@Preamble{
"\def \toenglish #1\endtoenglish{[{\em English:} #1\unskip]} " #
"\ifx \undefined \booktitle \def \booktitle #1{{{\em #1}}} \fi" #
"\ifx \undefined \circled \def \circled #1{(#1)} \fi" #
"\ifx \undefined \mathbb \def \mathbb #1{{\bf #1}} \fi" #
"\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}} \fi" #
"\ifx \undefined \mathrm \def \mathrm #1{{\rm #1}} \fi" #
"\ifx \undefined \operatorname \def \operatorname #1{{\rm #1}} \fi" #
"\ifx \undefined \pkg \def \pkg #1{{{\tt #1}}} \fi" #
"\ifx \undefined \r \let \r = \ocirc \fi" #
"\ifx \undefined \reg \def \reg {\circled{R}} \fi" #
"\ifx \undefined \texttt \def \texttt #1{{\tt #1}} \fi" #
"\ifx \undefined \TM \def \TM {${}^{\sc TM}$} \fi" #
"\hyphenation{
Cor-dic
COR-DIC
Gleit-komma
Gleit-komma-zahl-en
Gleit-komma-pro-zess-or
Gleit-komma-for-mat
Mikro-rech-en-tech-nik
Mikro-rech-ner-sys-tem-en
Mikro-rech-ner
Mi-yo-shi
Quad-rat-wurz-eln
Semi-nu-mer-i-cal
Swartz-lan-der
}"
}
@String{ack-jg = "Joe Grcar,
email: \path=jfgrcar@lbl.gov="}
@String{ack-jh = "John Harrison,
email: \path=johnh@ichips.intel.com="}
@String{ack-jr = "Jon Rokne,
Department of Computer Science,
The University of Calgary,
2500 University Drive N.W.,
Calgary, Alberta T2N 1N4,
Canada"}
@String{ack-kr = "Karin Remington,
National Institute of Standards and Technology,
Building 820, Room 365,
Gaithersburg, MD 20899, USA,
Tel: +1 301 975-5119,
FAX: +1 301 990-4127,
e-mail: \path|karin@cam.nist.gov|"}
@String{ack-mfc = "Michael F. Cowlishaw,
IBM UK (MP5),
PO Box 31,
Birmingham Road,
Warwick, CV34 5JL,
UK,
e-mail: \path|mfc@uk.ibm.com|,
URL: \path|http://www2.hursley.ibm.com/decimal|"}
@String{ack-nhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
e-mail: \path|beebe@math.utah.edu|,
\path|beebe@acm.org|,
\path|beebe@computer.org| (Internet),
URL: \path|https://www.math.utah.edu/~beebe/|"}
@String{ack-nj = "Norbert Juffa,
2445 Mission College Blvd.
Santa Clara, CA 95054
USA
email: \path=norbert@iit.com="}
@String{ack-pb = "Preston Briggs,
Tera Computer Company,
2815 Eastlake East,
Seattle, WA 98102,
USA,
Tel: +1 206 325-0800,
e-mail: \path|preston@tera.com|"}
@String{ack-rfb = "Ronald F. Boisvert,
Applied and Computational Mathematics Division,
National Institute of Standards and Technology,
Gaithersburg, MD 20899, USA,
Tel: +1 301 975 3812,
e-mail: \path=boisvert@cam.nist.gov="}
@String{ack-sfo = "Stuart F. Oberman,
e-mail: \path=stuart.oberman@amd.com="}
@String{inst-ANL = "Argonne National Laboratory"}
@String{inst-ANL:adr = "9700 South Cass Avenue, Argonne, IL
60439-4801, USA"}
@String{inst-ATT-BELL = "AT\&T Bell Laboratories"}
@String{inst-ATT-BELL:adr = "Murray Hill, NJ, USA"}
@String{inst-BERKELEY = "University of California"}
@String{inst-BERKELEY:adr = "Berkeley, CA, USA"}
@String{inst-BERKELEY-CPAM = "Center for Pure and Applied Mathematics,
University of California"}
@String{inst-BERKELEY-CPAM:adr = "Berkeley, CA, USA"}
@String{inst-BERKELEY-CS = "Department of Computer Science, University
of California"}
@String{inst-BERKELEY-CS:adr = "Berkeley, CA, USA"}
@String{inst-BERKELEY-EECS = "Department of Electrical Engineering and
Computer Science, University of California,
Berkeley"}
@String{inst-BERKELEY-EECS:adr = "Berkeley, CA, USA"}
@String{inst-BERKELEY-MATH-EECS = "Department of Mathematics and Department of
Electrical Engineering and Computer Science,
University of California, Berkeley"}
@String{inst-BERKELEY-MATH-EECS:adr = "Berkeley, CA, USA"}
@String{inst-CS-PURDUE = "Department of Computer Science, Purdue
University"}
@String{inst-CS-PURDUE:adr = "West Lafayette, IN 47907-2107, USA"}
@String{inst-CSC = "Center for Scientific Computing,
Department of Mathematics, University of
Utah"}
@String{inst-CSC:adr = "Salt Lake City, UT 84112, USA"}
@String{inst-ETH = "ETH Z{\"u}rich"}
@String{inst-ETH:adr = "Z{\"u}rich, Switzerland"}
@String{inst-HP = "Hewlett--Packard Corporation"}
@String{inst-HP:adr = "Palo Alto, CA, USA"}
@String{inst-INST-ADV-STUDY = "Institute for Advanced Study"}
@String{inst-INST-ADV-STUDY:adr = "Princeton, NJ, USA"}
@String{inst-INTEL = "Intel Corporation"}
@String{inst-INTEL:adr = "Santa Clara, CA, USA"}
@String{inst-LASL = "Los Alamos Scientific Laboratory"}
@String{inst-LASL:adr = "Los Alamos, NM, USA"}
@String{inst-LORIA-INRIA-LORRAINE = "LORIA/INRIA Lorraine"}
@String{inst-LORIA-INRIA-LORRAINE:adr = "B{\^a}timent A, Technop{\^o}le de
Nancy-Brabois, 615 rue du jardin
botanique, F-54602
Villers-l{\`e}s-Nancy Cedex, France"}
@String{inst-NLRC = "NASA Langley Research Center"}
@String{inst-NLRC:adr = "Hampton, VA, USA"}
@String{inst-NPL = "National Physical Laboratory"}
@String{inst-NPL:adr = "Teddington, Middlesex TW11 0LW, UK"}
@String{inst-MATHWORKS = "The MathWorks, Inc."}
@String{inst-MATHWORKS:adr = "3 Apple Hill Drive, Natick, MA 01760-2098,
USA"}
@String{inst-MRC-WISCONSIN = "Mathematics Research Center, University of
Wisconsin, Madison"}
@String{inst-MRC-WISCONSIN:adr = "Madison, WI, USA"}
@String{inst-PRINCETON = "Princeton University"}
@String{inst-PRINCETON:adr = "Princeton, NJ, USA"}
@String{inst-STAN-CS = "Stanford University, Department of
Computer Science"}
@String{inst-STAN-CS:adr = "Stanford, CA, USA"}
@String{inst-UT-CS = "Department of Computer Science,
University of Tennessee, Knoxville"}
@String{inst-UT-CS:adr = "Knoxville, TN 37996, USA"}
@String{j-ACTA-INFO = "Acta Informatica"}
@String{j-ACTA-NUMERICA = "Acta Numerica"}
@String{j-ACM-COMM-COMP-ALGEBRA = "ACM Communications in Computer Algebra"}
@String{j-ACM-J-EXP-ALGORITHMICS = "ACM Journal of Experimental Algorithmics"}
@String{j-ADA-LETT = "Ada Letters"}
@String{j-ADV-COMPUT-MATH = "Advances in Computational Mathematics"}
@String{j-ADV-SOFT-SCI-TECH = "Advances in software science and
technology"}
@String{j-ADV-THEORY-SIMUL = "Advanced Theory and Simulations"}
@String{j-ALGORITHMICA = "Algorithmica"}
@String{j-ALGORITHMS-BASEL = "Algorithms ({Basel})"}
@String{j-ALTA-FREQ = "Alta frequenza"}
@String{j-AM-J-MATH = "American Journal of Mathematics"}
@String{j-AM-SCI = "American Scientist"}
@String{j-AMER-J-PHYSICS = "American Journal of Physics"}
@String{j-AMER-MATH-MONTHLY = "American Mathematical Monthly"}
@String{j-AMER-STAT = "The American Statistician"}
@String{j-ANN-HIST-COMPUT = "Annals of the History of Computing"}
@String{j-ANN-MATH-ARTIF-INTELL = "Annals of Mathematics and Artificial
Intelligence"}
@String{j-ANN-MATH-STAT = "Annals of Mathematical Statistics"}
@String{j-ANN-NUM-MATH = "Annals of Numerical Mathematics"}
@String{j-APL-QUOTE-QUAD = "ACM SIGAPL APL Quote Quad"}
@String{j-APPL-ALGEBRA-ENG-COMMUN-COMPUT = "Applicable algebra in engineering,
communication and computing"}
@String{j-APPL-MATH-COMP = "Applied Mathematics and Computation"}
@String{j-APPL-MATH-LETT = "Applied Mathematics Letters"}
@String{j-APPL-NUM-MATH = "Applied Numerical Mathematics"}
@String{j-APPL-OPTICS = "Applied Optics"}
@String{j-APPL-STAT = "Applied Statistics"}
@String{j-ARCH-HIST-EXACT-SCI = "Archive for History of Exact Sciences"}
@String{j-ASTA-ADV-STAT-ANAL = "AStA. Advances in Statistical Analysis"}
@String{j-ASTRON-J = "Astronomical Journal"}
@String{j-AUSTRALIAN-COMP-J = "Australian Computer Journal"}
@String{j-AUTO-CTL-COMP-SCI = "Automatic Control and Computer Sciences"}
@String{j-AUTOMATION-REMOTE-CTL = "Automation and Remote Control"}
@String{j-BELL-LABS-RECORD = "Bell Laboratories Record"}
@String{j-BELL-SYST-TECH-J = "The Bell System Technical Journal"}
@String{j-BER-WISSENSCHAFTGESCH = "{Berichte zur Wissenschaftsgeschichte}"}
@String{j-BIOL-CYBERN = "Biological Cybernetics"}
@String{j-BIOMETRICS = "Biometrics"}
@String{j-BIT = "BIT (Nordisk tidskrift for
informationsbehandling)"}
@String{j-BIT-NUM-MATH = "BIT Numerical Mathematics"}
@String{j-BRITISH-J-HIST-MATH = "British Journal for the History of
Mathematics"}
@String{j-BRITISH-J-HIST-SCI = "British Journal for the History of Science"}
@String{j-BULL-AMS = "Bulletin of the American Mathematical
Society"}
@String{j-BULL-CALCUTTA-MATH-SOC = "Bulletin of the Calcutta Mathematical Society"}
@String{j-BYTE = "Byte Magazine"}
@String{j-C-R-ACAD-BULGARE-SCI = "Comptes rendus de l'Acad{\'e}mie bulgare
des sciences"}
@String{j-C-R-ACAD-SCI-PARIS-SER-I-MATH = "Comptes Rendus des S{\'e}ances de
l'Acad{\'e}mie des Sciences. S{\'e}rie I.
Math{\'e}matique"}
@String{j-CACM = "Communications of the Association for
Computing Machinery"}
@String{j-CAD = "Computer Aided Design"}
@String{j-CCCUJ = "C/C++ Users Journal"}
@String{j-CCPE = "Concurrency and Computation: Prac\-tice and
Experience"}
@String{j-CGF = "Com{\-}pu{\-}ter Graphics Forum"}
@String{j-COED = "CoED"}
@String{j-COLLEGE-MATH-J = "College Mathematics Journal"}
@String{j-COMBIN-PROBAB-COMPUT = "Combinatorics, Probability and Computing"}
@String{j-COMMUN-STAT-SIMUL-COMPUT = "Communications in Statistics: Simulation
and Computation"}
@String{j-COMMUN-STAT-THEORY-METH = "Communications in Statistics: Theory and
Methods"}
@String{j-COMP-ARCH-NEWS = "ACM SIGARCH Computer Architecture News"}
@String{j-COMP-DESIGN = "Computer Design"}
@String{j-COMP-EDU-J = "Computers in education journal"}
@String{j-COMP-GEOM = "Computational Geometry. Theory and
Applications"}
@String{j-COMP-GEOSCI = "Computers and Geosciences"}
@String{j-COMP-J = "The Computer Journal"}
@String{j-COMP-LANG-MAG = "Computer Language Magazine"}
@String{j-COMP-LANGS = "Computer Languages"}
@String{j-COMP-NET-AMSTERDAM = "Computer Networks (Amsterdam, Netherlands:
1999)"}
@String{j-COMP-PHYS-COMM = "Computer Physics Communications"}
@String{j-COMP-SURV = "ACM Computing Surveys"}
@String{j-COMPUT-AIDED-ENG = "Computer-aided engineering: CAE"}
@String{j-COMPUT-EDGE = "ComputingEdge"}
@String{j-COMPUT-ELECTR-ENG = "Computers and Electrical Engineering"}
@String{j-COMPUT-MATH-APPL = "Computers and Mathematics with Applications"}
@String{j-COMPUT-PHYS = "Computers in Physics"}
@String{j-COMPUT-SCI-ENG = "Computing in Science and Engineering"}
@String{j-COMPUT-SECUR = "Computers \& Security"}
@String{j-COMPUTE = "Compute"}
@String{j-COMPUTER = "Computer"}
@String{j-COMPUTING = "Computing: Archiv fur informatik und
numerik"}
@String{j-COMPUTING-SUPPLEMENTUM = "Computing. Supplementum"}
@String{j-CONG-NUM = "Congressus Numerantium"}
@String{j-CONTEMP-PHYS = "Contemporary physics"}
@String{j-CPE = "Concurrency: Prac\-tice and Experience"}
@String{j-CRYPTOLOGIA = "Cryptologia"}
@String{j-CT = "c't"}
@String{j-CUJ = "C Users Journal"}
@String{j-CYBER = "Cybernetics"}
@String{j-DDJ = "Dr. Dobb's Journal of Software Tools"}
@String{j-DEC-TECH-J = "Digital Technical Journal"}
@String{j-DEMOGRAPHY = "Demography"}
@String{j-DESIGNS-CODES-CRYPTOGR = "Designs, Codes, and Cryptography"}
@String{j-DIGIT-SIGNAL-PROCESS = "Digital Signal Processing"}
@String{j-DISCRETE-COMPUT-GEOM = "Discrete and Computational Geometry"}
@String{j-DOKL-AKAD-NAUK = "Doklady Akademii nauk SSSR"}
@String{j-DTRAP = "Digital Threats: Research and Practice
(DTRAP)"}
@String{j-EDN = "EDN"}
@String{j-EDUC-STUD-MATH = "Educational Studies in Mathematics"}
@String{j-ELECT-COMM-JAPAN-3-FUND-ELECT-SCI = "Electronics and communications in
Japan. Part 3, Fundamental electronic
science"}
@String{j-ELECT-LETTERS = "Electronics Letters"}
@String{j-ELECT-NOTES-THEOR-COMP-SCI = "Electronic Notes in Theoretical
Computer Science"}
@String{j-ELECTR-ENG = "Electrical Engineering (American Institute of
Electrical Engineers)"}
@String{j-ELECTRON-COMMUN-JPN = "Electronics and communications in Japan"}
@String{j-ELECTRON-ENG = "Electronic Engineering"}
@String{j-ELECTRON-TRANS-NUMER-ANAL = "Electronic Transactions on Numerical
Analysis"}
@String{j-ELECTRONIC-DESIGN = "Electronic Design"}
@String{j-ELECTRONIC-ENG-TIMES = "Electronic engineering times"}
@String{j-ELECTRONICS = "Electronics"}
@String{j-ELECTRONIK = "Elektronik"}
@String{j-ELEK-RECHENANLAGEN = "Elektronische Rechenanlagen"}
@String{j-ELEKTRONIKER = "Elektroniker (Switzerland)"}
@String{j-EMBED-SYS-PROG = "Embedded Systems Programming"}
@String{j-ENTROPY = "Entropy"}
@String{j-EURASIP-J-ADV-SIGNAL-PROCESS = "EURASIP Journal on Advances in Signal
Processing"}
@String{j-EURASIP-J-EMBED-SYS = "EURASIP Journal on Embedded Systems"}
@String{j-FIB-QUART = "Fibonacci Quarterly"}
@String{j-FORM-METHODS-SYST-DES = "Formal Methods in System Design"}
@String{j-FORTH-DIMENSIONS = "Forth Dimensions"}
@String{j-FORTRAN-FORUM = "ACM Fortran Forum"}
@String{j-FOUND-SCI = "Foundations of Science"}
@String{j-FUT-GEN-COMP-SYS = "Future Generation Computer Systems"}
@String{j-FUZZY-SETS-SYSTEMS = "Fuzzy Sets and Systems"}
@String{j-GAMM-MIT = "Mitteilungen der Gesellschaft f{\\\"u}r
Angewandte Mathematik und Mechanik"}
@String{j-GEOSCI-MODEL-DEV = "Geoscientific Model Development"}
@String{j-HIST-MATH = "Historia Mathematica"}
@String{j-HIST-SCI-2 = "Historia Scientiarum. Second Series.
International Journal of the History
of Science Society of Japan"}
@String{j-HIGH-PERFORM-SYST = "High performance systems"}
@String{j-HEWLETT-PACKARD-J = "Hewlett--Packard Journal"}
@String{j-HONEYWELL-COMP-J = "Honeywell Computer Journal"}
@String{j-IBM-JRD = "IBM Journal of Research and Development"}
@String{j-IBM-SYS-J = "IBM Systems Journal"}
@String{j-IBM-TDB = "IBM Technical Disclosure Bulletin"}
@String{j-IEE-PROC-COMPUT-DIGIT-TECH = "IEE Proceedings. Computers and Digital
Techniques"}
@String{j-IEE-PROC-E = "IEE proceedings, E: Computers and digital
techniques"}
@String{j-IEEE-ACCESS = "IEEE Access"}
@String{j-IEEE-ANN-HIST-COMPUT = "IEEE Annals of the History of Computing"}
@String{j-IEEE-APM = "IEEE Antennas and Propagation Magazine"}
@String{j-IEEE-CGA = "IEEE Computer Graphics and Applications"}
@String{j-IEEE-COMMUN-LET = "IEEE Communications Letters"}
@String{j-IEEE-COMPUT-ARCHIT-LETT = "IEEE Computer Architecture Letters"}
@String{j-IEEE-COMPUT-SCI-ENG = "IEEE Computational Science \& Engineering"}
@String{j-IEEE-DES-TEST-COMPUT = "IEEE Design \& Test of Computers"}
@String{j-IEEE-INT-CONF-ALG-ARCH-PAR-PROC = "IEEE International Conference on
Algorithms and Architectures for Parallel
Processing"}
@String{j-IEEE-J-EMERG-SEL-TOP-CIRCUITS-SYST = "IEEE Journal on Emerging and
Selected Topics in Circuits and Systems"}
@String{j-IEEE-J-SOLID-STATE-CIRCUITS = "IEEE Journal of Solid-State Circuits"}
@String{j-IEEE-MICRO = "IEEE Micro"}
@String{j-IEEE-POT = "IEEE Potentials"}
@String{j-IEEE-J-SEL-AREAS-COMMUN = "IEEE Journal on Selected Areas in
Communications"}
@String{j-IEEE-SIGNAL-PROCESS-LETT = "IEEE Signal Processing Letters"}
@String{j-IEEE-SIGNAL-PROCESS-MAG = "IEEE Signal Processing Magazine"}
@String{j-IEEE-SOFTWARE = "IEEE Software"}
@String{j-IEEE-SPECTRUM = "IEEE Spectrum"}
@String{j-IEEE-TIT = "IEEE Transactions on Information Theory"}
@String{j-IEEE-TRANS-ACOUST-SPEECH = "IEEE Transactions on Acoustics, Speech,
and Signal Processing"}
@String{j-IEEE-TRANS-AEROSP-ELECTRON-SYST = "IEEE Transactions on Aerospace
and Electronic Systems"}
@String{j-IEEE-TRANS-APPL-SUPERCOND = "IEEE Transactions on Applied
Superconductivity"}
@String{j-IEEE-TRANS-AUDIO-ELECTROACOUST = "IEEE Transactions on Audio and
Electroacoustics"}
@String{j-IEEE-TRANS-AUTOMAT-CONTR = "IEEE Transactions on Automatic Control"}
@String{j-IEEE-TRANS-BIOMED-ENG = "IEEE Transactions on Biomedical
Engineering"}
@String{j-IEEE-TRANS-BROADCAST = "IEEE Transactions on Broadcasting"}
@String{j-IEEE-TRANS-CAD-ICS = "IEEE Transactions on Computer-Aided Design
of Integrated Circuits and Systems"}
@String{j-IEEE-TRANS-CIRCUITS-SYST = "IEEE Transactions on Circuits and
Systems"}
@String{j-IEEE-TRANS-CIRCUITS-SYST-1 = "IEEE Transactions on Circuits and
Systems I: Regular Papers"}
@String{j-IEEE-TRANS-CIRCUITS-SYST-I-FUNDAM-THEORY-APPL = "IEEE Transactions on
Circuits and Systems I: Fundamental
Theory and Applications"}
@String{j-IEEE-TRANS-CIRCUITS-SYST-2 = "IEEE transactions on circuits and
systems. 2, Analog and digital signal
processing"}
@String{j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS = "IEEE Transactions on
Circuits and Systems II: Express Briefs"}
@String{j-IEEE-TRANS-CIRCUITS-SYST-VIDEO-TECH = "IEEE Transactions on Circuits
and Systems for Video Technology"}
@String{j-IEEE-TRANS-COMM = "IEEE Transactions on Communications"}
@String{j-IEEE-TRANS-COMPUT = "IEEE Transactions on Computers"}
@String{j-IEEE-TRANS-CONSUMER-ELECTRONICS = "IEEE Transactions on Consumer
Electronics"}
@String{j-IEEE-TRANS-CONTROL-SYST-TECHNOL = "IEEE Transactions on Control
Systems Technology"}
@String{j-IEEE-TRANS-ELEC-COMPUT = "IEEE Transactions on Electronic Computers"}
@String{j-IEEE-TRANS-EMERG-TOP-COMPUT = "IEEE Transactions on Emerging Topics in
Computing"}
@String{j-IEEE-TRANS-IND-ELECTRON = "IEEE Transactions on Industrial
Electronics"}
@String{j-IEEE-TRANS-INF-THEORY = "IEEE Transactions on Information Theory"}
@String{j-IEEE-TRANS-INSTRUM-MEAS = "IEEE Transactions on Instrumentation and
Measurement"}
@String{j-IEEE-TRANS-NEURAL-NETW = "IEEE Transactions on Neural Networks"}
@String{j-IEEE-TRANS-NUCL-SCI = "IEEE Transactions on Nuclear Science"}
@String{j-IEEE-TRANS-PAR-DIST-SYS = "IEEE Transactions on Parallel and
Distributed Systems"}
@String{j-IEEE-TRANS-PROF-COMMUN = "IEEE Transactions on Professional
Communication"}
@String{j-IEEE-TRANS-SIG-PROC = "IEEE Transactions on Signal Processing"}
@String{j-IEEE-TRANS-SOFTW-ENG = "IEEE Transactions on Software Engineering"}
@String{j-IEEE-TRANS-VEH-TECHNOL = "IEEE Transactions on Vehicular Technology"}
@String{j-IEEE-TRANS-VIS-COMPUT-GRAPH = "IEEE Transactions on Visualization and
Computer Graphics"}
@String{j-IEEE-TRANS-VLSI-SYST = "IEEE Transactions on Very Large Scale
Integration (VLSI) Systems"}
@String{j-IEEE-TRANS-WIREL-COMMUN = "IEEE Transactions on Wireless Communications"}
@String{j-IFIP-TRANS-A = "IFIP Transactions. A. Computer Science and
Technology"}
@String{j-IJQC = "International Journal of Quantum Chemistry"}
@String{j-IJSA = "The International Journal of Supercomputer
Applications"}
@String{j-IJHPCA = "The International Journal of High Performance
Computing Applications"}
@String{j-IMA-J-NUMER-ANAL = "IMA Journal of Numerical Analysis"}
@String{j-INC-STAT = "The Incorporated Statistician"}
@String{j-INF-CONTROL = "Information and Control"}
@String{j-INF-PROCESS-MACH = "Information processing machines"}
@String{j-INFO-PROC = "Journal of Information Processing (of
Japan??)"}
@String{j-INFO-PROC-LETT = "Information Processing Letters"}
@String{j-INFORM-THEOR-APPL = "RAIRO. Informatique th{\'e}orique et
applications := Theoretical
informatics and applications"}
@String{j-INFORMATIK-SPEKTRUM = "Informatik Spektrum"}
@String{j-INFORMS-J-COMPUT = "INFORMS Journal on Computing"}
@String{j-INT-J-COMPUT-GEOM-APPL = "International Journal of
Computational Geometry and Applications
(IJCGA)"}
@String{j-INT-J-COMP-APPL = "International Journal of Computer
Applications"}
@String{j-INT-J-COMP-RESEARCH = "International Journal of Computer Research"}
@String{j-INT-J-CONTROL = "International Journal of Control"}
@String{j-INT-J-ELECTRON = "International Journal of Electronics
Theoretical \& Experimental"}
@String{j-INT-J-FOUND-COMP-SCI = "International Journal of Foundations of
Computer Science"}
@String{j-INT-J-INFO-SEC = "International Journal of Information
Security"}
@String{j-INT-J-NUM-METH-FLUIDS = "Int. J. Num. Meth. Fluids"}
@String{j-INT-J-HIGH-SPEED-COMPUTING = "International Journal of High Speed
Computing"}
@String{j-INT-J-MINI-MICROCOMPUTERS = "International Journal of Mini and
Microcomputers"}
@String{j-INT-J-PAR-EMER-DIST-SYS = "International Journal of Parallel, Emergent
and Distributed Systems: IJPEDS"}
@String{j-INT-J-PARALLEL-PROG = "International Journal of Parallel
Programming"}
@String{j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER = "International Journal on
Software Tools for Technology Transfer:
STTT"}
@String{j-INT-J-SYST-SCI = "International Journal of Systems Science"}
@String{j-INTEGRATION-VLSI-J = "Integration, the VLSI journal"}
@String{j-INTEL-TECH-J = "Intel Technology Journal"}
@String{j-INTERVAL-COMP = "Interval Computations = Interval'nye
vychisleniia"}
@String{j-IRE-PROC = "IRE Proceedings"}
@String{j-IRE-TRANS-ELEC-COMPUT = "IRE Transactions on Electronic Computers"}
@String{j-ISIS = "Isis"}
@String{j-J-ACM = "Journal of the Association for Computing
Machinery"}
@String{j-J-ACOUST-SOC-AM = "Journal of the Acoustical Society of
America"}
@String{j-J-ADV-MODEL-EARTH-SYST = "Journal of Advances in Modeling Earth
Systems"}
@String{j-J-ALG = "Journal of Algorithms"}
@String{j-J-AM-STAT-ASSOC = "Journal of the American Statistical
Association"}
@String{j-J-APPL-MATH = "Journal of Applied Mathematics"}
@String{j-J-APPL-PROBAB = "Journal of Applied Probability"}
@String{j-J-APPL-STAT = "Journal of Applied Statistics"}
@String{j-J-APPROX-THEORY = "Journal of Approximation Theory"}
@String{j-J-AUSTRALIAN-MATH-SOC = "Journal of the Australian Mathematical
Society"}
@String{j-J-AUTOM-REASON = "Journal of Automated Reasoning"}
@String{j-J-CHINESE-INST-ENG = "Journal of the Chinese Institute of Engineers
= Chung-kuo kung ch'eng hsueh kan"}
@String{j-J-COMB-THEORY-A = "Journal of Combinatorial Theory (Series A)"}
@String{j-J-COMP-SYS-SCI = "Journal of Computer and System Sciences"}
@String{j-J-COMPUT-APPL-MATH = "Journal of Computational and Applied
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@String{pub-SUN:adr = "2550 Garcia Avenue, Mountain View,
CA 94043, USA"}
@String{pub-SV = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV:adr = "Berlin, Germany~/ Heidelberg,
Germany~/ London, UK~/ etc."}
@String{pub-SYNGRESS = "Syngress Publishing, Inc."}
@String{pub-SYNGRESS:adr = "Rockland, MA, USA"}
@String{pub-TEUBNER = "B. G. Teubner"}
@String{pub-TEUBNER:adr = "Stuttgart, Germany"}
@String{pub-TEWI = "te-wi"}
@String{pub-TEWI:adr = "M{\"u}nchen, Germany"}
@String{pub-TOMASH = "Tomash Publishers"}
@String{pub-TOMASH:adr = "Los Angeles, CA, USA"}
@String{pub-USENIX = "USENIX"}
@String{pub-USENIX-EL-CERRITO:adr = "P.O. Box 7, El Cerrito 94530, CA,
USA"}
@String{pub-USENIX:adr = "San Francisco, CA, USA"}
@String{pub-USGPO = "United States Government Printing Office"}
@String{pub-USGPO:adr = "Washington, DC, USA"}
@String{pub-VEB-VERLAG-TECHNIK = "VEB Verlag Technik"}
@String{pub-VEB-VERLAG-TECHNIK:adr = "Berlin, Germany"}
@String{pub-VIKING = "Viking"}
@String{pub-VIKING:adr = "New York, NY, USA"}
@String{pub-WCB = "William C. Brown Company Publishers"}
@String{pub-WCB:adr = "Dubuque, IA, USA"}
@String{pub-WEITEK = "Weitek Corporation"}
@String{pub-WEITEK:adr = "1060 E. Arques Ave., Sunnyvale, CA
94086-BRM-9759, USA"}
@String{pub-WESTERN-PERIODICALS = "Western Periodicals Co.,"}
@String{pub-WESTERN-PERIODICALS:adr = "North Hollywood, CA"}
@String{pub-WILEY = "Wiley"}
@String{pub-WILEY:adr = "New York, NY, USA"}
@String{pub-WILEY-INTERSCIENCE = "Wiley-In{\-}ter{\-}sci{\-}ence"}
@String{pub-WILEY-INTERSCIENCE:adr = "New York, NY, USA"}
@String{pub-WORLD-SCI = "World Scientific Publishing
Co. Pte. Ltd."}
@String{pub-WORLD-SCI:adr = "P. O. Box 128, Farrer Road,
Singapore 9128"}
@String{ser-APPL-MATH-SER-NBS = "Applied Mathematics Series / National Bureau
of Standards"}
@String{ser-LECT-NOTES-MATH = "Lecture Notes in Mathematics"}
@String{ser-LNCS = "Lecture Notes in Computer Science"}
@String{ser-LNCSE = "Lecture Notes in Computational
Science and Engineering"}
@String{ser-PROJECT-GUTENBERG = "Project Gutenberg"}
@String{ser-SIGPLAN = "ACM SIGPLAN Notices"}
@Article{Leibniz:1703:EAB,
author = "G.-W. Leibniz",
title = "Explication de {l'Arithm{\'e}tique} Binaire.
({French}) [{Explanation} of binary arithmetic]",
journal = "M{\'e}moires de math{\'e}matique et de physique de l
Acad{\'e}mie royale des sciences",
volume = "??",
number = "??",
pages = "85--89",
month = "????",
year = "1703",
bibdate = "Fri Mar 17 08:48:17 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Leibniz is often credited with the invention of the
binary number system, but there is other work from his
era, and detailed analysis of Leibniz's use of binary
numbers. See
\cite{Greve:1966:HLR,Glaser:1969:HMN,Glaser:1971:HBO,Lautz:1979:JLD,Glaser:1981:HBO,Esmay:2017:HNS,Strickland:2022:LBI,Zlatopolski:2023:PAV}",
URL = "https://hal.archives-ouvertes.fr/ads-00104781/document",
acknowledgement = ack-nhfb,
language = "French",
}
@Book{Pelicano:1712:APQ,
author = "Wenceslao Josepho Pelicano",
title = "Arithmeticus Perfectus Qui tria numerare nescit,
\ldots{}. ({Latin}) [{A} Perfect Arithmetic for who
does not know how to count to three]",
publisher = "????",
address = "Prague, Czechoslovakia",
pages = "????",
year = "1712",
bibdate = "Fri Mar 17 08:56:14 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://play.google.com/books/reader?id=cNxdAAAAcAAJ",
acknowledgement = ack-nhfb,
longtitle = "Arithmeticus Perfectus Qui tria numerare nescit, sen
Arithmetica dualis in qua Numerando non proceditur,
nisi ad duo, \& tamen omnes questiones Arithmetic{\ae}
negoti{\^o} facile enodar possunt ad perilsturem equite
Mathematic{\ae}. ({Latin}) [{A} Perfect Arithmetic for
who does not know how to count to three, is a dual
arithmetic in which he does not proceed to numbering
except to two, and yet all the questions of arithmetic
business can easily be entangled to the peril of the
mathematician]",
}
@Article{Colson:1726:SAN,
author = "John {Colson, F.R.S.}",
title = "A Short Account of Negativo-Affirmative Arithmetick",
journal = j-PHILOS-TRANS-R-SOC-LOND,
volume = "34",
number = "392--398",
pages = "161--173",
month = "????",
year = "1726",
CODEN = "PTRSAV",
DOI = "https://doi.org/10.1098/rstl.1726.0032",
ISSN = "0370-2316 (print), 2053-9207 (electronic)",
bibdate = "Tue Jul 28 14:21:05 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith22.gforge.inria.fr/slides/s2-ercegovac.pdf",
acknowledgement = ack-nhfb,
fjournal = "Philosophical transactions of the Royal Society of
London",
journal-URL = "http://rsta.royalsocietypublishing.org/",
remark = "Early work on signed-digit arithmetic, reported by
Milo{\v{s}} Ercegovac in a talk at the ARITH'22
conference, Lyon, France, June 2015.",
}
@Unpublished{Babbage:1837:MPC,
author = "Charles Babbage",
title = "On the mathematical powers of the calculating engine",
month = dec,
year = "1837",
bibdate = "Wed Oct 13 11:09:59 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Manuscript held by Museum of the History of Science,
Oxford, UK. Reprinted in \cite[\S
2.1]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@Book{Nystrom:1862:PNS,
author = "John W. (John William) Nystrom",
title = "Project of a new system of arithmetic, weight, measure
and coins, proposed to be called the tonal system, with
sixteen to the base",
publisher = "J. B. Lippincott and Co.",
address = "Philadelphia, PA, USA",
pages = "106",
year = "1862",
LCCN = "QC96 .N95",
bibdate = "Sat Oct 29 10:28:27 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://unifoundry.com/tonal/;
https://catalog.hathitrust.org/Record/011602816;
https://lccn.loc.gov/04025433",
acknowledgement = ack-nhfb,
author-dates = "Johan Vilhelm Nystr{\"o}m (1824--1885)",
remark = "Thanks to Paul Hardy of Unifoundry in San Diego, CA,
USA, for information about Nystrom's promotion of
hexadecimal arithmetic, and for creating a Web site
about Nystrom's tonal system, as well as developing
Unicode-compatible fonts to represent the additional
digits needed by the system.",
subject = "Weights and measures; Numeration; base-16 arithmetic;
hexadecimal arithmetic",
}
@Article{Anonymous:1875:AOM,
author = "Anonymous",
title = "The Arithmetical Operations of Multiplication and
Division",
journal = j-SCI-AMER,
volume = "32",
number = "3",
pages = "41--42",
day = "16",
month = jan,
year = "1875",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican01161875-41",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Fri May 17 10:29:24 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciam1870.bib",
URL = "http://www.nature.com/scientificamerican/journal/v32/n3/pdf/scientificamerican01161875-41.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@Article{Anonymous:1879:TRA,
author = "Anonymous",
title = "Three Rules for Abbreviating Multiplication",
journal = j-SCI-AMER,
volume = "41",
number = "12",
pages = "184--184",
day = "20",
month = sep,
year = "1879",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican09201879-184",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Fri May 17 10:36:54 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciam1870.bib",
URL = "http://www.nature.com/scientificamerican/journal/v41/n12/pdf/scientificamerican09201879-184.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@Article{Newcomb:1881:NFU,
author = "Simon Newcomb",
title = "Note on the frequency of use of the different digits
in natural numbers",
journal = j-AM-J-MATH,
volume = "4",
number = "1/4",
pages = "39--40",
year = "1881",
CODEN = "AJMAAN",
ISSN = "0002-9327 (print), 1080-6377 (electronic)",
ISSN-L = "0002-9327",
bibdate = "Thu Feb 15 16:35:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0002-9327%281881%294%3A1%2F4%3C39%3ANOTFOU%3E2.0.CO%3B2-K",
abstract = "That the ten digits do not occur with equal frequency
must be evident to any one making much use of
logarithmic tables, and noticing how much faster the
first pages wear out than the last ones. The first
significant figure is oftener 1 than any other digit,
and the frequency diminishes up to 9.",
acknowledgement = ack-nhfb,
fjournal = "American Journal of Mathematics",
journal-URL = "https://www.jstor.org/journal/amerjmath",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From p. 40: ``The law of probability of the occurrence
of numbers is such that all mantissas of their
logarithms are equally probable.''",
}
@Article{Holman:1888:DPM,
author = "Silas W. Holman",
title = "Discussion of the precision of measurement",
journal = "Technol. Q.",
volume = "1",
number = "??",
pages = "194--207",
month = "????",
year = "1888",
bibdate = "Mon May 21 17:12:03 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite[ref. 14]{Carter:2013:ESF}.",
}
@Book{Holman:1892:DPM,
author = "Silas W. Holman",
title = "Discussion of the Precision of Measurements: With
Examples Taken Mainly From Physics And Electrical
Engineering",
publisher = "Ferris Brothers Printers",
address = "New York, NY, USA",
pages = "????",
year = "1892",
bibdate = "Mon May 21 17:14:39 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite[ref. 15]{Carter:2013:ESF}.",
}
@Article{Anonymous:1893:IDb,
author = "Anonymous",
title = "The Instantaneous Divider",
journal = j-SCI-AMER,
volume = "68",
number = "21",
pages = "325--325",
day = "27",
month = may,
year = "1893",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican05271893-325a",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Wed May 22 19:04:00 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciam1890.bib",
URL = "http://www.nature.com/scientificamerican/journal/v68/n21/pdf/scientificamerican05271893-325a.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@Article{Felt:1893:MA,
author = "Dorr E. Felt",
title = "Mechanical Arithmetic",
journal = j-SCI-AMER,
volume = "69",
number = "20",
pages = "309--310",
day = "11",
month = nov,
year = "1893",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican11111893-309b",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Wed May 22 19:04:25 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciam1890.bib",
URL = "http://www.nature.com/scientificamerican/journal/v69/n20/pdf/scientificamerican11111893-309b.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@Article{Aley:1897:DES,
author = "Robert J. Aley",
title = "A Device for Extracting the Square Root of Certain
Surd Quantities",
journal = j-AMER-MATH-MONTHLY,
volume = "4",
number = "8/9",
pages = "204--208",
month = aug # "\slash " # sep,
year = "1897",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:37:08 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Anonymous:1898:OFA,
author = "Anonymous",
title = "Our Fingers as an Aid in Multiplication",
journal = j-SCI-AMER,
volume = "79",
number = "17",
pages = "265--266",
day = "22",
month = oct,
year = "1898",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican10221898-265",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Wed May 22 19:08:57 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciam1890.bib",
URL = "http://www.nature.com/scientificamerican/journal/v79/n17/pdf/scientificamerican10221898-265.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@Article{Ludgate:1909:PAM,
author = "P. E. Ludgate",
title = "On a proposed analytical machine",
journal = j-SCI-PROC-ROY-DUBLIN-SOC,
volume = "12",
number = "9",
pages = "77--91",
year = "1909",
CODEN = "SPRDAP",
ISSN = "0371-2303",
bibdate = "Wed Oct 13 11:14:08 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 2.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Scientific proceedings of the Royal Dublin Society",
}
@Article{Babbage:1910:BBA,
author = "H. P. Babbage",
title = "{Babbage}: {Babbage}'s analytical engine",
journal = j-MONTHLY-NOT-ROY-ASTRON-SOC,
volume = "70",
number = "??",
pages = "517--526, 645",
year = "1910",
CODEN = "MNRAA4",
ISSN = "0035-8711 (print), 1365-2966 (electronic)",
ISSN-L = "0035-8711",
bibdate = "Wed Oct 13 11:12:08 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 2.3]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Monthly Notices of the Royal Astronomical Society",
journal-URL = "https://academic.oup.com/mnras",
}
@Article{TorresyQuevedo:1915:EAS,
author = "L. {Torres y Quevedo}",
title = "Essais sur l'automatique. Sa definition. {{\'E}}tendue
th{\'e}orique de ses applications ({French}) [{Essays}
on automation. {Its} definition. {Theoretical} extent
of its applications]",
journal = j-REV-GEN-SCI-PURES-APPL,
volume = "??",
number = "??",
pages = "601--611",
day = "15",
month = nov,
year = "1915",
ISSN = "0370-7431",
bibdate = "Wed Oct 13 11:15:08 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 2.5]{Randell:1982:ODC}.
Translated by Mr. R. Basu.",
acknowledgement = ack-nhfb,
fjournal = "Revue G{\'e}n{\'e}rale des Sciences Pures et
Appliqu{\'e}es",
language = "French",
}
@Article{Barrow:1924:QDD,
author = "D. F. Barrow",
title = "Questions and Discussions: Discussions: On Taking
Square Roots of Integers",
journal = j-AMER-MATH-MONTHLY,
volume = "31",
number = "10",
pages = "482--484",
month = dec,
year = "1924",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:37:29 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Smith:1924:FPA,
author = "David Eugene Smith",
title = "The First Printed Arithmetic ({Treviso}, 1478)",
journal = j-ISIS,
volume = "6",
number = "3",
pages = "311--331",
month = "????",
year = "1924",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:57:26 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i211087;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1920.bib",
URL = "http://www.jstor.org/stable/224315",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Book{Karpinski:1925:HA,
author = "Louis Charles Karpinski",
title = "The History of Arithmetic",
publisher = "Rand McNally \& Company",
address = "New York, NY, USA",
pages = "xi + 200",
year = "1925",
bibdate = "Fri Nov 28 18:09:05 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@Article{Cajori:1926:BRB,
author = "Florian Cajori",
title = "Book Review: {{\booktitle{The History of Arithmetic}}
by Louis Charles Karpinski}",
journal = j-ISIS,
volume = "8",
number = "1",
pages = "231--232",
month = feb,
year = "1926",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:57:36 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i211094;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1920.bib",
URL = "http://www.jstor.org/stable/223706",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Article{Smith:1926:FGC,
author = "David Eugene Smith",
title = "The First Great Commercial Arithmetic",
journal = j-ISIS,
volume = "8",
number = "1",
pages = "41--49",
month = feb,
year = "1926",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:57:36 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i211094;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1920.bib",
URL = "http://www.jstor.org/stable/223673",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Article{Cajori:1927:EAP,
author = "Florian Cajori",
title = "The Earliest Arithmetic Published in {America}",
journal = j-ISIS,
volume = "9",
number = "3",
pages = "391--401",
month = dec,
year = "1927",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:57:45 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i214411;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1920.bib",
URL = "http://www.jstor.org/stable/330806",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Article{J:1930:RPRb,
author = "R. A. J.",
title = "Recent Publications: Reviews: {{\em Standard Table of
Square Roots}}, by {L. M. Milne-Thomson}",
journal = j-AMER-MATH-MONTHLY,
volume = "37",
number = "6",
pages = "314--314",
month = jun # "\slash " # jul,
year = "1930",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:35:55 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Laughlin:1930:LND,
author = "Harry H. Laughlin",
title = "Large-Number Division by Calculating Machine",
journal = j-AMER-MATH-MONTHLY,
volume = "37",
number = "6",
pages = "287--293",
month = jun # "\slash " # jul,
year = "1930",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:35:55 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Garver:1932:QDNb,
author = "Raymond Garver",
title = "Questions, Discussions, and Notes: a Square Root
Method and Continued Fractions",
journal = j-AMER-MATH-MONTHLY,
volume = "39",
number = "9",
pages = "533--535",
month = nov,
year = "1932",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:36:47 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Polachek:1932:MMU,
author = "H. Polachek",
title = "A method of multiplication used by {Saadia Gaon} in
the 10th century",
journal = j-SCRIPTA-MATH,
volume = "1",
number = "??",
pages = "245--246",
month = "????",
year = "1932",
ISSN = "0036-9713",
bibdate = "Thu Oct 26 11:15:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
acknowledgement = ack-nhfb,
ajournal = "Scripta Math.",
fjournal = "Scripta Mathematica: A Quarterly Journal Devoted to
the Philosophy, History, and Expository Treatment of
Mathematics",
jfm = "59.0019.03",
ZBmath = "2542288",
}
@Article{Simons:1932:IGA,
author = "T. E. Simons",
title = "{Isaac Greenwood}'s arithmetic",
journal = j-SCRIPTA-MATH,
volume = "1",
number = "??",
pages = "262--264",
month = "????",
year = "1932",
ISSN = "0036-9713",
bibdate = "Thu Oct 26 11:15:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
acknowledgement = ack-nhfb,
ajournal = "Scripta Math.",
fjournal = "Scripta Mathematica: A Quarterly Journal Devoted to
the Philosophy, History, and Expository Treatment of
Mathematics",
jfm = "59.0026.02",
ZBmath = "2542316",
}
@Book{Couffignal:1933:MCL,
author = "L. Couffignal",
title = "Les machines {\`a} calculer, leurs principes, leur
{\'e}volution. ({French}) [{Calculating} machines,
their principles, their evolution]",
publisher = "Gauthier-Villars",
address = "Paris, France",
year = "1933",
bibdate = "Wed Oct 13 11:19:11 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Extracts reprinted in \cite[\S 3.2]{Randell:1982:ODC}.
Translated by Mr. R. Basu.",
acknowledgement = ack-nhfb,
language = "French",
}
@Article{Kalbfell:1934:QDN,
author = "D. C. Kalbfell",
title = "Questions, Discussions and Notes: On a Method for
Calculating Square Roots",
journal = j-AMER-MATH-MONTHLY,
volume = "41",
number = "8",
pages = "504--506",
month = oct,
year = "1934",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:37:31 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Simons:1935:EEC,
author = "L. G. Simons",
title = "An early eighteenth century {American} readyreckoner",
journal = j-SCRIPTA-MATH,
volume = "3",
number = "??",
pages = "94--96",
month = "????",
year = "1935",
ISSN = "0036-9713",
bibdate = "Thu Oct 26 11:15:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
acknowledgement = ack-nhfb,
ajournal = "Scripta Math.",
fjournal = "Scripta Mathematica: A Quarterly Journal Devoted to
the Philosophy, History, and Expository Treatment of
Mathematics",
jfm = "61.0020.03",
ZBmath = "2531128",
}
@Article{Calvert:1936:DDS,
author = "H. R. Calvert",
title = "Decimal Division of Scales before the Metric System",
journal = j-ISIS,
volume = "25",
number = "2",
pages = "433--436",
month = sep,
year = "1936",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:21:25 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i211115;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1930.bib",
URL = "http://www.jstor.org/stable/225380",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Book{LeVita:1936:ALI,
author = "Maurice H. {Le Vita}",
title = "An Arithmetic of Life Insurance",
publisher = "Life Office Management Association",
address = "New York",
pages = "xii + 132",
year = "1936",
LCCN = "HG8781 .L43",
bibdate = "Sat Aug 12 14:42:20 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://hdl.handle.net/2027/mdp.39015017290688;
https://babel.hathitrust.org/cgi/pt?id=mdp.39015017290688",
abstract = "We have determined this item to be in the public
domain according to US copyright law through
information in the bibliographic record and/or US
copyright renewal records. The digital version is
available for all educational uses worldwide. Please
contact HathiTrust staff at hathitrust-help <at>
umich.edu with any questions about this item. Life
insurance--Mathematics. (LCCN)36034103.
(OCoLC)ocm03161649. HG8781 .L43. HG 8781 .L66.
Http://hdl.handle.net/2027/mdp.39015017290688.",
acknowledgement = ack-nhfb,
remark = "While not about computer arithmetic, this book is
about practical applications of arithmetic in the life
insurance industry. It considers compound interest
calculations, present values of financial instruments,
mortality tables, insurance premiums, bond returns, and
so on. In Table 1, which shows the growth of an
investment at 3 percent over 10 years, the author
[amusingly] comments ``Mathematicians have already
worked out the multiplications and have incorporated
them into a table. With the use of this table, the
result can be obtained by a single multiplication.''.
Although the MARC record indicates the book is in the
public domain, the URL only permits download of a
single page at a time, although it is possible to page
through the book.",
tableofcontents = "Preface / vii \\
Index to Tables / xi \\
Notes on the Solution of Problems / xii \\
\\
I. Interest and Discount / 1 \\
Interest \\
Discount \\
Examples \\
Observations \\
Problems \\
\\
II. The Mortality Table and Easy Problems in Rate
Calculation at Age 90 / 6 \\
Natural or Net One-Year Term Premium \\
Net One-Year Pure Endowment \\
Net Single Premium Whole Life \\
Fundamental Principle \\
Observations \\
Problems \\
\\
III. Single Premium Contracts --- Age 35 / 14 \\
Mortality Table \\
(Net) Single Premium 10-Year Term \\
(Net) Single Premium 10-Year Pure Endowment \\
(Net) Single Premium 10-Year Endowment \\
(Net) Single Premium Whole Life \\
(Net) Single Premium 10-Year Temporary Annuity \\
(Net) Single Premium Life Annuity \\
\\
IV. Development of Net Annual Premiums / 22 \\
Extension of Use of Discount \\
(Net) Annual Premium, Whole Life Policy \\
(Net) Annual Premium, 10-Payment Life \\
(Net) Annual Premium, 10-Year Term \\
(Net) Annual Premium, 10-Year Endowment \\
The ``Practical' and `More Exact' Premium \\
Alternative Method of Obtaining Net Annual Premiums \\
Problems \\
\\
V. More About Premiums / 30 \\
The Yearly Renewable Term Policy \\
Loading the Premium \\
Partial or Instalment Premiums \\
Problems \\
\\
VI. Net Level Premium Reserves / 34 \\
10-Year Term Policy \\
10-Year Endowment Policy \\
Whole Life Policy \\
10-Payment Life Policy \\
Yearly Renewable Term \\
Problems \\
\\
VII. Reserve Fund, Mortality Fund and Cost of Insurance
/ 44 \\
Reserve Credit \\
Payment of Death Claims \\
The Reserve Fund and Mortality Fund \\
Cost of Insurance \\
Problems \\
\\
VIII. Full Preliminary Term Valuation \\
Gross Level Annual Premiums \\
Preliminary Term \\
Terminal Reserves Policy P \\
Full Preliminary Term Valuation \\
Modified Preliminary Term \\
Problems \\
\\
IX. Initial, Mean, and Calendar Year Reserves \\
\\
Initial Reserve \\
Mean Reserve \\
Calendar Year Reserve \\
Initial and Mean Reserves, F.P.T. Basis \\
Problems \\
\\
X. Non-Foreiture Options; Cash VALUE; Paid-Up and
Extended Insurance; Loan Value / 61 \\
The Cash Value \\
What Happens When Policy is Surrendered \\
Non-Forfeiture Options (Option 1, Option 2, and Option
3) \\
Cash Values under F.P.T. Basis of Valuation \\
Loan Values \\
Problems \\
\\
XI. Profits to a Life Insurance Company / 67 \\
Actual and Expected Mortality \\
Actual and Expected Expenses \\
Actual and Expected Interest \\
Gain and Loss for the Year \\
Arithmetical Statement of Financial Status \\
Problems \\
\\
XII. Distribution of Surplus --- Dividend Options / 73
\\
Allocating Surplus to Policyholders \\
Share of Gain from Mortality, Loading and Interest \\
Dividend Formula \\
Variations in Dividend Formula \\
Dividend Options (Options 1 to 6) \\
Withdrawing the Dividend or Surrendering the Dividend
Credit \\
Problems \\
\\
XIII. Further Problems in Interest and Discount / 79
\\
Fundamental Principle \\
Annuity Certain (Present Value of) \\
Annuity Certain (Amount of) \\
Interest Compounded Oftener than Once a Year \\
Value of a Bond \\
Problems \\
\\
XIV. Deferred Annuity --- Certain and Continuous
Annuity --- Optional Modes of Settlement / 91 \\
Deferred Life Annuity \\
``Combination'' Annuity Contract \\
Optional Modes of Settlement \\
Problems \\
\\
XV. Mortality Rates and Mortality Tables / 94 \\
Rate of Mortality \\
Building the Table \\
Changing Number at Initial Age \\
Selection and Select Tables \\
Indicating the Age (for Mortality Analysis) \\
Select Table \\
Ultimate Tables and Select and Ultimate Tables \\
Problems \\
\\
XVI. More About Reserves / 103 \\
Fundamental Principle Amended \\
Corollary to Amended Principle \\
Prospective and Retrospective Method of Obtaining the
Reserve \\
Reserves on Single Premium Policies \\
Reserves on Substandard Policies \\
Percentage Mortality Rating Table \\
Problems. \\
\\
XVII. Modified Preliminary Term Valuation / 109 \\
M.P.T. Basis of Valuation \\
Method A: M.P.T. Whole Life Basis \\
Method B: M.P.T. 20-Payment Life Basis \\
Method C: M.P.T. Original Plan Basis \\
Illinois Standard System of Valuation \\
Ohio Standard System of Valuation \\
New Jersey Standard System of Valuation \\
Problems \\
\\
Appendices: \\
I. Miscellaneous Examples / 118 \\
II. Chart 3B --- Single Premium Life Insurance (Age 35)
/ 121 \\
III. Chart 5B -- Single Premium Life Annuity (Age 35) /
122 \\
IV. Answers to Problems and Miscellaneous Examples 123
\\
Index / 127",
usmarc540 = "[US Library of Congress record]: We have determined
this item to be in the public domain according to US
copyright law through information in the bibliographic
record and/or US copyright renewal records. The digital
version is available for all educational uses
worldwide.",
}
@Article{Phillips:1936:BC,
author = "E. W. Phillips",
title = "Binary calculation",
journal = j-J-INST-ACTUARIES,
volume = "67",
number = "??",
pages = "187--221",
year = "1936",
ISSN = "0020-2681",
bibdate = "Wed Oct 13 11:33:16 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.1]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Institute of Actuaries",
}
@Misc{Zuse:1936:VSD,
author = "K. Zuse",
title = "{Verfahren zur selbstt{\"a}tigen Durchfuhrung von
Rechnungen mit Hilfe von Rechenmaschinen}. ({German})
[{Procedure} for automatic execution of calculations by
calculating machines]",
howpublished = "German patent application Z23624.",
day = "11",
month = apr,
year = "1936",
bibdate = "Wed Oct 13 11:22:03 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 4.1]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Escott:1937:QDN,
author = "E. B. Escott",
title = "Questions, Discussions, and Notes: Rapid Method for
Extracting a Square Root",
journal = j-AMER-MATH-MONTHLY,
volume = "44",
number = "10",
pages = "644--646",
month = dec,
year = "1937",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:38:44 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Book{Millikan:1937:MMP,
author = "Robert A. Millikan and Duane E. Roller and Earnest C.
Watson",
title = "Mechanics, Molecular Physics, Heat, and Sound",
publisher = pub-MIT,
address = pub-MIT:adr,
pages = "????",
year = "1937",
bibdate = "Mon May 21 17:16:04 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See Appendix: Significant Figures and Notations by
Powers of Ten.",
acknowledgement = ack-nhfb,
remark = "Cited in \cite[ref. 22]{Carter:2013:ESF}.",
}
@MastersThesis{Shannon:1937:SAR,
author = "Claude Elwood Shannon",
title = "A Symbolic Analysis of Relay and Switching Circuits",
type = "{Master of Science}",
school = "Department of Electrical Engineering, MIT",
address = "Cambridge, MA, USA",
pages = "72",
day = "10",
month = aug,
year = "1937",
bibdate = "Thu Nov 18 10:35:20 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Not submitted until 1940",
URL = "http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425.pdf",
acknowledgement = ack-nhfb,
author-dates = "April 30, 1916--February 24, 2001",
remark = "Smiley \cite[p. 91]{Smiley:2010:MWI} claims: ``He
[Shannon] also had the insight, like Atanasoff, that
the binary arithmetic that relay switches represented
would simplify information systems. His master's
thesis, written when he as twenty-one and published
when he was twenty-two, is considered to be one of the
most important, if not the most important, master's
thesis of the twentieth century.''\par
Pages 59--61 of the thesis are a section called
``Electric Adder to the Base Two'', and pages 62--68,
``A Factor Table Machine'', describe a machine that
will print a table of factors and primes of all the
integers from 1 to 100,000,000. Shannon notes on page
68: ``As to the practicality of such a device, it might
be said that J. P. Kulik spent 20 years in constructing
a table of primes up to 100,000,000 and when finished
it was found to contain so many errors that it was not
worth publishing. The machine described here could
probably be made to handle 5 numbers per second so that
the table would require only about 2 months to
construct.''",
}
@Article{Benford:1938:LAN,
author = "Frank Benford",
title = "The Law of Anomalous Numbers",
journal = j-PROC-AMER-PHIL-SOC,
volume = "78",
number = "4",
pages = "551--572",
month = mar,
year = "1938",
CODEN = "PAPCAA",
ISSN = "0003-049X (print), 2326-9243 (electronic)",
ISSN-L = "0003-049X",
bibdate = "Thu Feb 15 16:28:28 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-G",
abstract = "It has been observed that the first pages of a table
of common logarithms show more wear than do the last
pages, indicating that more used numbers begin with the
digit 1 than with the digit 9. A compilation of some
20,000 first digits taken from widely divergent sources
shows that there is a logarithmic distribution of first
digits when the numbers are composed of four or more
digits. An analysis of the numbers from different
sources shows that the numbers taken from unrelated
subjects, such as a group of newspaper items, show a
much better agreement with a logarithmic distribution
than do numbers from mathematical tabulations or other
formal data. There is here the peculiar fact that
numbers that individually are without relationship are,
when considered in large groups, in good agreement with
a distribution law---hence the name ``Anomalous
Numbers.''\par
A further analysis of the data shows a strong tendency
for bodies of numerical data to fall into geometric
series. If the series is made up of numbers containing
three or more digits the first digits form a
logarithmic series. If the numbers contain only single
digits the geometric relation still holds but the
simple logarithmic relation no longer applies.\par
An equation is given showing the frequencies of first
digits in the different orders of numbers 1 to 10, 10
to 100, etc.\par
The equation also gives the frequency of digits in the
second, third + place of a multi-digit number, and it
is shown that the same law applies to
reciprocals.\par
There are many instances showing that the geometric
series, or the logarithmic law, has long been
recognized as a common phenomenon in factual literature
and in the ordinary affairs of life. The wire gauge and
drill gauge of the mechanic, the magnitude scale of the
astronomer and the sensory response curves of the
psychologist are all particular examples of a
relationship that seems to extend to all human affairs.
The Law of Anomalous Numbers is thus a general
probability law of widespread application.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
journal-URL = "http://www.jstor.org/journal/procamerphilsoci",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From \cite{Logan:1978:FDP}: ``Benford's paper was
published in 1938 in a journal of rather limited
circulation and not usually read by mathematicians. It
so happened that it was immediately followed in the
same issue by a physics paper which became of some
importance for secret nuclear work during World War II
[H. A. Bethe, M. E. Rose, and L. P. Smith, `The
Multiple Scattering of Electrons', Proc. Amer. Phil.
Soc. 78(4), 573--585 (1938)]. That is why Benford's
paper caught the attention of physicists in the early
1940's and was much discussed. This led to the notes in
Nature by Goudsmit and Furry [3] and Furry and Hurwitz
[4] containing an effort to explain Benford's law. We
considered it at that time merely a welcome diversion
and did not expect that over thirty papers would be
devoted to this subject in subsequent years.'' The 2006
bibliography \cite{Hurlimann:2006:BLB} cites 325
publications about Benford's Law.",
}
@PhdThesis{Couffignal:1938:AMA,
author = "L. Couffignal",
title = "Sur l'analyse m{\'e}canique. Application aux machines
{\`a} calculer et aux calculs de la m{\'e}canique
c{\'e}leste. ({French}) [{On} mechanical analysis.
Application to calculating machines and to calculation
in celestial mechanics]",
publisher = "Gauthier-Villars",
school = "Facult{\'e} des Sciences de Paris",
address = "Paris, France",
year = "1938",
bibdate = "Wed Oct 13 11:17:22 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Extracts reprinted in \cite[\S 2.7]{Randell:1982:ODC}.
Translated by Mr. R. Basu.",
acknowledgement = ack-nhfb,
language = "French",
}
@Book{Hardy:1938:ITN,
author = "G. H. (Godfrey Harold) Hardy and E. M. (Edward
Maitland) Wright",
title = "An Introduction to the Theory of Numbers",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xvi + 403",
year = "1938",
LCCN = "QA241 .H28",
bibdate = "Fri Nov 30 06:49:15 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Shannon:1938:SAR,
author = "Claude E. Shannon",
title = "A Symbolic Analysis of Relay and Switching Circuits",
journal = j-TRANS-AMER-INST-ELEC-ENG,
volume = "57",
number = "??",
pages = "713--723",
month = dec,
year = "1938",
CODEN = "TAEEA5",
ISSN = "0096-3860",
bibdate = "Sat Nov 20 08:54:12 2010",
bibsource = "http://www2.research.att.com/~njas/doc/shannonbio.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Institute of Electrical
Engineers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714",
remark = "This is Shannon's first published paper (his Master's
thesis). In 1940, it received the Alfred Noble Prize of
the combined engineering societies of the United
States, an award given each year to a person not over
thirty for a paper published in one of the journals of
the participating societies. H. H. Goldstine
\cite{Goldstine:1972:CPN} called this work ``one of the
most important master's theses ever written \ldots{} a
landmark in that it helped to change digital circuit
design from an art to a science.''",
}
@Article{Jager:1939:AAD,
author = "Robert Jager and Boyd C. Patterson",
title = "The Artificial Arithmetick in Decimals of {Robert
Jager} ({London}, 1651)",
journal = j-ISIS,
volume = "31",
number = "1",
pages = "25--31",
month = nov,
year = "1939",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:26:49 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302217;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1930.bib",
URL = "http://www.jstor.org/stable/226014",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Article{K:1939:BRBd,
author = "M. G. K.",
title = "Book Review: {{\booktitle{Duodecimal Arithmetic}}, by
George S. Terry}",
journal = j-J-R-STAT-SOC,
volume = "102",
number = "2",
pages = "299--300",
month = "????",
year = "1939",
DOI = "https://doi.org/10.2307/2980013",
ISSN = "0952-8385",
bibdate = "Sat Jan 24 11:18:08 MST 2015",
bibsource = "http://www.jstor.org/stable/i349540;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jrss-a-1930.bib",
URL = "http://www.jstor.org/stable/2980013",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society",
journal-URL = "http://www.jstor.org/journals/09528385.html",
}
@TechReport{Atanasoff:1940:CMS,
author = "J. V. Atanasoff",
title = "Computing machine for the solution of large systems of
linear algebraic equations",
type = "Unpublished memorandum",
institution = "Iowa State College",
address = "Ames, IA, USA",
month = aug,
year = "1940",
bibdate = "Wed Oct 13 11:36:11 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@Misc{Bush:1940:AM,
author = "V. Bush",
title = "Arithmetical Machine",
howpublished = "Vannevar Bush Papers, Container 18, Folder: Caldwell,
Samuel, 1939--1940",
year = "1940",
bibdate = "Wed Oct 13 11:37:32 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.3]{Randell:1982:ODC}.
Copyright interest in the unpublished writings of
Vannevar Bush has been dedicated to the public.",
acknowledgement = ack-nhfb,
}
@TechReport{Stibitz:1940:C,
author = "G. R. Stibitz",
title = "Computer",
type = "Unpublished memorandum",
institution = "Bell Telephone Laboratories",
address = "New York, NY, USA",
year = "1940",
bibdate = "Wed Oct 13 11:30:38 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.1]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@MastersThesis{Berry:1941:DED,
author = "Clifford Edward Berry",
title = "Design of electrical data recording and reading
mechanism",
type = "{M.S.} thesis",
school = "Iowa State College",
address = "Ames, IA, USA",
pages = "32",
year = "1941",
bibdate = "Thu Nov 18 11:18:18 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
author-dates = "1918--1963",
historical-note = "From
http://www.lib.iastate.edu/arch/rgrp/5-2-1-1.html:
``John Vincent Atanasoff received his M.S. (1926) in
Mathematics from Iowa State College (University) and
received his Ph.D. (1930) in Theoretical Physics from
the University of Wisconsin-Madison. He returned to
Iowa State in 1930 as Assistant Professor in
mathematics and physics and was promoted to Associate
Professor (1936). Atanasoff began developing concepts
for an electronic computing machine in 1937. It was
shortly thereafter that he, along with graduate student
Clifford Berry, started work on the world's first
electronic digital computer. The computer would later
be named the Atanasoff-Berry Computer (ABC).
Work on the machine stopped at the start of World War
II in 1941 and the ABC was never patented. Atanasoff
and Berry were both called to support the war effort
and left Iowa State. By the end of the decade, the ABC
was removed from the basement of Physics Hall and
dismantled.
Atanasoff and the ABC were part of a major court case
between Honeywell, Inc. and Sperry Rand Corporation
which occurred 1967-1973. The case involved the ENIAC
patent which covered basic ownership rights to the
design of electronic digital computers. During the
trial, the judge concluded that the invention of the
ENIAC was derived from the work of John Vincent
Atanasoff at Iowa State University.
A replica of the Atanasoff-Berry Computer was completed
and unveiled to the public in 1996. The ABC replica was
constructed by a team of Iowa State scientists at the
Ames Laboratory and was exhibited at museums throughout
the country over the next several years.''",
remark = "This thesis may be one of the earliest surviving
records of the ABC computer built by John Atanasoff and
Clifford Berry in the late 1930s. The one-of-a-kind ABC
was destroyed in 1948, and most of its parts were lost.
Also cited in ``Charles W. Bradley Collection on the
ENIAC Trial, 1930--1966'', (found in
http://discover.lib.umn.edu/): CWB as an attorney for
the group retained by Honeywell in the Honeywell v.
Sperry Rand ENIAC trial. The ABC had a 50-bit word.",
}
@Article{Lancaster:1942:MME,
author = "Otis E. Lancaster",
title = "Machine Method for the Extraction of Cube Root",
journal = j-J-AM-STAT-ASSOC,
volume = "37",
number = "217",
pages = "112--115",
month = mar,
year = "1942",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:24 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314096;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
URL = "http://www.jstor.org/stable/2279437",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@TechReport{Mauchly:1942:UHS,
author = "J. W. Mauchly",
title = "The use of high speed vacuum tube devices for
calculating",
type = "Privately circulated memorandum",
institution = "Moore School of Electrical Engineering, University of
Pennsylvania",
address = "Philadelphia, PA, USA",
month = aug,
year = "1942",
bibdate = "Wed Oct 13 11:52:54 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.6]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@TechReport{Rajchman:1942:REP,
author = "J. A. Rajchman and G. A. Morton and A. W. Vance",
title = "Report on Electronic Predictors for Anti-Aircraft Fire
Control",
institution = "Research Laboratories, R.C.A. Manufacturing Company,
Inc.",
address = "Camden, NJ, USA",
month = apr,
year = "1942",
bibdate = "Sat Feb 8 10:28:55 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@Article{Crawford:1943:DNS,
author = "W. S. H. Crawford",
title = "Discussions and Notes: Square Roots from a Table of
Cosines",
journal = j-AMER-MATH-MONTHLY,
volume = "50",
number = "3",
pages = "190--191",
month = mar,
year = "1943",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:36:57 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@TechReport{Rademacher:1943:MTI,
author = "Hans Rademacher",
title = "Mathematical Topics of Interest in {PX}, Part Two:
Summary of Articles Dealing with Rounding off Errors",
type = "{PX} Report",
number = "14",
institution = "Moore School of Electrical Engineering, Office of the
Director Records, University of Pennsylvania",
address = "Philadelphia, PA, USA",
day = "30",
month = nov,
year = "1943",
bibdate = "Fri Jun 15 17:39:28 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited on page 34 of Haigh, Priestley, and Rope,
\booktitle{ENIAC in Action} (2016) (ISBN 0-262-03398-4)
as an annotated bibliography of rounding errors.",
}
@Article{Goudsmit:1944:SFN,
author = "S. A. Goudsmit and W. H. Furry",
title = "Significant Figures of Numbers in Statistical Tables",
journal = j-NATURE,
volume = "154",
number = "3921",
pages = "800--801",
day = "23",
month = dec,
year = "1944",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/154800a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Sun Sep 18 11:57:19 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf",
abstract = "A rough qualitative explanation of this fact can
easily be given. If we consider tables in which the
entries become rarer the larger they are, we can draw
the obvious conclusion that in any interval, say,
between 10 and 99, or 10,000 and 99,999, there are more
entries on the small side than on the large side.",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Furry:1945:DND,
author = "W. H. Furry and Henry Hurwitz",
title = "Distribution of Numbers and Distribution of
Significant Figures",
journal = j-NATURE,
volume = "155",
number = "3924",
pages = "52--53",
day = "13",
month = jan,
year = "1945",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/155052a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Sun Sep 18 11:51:37 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@TechReport{vonNeumann:1945:FDR,
author = "John von Neumann",
title = "First Draft of a Report on the {EDVAC}",
institution = "University of Pennsylvania",
day = "30",
month = jun,
year = "1945",
bibdate = "Mon Jun 06 19:17:03 2005",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
remark = "This is the report that got von Neumann's name
associated with the serial, stored-program, general
purpose, digital architecture upon which 99.99\% of all
computers today are based.",
xxnote = "Report prepared for U.S. Army Ordinance Department
under Contract W-670-ORD-4926. Reprinted in
\cite[pp.~177--246]{Stern:1981:EUA},
\cite[pp.~399--413]{Randell:1982:ODC},
\cite{vonNeumann:1993:FDR}, and
\cite{Laplante:1996:GPC}.",
}
@Article{Aiken:1946:ASC,
author = "H. H. Aiken and G. M. Hopper",
title = "The {Automatic Sequence Controlled Calculator}",
journal = j-ELECTR-ENG,
volume = "65",
number = "??",
pages = "384--391, 449--454, 522--528",
year = "1946",
CODEN = "ELENAC",
ISSN = "0095-9197",
bibdate = "Wed Oct 13 11:26:29 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Electrical Engineering (American Institute of
Electrical Engineers)",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714",
}
@TechReport{Burks:1946:PDL,
author = "Arthur W. Burks and Herman H. Goldstine and John von
Neumann",
title = "Preliminary discussion of the logical design of an
electronic computing instrument",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "42",
day = "28",
month = jun,
year = "1946",
MRnumber = "MR22442",
bibdate = "Wed Oct 13 08:17:48 2004",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/arith.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Report to the U.S. Army Ordnance Department under
contract W-36-034-OKD-7481. Reprinted in \cite[Paper
2]{Taub:1963:JNCa}, \cite{Bell:1971:CSR}, \cite[pp.
221--259]{Swartzlander:1976:CDD} and \cite[pp.
97--146]{Aspray:1987:PJN}",
URL = "https://deepblue.lib.umich.edu/handle/2027.42/3972;
https://grch.com.ar/docs/p1/Apuntes/eng/Logical%20Design%20of%20an%20Electronic%20Computing%20Instrument.pdf",
acknowledgement = ack-nhfb,
author-dates = "John von Neumann (28 December 1903--8 February 1957)",
remark = "Discusses floating-point versus fixed-point
computation, and concludes that floating-point is
probably not justifiable. They wrote:\par
``There appear to be two major purposes in a `floating'
decimal point system both of which arise from the fact
that the number of digits in a word is a constant fixed
by design considerations for each particular machine.
The first of these purposes is to retain in a sum or
product as many significant digits as possible and the
second of these is to free the human operator from the
burden of estimating and inserting into a problem
`scale factors' --- multiplicative constants which
serve to keep numbers within the limits of the
machine.\par
There is, of course, no denying the fact that human
time is consumed in arranging for the introduction of
suitable scale factors. We only argue that the time so
consumed is a very small percentage of the total time
we will spend in preparing an interesting problem for
our machine. The first advantage of the floating point
is, we feel, somewhat illusory. In order to have such a
floating point, one must waste memory capacity which
could otherwise be used for carrying more digits per
word. It would therefore seem to us not at all clear
whether the modest advantages of a floating binary
point offset the loss of memory capacity and the
increased complexity of the arithmetic and control
circuits.''",
}
@Article{Cesareo:1946:RI,
author = "O. Cesareo",
title = "The Relay Interpolator",
journal = j-BELL-LABS-RECORD,
volume = "23",
number = "??",
pages = "457--460",
year = "1946",
CODEN = "BLRCAB",
ISSN = "0005-8564",
bibdate = "Wed Oct 13 11:31:47 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Bell Laboratories Record",
}
@Article{Comrie:1946:BDC,
author = "L. J. Comrie",
title = "{Babbage}'s Dream Come True",
journal = j-NATURE,
volume = "158",
number = "4017",
pages = "567--568",
day = "26",
month = oct,
year = "1946",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/158567a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Wed Aug 9 07:30:09 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The black mark earned by the government of the day
more than a hundred years ago for its failure to see
Charles Babbage's difference engine brought to a
successful conclusion has still to be wiped out. It is
not too much to say that it cost Britain the leading
place in the art of mechanical computing. Babbage then
conceived and worked on his `analytical engine',
designed to store numbers and operate on them according
to a sequence of processes conveyed to the machine by
cards similar to those used in the Jacquard loom. This,
however, was never completed.",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
remark = "The title in the Nature archive index is completely
wrong: it says ``A Manual of Operation for the
Automatic Sequence Controlled Calculator''. After the
critical introduction [see the abstract], the article
goes on to describe IBM's gift to Harvard of the
Automatic Sequence Controlled Calculator. It reports
about the ASCC: ``The machine contains seventy-two
storage counters, capable of holding twenty-three
digits and a sign. \ldots{} When working to the full
23-figure capacity of the machine, multiplication takes
about six seconds, and division twice as long;
additions and subtractions are done at the rate of
three a second, whatever their length.'' It then
describes the computation of logarithms via the Taylor
series expansion of $ \log (1 + x) $, and reports that
it can do exponential, trigonometric, and hyperbolic
functions as well.",
}
@TechReport{Dreyer:1946:REM,
author = "H.-J. Dreyer and A. Walther",
title = "{Der Rechenautomat Ipm. Entwicklung Mathematischer
Instrumente in Deutschland 1939 bis 1945}. ({German})
[{The} {Ipm} Calculator. {The} development of
mathematical instruments in {Germany} 1939--1945]",
type = "{Bericht}",
number = "A3",
institution = "Institut f{\"u}r Praktische Mathematik, Technische
Hochschule",
address = "Darmstadt, West Germany",
day = "19",
month = aug,
year = "1946",
bibdate = "Wed Oct 13 11:20:15 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 3.3]{Randell:1982:ODC}.
Translated by Mr. and Mrs. P. Jones",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Goldstine:1946:ENI,
author = "H. H. Goldstine and Adele Goldstine",
title = "The {Electronic Numerical Integrator and Computer
(ENIAC)}",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "2",
number = "15",
pages = "97--110",
month = jul,
year = "1946",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
note = "Reprinted in \cite[\S 7.7]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
ajournal = "Math. Tables Other Aids Comput.",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@TechReport{Goldstine:1947:PCPa,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument. {Part 1}, Vol. 1",
type = "Technical report",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "??",
month = "????",
year = "1947",
bibdate = "Fri Nov 16 16:35:14 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Goldstine:1947:PCPb,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument. {Part 2}, Vol. 1",
type = "Technical report",
number = "1",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "69",
day = "1",
month = apr,
year = "1947",
MRnumber = "MR22443",
bibdate = "Wed Jun 01 17:41:33 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Report prepared for U.S. Army Ordnance Department
under contract W-36-034-OKD-7481. Reprinted in
\cite[80--151]{Taub:1963:JNCa}. Knuth \cite[p.
278]{Knuth:1998:SA} cites pp. 142--151 of this report
as the first published treatment of double-precision
arithmetic on digital computers.",
acknowledgement = ack-nhfb,
}
@TechReport{Goldstine:1947:PCPc,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument. {Part 1}, Vol. 2",
type = "Technical report",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "??",
month = "????",
year = "1947",
bibdate = "Fri Nov 16 16:35:14 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Goldstine:1947:PCPd,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument. {Part 2}, Vol. 2",
type = "Technical report",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "??",
month = "????",
year = "1947",
bibdate = "Fri Nov 16 16:35:14 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Goldstine:1947:PCPe,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument. {Part 1}, Vol. 3",
type = "Technical report",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "??",
month = "????",
year = "1947",
bibdate = "Fri Nov 16 16:35:14 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Goldstine:1947:PCPf,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument. {Part 2}, Vol. 3",
type = "Technical report",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "??",
month = "????",
year = "1947",
bibdate = "Fri Nov 16 16:35:14 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{HUCL:1946:MOA,
author = "{Harvard University. Computation Laboratory}",
title = "A Manual of Operation for the {Automatic Sequence
Controlled Calculator}",
publisher = pub-HARVARD,
address = pub-HARVARD:adr,
pages = "561",
year = "1946",
LCCN = "QA3 .H3 v.1",
bibdate = "Mon Nov 4 07:46:57 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Its Annals v. 1",
acknowledgement = ack-nhfb,
keywords = "electronic digital computers; mathematics ---
bibliography",
}
@TechReport{Turing:1946:PEC,
author = "A. M. Turing",
title = "Proposed Electronic Calculator",
type = "Report",
number = "E882",
institution = inst-NPL,
address = inst-NPL:adr,
pages = "48",
year = "1946",
bibdate = "Fri Nov 25 16:22:27 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.emula3.com/docs/Turing_Report_on_ACE.pdf",
acknowledgement = ack-nhfb,
author-dates = "Alan Mathison Turing (23 June 1912--7 June 1954)",
xxnote = "Reprinted in \cite{Turing:1972:MTO}.",
}
@Article{Juley:1947:BC,
author = "J. Juley",
title = "The Ballistic Computer",
journal = j-BELL-LABS-RECORD,
volume = "24",
number = "??",
pages = "5--9",
year = "1947",
CODEN = "BLRCAB",
ISSN = "0005-8564",
bibdate = "Wed Oct 13 11:32:38 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.3]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Bell Laboratories Record",
}
@InProceedings{Mauchly:1947:PPE,
author = "J. W. Mauchly",
booktitle = "{Proceedings of a Symposium on Large Scale Digital
Calculating Machinery, 7--10 January 1947}",
title = "Preparation of problems for {EDVAC}-type machines",
publisher = "Harvard University Press",
address = "Cambridge, MA, USA",
year = "1947",
bibdate = "Wed Oct 13 11:55:58 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in {\em Annals of the Computation Laboratory
of Harvard University}, {\bf 16}, 203--207 (1948).
Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@Article{Richeson:1947:FAP,
author = "A. W. Richeson",
title = "The First Arithmetic Printed in {English}",
journal = j-ISIS,
volume = "37",
number = "1--2",
pages = "47--56",
month = may,
year = "1947",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:27:09 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302230;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1940.bib",
URL = "http://www.jstor.org/stable/226161",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
remark = "From the second paragraph: ``The earliest printed work
in English to discuss arithmetic, \booktitle{The
Myrrour of the World}, came from the press of William
Caxton in 1481. This work, however, contained only one
page devoted entirely to arithmetic. It is not until
1537 that we find another book printed in English
devoted entirely to arithmetic and dealing with the
Hindu--Arabic system of numbers. This is an anonymous
publication, from a press located at St. Albans, with
the title \booktitle{An Introduction for to Lerne to
Recken with the Pen, or with the Counters},'' This book
went through eight editions between 1537 and 1629. The
article quotes book sections on integer division.",
}
@Article{vonNeumann:1947:NIM,
author = "John von Neumann and Herman H. Goldstine",
title = "Numerical Inverting of Matrices of High Order",
journal = j-BULL-AMS,
volume = "53",
number = "11",
pages = "1021--1099",
month = nov,
year = "1947",
CODEN = "BAMOAD",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
MRclass = "65.0X",
MRnumber = "MR0024235 (9,471b)",
MRreviewer = "E. Bodewig",
bibdate = "Thu Nov 8 14:49:36 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/auto.diff.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.1.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/Matrix.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/sparse.linear.systems.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Goldstine:1951:NIM} for Part II. Reprinted
in \cite[vol. 5, pp. 479--557]{Taub:1961:JNCa}.",
URL = "http://projecteuclid.org/euclid.bams/1183511222",
ZMnumber = "0031.31402",
acknowledgement = ack-nhfb # " and " # ack-jg,
author-dates = "John von Neumann (28 December 1903--8 February 1957)",
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
kwds = "nla, linear system, rounding error",
referred = "[Markov1999a].",
remark = "This may be the first journal publication about the
use of double-precision arithmetic on computers, used
for the accumulation of inner products and matrix
products. On pp. 1035--1038, the authors show that when
the sum of $m$ products of two $s$-digit numbers is
accumulated in precision $ 2 s $, with rounding to $s$
digits only after the final sum is complete, then the
rounding error is essentially one unit in the last
place, instead of $m$ times that value. Cited in
\cite{Sterbenz:1974:FPC}.",
}
@Article{Alt:1948:BTLa,
author = "Franz L. Alt",
title = "A {Bell Telephone Laboratories}' Computing
Machine---{I}",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "3",
number = "21",
pages = "1--13",
month = jan,
year = "1948",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
note = "Reprinted in \cite[\S 6.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
ajournal = "Math. Tables Other Aids Comput.",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Eckert:1948:EC,
author = "W. J. Eckert",
title = "Electrons and computation",
journal = j-SCI-MONTHLY,
volume = "67",
number = "5",
pages = "315--323",
month = nov,
year = "1948",
CODEN = "SCMOAA",
ISSN = "0096-3771 (print), 2327-7513 (electronic)",
bibdate = "Wed Oct 13 11:27:40 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.3]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "The Scientific Monthly",
journal-URL = "http://www.jstor.org/journal/sciemont",
}
@InProceedings{Rademacher:1948:AEP,
author = "Hans A. Rademacher",
title = "On the Accumulation of Errors in Processes of
Integration on High-Speed Calculating Machines",
crossref = "Anonymous:1948:PSL",
pages = "176--187",
year = "1948",
bibdate = "Mon Jun 18 11:03:56 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "From page 186, remark by John W. Mauchly: ``I just
wanted to remark that this paper is probably one of the
first to appear as a result of the interaction between
computing machines and mathematics. I think many of us
have been looking forward with certainty to the day
when the advent of computing machines would influence
the course of mathematics, and there are still many
directions in which we can look forward to further such
impacts. This reaction is not, of course, one way.
Mathematics should also influence the computing
machine.''",
}
@TechReport{Tukey:1948:NSR,
author = "John W. Tukey",
title = "A note on the square-root iteration",
type = "SRG Memorandum report",
number = "10",
institution = inst-PRINCETON,
address = inst-PRINCETON:adr,
pages = "18",
year = "1948",
bibdate = "Tue May 15 08:00:09 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Turing:1948:REM,
author = "A. M. Turing",
title = "Rounding-Off Errors in Matrix Processes",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "1",
pages = "287--308",
month = sep,
year = "1948",
CODEN = "QJMMAV",
ISSN = "0033-5614 (print), 1464-3855 (electronic)",
ISSN-L = "0033-5614",
MRclass = "65.0X",
MRnumber = "MR0028100 (10,405c)",
MRreviewer = "E. Bodewig",
bibdate = "Sat Nov 19 12:09:58 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/a/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite{Turing:1992:PM} with summary and
notes (including corrections)",
URL = "http://turing.ecs.soton.ac.uk/browse.php/B/18",
ZMnumber = "0033.28501",
acknowledgement = ack-nhfb,
fjournal = "Quarterly Journal of Mechanics and Applied
Mathematics",
journal-URL = "http://qjmam.oxfordjournals.org/content/by/year",
mynote = "The notes are not very good. They mainly correct
errors and fill in the gaps of derivations. Much better
would have been higher level comments from a numerical
analyst, e.g. on where Turing's ideas/predictions were
wrong.",
}
@Article{Williams:1948:EDC,
author = "F. C. Williams and T. Kilburn",
title = "Electronic digital computers",
journal = j-NATURE,
volume = "162",
number = "4117",
pages = "487--487",
day = "25",
month = sep,
year = "1948",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/162487a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Wed Oct 13 12:00:02 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
remark = "Letter submitted 3 August 1948. Describes a small
prototype digital computer with 32 31-bit words for
instructions, data, and working storage.",
}
@Article{Davis:1949:MM,
author = "Harry M. Davis",
title = "Mathematical Machines",
journal = j-SCI-AMER,
volume = "180",
number = "4",
pages = "28--39",
month = apr,
year = "1949",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican0449-28",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Sat May 18 16:12:10 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciam1940.bib",
URL = "http://www.jstor.org/stable/24967160;
http://www.nature.com/scientificamerican/journal/v180/n4/pdf/scientificamerican0449-28.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
remark = "Description of counting devices before 1950, including
an introduction to the binary number system.",
}
@Article{Hartree:1949:NSR,
author = "Douglas R. (Douglas Rayner) Hartree",
title = "Note On Systematic Roundoff Errors in Numerical
Integration",
journal = "Journal of Research of the National Bureau of
Standards",
volume = "42",
number = "??",
pages = "62--??",
month = "????",
year = "1949",
bibdate = "Wed Feb 14 19:07:37 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Huskey:1949:PCP,
author = "H. D. Huskey",
title = "On the Precision of a Certain Procedure of Numerical
Integration",
journal = j-J-RES-NATL-BUR-STAND,
volume = "42",
number = "1",
pages = "57--62",
month = jan,
year = "1949",
CODEN = "JRNBAG",
DOI = "https://doi.org/10.6028/jres.042.005",
ISSN = "0091-0635 (print), 2376-5305 (electronic)",
ISSN-L = "0091-0635",
bibdate = "Fri Aug 20 09:32:34 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "With an appendix by Douglas R. Hartree.",
abstract = "An example of numerical integration is given that
shows very systematic effects in the less significant
digits. This lack of randomness gives rounding-off
errors that exceed the predicted standard deviation by
a factor of three. The example considered in this paper
shows that systematic rounding-off errors can occur in
numerical in integration, irrespective of the number of
digits kept in the contributions to the integral. In
the appendix this phenomenon is examined, and criteria
are set up to detect the cases in which it may arise to
a serious extent.",
acknowledgement = ack-nhfb,
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@TechReport{Tukey:1949:TRA,
author = "John W. Tukey and M. F. Freeman",
title = "Transformation related to the angular and the
square-root",
type = "SRG Memorandum report",
number = "24",
institution = inst-PRINCETON,
address = inst-PRINCETON:adr,
pages = "??",
year = "1949",
bibdate = "Tue May 15 08:00:09 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Stifler:1950:HSC,
editor = "W. W. {Stifler, Jr.}",
title = "High-speed computing devices",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xiii + 451",
year = "1950",
LCCN = "QA75 .E5",
bibdate = "Fri Aug 20 10:18:44 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Supervised by Charles Brown Tompkins and C. H.
Wakelin, Engineering Research Associates. The contents
of this volume were first assembled in the form of a
report to the Office of Naval Research, prepared under
a provision of contract N6-ONR-240, Task 1. Cited in
\cite{Sterbenz:1974:FPC}.",
subject = "computers",
}
@Article{Harrison:1950:BDC,
author = "J. O. {Harrison, Jr.}",
title = "Binary--Decimal Conversion on a Desk Calculator (in
Automatic Computing Machinery; Discussions)",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "4",
number = "32",
pages = "231--234",
month = oct,
year = "1950",
CODEN = "MTTCAS",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2002500",
acknowledgement = ack-nhfb,
ajournal = "Math. Tables Other Aids Comput.",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InProceedings{Wilkes:1950:E,
author = "M. V. Wilkes and W. Renwick",
booktitle = "{Report of a Conference on High Speed Automatic
Calculating Machines, 22--25 June 1949}",
title = "The {EDSAC}",
publisher = "University Mathematical Laboratory",
address = "Cambridge, UK",
pages = "9--11",
month = jan,
year = "1950",
bibdate = "Wed Oct 13 12:00:41 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.5]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@InProceedings{Worsley:1950:ED,
author = "B. H. Worsley",
booktitle = "Report of a Conference on High Speed Automatic
Calculating Machines, {22--25 June 1949}",
title = "The {EDSAC} demonstration",
publisher = "University Mathematical Laboratory",
address = "Cambridge, UK",
pages = "12--16",
month = jan,
year = "1950",
bibdate = "Wed Oct 13 11:39:09 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.6]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@Misc{Anonymous:1951:R,
author = "Anonymous",
title = "{RECIPROOT}",
howpublished = "Manchester University Electronic Computer Web
document.",
day = "9",
month = jul,
year = "1951",
bibdate = "Sat Aug 19 09:57:33 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "To calculate square roots and reciprocal square
roots.",
URL = "https://0x5f37642f.com/documents/ManchesterRecipRoot.pdf",
acknowledgement = ack-nhfb,
remark = "Code used on Ferranti Mark I.",
}
@Article{Booth:1951:SBM,
author = "A. D. Booth",
title = "A signed binary multiplication technique",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "4",
number = "2",
pages = "236--240",
month = "????",
year = "1951",
CODEN = "QJMMAV",
ISSN = "0033-5614 (print), 1464-3855 (electronic)",
ISSN-L = "0033-5614",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "Quarterly Journal of Mechanics and Applied
Mathematics",
journal-URL = "http://qjmam.oxfordjournals.org/content/by/year",
}
@InCollection{Brown:1951:HRR,
author = "G. W. Brown",
title = "History of {RAND}'s random digits",
crossref = "Householder:1951:MCM",
pages = "31--32",
year = "1951",
bibdate = "Sun Sep 18 12:02:43 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.rand.org/pubs/papers/2008/P113.pdf",
acknowledgement = ack-nhfb,
}
@Article{Gill:1951:PSS,
author = "S. Gill",
title = "A process for the step-by-step integration of
differential equations in an automatic digital
computing machine",
journal = j-PROC-CAMBRIDGE-PHIL-SOC,
volume = "47",
pages = "96--108",
year = "1951",
CODEN = "PCPSA4",
ISSN = "0008-1981",
bibdate = "Tue Aug 28 05:54:12 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Cambridge Philosophical Society.
Mathematical and physical sciences",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP",
keywords = "accurate floating-point summation; floating-point
arithmetic; rounding errors",
remark = "Higham \cite{Higham:1993:AFP} comments ``In 1951 Gill
[8] noticed that the rounding error in the sum of two
numbers could be estimated by subtracting one of the
numbers from the sum, and he made use of this estimate
in a Runge--Kutta code in a program library for the
EDSAC computer.''",
}
@Article{Goldstine:1951:NIM,
author = "Herman H. Goldstine and John von Neumann",
title = "Numerical Inverting of Matrices of High Order. {II}",
journal = j-PROC-AM-MATH-SOC,
volume = "2",
pages = "188--202",
year = "1951",
CODEN = "PAMYAR",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "65.0X",
MRnumber = "MR0041539 (12,861b)",
MRreviewer = "F. J. Murray",
bibdate = "Thu Nov 8 14:49:46 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{vonNeumann:1947:NIM} for Part I. Reprinted
in \cite[Paper 15, pp. 558--572]{Taub:1963:JNCa}.",
URL = "http://www.jstor.org/view/00029939/di970628/97p0185x/0",
ZMnumber = "043.12301",
acknowledgement = ack-nhfb,
author-dates = "John von Neumann (28 December 1903--8 February 1957)",
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
}
@Article{MacMillan:1951:FDC,
author = "Donald B. MacMillan and Richard H. Stark",
title = "``Floating Decimal'' Calculation on the {IBM} Card
Programmed Electronic Calculator (in Automatic
Computing Machinery; Discussions)",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "5",
number = "34",
pages = "86--92",
month = apr,
year = "1951",
CODEN = "MTTCAS",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Tables Other Aids Comput.",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InProceedings{Rademacher:1951:AEP,
author = "Hans Rademacher",
booktitle = "Proceedings of a Symposium on Large-scale Digital
Calculating Machinery",
title = "On the accumulation of errors in processes of
integration on high-speed calculating machines",
publisher = pub-HARVARD,
address = pub-HARVARD:adr,
pages = "176--185",
year = "1951",
bibdate = "Mon Jun 18 06:50:41 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Shirley:1951:BNB,
author = "John W. Shirley",
title = "Binary Numeration before {Leibniz}",
journal = j-AMER-J-PHYSICS,
volume = "19",
number = "8",
pages = "452--454",
month = nov,
year = "1951",
CODEN = "AJPIAS",
DOI = "https://doi.org/10.1119/1.1933042",
ISSN = "0002-9505 (print), 1943-2909 (electronic)",
ISSN-L = "0002-9505",
bibdate = "Sat Feb 8 10:29:20 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://scitation.aip.org/content/aapt/journal/ajp/19/8/10.1119/1.1933042",
abstract = "Though it is frequently stated that binary numeration
was first formally proposed by Leibniz as an
illustration of his dualistic philosophy, the
mathematical papers of Thomas Hariot (1560--1621) show
clearly that Hariot not only experimented with number
systems, but also understood clearly the theory and
practice of binary numeration nearly a century before
Leibniz's time.",
acknowledgement = ack-nhfb,
fjournal = "American Journal of Physics",
journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp",
remark = "Submitted 14 November 1950.",
}
@Book{Wilkes:1951:PPE,
author = "Maurice V. Wilkes and David J. Wheeler and Stanley
Gill",
title = "The Preparation of Programs for an Electronic Digital
Computer",
publisher = pub-AW,
address = pub-AW:adr,
pages = "167",
year = "1951",
LCCN = "QA76.5 .W55 1951",
bibdate = "Mon Feb 10 09:42:47 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also second edition \cite{Wilkes:1957:PPE}, and
reprint \cite{Wilkes:1982:PPE}.",
acknowledgement = ack-nhfb,
tableofcontents = "Part I \\
Chapter 1. The Design of Programs for Electronic
Computing Machines / 1 \\
1-1 Introduction / 1 \\
1-2 Types of automatic computing machines / 2 \\
1-3 Description of the EDSAC / 3 \\
1-4 The EDSAC order code / 5 \\
1-5 Notes on the order code / 6 \\
1-6 The use of conditional orders / 7 \\
1-7 Modification of orders by the program / 8 \\
1-8 Multiaddress codes / 11 \\
1-9 Binary--decimal conversion / 12 \\
1-10 Checking facilities / 14 \\
Chapter 2. Input of Orders / 15 \\
2-1 Initial orders / 15 \\
2-2 Pseudo-orders / 17 \\
2-3 Examples / 17 \\
2-4 Control combinations / 17 \\
2-5 Starting the program / 18 \\
2-6 Use of code letters / 19 \\
2-7 Constants / 20 \\
2-8 Notation / 20 \\
Chapter 3. Subroutines and Parameters / 22 \\
3-1 Open subroutines / 22 \\
3-2 closed subroutines / 22 \\
3-3 preset parameters / 23 \\
3-4 program parameters / 23 \\
Chapter 4. Library Subroutines and their Use in
Constructing Programs / 25 \\
4-1 Library catalog / 25 \\
4-2 Input and output subroutines / 25 \\
4-3 Division subroutines / 27 \\
4-4 Trigonometrical and other functions / 27 \\
4-5 Quadrature / 27 \\
4-6 Assembly subroutines / 27 \\
4-7 Integration of differential equations / 32 \\
4-8 Processes, Interpretive subroutines / 34 \\
Chapter 5. Pitfalls / 38 \\
5-1 Proofreading of programs, points to be checked / 38
\\
5-2 Location of mistakes in a program / 39 \\
5-3 Counting operations / 41 \\
Chapter 6. Use of the EDSAC \& Its Associated Equipment
/ 42 \\
6-1 Tape Punching \& editing facilities / 42 \\
6-2 Storage of library subroutines / 43 \\
6-3 EDSAC organization / 43 \\
6-4 EDSAC controls / 43 \\
Chapter 7. Examples / 45 \\
7-1 Example 1. Calculation of $\exp(-\sin x)$ / 45 \\
7-2 Example 2. Calculation of $\pi$ by evaluation of
definite integral / 48 \\
7-3 Alternative method for Example 2 / 52 \\
7-4 Example 2, with extra print orders for checking /
53 \\
7-5 Application of checking subroutine C11 to Example 2
/ 54 \\
7-6 Example of integration of an ordinary differential
equation / 46 \\
7-7 Evaluation of a definite integral / 61 \\
7-8 Program to facilitate the solution of algebraic
equation / 66 \\
Part II. Specifications of Library Subroutines / 72 \\
A. Subroutines to carry out floating point arithmetic /
73 \\
B. Subroutines to carry out arithmetical operations on
complex numbers / 78 \\
C. Checking subroutines / 79 \\
D. Division subroutines / 82 \\
E. Exponential subroutines / 83 \\
F. General routines relating to functions / 84 \\
G. Subroutines for integration of ordinary differential
equations / 86 \\
J. Subroutines for calculating special functions
[Legendre polynomials] / 88 \\
K. Subroutines for the summation of power series / 88
\\
L. Subroutines for evaluating logarithms / 91 \\
M. Miscellaneous subroutines / 91 \\
P. Print subroutines / 92 \\
Q. Quadrature subroutines / 95 \\
R. Input subroutines / 96 \\
S. Subroutines for evaluation of fractional powers / 98
\\
T. Subroutines for calculating trigonometrical
functions / 99 \\
U. Subroutines for counting operations / 101 \\
V1. Multiplication of vector by symmetric matrix / 102
\\
V2. Addition and subtraction of $n$ dimensional vectors
/ 103 \\
Part III. Programs of Selected Library Subroutines /
104 \\
Appendix A. Keyboard perforator code, etc. / 158 \\
Appendix B. The initial orders / 159 \\
Appendix C. Control combinations / 161 \\
Appendix D. Interpretive subroutines: example of
packing of orders / 162 \\
Appendix E. Methods of counting in a simple cycle / 164
\\
Index",
}
@InProceedings{Andrews:1952:RBL,
author = "E. G. Andrews",
editor = "J. C. McPherson",
booktitle = "Proceedings of the {AIEE-IRE '51}: Papers and
discussions presented at the December 10--12, 1951,
joint {AIEE-IRE} computer conference, Philadelphia,
{PA}: Review of electronic digital computers",
title = "A review of the {Bell Laboratories}' digital computer
developments",
publisher = pub-ACM,
address = pub-ACM:adr,
bookpages = "vi + 114",
pages = "101--105",
year = "1952",
DOI = "https://doi.org/10.1145/1434770.1434787",
LCCN = "????",
bibdate = "Fri Dec 03 09:17:58 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Bell Laboratories Model 1--5 relay computers; complex
fixed-point decimal arithmetic; complex floating-point
decimal arithmetic",
remark-1 = "From page 101: ``The Bell Telephone Laboratories have
designed and built seven digital computers.''",
remark-2 = "From page 101: ``George R. Stibitz \ldots{} designed
and \ldots{} called it a ``complex number computer.''",
remark-3 = "From page 101: ``This computer operated with binary
coded decimal notation, with the decimal digits 0 to 9
being represented by the binary numbers 0011 to 1100.
The input and output information consisted of eight
place numbers, but the calculator carried operations
out to ten places, the two extra places being used to
improve accuracy when accumulating the results of
several problems.''",
remark-4 = "From page 104: ``Besides these advantages in operation
ease, another has been developed but it has not yet
been incorporated into a computer as far as is known.
This is the self-correcting code for numerical data.
Dr. R. W. Hamming devised this principle of coding. A
computer with this feature would show an unattended
operation performance superior to anything we know
today.'' [Refers to ``Error Detecting and Error
Correcting Codes'', The Bell System Technical Journal
{\bf 29}(2) 147--160, April 1960,
doi:10.1002/j.1538-7305.1950.tb00463.x].",
}
@Article{Davis:1952:ARS,
author = "K. Davis and R. Biddulph and S. Balashek",
title = "Automatic Recognition of Spoken Digits",
journal = j-J-ACOUST-SOC-AM,
volume = "24",
number = "6",
pages = "637--642",
month = nov,
year = "1952",
CODEN = "JASMAN",
ISSN = "0001-4966",
ISSN-L = "0001-4966",
bibdate = "Fri Nov 28 16:38:51 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "Journal of the Acoustical Society of America",
journal-URL = "http://scitation.aip.org/content/asa/journal/jasa",
}
@Article{Hammersley:1952:CSS,
author = "J. M. Hammersley",
title = "The computation of sums of squares and products on a
desk calculator",
journal = j-BIOMETRICS,
volume = "8",
number = "??",
pages = "156--168",
year = "1952",
CODEN = "BIOMB6",
DOI = "https://doi.org/10.2307/3001930",
ISSN = "0006-341X (print), 1541-0420 (electronic)",
ISSN-L = "0006-341X",
MRclass = "65.0X",
MRnumber = "48908",
MRreviewer = "E. Lukacs",
bibdate = "Thu Jun 25 17:01:03 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/biometrics1950.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "Biometrics",
fjournal = "Biometrics",
journal-URL = "http://www.jstor.org/journal/biometrics",
}
@Article{Irani:1952:SMT,
author = "Rida A. K. Irani",
title = "A sexagesimal multiplication table in the {Arabic}
alphabetical system",
journal = j-SCRIPTA-MATH,
volume = "18",
number = "??",
pages = "92--93",
month = "????",
year = "1952",
ISSN = "0036-9713",
ISSN-L = "0036-9713",
MRclass = "01.0X",
MRnumber = "49109",
bibdate = "Thu Oct 26 11:15:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
ZMnumber = "0046.00102",
acknowledgement = ack-nhfb,
ajournal = "Scripta Math.",
fjournal = "Scripta Mathematica: A Quarterly Journal Devoted to
the Philosophy, History, and Expository Treatment of
Mathematics",
ZBmath = "3070983",
}
@Article{Michaelson:1952:BA,
author = "R. L. Michaelson",
title = "Binary Arithmetic",
journal = j-INC-STAT,
volume = "3",
number = "1",
pages = "35--40",
month = feb,
year = "1952",
CODEN = "????",
DOI = "https://doi.org/10.2307/2986591",
ISSN = "1466-9404",
ISSN-L = "1466-9404",
bibdate = "Thu Jan 22 18:10:18 MST 2015",
bibsource = "http://www.jstor.org/stable/i349863;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jrss-d-1950.bib",
URL = "http://www.jstor.org/stable/2986591",
acknowledgement = ack-nhfb,
fjournal = "The Incorporated Statistician",
journal-URL = "http://www.jstor.org/journals/14669404.html",
}
@Article{Morrill:1952:SEM,
author = "C. D. Morrill and R. V. Baum",
title = "A Stabilized Electronic Multiplier",
journal = j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT,
volume = "EC-1",
number = "??",
pages = "52--59",
month = dec,
year = "1952",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Jul 15 15:20:53 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the I.R.E. Professional Group on
Electronic Computers",
}
@InProceedings{Sheldon:1952:ICP,
author = "J. W. Sheldon and L. Tatum",
booktitle = "Review of Electronic Digital Computers. {Joint
AIEE--IRE Computer Conference. 10--12 December 1951}",
title = "The {IBM} card-programmed electronic calculator",
publisher = "American Institute of Electrical Engineers",
address = "New York, NY, USA",
pages = "30--36",
year = "1952",
bibdate = "Wed Oct 13 11:28:45 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@Article{Brooker:1953:FOE,
author = "R. A. Brooker and D. J. Wheeler",
title = "Floating Operations on the {EDSAC} (in Automatic
Computing Machinery; Discussions)",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "7",
number = "41",
pages = "37--47",
month = jan,
year = "1953",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1953-0052901-3",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
abstract = "The difficulties which arise when programming
calculations for large automatic calculating machines
which have a fixed decimal point are discussed. This
leads to a consideration of the possibility of using
floating decimal arithmetic for certain kinds of
calculations. A method by which floating decimal
arithmetic can be carried out with any fixed
decimal-point machine is outlined and the scheme
adopted for use with the EDSAC is described in
detail.",
acknowledgement = ack-nhfb,
ajournal = "Math. Tables Other Aids Comput.",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "floating-point decimal arithmetic",
remark-01 = "From page 38: ``The problem [of programmer-controlled
numeric scaling] does not arise with machines designed
to operate directly with numbers expressed in the
floating radix form. Numbers in this form are
represented by $a \cdot r^p$. The first machine of this
kind was the Bell Telephone Laboratories Relay Computer
Model V(1). This is a decimal machine (that is, $r =
10$) in which $1 > |a| > 0.1$, $19 > p > -19$ and $a$
is expressed to an accuracy of seven significant
figures. Since this was completed all important relay
machines have been equipped with similar facilities. No
electronic machine of this kind has yet been built but
we would remark that in our opinion an electronic
machine provided with a floating point arithmetical
unit would be a powerful computing instrument even if
it had a relatively slow store, a magnetic drum, for
example.''",
remark-02 = "From page 39: ``Two long and two short storage
locations are set aside to form a kind of `arithmetical
unit.' One long location holds the numerical part of a
number and one short location holds the exponent.
Together they form the {\em floating decimal
accumulator}. In a similar fashion the other long
location and the other short location form the {\em
floating decimal register}.''",
remark-03 = "From page 40: ``the floating decimal accumulator is
then `cleared' by replacing the number held in it by
zero, that is, by the special number $010^{-63}$.''",
remark-04 = "From page 40: `The use of two separate storage
locations for the floating decimal accumulator allows
the range and accuracy of numbers held therein to be
greater than those held in a single storage location
elsewhere. This enables products to be accumulated
without loss of accuracy due to intermediate
rounding-off errors.''",
remark-05 = "From the conclusion on page 46: ``From a direct
comparison it would seem that the floating 'orders,'
other than those used for reading and writing, are
about 60 times as slow as the machine orders and hence
that a programme using the interpretive subroutine
would be slower by the same factor. This is not
altogether true because in such a programme fewer
orders' are needed than would otherwise be necessary as
there are no scale factors to deal with and the
techniques for counting and for the modification of
orders' have been streamlined. Moreover, the time taken
by the C auxiliaries is about the same as that taken by
the corresponding subroutine in fixed decimal-point
working. These factors vary from problem to problem but
our experience has shown that the reduction in speed
varies from about 20 to 1 to about 4 to 1. The
reduction of the time taken to code a problem has to be
experienced to be believed!''",
}
@Book{IBM:1953:POT,
author = "{IBM Corporation}",
title = "Principles of Operation: Type 701 and Associated
Equipment",
publisher = pub-IBM,
address = pub-IBM:adr,
pages = "103",
year = "1953",
bibdate = "Wed Sep 14 23:17:49 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Samelson:1953:ORR,
author = "Klaus Samelson and Friedrich L. Bauer",
title = "{Optimale Rechengenauigkeit bei Rechenanlagen mit
gleitendem Komma}. ({German}) [{Optimal} calculation
accuracy for calculators with a floating point]",
journal = j-Z-ANGE-MATH-PHYS,
volume = "4",
number = "4",
pages = "312--316",
month = jul,
year = "1953",
CODEN = "ZAMPDB",
DOI = "https://doi.org/10.1007/bf02074638",
ISSN = "0044-2275 (print), 1420-9039 (electronic)",
ISSN-L = "0044-2275",
bibdate = "Sun Aug 16 18:04:35 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Digital automatic computing machines with floating
binary point are investigated with respect to their
accuracy. It is concluded that special devices can be
designed without difficulty, which guarantee the
highest accuracy obtainable with a fixed number of
digits. For binary computers, a modification of the
usual conversion routine is necessary, which is
discussed in detail.",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und Physik
= Journal of Applied Mathematics and Physics}",
journal-URL = "http://link.springer.com/journal/33",
keywords = "number base conversion",
language = "German",
}
@InCollection{Stiefel:1953:MCA,
author = "E. Stiefel",
booktitle = "Les machines {\`a} calculer et la pens{\'e}e humaine",
title = "La machine {\`a} calculer arithm{\'e}tique ``{Z4}'' de
l'{Ecole} {Polytechnique} {F}{\'e}d{\'e}rale {\`a}
{Zurich} ({Suisse}) et son application {\`a} la
r{\'e}solution d'une {\'e}quation aux d{\'e}riv{\'e}es
partielles de type elliptique. ({French}) [{The}
arithmetic calculator ``{Z4}'' of the {Swiss Federal
Polytechnical University in Zurich (Switzerland)} and
its application to the solution of an elliptical type
partial derivative equation]",
publisher = "Centre National de la Recherche Scientifique",
address = "Paris, France",
pages = "33--40",
year = "1953",
MRclass = "65.0X",
MRnumber = "0066093",
bibdate = "Wed Sep 2 16:23:13 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Colloques internationaux du Centre National de la
Recherche Scientifique, no 37",
acknowledgement = ack-nhfb,
author-dates = "Eduard Stiefel (21 April 1909--25 November 1978)",
language = "French",
}
@Article{Backus:1954:ISS,
author = "J. W. Backus",
title = "The {IBM 701 Speedcoding} System",
journal = j-J-ACM,
volume = "1",
number = "1",
pages = "4--6",
month = jan,
year = "1954",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Fri Nov 04 00:18:27 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://community.computerhistory.org/scc/projects/FORTRAN/paper/p4-backus.pdf",
abstract = "The IBM 701 Speedcoding System is a set of
instructions which causes the 701 to behave like a
three-address floating point calculator. Let us call
this the Speedcoding calculator. In addition to
operating in floating point, this Speedcoding
calculator has extremely convenient means for getting
information into the machine and for printing results;
it has an extensive set of operations to make the job
of programming as easy as possible. Speedcoding also
provides automatic address modification, flexible
tracing, convenient use of auxiliary storage, and
built-in checking.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Manual{Burroughs:1954:DH,
author = "{Burroughs Corporation.ElectroData}",
title = "Datatron handbooks",
organization = "The Division",
address = "Pasadena, CA, USA",
year = "1954",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "12 volumes in 1.",
acknowledgement = ack-nhfb,
keywords = "Datatron (Computer)",
remark = "Datatron programming and coding manual --- Datatron
operation manual --- Central computer handbook ---
Paper tape system handbook --- Card converter Model 500
handbook --- Magnetic tape system handbook ---
Cardatron system handbook --- Model 560 DATAFILE
handbook --- Control console and consolette handbook
--- Floating point control unit handbook --- External
switching unit handbook --- Tape preparation unit
handbook.",
}
@Article{Freeman:1954:TSA,
author = "H. Freeman and E. Parsons",
title = "Time-Sharing Analog Multiplier ({TSAM})",
journal = j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT,
volume = "EC-3",
number = "1",
pages = "11--17",
month = mar,
year = "1954",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Jul 15 15:20:53 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the I.R.E. Professional Group on
Electronic Computers",
remark = "Cited in US Patent 3,043,516 (10 July 1962): Time
Summing Device for Division, Multiplication, Root
Taking and Interpolation, by Harold W. Abbott and
Vernon P. Mathis.",
}
@Article{Gorn:1954:AAC,
author = "Saul Gorn",
title = "The Automatic Analysis and Control of Computing
Errors",
journal = j-J-SIAM,
volume = "2",
number = "2",
pages = "69--81",
month = jun,
year = "1954",
CODEN = "JSIMAV",
ISSN = "0368-4245 (print), 1095-712X (electronic)",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Society for Industrial and Applied
Mathematics",
journal-URL = "http://epubs.siam.org/loi/smjmap.1",
}
@Article{Kovach:1954:AMU,
author = "L. D. Kovach and W. Comley",
title = "An Analog Multiplier Using Thyrite",
journal = j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT,
volume = "EC-3",
number = "2",
pages = "42--45",
month = jun,
year = "1954",
CODEN = "????",
ISSN = "????",
bibdate = "Sun Jul 17 09:57:13 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the I.R.E. Professional Group on
Electronic Computers",
}
@Article{Mayer:1954:ODF,
author = "M. A. Mayer and B. M. Gordon and R. N. Nicola",
title = "An operational digital feedback divider",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-3",
number = "1",
pages = "17--20",
month = mar,
year = "1954",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Sun Jul 17 09:52:58 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Moshman:1954:GPR,
author = "Jack Moshman",
title = "The Generation of Pseudo-Random Numbers on a Decimal
Calculator",
journal = j-J-ACM,
volume = "1",
number = "2",
pages = "88--91",
month = apr,
year = "1954",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Fri Nov 04 00:18:27 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "decimal floating-point arithmetic",
}
@Article{Clenshaw:1955:NSC,
author = "C. W. Clenshaw",
title = "A note on the summation of {Chebyshev} series",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "9",
number = "51",
pages = "118--120",
year = "1955",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1955-0071856-0",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRclass = "65.0X",
MRnumber = "0071856",
bibdate = "Thu Feb 08 16:17:25 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib",
acknowledgement = ack-nhfb,
ajournal = "Math. Tables Other Aids Comput.",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Hidden inside \cite{Brenner:1955:TNS}, but important
in its own right for commentary on the recursive
algorithm for summation of Chebyshev series, and a
brief analysis of its accuracy.",
}
@Article{Crockett:1955:GMM,
author = "J. B. Crockett and H. Chernoff",
title = "Gradient Methods of Maximization",
journal = j-PAC-J-MATH,
volume = "5",
number = "??",
pages = "33--50",
year = "1955",
CODEN = "PJMAAI",
ISSN = "0030-8730 (print), 1945-5844 (electronic)",
ISSN-L = "0030-8730",
bibdate = "Fri Aug 20 08:54:24 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Pacific Journal of Mathematics",
journal-URL = "http://msp.org/pjm",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Book{Eckert:1955:FFS,
author = "W. J. (Wallace John) Eckert and Rebecca Bradley
Jones",
title = "Faster, faster; a simple description of a giant
electronic calculator and the problems it solves",
publisher = pub-IBM,
address = pub-IBM:adr,
pages = "160",
year = "1955",
LCCN = "QA76 .E25",
bibdate = "Fri Aug 20 08:57:56 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1902--1971",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
subject = "Computers",
xxaddress = pub-MCGRAW-HILL:adr,
xxpublisher = pub-MCGRAW-HILL,
}
@Book{Hastings:1955:ADC,
author = "Cecil B. {Hastings, Jr.} and Jeanne T. Hayward and
James P. {Wong, Jr.}",
title = "Approximations for Digital Computers",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "viii + 201",
year = "1955",
LCCN = "QA76 .H33",
bibdate = "Mon Sep 30 14:51:50 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Lenaerts:1955:ASR,
author = "E. H. Lenaerts",
title = "Automatic Square Rooting",
journal = j-ELECTRON-ENG,
volume = "27",
number = "??",
pages = "287--289",
month = jul,
year = "1955",
CODEN = "ELEGAP",
ISSN = "0013-4902",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Engineering",
}
@Article{Parsons:1955:SDC,
author = "Frances L. Parsons",
title = "A Simple Desk-Calculator Method for Checking Binary
Results of Digital Computer Arithmetic Operations",
journal = j-J-ACM,
volume = "2",
number = "3",
pages = "205--207",
month = jul,
year = "1955",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Wed Nov 09 01:00:34 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Book{Richards:1955:AOD,
author = "Richard Kohler Richards",
title = "Arithmetic Operations in Digital Computers",
publisher = "D. Van Nostrand",
address = "New York, NY, USA",
pages = "iv + 397",
year = "1955",
LCCN = "QA75 .R5 1955",
bibdate = "Fri Nov 28 18:46:37 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Robertson:1955:TCM,
author = "J. E. Robertson",
title = "Two's Complement Multiplication in Binary Parallel
Digital Computers",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-4",
number = "3",
pages = "118--119",
month = sep,
year = "1955",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/IRETELC.1955.5407911",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 15:10:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5407911",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Book{Stiefel:1955:RID,
author = "Eduard Stiefel",
title = "{Rechenautomaten im Dienste der Technik. Erfahrungen
mit dem Zuse-Rechenautomaten Z4}. ({German})
[{Calculating} machines in the service of technology.
{Experience} with the {Zuse}-calculator {Z4}]",
volume = "45",
publisher = "Westdeutscher Verlag",
address = "Cologne and Opladen, West Germany",
pages = "29--45; Diskussion 47--65",
year = "1955",
MRclass = "68.0X",
MRnumber = "0073311",
MRreviewer = "H. H. Goldstine",
bibdate = "Wed Sep 2 16:23:13 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Arbeitsgemeinschaft f{\"{u}}r Forschung des Landes
Nordrhein-Westfalen. Heft",
acknowledgement = ack-nhfb,
author-dates = "Eduard Stiefel (21 April 1909--25 November 1978)",
language = "German",
}
@Article{Estrin:1956:NHS,
author = "G. Estrin and B. Gilchrist and J. H. Pomerene",
title = "A Note on High-Speed Digital Multiplication",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-5",
number = "3",
pages = "140--140",
month = sep,
year = "1956",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1956.5219936",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 15:46:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219936",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Book{Hildebrand:1956:INA,
author = "Francis Begnaud Hildebrand",
title = "Introduction to Numerical Analysis",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "511",
year = "1956",
LCCN = "QA300 .H5",
bibdate = "Fri Aug 20 09:19:58 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "International series in pure and applied mathematics",
acknowledgement = ack-nhfb,
remark = "See also second edition
\cite{Hildebrand:1974:INA,Hildebrand:1987:INA}.",
subject = "Numerical analysis",
tableofcontents = "1. Introduction (significant figures, random
errors, error bounds, etc.) \\
2. Interpolation with divided differences \\
3. Lagrangian methods \\
4. Finite-difference interpolation \\
5. Operations with finite differences \\
6. Numerical solution of ordinary differential
equations \\
7. Least-squares polynomial approximation \\
8. Gaussian quadrature and related topics \\
9. Approximations of various types \\
10. Numerical solution of equations \\
Appendix: Justification of the Crout reduction",
}
@TechReport{Lazarus:1956:MI,
author = "R. B. Lazarus and N. Metropolis and W. Orvedahl and J.
H. Richardson and W. {Spack, Jr.} and R. L. Bivins and
J. V. Caulfield and I. Kral and A. F. Malmberg and G.
T. McKinley and R. E. Williamson",
title = "{MANIAC II}",
type = "Report",
number = "LA-2083",
institution = inst-LASL,
address = inst-LASL:adr,
pages = "54",
day = "1",
month = oct,
year = "1956",
bibdate = "Tue Mar 20 11:14:15 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://sgp.fas.org/othergov/doe/lanl/lib-www/la-pubs/00320765.pdf",
acknowledgement = ack-nhfb,
remark-1 = "OSTI ID: 4382471",
remark-2 = "From page 9: ``The Maniac II \ldots{} has 12,288
48-bit words. It is asynchronous and has no clock. Its
speed is that appropriate to (1) a memory cycle of 8
microseconds, (2) a basic add time of 6 microseconds,
and (3) a shift time of about 1.3 microseconds per
stage. The average multiply time is about 160
microseconds.''",
remark-3 = "From page 14, the 48-bit floating-point word consists
of a 1-bit sign, a 3-bit exponent-of-65536, a 1-bit
sign of the exponent, and a 43-bit fraction in [0,1).
The range of nonzero numbers is (0x1p-155, 0x1p112), or
roughly (2e-47, 5e33). The report notes: ``Although
such a large base implies of possibility of as many as
15 lead[ing] zeros, the large word size of 48 bits
guarantees adequate significance.''",
}
@Article{Lilamand:1956:TDM,
author = "M. Lejet Lilamand",
title = "A Time-Division Multiplier",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-5",
number = "1",
pages = "26--34",
month = mar,
year = "1956",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1956.5219789",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 15:46:18 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219789",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Perkins:1956:EPC,
author = "Robert Perkins",
title = "{EASIAC}, {A} Pseudo-Computer",
journal = j-J-ACM,
volume = "3",
number = "2",
pages = "65--72",
month = apr,
year = "1956",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Fri Nov 04 23:46:26 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "One of the primary functions of the MIDAC installation
at the University of Michigan is the instruction of
beginners in the various aspects of digital machine use
including programming and coding. \ldots{} In
conducting these courses it was soon found to be
extremely difficult, in five or six instruction
periods, to bring a complete newcomer up to the point
where he can code and check out on MIDAC anything more
than a rather trivial routine. As might be expected the
difficulty centers around problems of scaling,
instruction modification and binary representation.
\ldots{} To alleviate these problems it was decided
that a new computer was needed: one designed to make
programming easier. At the cost of some of MIDAC's
speed and capacity plus two or three man-months of
programming time EASIAC, the EASy Instruction Automatic
Computer, was realized as a translation-interpretation
program in MIDAC.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "decimal floating-point arithmetic",
remark = "Early example of a decimal floating-point machine.",
}
@Article{Robertson:1956:NCD,
author = "J. E. Robertson",
title = "A new class of digital division methods",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-5",
number = "??",
pages = "65--73",
month = jun,
year = "1956",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Fri Nov 09 19:14:45 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Stegun:1956:PC,
author = "Irene A. Stegun and Milton Abramowitz",
title = "Pitfalls in computation",
journal = "Journal of the Society for Industrial and Applied
Mathematics",
volume = "4",
pages = "207--219",
year = "1956",
bibdate = "Tue Aug 28 06:16:28 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Sydnor:1956:AMS,
author = "R. L. Sydnor and T. R. O'Meara and J. Strathman",
title = "Analog Multipliers and Squarers Using a Multigrid
Modulator",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-5",
number = "2",
pages = "82--85",
month = jun,
year = "1956",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1956.5219804",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 15:46:21 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219804",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Weinberger:1956:OMA,
author = "A. Weinberger and J. L. Smith",
title = "A One-Microsecond Adder Using One-Megacycle
Circuitry",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-5",
number = "??",
pages = "65--73",
month = jun,
year = "1956",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Fri Nov 09 19:38:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Wolontis:1956:CFD,
author = "V. M. Wolontis",
title = "A Complete Floating-Decimal Interpretive System for
the {IBM 650 Magnetic Drum Calculator}",
journal = "IBM Technical Newsletter",
volume = "??",
number = "11",
pages = "xxi + 63",
month = mar,
year = "1956",
bibdate = "Mon Sep 04 13:55:28 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://babel.hathitrust.org/cgi/pt?id=coo.31924003945759&seq=7",
acknowledgement = ack-nhfb,
}
@Book{Alt:1957:EDC,
editor = "Franz L. Alt",
title = "Electronic Digital Computers: Their Use in Science and
Engineering",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "x + 335",
year = "1957",
bibdate = "Sun Jun 17 18:53:23 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Section 2.3 discusses number representation and
decimal versus binary arithmetic.",
xxnote = "Check page count: incomplete view in Google books.
Price bibliography says 1958.",
}
@Article{Ercoli:1957:EDO,
author = "Paolo Ercoli and Roberto Vacca",
title = "Errors Due to Overflow in Arithmetic Operations
Particularly as Regards {FINAC} Electronic Computer",
journal = j-J-ACM,
volume = "4",
number = "4",
pages = "450--455",
month = oct,
year = "1957",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Thu Dec 08 09:28:48 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See letter \cite{Ercoli:1960:LEE}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "floating-point arithmetic; overflow",
}
@Article{Gini:1957:SFD,
author = "Corrado Gini",
title = "Sulla frequenza delle cifre iniziali dei numeri
osservati. ({Italian}) [{On} the frequency of initial
digits of observed numbers]",
journal = "Bull. Inst. Internat. Stat.",
volume = "35",
number = "??",
pages = "57--76",
year = "1957",
bibdate = "Sun Sep 18 11:54:25 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "29th session, 2nd delivery, Rio de Janerio.",
URL = "",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
language = "Italian",
}
@Article{Herzel:1957:SDD,
author = "Amato Herzel",
title = "Sulla distribuzione della cifre iniziali dei numeri
statistici. ({Italian}) [{On} the frequency of initial
digits of statistical numbers]",
journal = "Atti dell XV e XVII Riunione, Societa Italiana di
Statistica",
volume = "??",
number = "??",
pages = "??--??",
year = "1957",
bibdate = "Sun Sep 18 12:00:07 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
language = "Italian",
}
@Article{Howe:1957:TRA,
author = "R. M. Howe and E. G. Gilbert",
title = "Trigonometric Resolution in Analog Computers by Means
of Multiplier Elements",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-6",
number = "2",
pages = "86--92",
month = jun,
year = "1957",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1957.5221576",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 16:07:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221576",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Kalbfell:1957:EAM,
author = "David C. Kalbfell",
title = "An Electronic Analog Multiplier",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-6",
number = "2",
pages = "100--103",
month = jun,
year = "1957",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1957.5221579",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 16:07:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221579",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Kogbetliantz:1957:CEN,
author = "E. G. Kogbetliantz",
title = "Computation of $ e^n $ for $ - \infty < n < + \infty $
Using an Electronic Computer",
journal = j-IBM-JRD,
volume = "1",
number = "2",
pages = "110--115",
month = apr,
year = "1957",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Sep 06 18:04:49 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Lehman:1957:HSD,
author = "M. Lehman",
title = "High-Speed Digital Multiplication",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-6",
number = "3",
pages = "204--205",
month = sep,
year = "1957",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1957.5222025",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 16:07:34 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222025",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Luke:1957:CLZ,
author = "Y. L. Luke",
title = "On the Computation of $ \log {Z} $ and $ \arctan {Z}
$",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "??",
pages = "16--18",
month = "????",
year = "1957",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "Math. Tables Other Aids Comput.",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@TechReport{Metze:1957:SPO,
author = "G. Metze",
title = "A Study of Parallel One's Complement Arithmetic Units
with Separate Carry or Borrow Storage",
type = "Report",
number = "81",
institution = "Digital Computer Laboratory, University of Illinois",
address = "Urbana, IL, USA",
pages = "77",
year = "1957",
bibdate = "Thu Nov 18 09:07:07 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Flores' book \cite[p. 485]{Flores:1963:LCA} cites this
report, and says that its conclusion is that the
disadvantages of one's complement arithmetic outweigh
the advantages.",
}
@Article{Murphy:1957:PIA,
author = "R. W. Murphy",
title = "A Positive-Integer Arithmetic for Data Processing",
journal = j-IBM-JRD,
volume = "1",
number = "2",
pages = "158--170",
month = apr,
year = "1957",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.12.0158",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "68.0X",
MRnumber = "18,939d",
bibdate = "Tue Sep 11 15:35:33 MDT 2012",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392735;
http://www.research.ibm.com/journal/rd/012/ibmrd0102G.pdf",
abstract = "It is hypothesized that positive numbers suffice for
the expression of quantities in accounting. New
arithmetic operations are devised that yield
non-negative results in computation, and the
applicability of these operations to data processing is
studied. These operations permit a wide variety of
functions to be computed with fewer and less complex
steps and imply the feasibility of constructing less
complex data-processing machines.",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
reviewer = "C. C. Gotlieb",
}
@Article{Pawlak:1957:UEN,
author = "Z. Pawlak",
title = "Use of expansions with a negative basis in the
arithmometer of a digital computer",
journal = "Bull. Acad. Pol. Sci., Ser. Sci. Tech.",
volume = "5",
number = "??",
pages = "232--236",
month = "????",
year = "1957",
bibdate = "Thu Nov 06 05:56:32 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "negative base",
}
@TechReport{Taylor:1957:CCA,
author = "W. Bruce Taylor",
title = "{COIN} (Compile-Interpreter): an automatic
programming, fixed and floating-point library of
subroutines for the {ERA} 1103 computer",
institution = "Operations Research Office, Johns Hopkins University",
address = "Bethesda, MD, USA",
pages = "43",
year = "1957",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Staff paper / Johns Hopkins University, Operations
Research Office; ORO-SP-32 Staff paper (Johns Hopkins
University. Operations Research Office); ORO-SP-32.",
acknowledgement = ack-nhfb,
keywords = "Military art and science --- Data processing.;
Military research --- Data processing.",
remark = "Cover title. ``Operating under contract with the
Department of the Army.'' ``Project COMPLAB.''
``October 1957.'' ORO-SP-32",
}
@Article{Wadel:1957:NBN,
author = "L. B. Wadel",
title = "Negative base number systems",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-6",
number = "??",
pages = "123--??",
month = jun,
year = "1957",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Thu Nov 06 05:53:55 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
keywords = "negative base",
}
@Article{Walker:1957:EMA,
author = "R. M. Walker and D. E. Rosenheim and P. A. Lewis and
A. G. Anderson",
title = "An Experimental 50-Megacycle Arithmetic Unit",
journal = j-IBM-JRD,
volume = "1",
number = "3",
pages = "257--278",
month = jul,
year = "1957",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.13.0257",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Sep 11 15:35:35 MDT 2012",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392687;
http://www.research.ibm.com/journal/rd/013/ibmrd0103H.pdf",
abstract = "An experimental 50-megacycle arithmetic unit has been
built which performs a repetitive multiplication
program and checks the results for errors. The unit
uses pulse circuitry which has been developed to
perform digital operations at a 50-megacycle
pulse-repetition rate. This paper describes the
arithmetic system and the circuits which perform the
required functions. These circuits include a full
binary adder, a phase-locked frequency divider which
provides a 3.125-megacycle secondary timing source, a
reshaping and retiming circuit using germanium diodes
and capacitive storage, a high-speed shift register, a
high-speed indicator register, and a binary word
generator.\par
Various novel features of a digital system operating at
these high speeds are described. These include the use
of coaxial delay lines for the distribution of signals
and as storage elements, and the use of secondary
emission tubes in amplifier and multivibrator
circuits.\par
In a 50-megacycle system the interdependence of the
space and time dimensions is marked, and although this
introduces problems which are not ordinarily
encountered in computing systems, it may be used
advantageously to provide features such as the
variable-phase clock system used in the arithmetic
unit.\par
The performance and reliability of the arithmetic unit
are discussed as well as the reliability of the
components and circuits which make up the system.
Although the techniques and circuitry discussed here
have been applied only to a relatively simple
arithmetic unit, it is felt that they could be useful
in a variety of high-speed computing and measurements
applications.",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Weibel:1957:EAM,
author = "Erich S. Weibel",
title = "An Electronic Analog Multiplier Using Carriers",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-6",
number = "1",
pages = "30--34",
month = mar,
year = "1957",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1957.5221558",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 16:07:23 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221558",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Book{Wilkes:1957:PPE,
author = "Maurice V. Wilkes and David J. Wheeler and Stanley
Gill",
title = "The Preparation of Programs for an Electronic Digital
Computer",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Second",
pages = "xiv + 238",
year = "1957",
LCCN = "QA76.5 .W52 1957",
bibdate = "Mon Feb 10 09:42:47 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also first edition \cite{Wilkes:1951:PPE}.",
URL = "https://b-ok.org/book/3668116/b363ff",
acknowledgement = ack-nhfb,
remark-1 = "According to \cite{Anderson:2019:SAM}, this book
discusses the computation of integer population counts
on the Electronic Delay Storage Automatic Calculator
(EDSAC) computer using a recursive divide-and-conquer
algorithm. See also somewhat negative 1958 review by
Fernando J. Corbat{\'o}
\url{https://doi.org/10.1063/1.3062687}. Floating-point
arithmetic is discussed on pages 60, 90--91, and
135--137.",
remark-2 = "From page 5: ``Each storage location in the EDSAC
holds 17 binary digits. In words representing numbers,
the binary point is regarded as being to the right of
the extreme left-hand digit; this digit (the most
significant digit) is used as a sign indicator and is
referred to as the sign digit. \ldots{} the capacity of
the accumulator is 70 digits; there is, therefore,
plenty of room to hold the full 33-digit product of two
17-digit numbers. \ldots{} A negative number $-x$
(where $O < x \leq 1$) is represented by a $1$ in the
sign-digit position, followed by the digits of $(1 -
x)$; for example, $1.1100\ldots{}$ represents $-(1 -
3/4) = -1/4$. \ldots{} Another way of explaining the
representation of negative numbers is to regard the
sign digit as an ordinary numerical digit, and to say
that $-x$ is stored as the number $(2 - x)$. Note in
particular that $1.0000\ldots{}$ represents $-1$.''
[Page 59 calls this a {\em True complements}
representation, distinguished from one's complement.]",
remark-3 = "From page 35: ``The EDSAC has a facility which enables
an even-numbered storage location and the following
odd-numbered storage to be used as a single storage
location holding 35 binary digits.'' [This suggests the
word size in 18, not 17 as page 5 suggests. The
Wikipedia article on the EDSAC reports: ``The EDSAC's
main memory consisted of 1024 locations, though only
512 locations were initially installed. Each contained
18 bits, but the topmost bit was always unavailable due
to timing problems, so only 17 bits were used.'']",
remark-4 = "From page 36: ``The multiplier register of the
arithmetical unit is of sufficient capacity to hold a
long number, and the accumulator is of sufficient
capacity to hold the complete (69) binary digit
[including the sign bit] product of two long
numbers.''",
remark-5 = "From page 36: ``In some calculations, long numbers may
not provide sufficient precision. In such cases, the
programmer may make use of what is known as
double-length or double-precision working, in which two
long storage locations are used to hold the digits of a
single number.'' [this would be a quad-word number
holding 69 bits, including the sign bit.].",
remark-6 = "From page 60: ``\ldots{} two double-length numbers,
each stored in two locations, can be added and the
result put in two locations in the store, by means of
six orders''.",
remark-7 = "From page 90: ``Each number is expressed in the form
$a \cdot 10^p$, where $-10 \leq a \leq 10$ and $63 \leq
p < 63$ and is represented in the store by $a \cdot
2^{-11} + p \cdot 2^{-6}$.''",
remark-8 = "From page 91: ``Numbers are expressed in the form $a
\cdot 10^p$, where $a$ and $p$ are packed into a single
storage location. The number of digits defining $p$ may
be varied from 4 to 15 by means of a preset parameter,
so that a suitable value for the permissible range of
variation of numbers may be selected for a given
calculation.''",
remark-9 = "From page 91: ``Although the use of floating-point
operation can simplify the programmer's task by
relieving him of undue preoccupation with scaling, it
must not be thought that it solves all his
difficulties. In particular, the loss of significant
digits resulting from the subtraction of a number from
a nearly equal number can have serious consequences
unless proper precautions are taken.''",
tableofcontents = "CHAPTER 1. THE ELEMENTS OF PROGRAM DESIGN / 1 \\
1-1 Introduction / 1 \\
1-2 Types of automatic computing machine / 1 \\
1-3 The EDSAC / 3 \\
1-4 Store / 5 \\
1-5 Arithmetical unit / 5 \\
1-6 Form of numbers in the machine / 5 \\
1-7 Form of orders in the machine / 6 \\
1-8 Storage of orders / 6 \\
1-9 Written form of orders / 7 \\
1-10 Some simple examples / 7 \\
Exercises A / 9 \\
1-11 Jump orders / 9 \\
Exercises B / 11 \\
1-12 Repeated groups of orders / 11 \\
1-13 The use of the B-register / 15 \\
Exercises C / 18 \\
1-14 Equivalence between orders and numbers;
pseudo-orders / 18 \\
1-15 Use of the arithmetical unit for constructing or
modifying orders / 20 \\
1-16 The mix order / 23 \\
Exercises D / 24 \\
CHAPTER 2. SUBROUTINES / 25 \\
2-1 Introduction / 25 \\
2-2 Relative numbering of addresses / 25 \\
2-3 Internal and external forms of orders / 26 \\
2-4 Reading of orders from the input tape / 28 \\
2-5 Open and closed subroutines / 29 \\
2-6 Entering and leaving a closed subroutine / 29 \\
2-7 Closed B subroutines / 30 \\
2-8 Closed A subroutines / 31 \\
2-9 Use of library subroutines / 32 \\
Exercises E / 33 \\
2-10 Long numbers / 35 \\
2-11 Some further orders in the order code / 36 \\
2-12 Scale factors / 38 \\
2-13 Control combinations / 39 \\
Exercises F / 40 \\
2-14 Relative addresses in control combinations / 41
\\
2-15 Extension of the use of relative addresses / 41
\\
2-16 Setting of the constants to be added by terminal
code letters / 43 \\
2-17 Complete table of terminal code letters / 44 \\
2-18 Parameters / 45 \\
2-19 Preset parameters / 46 \\
2-20 Program parameters / 46 \\
2-21 Standard procedure for setting preset parameters /
46 \\
2-22 Interpretive subroutines / 47 \\
Exercises G / 49 \\
CHAPTER 3. PROGRAMMING FOR OTHER MACHINES / 51 \\
3-1 Introduction / 51 \\
3-2 Single-address codes / 52 \\
3-3 Multi-address codes / 53 \\
3-4 Multiplication and division / 56 \\
3-5 Source-destination codes / 57 \\
3-6 Representation of negative numbers / 59 \\
3-7 Miscellaneous facilities / 60 \\
3-8 Minimum-access coding / 61 \\
3-9 The evaluation of an order code / 63 \\
3-10 Use of an auxiliary store / 64 \\
CHAPTER 4. INPUT AND OUTPUT / 66 \\
4-1 Introduction / 66 \\
4-2 Input of numbers / 66 \\
4-3 Output of numbers / 67 \\
4-4 Input of orders / 69 \\
4-5 Recognition of the code letter S / 72 \\
4-6 Economy of input and output time / 72 \\
4-7 Some features of input systems used with other
machines / 73 \\
4-8 Punched tape / 73 \\
4-9 Punched cards / 75 \\
CHAPTER 5. THE LIBRARY OF SUBROUTINES / 80 \\
5-1 Introduction / 80 \\
5-2 Library catalog / 80 \\
5-3 Input subroutines / 81 \\
5-4 Output subroutines / 81 \\
5-5 Division subroutines / 82 \\
5-6 Trigonometric and other functions / 82 \\
5-7 The economization of a power series by the use of
Chebyshev polynomials / 83 \\
5-8 Quadrature / 86 \\
5-9 Integration of ordinary differential equations / 87
\\
5-10 Library subroutines Gl2 and G13: Runge--Kutta
processes / 88 \\
5-11 The independent variable / 88 \\
5-12 Definition of the Runge--Kutta--Gill process / 89
\\
5-13 Taylor-series method / 90 \\
5-14 Interpretive subroutines / 90 \\
5-15 Floating-point subroutines / 90 \\
CHAPTER 6. DIAGNOSIS OF ERRORS IN PROGRAM / 92 \\
6-1 Introduction / 92 \\
6-2 Proofreading of programs / 93 \\
6-3 Punching / 93 \\
6-4 Locating mistakes in a program- / 94 \\
6-5 Subroutines for checking programs / 96 \\
6-6 The development of a program / 97 \\
CHAPTER 7. EXAMPLES OF COMPLETE PROGRAMS FOR THE EDSAC
/ 99 \\
EXAMPLE 1 Calculation of $e^{-\sin x}$ / 99 \\
EXAMPLE 2 The evaluation of a definite integral / 102
\\
EXAMPLE 3 Integration of an ordinary differential
equation / 108 \\
EXAMPLE 4 Evaluation of a Fourier transform / 113 \\
EXAMPLE 5 Evaluation of a definite integral / 118 \\
CHAPTER 8. AUTOMATIC PROGRAMMING / 126 \\
8-1 Introduction / 126 \\
8-2 Conversion versus interpretation / 127 \\
8-3 Assembly of a program / 127 \\
8-4 Floating addresses / 129 \\
8-5 Formula recognition / 136 \\
Part Two: SPECIFICATIONS OF EDSAC LIBRARY SUBROUTINES /
139 \\
CATEGORY A. Subroutines to carry out floating-point
arithmetic / 140 \\
CATEGORY B. Subroutines to perform arithmetical
operations on complex numbers / 142 \\
CATEGORY C. Error-diagnosis subroutines / 144 \\
CATEGORY D. Division subroutines / 146 \\
CATEGORY E. Exponential subroutines / 148 \\
CATEGORY F. General subroutines relating to functions /
148 \\
CATEGORY G. Subroutines for the integration of
differential equations / 150 \\
CATEGORY L. Subroutines for evaluating logarithms / 153
\\
CATEGORY M. Miscellaneous subroutines / 154 \\
CATEGORY N. Operations on double-length numbers / 156
\\
CATEGORY P. Print subroutines / 158 \\
CATEGORY Q. Quadrature subroutines / 162 \\
CATEGORY R. Input subroutines / 164 \\
CATEGORY s. Subroutines for evaluating fractional
powers / 168 \\
CATEGORY T. Subroutines for calculating trigonometric
functions / 169 \\
CATEGORY Z. Post-mortem routines / 170 \\
PART THREE: PROGRAMS OF SELECTED EDSAC LIBRARY
SUBROUTINES / 173 \\
APPENDIX 1. Input and output codes of the EDSAC / 212
\\
APPENDIX 2. Order code and controls of the EDSAC / 214
\\
APPENDIX 3. The initial input routine of the EDSAC /
218 \\
APPENDIX 4. Control combinations / 221 \\
APPENDIX 5. Specimen solutions to programming exercises
/ 223 \\
BIBLIOGRAPHY / 233 \\
INDEX / 237",
}
@TechReport{Anonymous:1958:ARM,
author = "Anonymous",
title = "Analysis and research memorandum 294",
type = "{AR} Memo",
number = "294 (AD 207929)",
institution = "Massachusetts Institute of Technology, Naval
Supersonic Laboratory",
address = "Cambridge, MA, USA",
pages = "7",
day = "23",
month = oct,
year = "1958",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Error functions.; Floating-point arithmetic.",
}
@Article{Bemer:1958:MMS,
author = "Robert W. Bemer",
title = "A Machine Method for Square-Root Computation",
journal = j-CACM,
volume = "1",
number = "1",
pages = "6--7",
month = jan,
year = "1958",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 15 18:35:46 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Bemer:1958:SMC,
author = "R. W. Bemer",
title = "A Subroutine Method for Calculating Logarithms",
journal = j-CACM,
volume = "1",
number = "5",
pages = "5--7",
month = may,
year = "1958",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Couleur:1958:BBD,
author = "J. F. Couleur",
title = "{BIDEC} --- a Binary-to-Decimal or Decimal-to-Binary
Converter",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-7",
pages = "313--316",
year = "1958",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Fri Nov 28 16:28:12 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
keywords = "decimal floating-point arithmetic",
}
@Article{Delury:1958:CAN,
author = "Daniel B. Delury",
title = "Computation with Approximate Numbers",
journal = j-MATH-TEACH,
volume = "51",
pages = "521--530",
month = nov,
year = "1958",
ISSN = "0025-5769 (print), 2330-0582 (electronic)",
bibdate = "Fri Nov 28 11:47:47 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "The Mathematics Teacher",
}
@Article{Ershov:1958:PAO,
author = "Andrei P. Ershov",
title = "On Programming of Arithmetic Operations",
journal = j-CACM,
volume = "1",
number = "8",
pages = "3--6",
month = aug,
year = "1958",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:21 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Ershov58;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Ershov58",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Ershov58",
}
@Article{Gower:1958:NIM,
author = "J. C. Gower",
title = "A Note on an Iterative Method for Root Extraction",
journal = j-COMP-J,
volume = "1",
pages = "142--143",
year = "1958",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Thu Sep 15 18:36:55 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
xxmonth = "(none)",
xxnumber = "(none)",
}
@Article{Hammer:1958:PST,
author = "Franz Hammer",
title = "{Nicht Pascal sondern der T{\"u}binger Professor
Wilhelm Schickard erfand die Rechenmaschine!}.
({German}) [{Not Pascal}, but the {T{\"u}bingen}
professor {William Schickard}, invented the
calculator!]",
journal = "{B{\"u}romarkt}",
volume = "20",
number = "??",
pages = "1023--1025",
month = "????",
year = "1958",
ISSN = "0007-3148",
ISSN-L = "0007-3148",
bibdate = "Sat Jul 27 11:05:26 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/scicontext.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Kogbetliantz:1958:CANa,
author = "E. G. Kogbetliantz",
title = "Computation of Arctan {$N$} for $ - \infty < {N} < +
\infty $ Using an Electronic Computer",
journal = j-IBM-JRD,
volume = "2",
number = "1",
pages = "43--53",
month = jan,
year = "1958",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Kogbetliantz:1958:CANb,
author = "E. G. Kogbetliantz",
title = "Computation of Arcsin {$N$} for $ 0 < {N} < 1 $ Using
an Electronic Computer",
journal = j-IBM-JRD,
volume = "2",
number = "3",
pages = "218--222",
month = jul,
year = "1958",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Metropolis:1958:SDC,
author = "N. Metropolis and R. L. Ashenhurst",
title = "Significant Digit Computer Arithmetic",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-7",
number = "4",
pages = "265--267",
month = dec,
year = "1958",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1958.5222657",
ISSN = "0367-9950",
bibdate = "Wed Feb 14 19:23:38 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222657",
abstract = "The usual floating point arithmetic makes error
analysis difficult. This paper describes an alternative
system which offers a means of analyzing floating point
calculations more effectively and which also possesses
certain advantages from an equipment standpoint.",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
keywords = "MANIAC III",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Robertson:1958:NCDa,
author = "J. E. Robertson",
title = "A new class of digital division methods",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-7",
number = "3",
pages = "88--92",
month = sep,
year = "1958",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Robertson:1958:NCDb,
author = "James E. Robertson",
title = "A New Class of Digital Division Methods",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-7",
number = "3",
pages = "218--222",
month = sep,
year = "1958",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1958.5222579",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222579",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Schmid:1958:TFQ,
author = "Hermann Schmid",
title = "A Transistorized Four-Quadrant Time-Division
Multiplier with an Accuracy of 0.1 Per Cent",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-7",
number = "1",
pages = "41--47",
month = mar,
year = "1958",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1958.5222094",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222094",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Sisson:1958:IDR,
author = "Roger L. Sisson",
title = "An Improved Decimal Redundancy Check",
journal = j-CACM,
volume = "1",
number = "5",
pages = "10--12",
month = may,
year = "1958",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:22:12 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Sisson58;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "As more emphasis is placed on improving the accuracy
of data fed into automatic computing systems, more
emphasis will be placed on redundancy checking of
predictable fields within the input. Two systems (at
least) of checking a field of decimal digits have been
proposed. In both of these it is assumed that the field
to be checked is all numeric and that the redundancy
must be of only one digit.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "decimal floating-point arithmetic",
oldlabel = "Sisson58",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sisson58",
}
@Article{Tocher:1958:TMD,
author = "K. D. Tocher",
title = "Techniques of Multiplication and Division for
Automatic Binary Computers",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "11",
number = "3",
pages = "364--384",
month = "????",
year = "1958",
CODEN = "QJMMAV",
ISSN = "0033-5614 (print), 1464-3855 (electronic)",
ISSN-L = "0033-5614",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "Quarterly Journal of Mechanics and Applied
Mathematics",
journal-URL = "http://qjmam.oxfordjournals.org/content/by/year",
}
@Article{Wadey:1958:TSR,
author = "W. G. Wadey",
title = "Two Square-Root Approximations",
journal = j-CACM,
volume = "1",
number = "11",
pages = "13--14",
month = nov,
year = "1958",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Wadey58;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Wadey58",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Wadey58",
}
@Article{Ashenhurst:1959:UFP,
author = "Robert L. Ashenhurst and Nicholas Metropolis",
title = "Unnormalized Floating Point Arithmetic",
journal = j-J-ACM,
volume = "6",
number = "3",
pages = "415--428",
month = jul,
year = "1959",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/320986.320996",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "68.00",
MRnumber = "MR0105833 (21 \#4568)",
MRreviewer = "H. H. Goldstine",
bibdate = "Fri Dec 08 13:06:24 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jacm.bib",
ZMnumber = "0121.12102",
abstract = "Algorithms for floating point computer arithmetic are
described, in which fractional parts are not subject to
the usual normalization convention. These algorithms
give results in a form which furnishes some indication
of their degree of precision. An analysis of one-stage
error propagation is developed for each operation; a
suggested statistical model for long-run error
propagation is also set forth.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Buchholz:1959:FFC,
author = "Wilfried Buchholz",
title = "Fingers or Fists? (The Choice of Decimal or Binary
Representation)",
journal = j-CACM,
volume = "2",
number = "12",
pages = "3--11",
month = "????",
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:28:45 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Buchholz59;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "decimal floating-point arithmetic",
oldlabel = "Buchholz59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Buchholz59",
xxnote = "Check author first name: article has W. Buchholz; I
think it should be Werner, not Wilfried.",
}
@Article{Carr:1959:EAF,
author = "John W. {Carr III}",
title = "Error Analysis in Floating Point Arithmetic",
journal = j-CACM,
volume = "2",
number = "5",
pages = "10--15",
month = may,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:23 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Carr59a;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Carr59a",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Carr59a",
}
@InCollection{Carr:1959:PC,
author = "John W. {Carr III}",
editor = "Eugene M. Grabbe and Simon Ramo and Dean E.
Wooldridge",
booktitle = "Handbook of Automation, Computation, and Control",
title = "Programming and Coding",
publisher = pub-WILEY,
address = pub-WILEY:adr,
bookpages = "????",
year = "1959",
LCCN = "TJ213 .G72",
bibdate = "Fri Aug 20 08:41:16 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "Chapter 2.",
acknowledgement = ack-nhfb,
remark = "1958--1961: Volume 1. Control fundamentals. Volume 2.
Computers and data processing. Volume 3. Systems and
components. Cited in \cite{Sterbenz:1974:FPC}.",
subject = "automation; mathematics; computers; operations
research",
}
@Article{Daggett:1959:DBC,
author = "D. H. Daggett",
title = "Decimal-Binary Conversions in {CORDIC}",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "5",
pages = "335--339",
month = sep,
year = "1959",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Thu Sep 08 08:14:00 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
keywords = "decimal floating-point arithmetic",
}
@Article{Ercoli:1959:BAD,
author = "Paolo Ercoli and Roberto Vacca",
title = "Binary Arithmetic for Discretely Variable Word Length
in a Serial Computer",
journal = j-CACM,
volume = "2",
number = "4",
pages = "13--15",
month = apr,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#ErcoliV59;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "ErcoliV59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/ErcoliV59",
}
@Article{Forsythe:1959:RNR,
author = "George E. Forsythe",
title = "Reprint of a Note on Rounding-Off Errors",
journal = j-SIAM-REVIEW,
volume = "1",
number = "1",
pages = "66--67",
month = jan,
year = "1959",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1001011",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65.00",
MRnumber = "MR0099119 (20 \#5563)",
bibdate = "Thu Mar 27 09:04:24 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/1/1;
https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
ZMnumber = "0168.14002",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
keywords = "numerical analysis; random rounding-off procedure",
onlinedate = "January 1959",
received = "7 February 1958",
remark = "From a footnote on the cover page: ``This note was
written in June 1950 at the National Bureau of
Standards, Los Angeles, and a few copies were
distributed in multilithed form by that organization as
an appendix to a reproduction of a well-known article
by Rademacher [1]. The note was abstracted in Math.
Reviews, Vol. 12 (1951), p. 208. Because he receives
frequent requests for copies of the note, which are
unavailable, the author has asked the editors to
reprint it in essentially its original form.''",
}
@Article{Garner:1959:RMS,
author = "Harvey L. Garner",
title = "A Ring Model for the Study of Multiplication for
Complement Codes",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "1",
pages = "25--30",
month = mar,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5222757",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:44 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222757",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Garner:1959:RNS,
author = "Harvey L. Garner",
title = "The Residue Number System",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "2",
pages = "140--147",
month = jun,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5219515",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:44 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219515",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@InProceedings{Gray:1959:NFP,
author = "H. L. Gray and C. Harrison",
booktitle = "Proceedings of the Eastern Joint Computer Conference,
Boston, {MA}, December 1--3, 1959",
title = "Normalized floating-point arithmetic with an index of
significance",
volume = "16",
publisher = pub-AFIPS,
address = pub-AFIPS:adr,
pages = "244--248",
year = "1959",
LCCN = "TK7885.A1 J6",
bibdate = "Tue Oct 09 09:43:31 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Henrici:1959:TES,
author = "Peter Henrici",
editor = "????",
booktitle = "Proceedings of the International Conference on
Information Processing, {UNESCO}",
title = "Theoretical and Experimental Studies on the
Accumulation of Error in the Numerical Solution of
Initial Value Problems for Systems of Ordinary
Differential Equations",
publisher = "????",
address = "????",
pages = "36--43",
year = "1959",
LCCN = "????",
bibdate = "Fri Aug 20 09:11:32 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Kogbetliantz:1959:CSC,
author = "E. G. Kogbetliantz",
title = "Computation of $ \sin {N} $, $ \cos {N} $, and {$M$
th} Root of {$N$} Using an Electronic Computer",
journal = j-IBM-JRD,
volume = "3",
number = "2",
pages = "147--152",
month = apr,
year = "1959",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Lucal:1959:AOD,
author = "Harold M. Lucal",
title = "Arithmetic Operations for Digital Computers Using a
Modified Reflected Binary Code",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "4",
pages = "449--458",
month = dec,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5222057",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222057",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Muller:1959:CMG,
author = "Mervin E. Muller",
title = "A Comparison of Methods for Generating Normal Deviates
on Digital Computers",
journal = j-J-ACM,
volume = "6",
number = "3",
pages = "376--383",
month = jul,
year = "1959",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Tue Nov 1 09:33:26 1994",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
descriptors = "RVG",
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Pawlak:1959:EDC,
author = "Z. Pawlak",
title = "An electronic digital computer based on the `$ - 2 $'
system",
journal = "Bull. Acad. Pol. Sci., Ser. Sci. Tech.",
volume = "7",
number = "??",
pages = "713--722",
month = "????",
year = "1959",
bibdate = "Thu Nov 06 05:58:31 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "negative base",
}
@Article{Pfeiffer:1959:FQM,
author = "Paul E. Pfeiffer",
title = "A Four-Quadrant Multiplier Using Triangular Waves,
Diodes, Resistors, and Operational Amplifiers",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "2",
pages = "222--227",
month = jun,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5219526",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219526",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Rothstein:1959:RBN,
author = "Jerome Rothstein",
title = "Residues of Binary Numbers Modulo Three",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "2",
pages = "229--229",
month = jun,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5219529",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219529",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Sarafyan:1959:NMC,
author = "Diran Sarafyan",
title = "A New Method of Computation of Square Roots Without
Using Division",
journal = j-CACM,
volume = "2",
number = "11",
pages = "23--24",
month = nov,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:24 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sarafyan59;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See comments \cite{Traub:1960:CNM}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Sarafyan59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sarafyan59",
}
@Article{Sheridan:1959:ATC,
author = "Peter B. Sheridan",
title = "The Arithmetic Translator Compiler of the {IBM FORTRAN
Automatic Coding System}",
journal = j-CACM,
volume = "2",
number = "2",
pages = "9--21",
month = feb,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sheridan59;
http://ei.cs.vt.edu/~cs4304/bibliography.html;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Sheridan59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sheridan59",
}
@Article{Strachey:1959:TSR,
author = "C. Strachey",
title = "On taking the square root of a complex number",
journal = j-COMP-J,
volume = "2",
number = "2",
pages = "89--89",
month = jul,
year = "1959",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/2.2.89",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:55:11 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/020089.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/tiff/89.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
remark = "This 1/4-page note comments that if $ \sqrt {x + i y}
= u + i v $, then $ u = \sqrt {[\sqrt {x^2 + y^2} + x]
/ 2} $ and $ v = \sqrt {[\sqrt {x^2 + y^2} - x] / 2}
$, where both inner and outer square roots should be
evaluated to twice working precision.",
}
@Article{Taranto:1959:BCF,
author = "Donald Taranto",
title = "Binary Conversion, with Fixed Decimal Precision, of a
Decimal Fraction",
journal = j-CACM,
volume = "2",
number = "7",
pages = "27--27",
month = jul,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:25:37 MST 2001",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Taranto59;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "decimal floating-point arithmetic",
oldlabel = "Taranto59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Taranto59",
}
@Article{Volder:1959:CTC,
author = "J. E. Volder",
title = "The {CORDIC} Trigonometric Computing Technique",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "5",
pages = "330--334",
month = sep,
year = "1959",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Wensley:1959:CNA,
author = "J. H. Wensley",
title = "A Class of Non-Analytical Iterative Processes",
journal = j-COMP-J,
volume = "1",
number = "4",
pages = "163--167",
month = jan,
year = "1959",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:55:07 MDT 2000",
bibsource = "Compiler/semantics.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/010163.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/163.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/164.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/165.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/166.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/167.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Wilkinson:1959:EZIa,
author = "J. H. Wilkinson",
title = "The evaluation of the zeros of ill-conditioned
polynomials. {I}",
journal = j-NUM-MATH,
volume = "1",
pages = "150--166",
month = dec,
year = "1959",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01386381",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.00",
MRnumber = "MR0109435 (22 \#321)",
MRreviewer = "H. Rutishauser",
bibdate = "Mon Oct 18 01:28:20 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Wilkinson:1959:EZIb,
author = "J. H. Wilkinson",
title = "The evaluation of the zeros of ill-conditioned
polynomials. {II}",
journal = j-NUM-MATH,
volume = "1",
pages = "167--180",
month = dec,
year = "1959",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01386382",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.00",
MRnumber = "MR0109435 (22 \#321)",
MRreviewer = "H. Rutishauser",
bibdate = "Mon Oct 18 01:28:20 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@MastersThesis{Young:1959:SSM,
author = "John Mackay Young",
title = "A study of some methods of numerical integration using
floating point arithmetic",
type = "Thesis ({M.S. in Mathematics})",
school = "Texas A.\&M. College",
address = "College Station, TX, USA",
pages = "50",
year = "1959",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Bockstaele:1960:NFA,
author = "P. Bockstaele",
title = "Notes on the First Arithmetics Printed in {Dutch} and
{English}",
journal = j-ISIS,
volume = "51",
number = "3",
pages = "315--321",
month = sep,
year = "1960",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:28:03 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302265;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1960.bib",
URL = "http://www.jstor.org/stable/226510",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Article{Brown:1960:EDC,
author = "David T. Brown",
title = "Error Detecting and Correcting Binary Codes for
Arithmetic Operations",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-9",
number = "3",
pages = "333--337",
month = sep,
year = "1960",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1960.5219855",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:34:12 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219855",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Cohen:1960:EAF,
author = "Eckford Cohen",
title = "The elementary arithmetical functions",
journal = j-SCRIPTA-MATH,
volume = "25",
number = "??",
pages = "221--228",
month = "????",
year = "1960",
ISSN = "0036-9713",
ISSN-L = "0036-9713",
MRclass = "10.00",
MRnumber = "118694",
MRreviewer = "H. Bergstr{\"{o}}m",
bibdate = "Thu Oct 26 11:15:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
ZMnumber = "0116.27101",
acknowledgement = ack-nhfb,
ajournal = "Scripta Math.",
fjournal = "Scripta Mathematica: A Quarterly Journal Devoted to
the Philosophy, History, and Expository Treatment of
Mathematics",
xxpages = "221--227",
ZBmath = "3189455",
}
@Article{Croy:1960:IAD,
author = "John E. Croy",
title = "Improved Arrangement of a Decimal Multiplier",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-9",
number = "2",
pages = "263--263",
month = jun,
year = "1960",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1960.5219830",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:34:11 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219830",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Ercoli:1960:LEE,
author = "Paolo Ercoli",
title = "Letter to the {Editor}: {Errors} Due to Overflow in
Arithmetic Operations",
journal = j-CACM,
volume = "3",
number = "12",
pages = "A9--A9",
month = dec,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:29 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Ercoli:1957:EDO}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Gurzi:1960:HSM,
author = "Fred Gurzi",
title = "A High-Speed Multiplication Process for Digital
Computers",
journal = j-CACM,
volume = "3",
number = "4",
pages = "241--245",
month = apr,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:26 MST 2005",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Gurzi60;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Gurzi60",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Gurzi60",
}
@TechReport{Jensen:1960:CIF,
author = "B. A. Jensen",
title = "Coding instructions for floating point trigonometric,
inverse trigonometric hyperbolic and exponential
functions",
type = "Group report",
number = "30G-0009",
institution = "Massachusetts Institute of Technology, Lincoln
Laboratory",
address = "Lexington, MA, USA",
pages = "7",
year = "1960",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Trigonometrical functions --- Computer programs.",
remark = "Cover title. ``Millstone Hill Radar Station.'' ``1
November 1960.'' Air Force Contract",
}
@Article{Kanner:1960:NUA,
author = "Herbert Kanner",
title = "A Note on the Use of the Abacus in Number Conversion",
journal = j-CACM,
volume = "3",
number = "3",
pages = "167--167",
month = mar,
year = "1960",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/367149.367166",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:26 MST 2005",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Kanner60;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Conversion of integers in both directions between the
base ten and any desired base can be accomplished with
remarkable simplicity by use of the abacus. In fact,
the conversion procedures are far more cumbersome on
the electric desk calculator, for reasons which will be
apparent.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "number base conversion",
oldlabel = "Kanner60",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kanner60",
}
@Article{Knuth:1960:INS,
author = "Donald E. Knuth",
title = "An Imaginary Number System",
journal = j-CACM,
volume = "3",
number = "4",
pages = "245--247",
month = apr,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.99",
MRnumber = "23\#B554",
MRreviewer = "C. B. Haselgrove",
bibdate = "Fri Nov 25 18:19:26 MST 2005",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Knuth60;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
note = "Errata, {\sl Commun\-i\-ca\-tions of the ACM\/ \bf 4}
(August 1961), 355 \cite{Knuth:1961:EIN}. See
\cite{Nadler:1961:DSR} for extension to division and
square root.",
abstract = "For centuries the decimal number system reigned
supreme, except, perhaps, among the Mayan Indians,
until the advent of digital computers brought the
binary and octal systems into the limelight. This paper
introduces another number system which may prove useful
for manipulating complex numbers on machines.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Knuth60",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Knuth60",
ZMreviewer = "C. B. Haselgrove",
}
@Article{Lowan:1960:PREa,
author = "Arnold N. Lowan",
title = "On the Propagation of Round-Off Errors in the
Numerical Integration of the Heat Equation",
journal = j-MATH-COMPUT,
volume = "14",
number = "70",
pages = "139--146",
month = apr,
year = "1960",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Lowan:1960:PREb,
author = "Arnold N. Lowan",
title = "On the Propagation of Round-Off Errors in the
Numerical Treatment of the Wave Equation",
journal = j-MATH-COMPUT,
volume = "14",
number = "71",
pages = "223--228",
month = jul,
year = "1960",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Pawlak:1960:ODC,
author = "Z. Pawlak",
title = "The organization of a digital computer based on the `$
- 2 $' system",
journal = "Bull. Acad. Pol. Sci., Ser. Tech. Sci.",
volume = "8",
number = "??",
pages = "253--258",
month = "????",
year = "1960",
bibdate = "Thu Nov 06 06:00:08 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "negative base",
}
@Article{Perlin:1960:HPC,
author = "I. E. Perlin and J. R. Garrett",
title = "High Precision Calculation of $ \operatorname {Arcsin}
x $, $ \operatorname {Arccos} x $, and $ \operatorname
{Arctan} x $ (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "14",
number = "71",
pages = "270--274",
month = jul,
year = "1960",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nj # " and " # ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Perry:1960:CBF,
author = "C. Perry",
title = "Conversion between floating point representations",
journal = j-CACM,
volume = "3",
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "352.68.00",
MRnumber = "22\#8714",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Pope:1960:MPA,
author = "D. A. Pope and M. L. Stein",
title = "Multiple Precision Arithmetic",
journal = j-CACM,
volume = "3",
number = "12",
pages = "652--654",
month = dec,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@InCollection{Reitwiesner:1960:BA,
author = "G. W. Reitwiesner",
title = "Binary arithmetic",
crossref = "Alt:1960:AC",
pages = "231--308",
year = "1960",
bibdate = "Sat May 18 14:36:56 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Sarafyan:1960:DCS,
author = "Diran Sarafyan",
title = "Divisionless computation of square roots through
continued squaring",
journal = j-CACM,
volume = "3",
number = "5",
pages = "319--321",
month = may,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.00",
MRnumber = "22\#8639",
bibdate = "Fri Nov 25 18:19:26 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions",
ZMreviewer = "M. Lotkin",
}
@Article{Silver:1960:LER,
author = "Roland Silver",
title = "Letter to the {Editor}: Rounding in Floating-Point
Arithmetic",
journal = j-CACM,
volume = "3",
number = "12",
pages = "A9--A9",
month = dec,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:29 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Sklansky:1960:CSA,
author = "J. Sklansky",
title = "Conditional Sum Addition Logic",
journal = j-TRANS-IRE,
volume = "EC-9",
number = "2",
pages = "226--230",
month = jun,
year = "1960",
bibdate = "Fri Nov 09 19:17:08 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the IRE",
}
@Article{Traub:1960:CNM,
author = "J. F. Traub",
title = "Comments on a recent paper [{``A New Method of
Computation of Square Roots Without Using
Division''}]",
journal = j-CACM,
volume = "3",
number = "2",
pages = "86--86",
month = feb,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:25 MST 2005",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Traub60;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Sarafyan:1959:NMC}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Traub60",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Traub60",
}
@Article{Wadey:1960:FA,
author = "W. G. Wadey",
title = "Floating-Point Arithmetics",
journal = j-J-ACM,
volume = "7",
number = "2",
pages = "129--139",
month = apr,
year = "1960",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "65.00 (68.00)",
MRnumber = "22\#6090",
bibdate = "Fri Dec 08 14:44:46 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Three types of floating-point arithmetics with error
control are discussed and compared with conventional
floating-point arithmetic. General multiplication and
division shift criteria are derived (for any base) for
Metropolis-style arithmetics. The limitations and most
suitable range of application for each arithmetic are
discussed.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
reviewer = "C. B. Haselgrove",
xxmonth = "none",
xxnumber = "none",
}
@Article{Wilkinson:1960:EAF,
author = "J. H. Wilkinson",
title = "Error Analysis of Floating-Point Computation",
journal = j-NUM-MATH,
volume = "2",
pages = "319--340",
month = dec,
year = "1960",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.00",
MRnumber = "MR0116477 (22 \#7264)",
MRreviewer = "C. B. Haselgrove",
bibdate = "Fri May 14 17:18:08 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Amble:1961:AFP,
author = "O. Amble and Jan V. Garwick",
title = "On the Accuracy of Floating Point Computers {[BIT {\bf
1}(2), 1961, pp. 87--88]}",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "3",
pages = "220--222",
month = sep,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01933434",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=3;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Garwick:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=3&spage=220",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
xxpages = "220--221??",
}
@TechReport{Anonymous:1961:MCM,
author = "Anonymous",
title = "Modern Computing Methods",
type = "Notes on Applied Science",
number = "16",
institution = "National Physical Laboratory",
address = "Her Majesty's Stationery Office, London",
year = "1961",
bibdate = "Fri Aug 20 10:05:25 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Avizienis:1961:SDN,
author = "Algirdas Avi{\v{z}}ienis",
title = "Signed-Digit Number Representations for Fast Parallel
Arithmetic",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "3",
pages = "389--400",
month = sep,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219227",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219227",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Cheney:1961:DCB,
author = "Philip Warren Cheney",
title = "A Digital Correlator Based on the Residue Number
System",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "1",
pages = "63--70",
month = mar,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219154",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219154",
abstract = "A system design for a digital correlator based on the
application of the residue number system for
computation is presented. Areas of investigation
include sampling, analog-to-residue conversion, logical
design of the arithmetic units, residue-to-analog
conversion, and modes of operation of the proposed
digital correlator. The advantages of speed of
computation and simplicity of logic due to the use of a
residue number system are shown to result in a
significantly faster and simpler system than if a
conventional number system were used. The resulting
digital correlator is designed for megacycle sampling
and computation with a 0.1 per cent system precision.",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Cheney:1961:TNA,
author = "E. W. Cheney and H. L. Loeb",
title = "Two new algorithms for rational approximation",
journal = j-NUM-MATH,
volume = "3",
number = "1",
pages = "72--75",
month = dec,
year = "1961",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01386002",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 19:01:15 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Clarkson:1961:DMI,
author = "W. K. Clarkson",
title = "A Divisionless Method of Integer Conversion",
journal = j-CACM,
volume = "4",
number = "7",
pages = "315--316",
month = jul,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 08:14:59 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Cox:1961:NMP,
author = "Albert G. Cox and H. A. Luther",
title = "A Note on Multiple Precision Arithmetic",
journal = j-CACM,
volume = "4",
number = "8",
pages = "353--353",
month = aug,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/366678.366693",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Dec 03 14:07:44 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Since computers have means to detect overflow on
addition or subtraction, this can be used in a multiple
precision addition-subtraction subroutine to obviate a
sign analysis. Consider all integers in the computer to
be expressed ``radix t'', that is, in the form $ a =
a_0 + a_1 t + \cdots + a_n t^n $ where $ a_i $ are of
like sign and have magnitudes less than $t$. $t$ is a
positive integer determined by the word length of the
computer. Consider the expression $ c = a \pm b = (a_0
\pm b_0) + (a_1 \pm b_1)t + \cdots + (a_n \pm b_n)t^n$.
Here $ a_i \pm b_i$ may exceed the storage capacity of
one word or may have a sign different from $c$.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Croy:1961:RTM,
author = "John E. Croy",
title = "Rapid Technique of Manual or Machine Binary-to-Decimal
Integer Conversion Using Decimal Radix Arithmetic",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "4",
pages = "777--777",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219286",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:05 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219286",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Freiman:1961:SAC,
author = "C. V. Freiman",
title = "Statistical analysis of certain binary division
algorithms",
journal = j-IRE-PROC,
volume = "49",
number = "1",
pages = "91--103",
month = jan,
year = "1961",
bibdate = "Mon Sep 16 16:12:21 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IRE Proceedings",
xxnote = "Check author name: I have found this paper cited both
as Freiman and as Frieman?? Hennessy and Patterson
\cite{Hennessy:2002:CAQ} have Freiman.",
}
@TechReport{Garner:1961:RNS,
author = "H. L. Garner and R. F. Arnold and B. C. Benson and C.
G. Brockus and R. J. Gonzalez and D. P. Rozenberg",
title = "Residue number systems for computers",
type = "{ASD} Technical Report",
number = "61-483",
institution = "Electronic Technology Laboratory, The University of
Michigan",
address = "Ann Arbor, MI, USA",
month = oct,
year = "1961",
bibdate = "Thu Nov 18 09:27:06 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txt",
abstract = "The purpose of the research performed under this
contract was to investigate the feasibility of residue
number systems in their applications to digital
computers. The problems of such an application are the
ones of magnitude determination, sign determination,
overflow, scaling, and division. These problems are not
independent, but are found to be quite interrelated. A
theoretical treatment of residue number systems is
given which lays the foundation for a unified study of
the complete problem. Treatments of an organizational
nature are given which deal with multiplication,
division, and scaling. The matter of correlating the
theoretical and organizational studies to physical
realizations involving networks is treated also. The
question of whether the residue number system can be
successfully applied to general purpose computers is
still an open one. Their application to special purpose
machines is considered both feasible and practical.",
acknowledgement = ack-nhfb,
remark = "This report represents the results of research
performed by the group at The University of Michigan
under the direction of Professor H. L. Garner.
Concurrently, research on the same subject was being
conducted at Harvard University under the direction of
Professor Howard Aiken, and at the Lockheed Missile
System Division under the direction of Dr. Richard
Tanaka. There was a considerable exchange of
information among the above groups during the course of
the research effort. The efforts attained exhibit
little overlap, rather they are complementary. A
portion of this report was extracted from the doctoral
dissertation of D. P. Rozenberg. His work was supported
by this contract, and led to the Ph.D..",
}
@Article{Garwick:1961:AFP,
author = "Jan V. Garwick",
title = "The Accuracy of Floating Point Computers",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "2",
pages = "87--88",
month = jun,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01939221",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=2;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also comment and reply
\cite{Amble:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=2&spage=87",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
}
@Article{Garwick:1961:RAF,
author = "J. V. Garwick",
title = "Reply to {``On the Accuracy of Floating Point
Computers'' [BIT {\bf 1}(3), 1961, pp. 220--221]}",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "3",
pages = "222--222",
year = "1961",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon Nov 16 14:36:22 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Garwick:1961:AFP,Amble:1961:AFP}.",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
}
@InProceedings{Henderson:1961:RCE,
author = "D. S. Henderson",
booktitle = "{Proceedings of the 1961 16th ACM national meeting}",
title = "Residue class error checking codes",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "132.101--132.104",
year = "1961",
DOI = "https://doi.org/10.1145/800029.808563",
bibdate = "Thu Aug 07 19:04:58 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Error checking codes based on residues have the
advantage over parity-based codes of monitoring
arithmetic as well as transmission operations. Codes
may be devised to detect burst-type errors, to correct
single errors in a binary arithmetic operation, to
correct burst errors and finally to correct any
single-digit error in a decimal operation.",
acknowledgement = ack-nhfb,
keywords = "decimal arithmetic",
}
@Article{Kettel:1961:AAM,
author = "E. Kettel and W. Schneider",
title = "An Accurate Analog Multiplier and Divider",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "2",
pages = "269--272",
month = jun,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219198",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:03 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219198",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Knuth:1961:EIN,
author = "Donald E. Knuth",
title = "Errata: {``An imaginary number system''}",
journal = j-CACM,
volume = "4",
number = "8",
pages = "355--355",
month = aug,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Jan 09 07:10:22 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1960:INS}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Kovatch:1961:HEA,
author = "G. Kovatch and W. E. Meserve",
title = "The {Hall-Effect} Analog Multiplier",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "3",
pages = "512--515",
month = sep,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219240",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219240",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Lehman:1961:STH,
author = "M. Lehman and N. Burla",
title = "Skip Techniques for High-Speed Carry-Propagation in
Binary Arithmetic Units",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "4",
pages = "691--698",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219274",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219274",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{MacSorley:1961:HSA,
author = "O. L. MacSorley",
title = "High-speed arithmetic in binary computers",
journal = j-IRE-PROC,
volume = "49",
number = "??",
pages = "67--91",
month = jan,
year = "1961",
bibdate = "Sat May 18 14:34:55 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite{Swartzlander:1976:CDD}.",
acknowledgement = ack-nhfb,
fjournal = "IRE Proceedings",
}
@Book{Morrison:1961:CBP,
editor = "Philip Morrison and Emily Morrison",
title = "{Charles Babbage} on the principles and development of
the calculator: and other seminal writings",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xxxviii + 400",
year = "1961",
ISBN = "0-486-24691-4 (paperback)",
ISBN-13 = "978-0-486-24691-8 (paperback)",
LCCN = "QA75 .C52 1961",
bibdate = "Sat Jan 12 22:30:15 MST 2013",
bibsource = "clio-db.cc.columbia.edu:7090/Voyager;
https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$7.95",
acknowledgement = ack-nhfb,
subject = "Calculators; Babbage, Charles",
subject-dates = "Charles Babbage (26 December 1791--18 October 1871)",
tableofcontents = "Chapters from Passages from the life of a
philosopher \\
Selections from Babbage's calculating engines \\
Appendix of miscellaneous papers",
}
@Article{Nadler:1961:DSR,
author = "Morton Nadler",
title = "Division and square root in the quater-imaginary
number system",
journal = j-CACM,
volume = "4",
number = "4",
pages = "192--193",
month = apr,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.99",
MRnumber = "23\#B555",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1960:INS}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions",
ZMreviewer = "C. B. Haselgrove",
}
@Article{Pinkham:1961:DFS,
author = "Roger S. Pinkham",
title = "On the Distribution of First Significant Digits",
journal = j-ANN-MATH-STAT,
volume = "32",
number = "4",
pages = "1223--1230",
month = dec,
year = "1961",
CODEN = "AASTAD",
ISSN = "0003-4851 (print), 2168-8990 (electronic)",
ISSN-L = "0003-4851",
bibdate = "Thu Feb 15 15:07:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0003-4851%28196112%2932%3A4%3C1223%3AOTDOFS%3E2.0.CO%3B2-T",
abstract = "It has been noticed by astute observers that well used
tables of logarithms are invariably dirtier at the
front than at the back. Upon reflection one is led to
inquire whether there are more physical constants with
low order first significant digits than high. Actual
counts by Benford [2] show that not only is this the
case but that it seems to be an empirical truth that
whenever one has a large body of physical data,
Farmer's Almanac, Census Reports, Chemical Rubber
Handbook, etc., the proportion of these data with first
significant digit $n$ or less is approximately $
\log_{10}(n + 1) $. Any reader formerly unaware of this
``peculiarity'' will find an actual sampling experiment
wondrously tantalizing. Thus, for example,
approximately $ 0.7 $ of the physical constants in the
Chemical Rubber Handbook begin with $4$ or less ($
\log_{10}(4 + 1) = 0.699 $). This is to be contrasted
with the widespread intuitive evaluation $ 4 / 9 $
ths.",
acknowledgement = ack-nhfb,
fjournal = "Annals of Mathematical Statistics",
journal-URL = "http://projecteuclid.org/all/euclid.aoms/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From p. 1223: ``\ldots{} the proportion of these data
with first significant digit $n$ or less is
approximately $ \log_{10}(n + 1) $.''\par
\ldots{} ``The only distribution for first significant
digits which is invariant under scale change of the
underlying distribution is $ \log_{10}(n + 1) $.
Contrary to suspicion this is a non-trivial
mathematical result, for the variable $n$ is
discrete.''.\par
From p. 1230: ``The foregoing results bear on questions
of round-off in computing machines. Since $ d(u v) = u
d v + v d u $, the error resulting from multiplying two
rounded numbers will be governed primarily by the first
significant digits of the two numbers being multiplied.
Now the distribution of first significant digits,
favoring as it does low order digits, tends to produce
less error than would be the case if first significant
digits were uniform as has sometimes been
assumed.''\par
Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Rabinowitz:1961:MPD,
author = "Philip Rabinowitz",
title = "Multiple-Precision Division",
journal = j-CACM,
volume = "4",
number = "2",
pages = "98--98",
month = feb,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/366105.366171",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 00:29:25 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Saltman:1961:RCT,
author = "Roy G. Saltman",
title = "Reducing Computing Time for Synchronous Binary
Division",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "2",
pages = "169--174",
month = jun,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219186",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:03 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219186",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Spielberg:1961:ECF,
author = "Kurt Spielberg",
title = "Efficient Continued Fraction Approximations To
Elementary Functions",
journal = j-MATH-COMPUT,
volume = "15",
number = "76",
pages = "409--417",
month = oct,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nj # " and " # ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Spielberg:1961:RPS,
author = "K. Spielberg",
title = "Representation of Power Series in Terms of
Polynomials, Rational Approximations and Continued
Fractions",
journal = j-J-ACM,
volume = "8",
number = "4",
pages = "613--627",
month = oct,
year = "1961",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Sat Dec 09 14:01:44 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Thacher:1961:ISR,
author = "Henry C. {Thacher, Jr.}",
title = "Iterated Square Root Expansions for the Inverse Cosine
and Inverse Hyperbolic Cosine",
journal = j-MATH-COMPUT,
volume = "15",
number = "76",
pages = "399--403",
month = oct,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@TechReport{Weik:1961:TSD,
author = "Martin H. Weik",
title = "A Third Survey of Domestic Electronic Digital
Computing Systems",
type = "Report",
number = "1115",
institution = "Ballistic Research Laboratories",
address = "Aberdeen Proving Ground, MD, USA",
pages = "1131",
month = mar,
year = "1961",
bibdate = "Fri Nov 28 19:37:51 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Based on the results of a third survey, the
engineering and programming characteristics of two
hundred twenty-two different electronic digital
computing systems are given. The data are presented
from the point of view of application, numerical and
arithmetic characteristics, input, output and storage
systems, construction and checking features, power,
space, weight, and site preparation and personnel
requirements, production records, cost and rental
rates, sale and lease policy, reliability, operating
experience, and time availability, engineering
modifications and improvements and other related
topics. An analysis of the survey data, fifteen
comparative tables, a discussion of trends, a revised
bibliography, and a complete glossary of computer
engineering and programming terminology are included.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@Article{Wilson:1961:ARB,
author = "J. B. Wilson and R. S. Ledley",
title = "An Algorithm for Rapid Binary Division",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "4",
pages = "662--670",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219271",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219271",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@InProceedings{Ashenhurst:1962:MIA,
author = "R. L. Ashenhurst",
title = "The {Maniac III} Arithmetic System",
crossref = "AFIPS:1962:APS",
pages = "192--202",
year = "1962",
bibdate = "Wed Feb 14 17:14:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Buchholz:1962:PCS,
editor = "Werner Buchholz",
title = "Planning a Computer System: {Project Stretch}",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xvii + 322",
year = "1962",
LCCN = "1876",
bibdate = "Fri Nov 19 10:02:31 MST 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
library.ox.ac.uk:210/ADVANCE",
note = "This important book is the primary description of the
influential IBM 7030 Stretch computer, written by its
architects. See also a detailed critical review
\cite{Strachey:1962:BRP}.",
URL = "http://ed-thelen.org/comp-hist/IBM-7030-Planning-McJones.pdf",
acknowledgement = ack-nhfb,
remark = "The text of the book is in the public domain, with the
permission of the author in 2003.
See \cite{MacKenzie:1991:IAL} for a remark about the
noisy mode for floating-point arithmetic in the IBM
7030 Stretch. That mode is first mentioned on page 25
of this book, and described in detail on page 102,
which states:
``By definition of ordinary normalized FLP operations,
numbers are frequently extended on the right by
attaching zeros. During addition the n-digit operand
that is not preshifted is extended with n zeros, so as
to provide the extra positions to which the preshifted
operand can be added. Any operand or result that is
shifted left to be normalized requires a corresponding
number of zeros to be shifted in at the right. Both
sets of zeros tend to produce numbers smaller in
absolute value than they would have been if more digits
had been carried. In the noisy mode these numbers are
simply extended with 1's instead of zeros (1's in a
binary machine, 9's in a decimal machine). So all
numbers tend to be too large in absolute value. The
true value, if there had been no significance loss,
should lie between these two extremes. Hence, two runs,
one made without and one made with the noisy mode,
should show differences in result that indicate which
digits may have been affected by significance loss.
The principal weakness of the noisy-mode procedure is
that it requires two runs for the same problem. A much
less important weakness is that the loss of
significance cannot be guaranteed to show up --- it
merely has a very high probability of showing up ---
whereas built-in significance checks can be made
slightly pessimistic, so that actual significance loss
will not be greater than indicated. On the other hand,
little extra hardware and no extra storage are required
for the noisy-mode approach. Furthermore, significance
loss is relatively rare, so that running a problem
twice when Significance loss is suspected does not pose
a serious problem. What is serious is the possibility
of unsuspected significance loss.
In discussions of significance two points are often
overlooked. The first of these is trivial: the best way
of ensuring significant results is to use an adequate
number of fraction digits. The second is almost equally
mundane: for a given procedure, normalized FLP
arithmetic will ordinarily produce the greatest
precision possible for the number of fraction digits
used. Normalized FLP arithmetic has been criticized
with respect to significance loss, because such loss is
not indicated by the creation of leading zeros, as it
is with fixed-point arithmetic. In other words, the
contention is not that normalized FLP arithmetic is
more prone to significance loss than equivalent
fixed-point arithmetic, which would be untrue, but that
an equivalent indication of such loss is not provided.
Loss of significance, however, is also a serious
problem in fixed-point arithmetic; multiplication and
division do not handle it at all correctly by means of
leading zeros. (In particular, fixed-point
multiplication may lead to serious or even total
significance loss, which would not have occurred with
normalized FLP arithmetic: and although leading zeros
in addition and subtraction of fixed-point operands do
give correct significance indications, the use of other
operations and of built-in scaling loops frequently
destroys entirely the leading-zeros method of counting
significance.)''",
subject = "Computer architecture",
tableofcontents = "Foreword v \\
Preface vii \\
1. Project Stretch 1 \\
[by W. Buchholz] \\
2. Architectural Philosophy 5 \\
[by F. P. Brooks, Jr.] \\
2.1. The Two Objectives of Project Stretch 5 \\
2.2. Resources 6 \\
2.3. Guiding Principles 7 \\
2.4. Contemporary Trends in Computer Architecture 10
\\
2.5. Hindsight 15 \\
3. System Summary of IBM 7030 17 \\
[by W. Buchholz] \\
3.1. System Organization 17 \\
3.2. Memory Units 17 \\
3.3. Index Memory 19 \\
3.4. Special Registers 19 \\
3.5. Input and Output Facilities 19 \\
3.6. High-speed Disk Units 20 \\
3.7. Central Processing Unit 20 \\
3.8. Instruction Controls 21 \\
3.9. Index-arithmetic Unit 21 \\
3.10. Instruction Look-ahead 21 \\
3.11. Arithmetic Unit 22 \\
3.12. Instruction Set 24 \\
3.13. Data Arithmetic 24 \\
3.14. Radix-conversion Operations 27 \\
3.15. Connective Operations 27 \\
3.16. Index-arithmetic Operations 27 \\
3.17. Branching Operations 28 \\
3.18. Transmission Operations 28 \\
3.19. Input-Output Operations 29 \\
3.20. New Features 29 \\
3.21. Performance 32 \\
4. Natural Data Units 33 \\
[by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
\\
4.1. Lengths and Structures of Natural Data Units 33
\\
4.2. Procedures for Specifying Natural Data Units 36
\\
4.3. Data Hierarchies 39 \\
4.4. Classes of Operations 40 \\
5. Choosing a Number Base 42 \\
[by W. Buchholz] \\
5.1. Introduction 42 \\
5.2. Information Content 45 \\
5.3. Arithmetic Speed 49 \\
5.4. Numerical Data 50 \\
5.5. Nonnumerical Data 51 \\
5.6. Addresses 52 \\
5.7. Transformation 53 \\
5.8. Partitioning of Memory 54 \\
5.9. Program Interpretation 56 \\
5.10. Other Number Bases 58 \\
5.11. Conclusion 58 \\
6. Character Set 60 \\
[by R. W. Bemer and W. Buchholz] \\
6.1. Introduction 60 \\
6.2. Size of Set 62 \\
6.3. Subsets 62 \\
6.4. Expansion of Set 63 \\
6.5. Code 63 \\
6.6. Parity Bit 66 \\
6.7. Sequence 66 \\
6.8. Blank 67 \\
6.9. Decimal Digits 68 \\
6.10. Typewriter Keyboard 68 \\
6.11. Adjacency 69 \\
6.12. Uniqueness 69 \\
6.13. Signs 70 \\
6.14. Tape-recording Convention 71 \\
6.15. Card-punching Convention 71 \\
6.16. List of 7030 Character Set 72 \\
7. Variable-field-length Operation 75 \\
[by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
\\
7.1. Introduction 75 \\
7.2. Addressing of Variable-field-length Data 76 \\
7.3. Field Length 77 \\
7.4. Byte Size 78 \\
7.5. Universal Accumulator 79 \\
7.6. Accumulator Operand 79 \\
7.7. Binary and Decimal Arithmetic 80 \\
7.8. Integer Arithmetic 81 \\
7.9. Numerical Signs 82 \\
7.10. Indicators 84 \\
7.11. Arithmetical Operations 85 \\
7.12. Radix-conversion Operation 87 \\
7.13. Logical Connectives of Two Variables 87 \\
7.14. Connective Operations 89 \\
8. Floating-point Operation 92 \\
[by S. G. Campbell] \\
General Discussion \\
8.1. Problems of Fixed-point Arithmetic 92 \\
8.2. Floating-point Arithmetic 94 \\
8.3. Normalization 97 \\
8.4. Floating-point Singularities 98 \\
8.5. Range and Precision 99 \\
8.6. Round-off Error 100 \\
8.7. Significance Checks 101 \\
8.8. Forms of Floating-point Arithmetic 103 \\
8.9. Structure of Floating-point Data 104 \\
Floating-point Features of the 7030 \\
8.10. Floating-point Instruction Format 106 \\
8.11. Floating-point Data Formats 106 \\
8.12. Singular Floating-point Numbers 108 \\
8.13. Indicators 112 \\
8.14. Universal Accumulator 113 \\
8.15. Fraction Arithmetic 114 \\
8.16. Floating-point-arithmetic Operations 114 \\
8.17. Fixed-point Arithmetic Using Unnormalized \\
Floating-point Operations 118 \\
8.18. Special Functions and Forms of Arithmetic 119 \\
8.19. Multiple-precision Arithmetic 119 \\
8.20. General Remarks 121 \\
9. Instruction Formats 122 \\
[by W. Buchholz] \\
9.1. Introduction 122 \\
9.2. Earlier Instruction Languages 122 \\
9.3. Evolution of the Single-address Instruction 124
\\
9.4. Implied Addresses 125 \\
9.5. Basic 7030 Instruction Formats 126 \\
9.6. Instruction Efficiency 127 \\
9.7. The Simplicity of Complexity 131 \\
9.8. Relationship to Automatic Programming Languages
132 \\
10. Instruction Sequencing 133 \\
[by F. P. Brooks, Jr.] \\
10.1. Modes of Instruction Sequencing 133 \\
10.2. Instruction Counter 134 \\
10.3. Unconditional Branching 135 \\
10.4. Conditional Branching 136 \\
10.5. Program-interrupt System 136 \\
10.6. Components of the Program-interrupt System 137
\\
10.7. Examples of Program-interrupt Techniques 140 \\
10.8. Execute Instructions 146 \\
10.9. Execute Operations in the 7030 148 \\
11. Indexing 150 \\
[by G. P. Blaauw] \\
11.1. Introduction 150 \\
11.2. Indexing Functions 151 \\
11.3. Instruction Format for Indexing 155 \\
11.4. Incrementing 157 \\
11.5. Counting 159 \\
11.6. Advancing by One 161 \\
11.7. Progressive Indexing 161 \\
11.8. Data Transmission 162 \\
11.9. Data Ordering 163 \\
11.10. Refilling 165 \\
11.11. Indirect Addressing and Indirect Indexing 167
\\
11.12. Indexing Applications 169 \\
11.13. Record-handling Applications 172 \\
11.14. File Maintenance 175 \\
11.15. Subroutine Control 177 \\
11.16. Conclusion 178 \\
12. Input-Output Control 179 \\
[by W. Buchholz] \\
12.1. A Generalized Approach to Connecting \\
Input-Output and External Storage 179 \\
12.2. Input-Output Instructions 180 \\
12.3. Defining the Memory Area 181 \\
12.4. Writing and Reading 182 \\
12.5. Controlling and Locating 183 \\
12.6. An Alternative Approach 184 \\
12.7. Program Interruptions 184 \\
12.8. Buffering 180 \\
12.9. Interface 188 \\
12.10. Operator Control of Input-Output Units 190 \\
13. Multiprogramming 192 \\
[by E. F. Codd, E. S. Lowry, E. McDonough, and C. A.
Scalzi] \\
13.1. Introduction 192 \\
13.2. Multiprogramming Requirements 193 \\
13.3. 7030 Features that Assist Multiprogramming 195
\\
13.4. Programmed Logic 197 \\
13.5. Concluding Remarks 200 \\
13.6. References 201 \\
14. The Central Processing Unit 202 \\
[by E. Bloch] \\
14.1. Concurrent System Operation 202 \\
14.2. Concurrency within the Central Processing Unit
204 \\
14.3. Data Flow 204 \\
14.4. Arithmetic Unit 208 \\
14.5. Checking 216 \\
14.6. Component Count 216 \\
14.7. Performance 217 \\
14.8. Circuits 218 \\
14.9. Packaging 223 \\
15. The Look-ahead Unit 228 \\
[by R. S. Balance, J. Cocke, and H. G. Kolsky] \\
15.1. General Description 228 \\
15.2. Timing-simulation Program 230 \\
15.3. Description of the Look-ahead Unit 238 \\
15.4. Forwarding 240 \\
15.5. Counter Sequences 241 \\
15.6. Recovery after Interrupt 246 \\
15.7. A Look-back at the Look-ahead 247 \\
16. The Exchange 248 \\
[by W. Buchholz] \\
16.1. General Description 248 \\
16.2. Starting a WRITE or READ Operation 250 \\
16.3. Data Transfer during Writing 250 \\
16.4. Data Transfer during Reading 251 \\
16.5. Terminating a WRITE or READ Operation 252 \\
16.6. Multiple Operations 252 \\
16.7. CONTROL and LOCATE Operations 252 \\
16.8. Interrogating the Control Word 253 \\
16.9. Forced Termination 253 \\
17. A Nonarithmetical System Extension 254 \\
[by S. G. Campbell, P. S. Herwitz, and J. H. Pomerene]
\\
17.1. Nonarithmetical Processing 254 \\
17.2. The Set-up Mode 258 \\
17.3. Byte-sequence Formation 259 \\
17.4. Pattern Selection 260 \\
17.5. Transformation Facilities 261 \\
17.6. Statistical Aids 263 \\
17.7. The BYTE-BY-BYTE Instruction 263 \\
17.8. Monitoring for Special Conditions 264 \\
17.9. Instruction Set 265 \\
17.10. Collating Operations 266 \\
17.11. Table Look-up Operations 267 \\
17.12. Example 267 \\
Appendix A. Summary Data 273 \\
A.1. List of the Larger IBM Stored-program Computers
273 \\
A.2. Instruction Formats 275 \\
A.3. List of Registers and Special Addresses 276 \\
A.4. Summary of Operations and Modifiers 277 \\
A.5. Summary of Indicators 287 \\
Appendix B. Programming Examples 292 \\
Notation 292 \\
B.1. Polynomial Evaluation 295 \\
B.2. Cube-root Extraction 296 \\
B.3. Matrix Multiplication 298 \\
B.4. Conversion of Decimal Numbers to a \\
Floating-point Normalized Vector 299 \\
B.5. Editing a Typed Message 301 \\
B.6. Transposition of a Large Bit Matrix 303 \\
Index 305",
}
@InCollection{Campbell:1962:FPO,
author = "S. G. Campbell",
editor = "Werner Buchholz",
booktitle = "Planning a Computer System: {Project Stretch}",
title = "Floating-Point Operation",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
bookpages = "322",
pages = "92--121",
year = "1962",
LCCN = "QA76.8.I2 I5",
bibdate = "Wed Feb 14 17:24:27 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "IBM 7030 (Computer); IBM Stretch",
}
@Article{Cantor:1962:LEF,
author = "D. Cantor and G. Estrin and R. Turn",
title = "Logarithmic and Exponential Function Evaluation in a
Variable Structure Digital Computer",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "2",
pages = "155--164",
month = apr,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219348",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:49 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219348",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@TechReport{Descloux:1962:REF,
author = "J. Descloux",
title = "Remarks on errors in first order iterative processes
with floating-point computers",
institution = "University of Illinois Graduate College, Digital
Computer Laboratory",
address = "Urbana, IL, USA",
pages = "7",
year = "1962",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Report / University of Illinois, Digital Computer
Laboratory; no. 113 Report (University of Illinois
(Urbana-Champaign campus). Digital Computer
Laboratory); no. 113.",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers.; Numerical
calculations.",
remark = "Supported by: National Science Foundation under grant
G16489. ``March 22, 1962.''",
}
@Article{Fischler:1962:TRA,
author = "M. A. Fischler and E. A. Poe",
title = "Threshold Realization of Arithmetic Circuits",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "2",
pages = "287--288",
month = apr,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219366",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:50 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219366",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Fraser:1962:CRA,
author = "W. Fraser and J. F. Hart",
title = "On the computation of rational approximations to
continuous functions",
journal = j-CACM,
volume = "5",
number = "7",
pages = "401--403",
month = jul,
year = "1962",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/368273.368578",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:39 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\abs(x)$; $\cos(x)$; $\Gamma(1+x)$; $\sin(x)$;
elementary functions; Remes algorithm; special
functions",
}
@Article{Grau:1962:FNR,
author = "A. A. Grau",
title = "On a floating-point number representation for use with
algorithmic languages",
journal = j-CACM,
volume = "5",
number = "3",
pages = "160--161",
month = mar,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00",
MRnumber = "26\#4506",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Algorithmic languages, such as ALGOL, make provision
for two types of numbers, real and integer, which are
usually implemented on the computer by means of
floating-point and fixed-point numbers respectively.
The concepts real and integer, however, are taken from
mathematics, where the set of integers forms a proper
subset of the set of real numbers. In implementation a
real problem is posed by the fact that the set of
fixed-point numbers is not a proper subset of the set
of floating-point numbers; this problem becomes very
apparent in attempts to implement ALGOL 60.
Furthermore, the {\em one\/} mathematical operation of
addition is implemented in the machine by one of {\em
two\/} machine operations, fixed-point addition or
floating-point addition.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
reviewer = "R. L. Ashenhurst",
}
@Article{Guffin:1962:CSL,
author = "Ronald M. Guffin",
title = "A Computer for Solving Linear Simultaneous Equations
Using the Residue Number System",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "2",
pages = "164--173",
month = apr,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219349",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:49 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219349",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Book{Hamming:1962:NMS,
author = "R. W. (Richard Wesley) Hamming",
title = "Numerical methods for scientists and engineers",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "411",
year = "1962",
LCCN = "QA297 .H28",
bibdate = "Fri Aug 20 09:12:08 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "International series in pure and applied mathematics",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
subject = "Numerical analysis; Electronic digital computers",
}
@Article{Jones:1962:FPF,
author = "F. B. Jones and A. W. Wymore",
title = "Floating Point Feature on the {IBM Type 1620}",
journal = j-IBM-TDB,
volume = "05-62",
pages = "43--46",
month = may,
year = "1962",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Fri Nov 28 11:26:02 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
keywords = "decimal floating-point arithmetic",
remark = "The IBM 1620 normalized variable-precision arithmetic
provides up to 100 decimal digits with an exponent
range of $ \pm 99 $.",
}
@Article{Karatsuba:1962:MMN,
author = "A. Karatsuba and Y. Ofman",
title = "Multiplication of multidigit numbers on automata",
journal = j-DOKL-AKAD-NAUK,
volume = "145",
number = "??",
pages = "293--294",
month = "????",
year = "1962",
CODEN = "DANKAS",
ISSN = "0002-3264",
bibdate = "Tue Jul 05 10:35:11 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Doklady Akademii nauk SSSR",
journal-URL = "http://istina.msu.ru/journals/366838/",
}
@Article{Keir:1962:DOD,
author = "Y. A. Keir and P. W. Cheney and M. Tannenbaum",
title = "Division and overflow detection in residue number
systems",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "4",
pages = "501--507",
month = aug,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219389",
ISSN = "0367-9950",
MRclass = "68.00",
MRnumber = "MR0150990 (27 \#976)",
MRreviewer = "N. H. Choksy",
bibdate = "Thu Jul 14 09:11:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219389",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Kesner:1962:FPA,
author = "O. Kesner",
title = "Floating-point arithmetic in {COBOL}",
journal = j-CACM,
volume = "5",
number = "5",
pages = "269--271",
month = may,
year = "1962",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/367710.367739",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:38 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Knuth:1962:EPC,
author = "Donald E. Knuth",
title = "Evaluation of polynomials by computer",
journal = j-CACM,
volume = "5",
number = "12",
pages = "595--599",
month = dec,
year = "1962",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355580.369074",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00 (12.00)",
MRnumber = "27 \#970",
bibdate = "Thu Dec 08 11:11:03 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
note = "See letter \cite{Knuth:1963:LEE}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "The author that Motzkin (1962) showed that Horner's
rule for polynomial evaluation may not be optimal, and
develops the idea further for arbitrary polynomials,
but also observes that the coefficients of the revised
polynomials may be difficult to find. He also asks
about, but does not answer, the question of error
analysis of the various methods.",
}
@Article{Lake:1962:LEH,
author = "G. T. Lake",
title = "Letter to the Editor: Hardware Conversion of Decimal
and Binary Numbers",
journal = j-CACM,
volume = "5",
number = "9",
pages = "468--469",
month = sep,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 28 18:16:30 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "decimal floating-point arithmetic",
}
@Article{Lynch:1962:WBD,
author = "W. C. Lynch",
title = "On a Wired-In Binary-to-Decimal Conversion Scheme",
journal = j-CACM,
volume = "5",
number = "3",
pages = "159--159",
month = mar,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 28 18:21:41 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "decimal floating-point arithmetic",
}
@Article{MacSorley:1962:RBA,
author = "O. L. MacSorley",
title = "Review: \booktitle{An Algorithm for Rapid Binary
Division}, by {J. B. Wilson and R. S. Ledley}",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "3",
pages = "420--420",
month = jun,
year = "1962",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Sat Jul 16 20:52:08 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{McGee:1962:BM,
author = "W. C. McGee",
title = "A Binary Multiplication",
journal = j-SIAM-REVIEW,
volume = "4",
number = "3",
pages = "256--256",
month = "????",
year = "1962",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1004066",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:04:54 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/4/3;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "July 1962",
}
@Article{Meggitt:1962:PDP,
author = "J. E. Meggitt",
title = "Pseudo Division and Pseudo Multiplication Processes",
journal = j-IBM-JRD,
volume = "6",
number = "2",
pages = "210--226",
month = apr,
year = "1962",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Metze:1962:CBD,
author = "Gernot Metze",
title = "A Class of Binary Divisions Yielding Minimally
Represented Quotients",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "6",
pages = "761--764",
month = dec,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219460",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:53 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219460",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Mitchell:1962:CMD,
author = "John N. Mitchell",
title = "Computer Multiplication and Division Using Binary
Logarithms",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "4",
pages = "512--517",
month = aug,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219391",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219391",
abstract = "A method of computer multiplication and division is
proposed which uses binary logarithms. The logarithm of
a binary number may be determined approximately from
the number itself by simple shifting and counting. A
simple add or subtract and shift operation is all that
is required to multiply or divide. Since the logarithms
used are approximate there can be errors in the result.
An error analysis is given and a means of reducing the
error for the multiply operation is show",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Rozier:1962:DBC,
author = "Charles P. Rozier",
title = "Decimal-to-Binary Conversion Using Octal Radix
Arithmetic",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "5",
pages = "708--709",
month = oct,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219436",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:52 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219436",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Shanks:1962:CD,
author = "Daniel Shanks and John W. {Wrench, Jr.}",
title = "Calculation of $ \pi $ to 100,000 Decimals",
journal = j-MATH-COMPUT,
volume = "16",
number = "77",
pages = "76--99",
month = jan,
year = "1962",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Misc{Sierra:1962:FDP,
author = "Huberto M. Sierra",
title = "Floating Decimal Point Arithmetic Control Means for
Calculator",
howpublished = "US Patent 3,037,701",
day = "5",
month = jun,
year = "1962",
bibdate = "Sat Mar 24 05:59:45 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://patents.google.com/patent/US3037701A",
abstract = "The invention relates to digital computers and more
particularly to digital computers for making
calculations with numbers having a wide range of values
with a limited number of digit storing positions.",
acknowledgement = ack-nhfb,
remark = "US Patent filed 21 November 1956, granted to IBM on 5
June 1962, expired 5 June 1979 (17 years after grant).
This may be the earliest US patent on floating-point
arithmetic.",
}
@Article{Smith:1962:ACDa,
author = "Robert L. Smith",
title = "{Algorithm 116}: {Complex} Division",
journal = j-CACM,
volume = "5",
number = "8",
pages = "435--435",
month = aug,
year = "1962",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/368637.368661",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:40 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Spielberg:1962:PCF,
author = "Kurt Spielberg",
title = "Polynomial and Continued-Fraction Approximations for
Logarithmic Functions",
journal = j-MATH-COMPUT,
volume = "16",
number = "78",
pages = "205--217",
month = apr,
year = "1962",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nj # " and " # ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Strachey:1962:BRP,
author = "Christopher Strachey",
title = "Book Reviews: {{\booktitle{Planning a Computer System:
Project Stretch}}. Edited by Werner Buchholz. 322
pp.(London: McGraw-Hill)}",
journal = j-COMP-J,
volume = "5",
number = "2",
pages = "152--153",
month = aug,
year = "1962",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/5.2.152",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Wed Sep 25 09:59:25 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
note = "See \cite{Buchholz:1962:PCS}.",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "IBM 7030 (Stretch); IBM 7950 (Harvest)",
}
@Article{Wynn:1962:AAP,
author = "P. Wynn",
title = "An Arsenal of {ALGOL} Procedures for Complex
Arithmetic",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "2",
number = "4",
pages = "232--255",
month = dec,
year = "1962",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01940171",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=2&issue=4;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=2&issue=4&spage=232",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "ALGOL; complex arithmetic; confluence hypergeometric
function; continued fractions; incomplete beta
function; incomplete gamma function; Stieltjes
$S$-fractions; Weber parabolic cylinder function",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@InCollection{Zuse:1962:ERE,
author = "K. Zuse",
editor = "W. Hoffman",
booktitle = "{Digitale Informationswandler}",
title = "{Entwicklungslinien einer Rechenger{\"a}te-Entwicklung
von der Mechanik zur Elektronik}. ({German}) [Lines of
development of computing equipment development from
mechanics to electronics]",
publisher = "Vieweg \& Sohn, GmbH",
address = "Braunschweig, West Germany",
pages = "508--532",
year = "1962",
bibdate = "Wed Oct 13 11:23:04 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 4.3]{Randell:1982:ODC}.
Translated by Mr. and Mrs. P. Jones.",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Bemer:1963:NRT,
author = "R. W. Bemer",
title = "A Note on Range Transformations for Square Root and
Logarithm",
journal = j-CACM,
volume = "6",
number = "6",
pages = "306--307",
month = jun,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:47 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\log(x)$; $\sqrt(x)$; elementary functions",
}
@Article{Clenshaw:1963:ASF,
author = "C. W. Clenshaw and G. F. Miller and M. Woodger",
title = "Algorithms for Special Functions {I}",
journal = j-NUM-MATH,
volume = "4",
pages = "403--419",
year = "1963",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Sep 16 10:21:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
xxmonth = "(none)",
xxnumber = "(none)",
}
@Article{Daly:1963:HSA,
author = "W. G. Daly and J. F. Kruy",
title = "A High-Speed Arithmetic Unit Using Tunnel Diodes",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-12",
number = "5",
pages = "503--511",
month = oct,
year = "1963",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1963.263644",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:42 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037964",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Descloux:1963:NRE,
author = "J. Descloux",
title = "Note on the Round-Off Errors in Iterative Processes",
journal = j-MATH-COMPUT,
volume = "17",
number = "81",
pages = "18--27",
month = jan,
year = "1963",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Dietmeyer:1963:CPN,
author = "Donald L. Dietmeyer",
title = "Conversion from Positive to Negative and Imaginary
Radix",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-12",
number = "1",
pages = "20--22",
month = feb,
year = "1963",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1963.263391",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:36 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037765",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
keywords = "imaginary base; negative base",
}
@Article{Eisman:1963:PER,
author = "S. H. Eisman",
title = "Polynomial Evaluation Revisited",
journal = j-CACM,
volume = "6",
number = "7",
pages = "384--385",
month = jul,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Eve:1963:SAI,
author = "J. Eve",
title = "Starting Approximations for the Iterative Calculation
of Square Roots",
journal = j-COMP-J,
volume = "6",
number = "3",
pages = "274--276",
month = nov,
year = "1963",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/6.3.274",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:30 MST 2012",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://comjnl.oxfordjournals.org/content/6/3.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_03/;
https://www.math.utah.edu/pub/tex/bib/compj1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Several starting approximations are given which, in
conjunction with a well-known iterative process, lead
to square root approximations, with a relative error in
the range $ (2^{-55}, 2^{-45}) $, at the expense of
three divisions. More accurate approximations are given
which require in addition a single multiplication.",
acknowledgement = ack-nhfb # " and " # ack-nj,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Book{Flores:1963:LCA,
author = "I. Flores",
title = "The Logic of Computer Arithmetic",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xii + 493",
year = "1963",
LCCN = "QA76.5 .F46",
bibdate = "Thu Sep 1 10:12:51 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Geier:1963:ACD,
author = "A. Geier and I. Sturz",
title = "The approximate calculation of a definite integral
with automatic choice of integration steps (intervals).
The program for the computer {$ {\rm MECIPTI} $} in a
floating point regime. ({Romanian})",
journal = "An. Univ. Timi{\c{s}}oara Ser. {\c{S}}ti. Mat.-Fiz.",
volume = "1",
pages = "133--139",
year = "1963",
MRclass = "68.00",
MRnumber = "30\#3588",
bibdate = "Fri Dec 08 13:52:47 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "R. N. Goss",
}
@Article{Goldstein:1963:SAD,
author = "Max Goldstein",
title = "Significance arithmetic on a digital computer",
journal = j-CACM,
volume = "6",
number = "3",
pages = "111--117",
month = mar,
year = "1963",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/366274.366339",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:45 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The 7090 at NYU has been modified to include a
``Significance Mode'' of operation which is intended to
facilitate the identification of significant bits in
the results of floating-point arithmetic operations.
The manner in which floating-point arithmetic is
handled in this mode is discussed. Several numerical
experiments using this mode are described and
comparisons are made with the ordinary ``normalized
mode.'' Examples include power series evaluation,
linear equations solution, determinant evaluation and
matrix inversion.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Knuth:1963:LEE,
author = "Donald E. Knuth",
title = "Letter to the {Editor}: {Evaluation} of polynomials by
computer",
journal = j-CACM,
volume = "6",
number = "2",
pages = "51--51",
month = feb,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Dec 26 16:31:38 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1962:EPC}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Krishnamurthy:1963:CMD,
author = "E. V. Krishnamurthy",
title = "On Computer Multiplication and Division Using Binary
Logarithms",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-12",
number = "3",
pages = "319--320",
month = jun,
year = "1963",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1963.263572",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037874",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Lehman:1963:MAB,
author = "M. Lehman",
title = "The Minimization of Assimilations in Binary
Carry-Storage Arithmetic Units",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-12",
number = "4",
pages = "409--410",
month = aug,
year = "1963",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1963.263479",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:40 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037921",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Lehmer:1963:RDO,
author = "D. H. Lehmer",
title = "{R63--17} Division and Overflow Detection in Residue
Number Systems",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-12",
number = "1",
pages = "36--37",
month = feb,
year = "1963",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1963.263493",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:36 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037786;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4037754",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
keywords = "residue arithmetic; residue number system",
}
@Article{Lindamood:1963:MCO,
author = "George E. Lindamood and George Shapiro",
title = "Magnitude Comparison and Overflow Detection in Modular
Arithmetic Computers",
journal = j-SIAM-REVIEW,
volume = "5",
number = "4",
pages = "342--350",
month = "????",
year = "1963",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1005095",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:05:07 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/5/4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "October 1963",
}
@Article{Metropolis:1963:BOU,
author = "N. Metropolis and R. L. Ashenhurst",
title = "Basic Operations in an Unnormalized Arithmetic
System",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-12",
number = "6",
pages = "896--904",
month = dec,
year = "1963",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1963.263593",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:44 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038037",
ZMnumber = "0124.07910",
abstract = "A particular set of unnormalized arithmetic operations
termed ``basic'' are described, in the context of the
University of Chicago Maniac III Computer. Each basic
operation involves three operand words and generates
two result words, all in unnormalized floating point
format. The use of these operations in the
implementation of multi-precision arithmetic is
explained; in particular, it is demonstrated that
multiprecision division can be effected in a
nontentative manner with their aid.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753",
keywords = "MANIAC III",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Book{Mood:1963:ITS,
author = "Alexander McFarlane Mood and Franklin A. Graybill",
title = "Introduction to the theory of statistics",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
edition = "Second",
pages = "443",
year = "1963",
LCCN = "HA29 .M75 1963",
bibdate = "Fri Aug 20 10:02:03 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "McGraw-Hill series in probability and statistics",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
subject = "Mathematical statistics",
}
@Article{Stern:1963:CSR,
author = "T. E. Stern and R. M. Lerner",
title = "A circuit for the square root of the sum of the
squares",
journal = j-PROC-IEEE,
volume = "51",
number = "4",
pages = "593--596",
month = apr,
year = "1963",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "A piecewise-linear network can produce an output
proportional to the square root of the sum of the
squares of a set of input voltages, using resistors and
diodes alone. The required relationship between
voltages can be represented by a multi- \ldots{}",
}
@Article{Stroud:1963:MPF,
author = "A. H. Stroud and D. Secrest",
title = "A multiple-precision floating-point interpretive
program for the {Control Data} 1604",
journal = j-COMP-J,
volume = "6",
number = "1",
pages = "62--66",
month = apr,
year = "1963",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:55:45 MDT 2000",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/060062.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/62.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/63.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/64.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/65.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/66.tif",
acknowledgement = ack-nhfb # " and " # ack-nj,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Svoboda:1963:AD,
author = "A. Svoboda",
title = "An algorithm for division",
journal = j-INF-PROCESS-MACH,
volume = "9",
number = "??",
pages = "25--33",
month = "????",
year = "1963",
CODEN = "IPRMDD",
ISSN = "0373-885X",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "Information processing machines",
}
@InProceedings{Wilkinson:1963:PSA,
author = "J. H. Wilkinson",
title = "Plane rotations in floating-point arithmetic",
crossref = "Metropolis:1963:PFS",
pages = "185--198",
year = "1963",
MRclass = "65.35",
MRnumber = "28\#1744",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "A. S. Householder",
}
@Article{Aiken:1964:PAC,
author = "H. H. Aiken and A. G. Oettinger and T. C. Bartee",
title = "Proposed automatic calculating machine",
journal = j-IEEE-SPECTRUM,
volume = "1",
number = "8",
pages = "62--69",
month = aug,
year = "1964",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1964.6500770",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Tue Jan 14 11:14:17 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
note = "Previously unpublished memorandum written by Aiken and
dated by an unknown recipient as 4 November 1937.
Reprinted in \cite[\S 5.1]{Randell:1982:ODC}.",
abstract = "Here presented is the memorandum that 20 years ago
initiated a series of events whose revolutionary
implications are only beginning to manifest themselves
a description of the first large-scale general-purpose
automatic digital computer. Twenty years ago, on August
7, 1944, Mark I, the first large-scale general-purpose
automatic digital computer ever to be put in operation
was dedicated at Harvard University by James B. Conant,
then president of Harvard, and the late Thomas J.
Watson, founder of IBM.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
remark = "Pages 66--69 discuss computation of the elementary
functions with minimal intermediate storage: recipes
are given for integral and fractional power, log,
exponential, trigonometric, inverse trigonometric,
hyperbolic, and inverse hyperbolic. Mention is also
made of the probability integral, elliptic functions,
and Bessel functions, but the text says they will be
discussed later (meaning, in a future publication). The
methods involve recurrences and series summations, and
thus, can be regarded as precision independent.",
}
@Manual{Anonymous:1964:PPF,
author = "Anonymous",
title = "{PINT}: {Purdue} floating point interpretive system:
for the {RPC 4000 General Precision} electronic
computer",
organization = "General Precision, Inc.",
address = "West Lafayette, IN, USA",
pages = "45",
year = "1964",
bibdate = "Mon May 06 10:24:31 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.; Purdue
University School of Electrical Engineering; RPC 4000
(Computer)",
remark = "Program no. H1-02.0",
}
@Article{Ashenhurst:1964:FEU,
author = "R. L. Ashenhurst",
title = "Function Evaluation in Unnormalized Arithmetic",
journal = j-J-ACM,
volume = "11",
number = "2",
pages = "168--187",
month = apr,
year = "1964",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Thu Nov 03 22:33:52 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Baer:1964:MPA,
author = "Robert M. Baer and Martin G. Redlich",
title = "Multiple-precision arithmetic and the exact
calculation of the $ 3 - j $, $ 6 - j $ and $ 9 - j $
symbols",
journal = j-CACM,
volume = "7",
number = "11",
pages = "657--659",
month = nov,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.25",
MRnumber = "31\#865",
bibdate = "Mon Oct 24 09:33:02 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Described in this paper is a system of general-purpose
multiple-precision fixed-point routines and their use
in subroutines which calculate exactly the
quantum-mechanical 3-j, 6-j and 9-j symbols of large
arguments.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@MastersThesis{Bookhart:1964:SFP,
author = "Thomas Woodward Bookhart",
title = "A study of floating point arithmetic",
type = "Thesis ({M.S. in Math.})",
school = "Georgia Institute of Technology",
address = "Atlanta, GA, USA",
pages = "51",
year = "1964",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers.; Number theory.;
Numerical calculations --- Computer programs.",
}
@Article{Brooker:1964:PPS,
author = "R. A. Brooker",
title = "A programming package for some general modes of
arithmetic",
journal = j-CACM,
volume = "7",
number = "2",
pages = "119--127",
month = feb,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Oct 24 09:33:00 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An interpretive programming package is described for
computation with operands which may be real, complex,
single or double precision, or real multiple precision.
It also performs operations on matrices formed from
these elements. A simple language structure is used to
describe the computation.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Manual{Burroughs:1964:BBI,
author = "{Burroughs Corporation}",
title = "{Burroughs B5500} Information Processing Systems
Reference Manual",
organization = "Burroughs Corporation",
address = "Detroit, MI, USA",
year = "1964",
bibdate = "Wed Nov 22 21:15:11 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "The B5500 uses a decimal integer or fixed-point
coefficient of 21 or 22 digits, with an exponent range
of $ \pm 63 $.",
}
@Article{Cody:1964:DPS,
author = "W. J. {Cody, Jr.}",
title = "Double-Precision Square Root for the {CDC-3600}",
journal = j-CACM,
volume = "7",
number = "12",
pages = "715--718",
month = dec,
year = "1964",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355588.365122",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In January of 1960, the late Hans J. Maehly completed
a summary of approximations to the elementary functions
for the CDC-1604 computer. The approximations and
techniques suggested by Maehly are equally applicable
to the second large computer in the CDC line, the 3600.
Unlike the 1604, however, the 3600 has built-in
double-precision floating-point arithmetic. The present
work, largely inspired by the successes of Maehly and
his associates, concerns the extension of one of
Maehly's ideas to a double-precision subroutine for the
3600.",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$sqrt(x)$; CDC 3600; elementary functions",
}
@Article{Cowgill:1964:LEB,
author = "D. Cowgill",
title = "Logic Equations for a Built-In Square Root Method",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "2",
pages = "156--157",
month = apr,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263791",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:56:59 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038119",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Eve:1964:EP,
author = "J. Eve",
title = "The Evaluation of Polynomials",
journal = j-NUM-MATH,
volume = "6",
pages = "17--21",
year = "1964",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Sep 16 10:21:47 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
xxmonth = "(none)",
xxnumber = "(none)",
}
@MastersThesis{Goldschmidt:1964:ADC,
author = "Robert E. Goldschmidt",
title = "Applications of Division by Convergence",
type = "Thesis ({M.S.})",
school = "Department of Electrical Engineering, Massachusetts
Institute of Technology",
address = "Cambridge, MA, USA",
pages = "44",
month = jun,
year = "1964",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://dspace.mit.edu/handle/1721.1/11113",
acknowledgement = ack-sfo # " and " # ack-nhfb,
advisor = "Alfred K. Susskind",
remark = "This thesis introduced the quadratically convergent
Goldschmidt algorithm for iterative division, as an
alternative to Newton--Raphson iteration: see
\cite{Flynn:1966:VHS, Anderson:1967:ISMb,
Flynn:1970:DFI, Ito:1995:EIAb, Oberman:1996:FIR,
Ercegovac:1999:IGD, Ercegovac:2000:IGD,
Gallagher:2000:FTN, Even:2003:PEA, Markstein:2004:SDS,
Even:2005:PEA, Piso:2006:OMD, Schulte:2007:FPD,
Kong:2008:RMI, Piso:2008:FOS, Piso:2008:NRA,
Ruiz:2008:EIR, Kong:2010:RMR, Kong:2011:GDM,
Piso:2011:VLG, Panhaleux:2012:CFP} for improvements and
error analysis. For computing $ Q = N / D $,
Newton--Raphson starts with $ Y \approx 1 / D $, and
iterates $ Y \leftarrow (2 - Y D) Y $, or equivalently,
$ Y \leftarrow Y - (Y (Y D - 1)) $. With the same
starting point, Goldschmidt instead iterates $ N
\leftarrow N Y $, $ D \leftarrow D Y $, $ Y = 2 - D $,
which converges to $ Y = 1 $. When parallel multipliers
are available, the two multiplies can be done at the
same time, whereas Newton--Raphson requires two
sequential multiplies. In addition, the update $ 2 D $
can be computed in hardware by a fast bitwise two's
complement operation, instead of a slower
floating-point subtraction. The Goldschmidt algorithm
has been used in CPUs of the IBM S/360 model 91 and the
AMD K7. Unfortunately, unlike Newton--Raphson, each
iteration of the Goldschmidt algorithm increases
rounding error. Numerical tests of the Goldschmidt
algorithm show worst-case errors in ulps roughly equal
to the number of iterations. Without an FMA, the
Newton--Raphson worst case errors are about 1.7 ulps,
and with an FMA, about 1.0 ulps. In hardware in both
cases, a few bits of extra intermediate precision can
lead to correctly rounded results. Without extra
precision, additional fixups are needed for correct
rounding.",
}
@Article{Gram:1964:RZF,
author = "Christian Gram",
title = "On the Representation of Zero in Floating-Point
Arithmetic",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "4",
number = "3",
pages = "156--161",
month = sep,
year = "1964",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01956026",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "68.00",
MRnumber = "29\#5412",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=4&issue=3&spage=156",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Gregory:1964:FAN,
author = "Robert T. Gregory and James L. Raney",
title = "Floating-point arithmetic with $ 84 $-bit numbers",
journal = j-CACM,
volume = "7",
pages = "10--13",
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00",
MRnumber = "30\#2706",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Book{Henrici:1964:ENA,
author = "Peter Henrici",
title = "Elements of numerical analysis",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xv + 328",
year = "1964",
LCCN = "QA297 .H4",
bibdate = "Fri Aug 20 09:17:19 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Based on the author's lecture notes for a course
entitled {\em Numerical Mathematical Analysis\/} at the
University of California, Los Angeles. Cited in
\cite{Sterbenz:1974:FPC}.",
subject = "Numerical analysis",
}
@Article{Jacobsohn:1964:SFM,
author = "D. Jacobsohn",
title = "A Suggestion for a Fast Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "6",
pages = "754--754",
month = dec,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263942",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:57:06 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038318",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Book{Khinchin:1964:CF,
author = "Aleksandr Iakovlevich Khinchin",
title = "Continued fractions",
publisher = "P. Noordhoff",
address = "Groningen, The Netherlands",
pages = "101",
year = "1964",
LCCN = "QA295 .K513 1964a",
bibdate = "Fri Nov 30 06:55:53 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "Translated by Peter Wynn",
URL = "http://www.loc.gov/catdir/description/dover032/97008056.html;
http://www.loc.gov/catdir/toc/dover031/97008056.html",
acknowledgement = ack-nhfb,
author-dates = "1894--1959",
}
@Article{Klokacev:1964:RNF,
author = "I. V. Kloka{\v{c}}ev",
title = "A refinement of the normalized floating point number
notation on digital computers. ({Russian})",
journal = "{\v{Z}}. Vy{\v{c}}isl. Mat. i Mat. Fiz.",
volume = "4",
pages = "192--194",
year = "1964",
MRclass = "68.00",
MRnumber = "28\#4694",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Kundu:1964:TMD,
author = "P. Kundu and S. Banerji",
title = "Transistorized Multiplier and Divider and Its
Applications",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "3",
pages = "288--295",
month = jun,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263919",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:57:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038157",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Lamson:1964:DAD,
author = "Roger C. Lamson",
title = "A Division Algorithm for a Digital Differential
Analyzer",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "1",
pages = "54--55",
month = feb,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263838",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:56:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038079",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Lynn:1964:REM,
author = "M. Stuart Lynn",
title = "On the Round-Off Error in the Method of Successive
Over-Relaxation",
journal = j-MATH-COMPUT,
volume = "18",
number = "85",
pages = "36--49",
month = jan,
year = "1964",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Maley:1964:MDC,
author = "Gerald A. Maley and Edward J. Skiko",
title = "Modern digital computers",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xiv + 216",
year = "1964",
LCCN = "QA76.5 .M192",
bibdate = "Thu Nov 18 10:04:00 MST 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "Prentice-Hall electrical engineering series",
acknowledgement = ack-nhfb,
keywords = "binary arithmetic",
subject = "Electronic digital computers",
}
@Book{McCracken:1964:NMF,
author = "Daniel D. McCracken and William S. Dorn",
title = "Numerical methods and {FORTRAN} programming, with
applications in engineering and science",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xii + 457",
year = "1964",
bibdate = "Sat Jan 27 13:40:57 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Numerical analysis --- Data processing.; {Fortran}
(Computer program language)",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Merrill:1964:IDC,
author = "Roy D. Merrill",
title = "Improving Digital Computer Performance Using Residue
Number Theory",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "2",
pages = "93--101",
month = apr,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263776;
https://doi.org/10.1109/PGEC.1964.263777",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:56:58 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038105;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4038099",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
keywords = "residue arithmetic; residue number system",
summary = "Residue arithmetic has the interesting characteristic
that in multiplication, addition and subtraction any
digit in the result is dependent only on its two
corresponding operand digits. Consequently, for these
operations, residue arithmetic is \ldots{}",
}
@Article{Miller:1964:ESD,
author = "R. H. Miller",
title = "An example in ``significant-digit'' arithmetic",
journal = j-CACM,
volume = "7",
number = "1",
pages = "21--21",
month = jan,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Oct 24 09:33:00 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Different methods of handling the summing process for
the geometric series are shown to give results
indicating widely differing significances when carried
out in a machine incorporating ``significant-digit''
arithmetic.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@MastersThesis{Moss:1964:RDC,
author = "George Joseph {Moss, Jr.}",
title = "Recording digital counter with floating point output
format",
type = "Thesis ({M.S.})",
school = "University of Maryland",
address = "College Park, MD, USA",
pages = "155",
year = "1964",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Rice:1964:AFV,
author = "John R. Rice",
title = "The Approximation of Functions",
volume = "1",
publisher = pub-AW,
address = pub-AW:adr,
pages = "various",
year = "1964",
LCCN = "QA221 .R5 V.1-2",
bibdate = "Fri Dec 08 13:02:52 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Santos:1964:BVB,
author = "J. Santos and H. Arango",
title = "Base $3$ vs Base $2$ Synchronous Arithmetic Units",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "5",
pages = "608--609",
month = oct,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263734",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:57:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038256",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Stein:1964:DCM,
author = "M. L. Stein",
title = "Divide-and-Correct Methods for Multiple Precision
Division",
journal = j-CACM,
volume = "7",
number = "8",
pages = "472--474",
month = aug,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@MastersThesis{Sweo:1964:SFP,
author = "David Ernest Sweo",
title = "A study of floating point arithmetic with the residue
number system",
type = "Thesis ({M.S.})",
school = "UCLA - Engineering",
address = "Los Angeles, CA, USA",
pages = "89",
year = "1964",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Congruences and residues.; Electronic digital
computers --- Programming.",
}
@Article{Wallace:1964:SFM,
author = "C. S. Wallace",
title = "A Suggestion for a Fast Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "1",
pages = "14--17",
month = feb,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263830",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:56:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038071",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Wolfe:1964:RTE,
author = "Jack M. Wolfe",
title = "Reducing Truncation Errors by Programming",
journal = j-CACM,
volume = "7",
number = "6",
pages = "355--356",
month = jun,
year = "1964",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/512274.512287",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:54 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In accumulating a sum such as in a numerical
integration with a large number of intervals, the sum
itself becomes much larger than the individual addends.
This may produce a less accurate sum as the number of
intervals is increased. Separate variables can be
established as accumulators to hold partial sums within
various distinct intervals. Thus, the extensive
successive truncations are eliminated.",
acknowledgement = ack-nhfb # " and " # ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point arithmetic; truncation errors",
remark = "This algorithm is a precursor of Kahan's compensated
summation algorithm \cite{Kahan:1965:PFR}; see \cite[p.
384]{Lange:2020:NDF} for a discussion.",
}
@Article{Ashenhurst:1965:EEC,
author = "R. L. Ashenhurst and N. Metropolis",
title = "Error Estimation in Computer Calculation",
journal = j-AMER-MATH-MONTHLY,
volume = "72",
number = "2 (Part 2)",
pages = "47--58",
year = "1965",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "65.80",
MRnumber = "MR0192671 (33 \#896)",
MRreviewer = "James H. Wilkinson",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in Department of Economics, Graduate School
of Business, University of Chicago, Center for
Mathematical Studies in Business and Economics, number
45.",
ZMnumber = "0216.49602",
acknowledgement = ack-jr,
fjournal = "The American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
keywords = "error estimation; floating-point arithmetic",
}
@InProceedings{Ashenhurst:1965:EIU,
author = "R. L. Ashenhurst",
editor = "L. B. Rall",
booktitle = "Error in digital computation",
title = "Experimental investigation of unnormalized
arithmetic",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "3--37",
year = "1965",
bibdate = "Thu Nov 8 14:49:59 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARI FLP",
}
@InProceedings{Ashenhurst:1965:TAE,
author = "R. L. Ashenhurst",
editor = "L. B. Rall",
booktitle = "Error in digital computation",
title = "Techniques for automatic error monitoring and
control",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "43--59",
year = "1965",
bibdate = "Tue Oct 9 09:42:56 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARI FLP",
}
@Article{Atrubin:1965:ODR,
author = "A. J. Atrubin",
title = "A One-Dimensional Real-Time Iterative Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "3",
pages = "394--399",
month = jun,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264145",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:33 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038457",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Blum:1965:EAP,
author = "B. I. Blum",
title = "An Extended Arithmetic Package",
journal = j-CACM,
volume = "8",
number = "5",
pages = "318--320",
month = may,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 8 08:20:53 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Combet:1965:CBT,
author = "M. Combet and H. {Van Zonneveld} and L. Verbeek",
title = "Computation of the Base Two Logarithm of Binary
Numbers",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "6",
pages = "863--867",
month = dec,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264080",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:41 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038605",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Dadda:1965:SSP,
author = "Luigi Dadda",
title = "Some Schemes for Parallel Multipliers",
journal = j-ALTA-FREQ,
volume = "34",
number = "??",
pages = "349--356",
month = mar,
year = "1965",
CODEN = "ALFRAJ",
ISSN = "0002-6557",
ISSN-L = "0002-6557",
bibdate = "Fri Nov 09 10:47:42 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[pages
118--225]{Swartzlander:1990:CAa}.",
URL = "http://en.wikipedia.org/wiki/Dadda_multiplier;
http://en.wikipedia.org/wiki/luigi_dadda",
acknowledgement = ack-nhfb,
author-dates = "29 April 1923--26 October 2012",
fjournal = "Alta frequenza",
remark = "According to an ARITH'21 conference attendee, this is
a recommended article for understanding the Wallace and
Dadda multipliers.",
}
@Article{Deiters:1965:ODD,
author = "Robert M. Deiters",
title = "Optimum Design of a Diode Squarer by Applying the
Criterion of Square Root of the Integral of Per Cent
Error Squared",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "3",
pages = "456--463",
month = jun,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264153",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:34 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038465",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Dodd:1965:RSB,
author = "George G. Dodd",
title = "Remarks on Simulation of {Boolean} Functions",
journal = j-CACM,
volume = "8",
number = "8",
pages = "517--517",
month = aug,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:01 MST 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Recently M. Morris Mano presented a method for
performing Boolean OR, AND and NOT operations by means
of arithmetic and conditional transfer operations in a
decimal computer lacking builtin logical
instructions.",
acknowledgement = ack-nhfb,
checked = "19940407",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Boolean operations; decimal arithmetic",
sjb = "Commenting on \cite{Mano:1965:PSB}.",
}
@Article{Earle:1965:LCS,
author = "J. G. Earle",
title = "Latched Carry-Save Adder",
journal = j-IBM-TDB,
volume = "7",
number = "??",
pages = "909--910",
month = mar,
year = "1965",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Fri Nov 09 10:49:36 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
}
@InCollection{Garner:1965:NSA,
author = "H. L. Garner",
title = "Number systems and arithmetic",
crossref = "Alt:1965:AC",
volume = "6",
pages = "131--194",
year = "1965",
bibdate = "Sat May 18 14:18:19 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Garner:1965:RID,
author = "H. L. Garner",
title = "{R65-22} Improving Digital Computer Performance Using
Residue Number Theory",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
pages = "277--277",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.263975",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:23 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038430;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4038385",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
keywords = "residue arithmetic; residue number system",
}
@Article{Hammel:1965:RLC,
author = "D. Hammel",
title = "{R65-54} The Logic of Computer Arithmetic",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "4",
pages = "670--670",
month = aug,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264031",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:40 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038535",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Hammer:1965:BRBa,
author = "Preston C. Hammer",
title = "Book Review: {{\booktitle{Experimental Arithmetic,
High Speed Computing and Mathematics}} by N. C.
Metropolis; A. H. Taub; John Todd; C. B. Tompkins}",
journal = j-TECHNOMETRICS,
volume = "7",
number = "1",
pages = "82--82",
month = feb,
year = "1965",
CODEN = "TCMTA2",
DOI = "https://doi.org/10.2307/1266139",
ISSN = "0040-1706 (print), 1537-2723 (electronic)",
ISSN-L = "0040-1706",
bibdate = "Sat Jun 21 13:17:45 MDT 2014",
bibsource = "http://www.jstor.org/journals/00401706.html;
http://www.jstor.org/stable/i254241;
https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib",
URL = "http://www.jstor.org/stable/1266139",
acknowledgement = ack-nhfb,
fjournal = "Technometrics",
journal-URL = "http://www.jstor.org/journals/00401706.html",
}
@Article{Hammer:1965:BRBb,
author = "Preston C. Hammer",
title = "Book Review: {{\booktitle{Experimental Arithmetic,
High Speed Computing and Mathematics}} by N. C.
Metropolis, A. H. Taub, John Todd, and C. B.
Tompkins}",
journal = j-TECHNOMETRICS,
volume = "7",
number = "1",
pages = "82--82",
month = feb,
year = "1965",
CODEN = "TCMTA2",
ISSN = "0040-1706 (print), 1537-2723 (electronic)",
ISSN-L = "0040-1706",
bibdate = "Tue Mar 20 13:44:52 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib",
URL = "http://links.jstor.org/sici?sici=0040-1706%28196502%297%3A1%3C82%3AEAHSCA%3E2.0.CO%3B2-9",
acknowledgement = ack-nhfb,
fjournal = "Technometrics",
journal-URL = "http://www.jstor.org/journals/00401706.html",
}
@Article{Hamming:1965:NLB,
author = "R. W. Hamming and W. L. Mammel",
title = "A Note on the Location of the Binary Point in a
Computing Machine",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
pages = "260--261",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264258",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038414",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
remark = "The authors consider the low-level multiplication
circuit efficiency of placing the binary point before
or after the first bit. If the leading bit is equally
likely to be a 0 or a 1, then their analysis shows that
it is better to place the point before the leading bit.
However, they report that a more likely distribution is
logarithmic (as predicted by Benford's Law, although
the Newcomb / Benford work is neither mentioned nor
cited), in which case there is no advantage for either
choice of placement of the binary point. The conclude
that it would be humane to place it after the leading
digit, by analogy with how people learn decimal
arithmetic.",
}
@Article{Ikebe:1965:NTP,
author = "Yasuhiko Ikebe",
title = "Note on Triple-Precision Floating-Point Arithmetic
with 132-Bit Numbers",
journal = j-CACM,
volume = "8",
number = "3",
pages = "175--177",
month = mar,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00",
MRnumber = "30\#2707",
bibdate = "Fri Dec 08 14:32:51 1995",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In a recent paper, Gregory and Raney described a
technique for double-precision floating-point
arithmetic. A similar technique can be developed for
triple-precision floating-point arithmetic and its is
the purpose of this note to describe this technique.
Only the multiplication and the division algorithms are
described, since the addition-subtraction algorithm can
be obtained by a trivial modification of the algorithm
in Gregory's and Raney's paper.",
acknowledgement = ack-nhfb,
checked = "19940404",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{James:1965:GSR,
author = "Wendy James and P. Jarratt",
title = "The Generation of Square Roots on a Computer with
Rapid Multiplication Compared with Division (in
{Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "19",
number = "91",
pages = "497--500",
month = jul,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nj # " and " # ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InCollection{Kahan:1965:FPO,
author = "W. Kahan",
booktitle = "Programmer's Reference Manual",
title = "The Floating-Point Over\slash Underflow Trap Routine
{{\tt FPTRP}}",
publisher = "Institute of Computer Science, University of Toronto",
address = "Toronto, Ontario, Canada",
year = "1965",
LCCN = "????",
bibdate = "Wed Feb 14 19:11:11 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Section 4.1.",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Kahan:1965:PFR,
author = "W. Kahan",
title = "Pracniques: {Further} Remarks on Reducing Truncation
Errors",
journal = j-CACM,
volume = "8",
number = "1",
pages = "40--40",
month = jan,
year = "1965",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363707.363723",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 00:18:17 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point arithmetic; truncation errors",
remark = "Gives summation error estimate formula `s = fl(a + b);
error = (a - s) + b', also discovered independently by
\cite{Moller:1965:QDP}. Extends Gill's earlier
fixed-point result \cite{Gill:1951:PSS}. See
improvement \cite{Ozawa:1993:SAE}.",
}
@Article{Kanner:1965:NBC,
author = "Herbert Kanner",
title = "Number Base Conversion in Significant Digit
Arithmetic",
journal = j-J-ACM,
volume = "12",
number = "2",
pages = "242--246",
month = apr,
year = "1965",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Thu Nov 03 08:47:50 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{King:1965:LED,
author = "R. King",
title = "Letter to the {Editor}: On the Double-Precision Square
Root Routine",
journal = j-CACM,
volume = "8",
number = "4",
pages = "202",
month = apr,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions; floating-point
arithmetic",
}
@Article{Krishnamurthy:1965:DCM,
author = "E. V. Krishnamurthy",
title = "On a Divide-and-Correct Method for Variable Precision
Division",
journal = j-CACM,
volume = "8",
number = "3",
pages = "179--181",
month = mar,
year = "1965",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363791.363829",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00",
MRnumber = "30\#2709",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Described in this paper is a divide-and-correct method
for variable precision division in digital computers.
Unlike the earlier methods of Stein and Pope, the
present method uses a suitably rounded form of the
normalized divisor for getting an estimate of the
quotient characters. This result is a correction of at
most plus or minus one to the estimate, to obtain the
exact quotient character. It is believed that this
method will be widely applicable for division
operations in variable word-length character-oriented
machines.",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "correct rounding; floating-point arithmetic",
}
@TechReport{Lederer:1965:FPP,
author = "E. Lederer",
title = "Floating-point-Pegasus, {FLPPEG}",
type = "{ISD-Bericht}",
number = "12",
institution = "ISD, Inst. f{\"u}r Statik u. Dynamik d. Luft- u.
Raumfahrtkonstruktionen, Universit{\"a}t Stuttgart",
address = "Stuttgart, Germany",
pages = "5",
year = "1965",
bibdate = "Thu May 09 09:05:51 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Lehman:1965:SAT,
author = "M. Lehman",
title = "Serial Arithmetic Techniques",
crossref = "AFIPS:1965:FJC",
pages = "715--725",
year = "1965",
bibdate = "Tue Jan 08 23:08:35 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Liddiard:1965:DPF,
author = "Lawrence Anthony Liddiard",
title = "Double precision floating point arithmetic",
type = "Thesis ({M.S.})",
school = "University of Minnesota",
address = "????",
pages = "various",
year = "1965",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Calculators.; Numerical calculations.",
}
@Book{Lyusternik:1965:HCE,
author = "L. A. Lyusternik and O. A. Chervonenkis and A. R.
Yanpolski",
title = "Handbook for Computing Elementary Functions",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "xiii + 251",
year = "1965",
LCCN = "QA221.L513",
bibdate = "Thu Sep 1 10:13:16 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Translated from the Russian by G. J. Tee. Translation
edited by K. L. Stewart.",
acknowledgement = ack-nj,
}
@Article{Mano:1965:PSB,
author = "M. Morris Mano",
title = "Pracniques: {Simulation} of {Boolean} functions in a
decimal computer",
journal = j-CACM,
volume = "8",
number = "1",
pages = "39--40",
month = jan,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:58 MST 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See remarks \cite{Dodd:1965:RSB}.",
acknowledgement = ack-nhfb,
checked = "19940304",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
sjb = "Describes how to perform Boolean operations by means
of arithmetic and conditional transfer operations on a
decimal computer lacking any built in logical
instructions. See also \cite{Dodd:cacm:65}.",
}
@Article{Martin:1965:SHS,
author = "A. R. Martin and A. B. Rosenstein",
title = "A Shiftrix for High-Speed Multiplication",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "4",
pages = "639--643",
month = aug,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264010",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038521",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@InProceedings{Metropolis:1965:AIE,
author = "N. Metropolis",
title = "Analysis of Inherent Errors in Matrix Decomposition
Using Unnormalized Arithmetic",
crossref = "Kalenich:1965:IPP",
volume = "2",
pages = "441--442",
year = "1965",
bibdate = "Wed Feb 14 19:21:38 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0161.35502",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Metropolis:1965:AUA,
author = "N. Metropolis",
title = "Algorithms in unnormalized arithmetic. {I}.
{Recurrence} relations",
journal = j-NUM-MATH,
volume = "7",
number = "2",
pages = "104--112",
month = apr,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "68.00",
MRnumber = "MR0178589 (31 \#2846)",
MRreviewer = "G. Dahlquist",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See erratum \cite{Metropolis:1965:BAU}.",
ZMnumber = "0128.36301",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Metropolis:1965:BAU,
author = "N. Metropolis",
title = "Berichtigung: {Algorithms} in unnormalized arithmetic.
{I}. {Recurrence} relations",
journal = j-NUM-MATH,
volume = "7",
number = "4",
pages = "354",
month = aug,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "Contributed Item",
MRnumber = "MR1553943",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Metropolis:1965:RCU,
author = "N. Metropolis and R. L. Ashenhurst",
title = "Radix Conversion in an Unnormalized Arithmetic
System",
journal = j-MATH-COMPUT,
volume = "19",
number = "91",
pages = "435--441",
month = jul,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
URL = "http://links.jstor.org/sici?sici=0025-5718%28196507%2919%3A91%3C435%3ARCIAUA%3E2.0.CO%3B2-D",
ZMnumber = "0146.14607",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Metze:1965:MSR,
author = "Gernot Metze",
title = "Minimal Square Rooting",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
pages = "181--185",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.263963",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038397",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Miller:1965:ASF,
author = "G. F. Miller",
title = "Algorithms for Special Functions {II}",
journal = j-NUM-MATH,
volume = "7",
pages = "194--196",
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Sep 16 10:22:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
xxmonth = "(none)",
xxnumber = "(none)",
}
@Article{Moller:1965:NQD,
author = "Ole M{\o}ller",
title = "Note on Quasi Double-Precision",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "5",
number = "4",
pages = "251--255",
year = "1965",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Sat Nov 14 09:14:57 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Moller:1965:QDP}.",
acknowledgement = ack-nj # " and " # ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Moller:1965:QDP,
author = "Ole M{\o}ller",
title = "Quasi Double-Precision in Floating Point Addition",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "5",
number = "1",
pages = "37--50",
month = mar,
year = "1965",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01975722",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65.80",
MRnumber = "MR0181130 (31 \#5359)",
bibdate = "Wed Jan 4 18:52:08 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=5&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Moller:1965:NQD}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=5&issue=1&spage=37",
acknowledgement = ack-nj # " and " # ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "accurate floating-point summation; floating-point
arithmetic; rounding errors",
remark = "Gives summation error estimate formula `s = fl(a + b);
error = (a - s) + b', also discovered independently by
\cite{Kahan:1965:PFR}. Extends Gill's earlier
fixed-point result \cite{Gill:1951:PSS}.",
}
@InCollection{Moore:1965:AACa,
author = "Ramon E. Moore",
title = "The automatic analysis and control of error in digital
computing based on the use of interval numbers",
crossref = "Rall:1965:EDCa",
chapter = "2",
bookpages = "????",
pages = "61--130",
year = "1965",
MRclass = "65.61 (65.80)",
MRnumber = "MR0176614 (31 \#886)",
MRreviewer = "T. E. Hull",
bibdate = "Thu Jun 20 10:51:40 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://interval.louisiana.edu/Moores_early_papers/Moore_in_Rall_V1.pdf",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@InCollection{Moore:1965:AACb,
author = "Ramon E. Moore",
title = "Automatic local coordinate transformations to reduce
the growth of error bounds in interval computation of
solutions of ordinary differential equations",
crossref = "Rall:1965:EDCb",
chapter = "2",
pages = "103--140",
year = "1965",
MRclass = "65.80 (65.60)",
MRnumber = "MR0185839 (32 \#3299)",
MRreviewer = "T. E. Hull",
bibdate = "Thu Jun 20 10:51:40 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://interval.louisiana.edu/Moores_early_papers/Moore_in_Rall_V2.pdf",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Morrison:1965:MCC,
author = "D. R. Morrison",
title = "A Method for Computing Certain Inverse Functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "10",
number = "??",
pages = "202--208",
month = "????",
year = "1965",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "Math. Tables Other Aids Comput.",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Nathan:1965:CM,
author = "Amos Nathan",
title = "The Cascade Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
pages = "243--247",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264250",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038406",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Penney:1965:BSC,
author = "Walter Penney",
title = "A {``Binary''} System for Complex Numbers",
journal = j-J-ACM,
volume = "12",
number = "2",
pages = "247--248",
month = apr,
year = "1965",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Thu Nov 03 08:47:50 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Book{Ralston:1965:FCN,
author = "Anthony Ralston",
title = "A first course in numerical analysis",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xix + 578",
year = "1965",
LCCN = "QA297 .R3",
bibdate = "Fri Aug 20 10:13:32 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "International series in pure and applied mathematics",
acknowledgement = ack-nhfb,
remark = "See also second edition
\cite{Ralston:1978:FCN,Ralston:2001:FCN}. Cited in
\cite{Sterbenz:1974:FPC}.",
subject = "Numerical analysis",
}
@Article{Riordan:1965:UAT,
author = "R. H. S. Riordan and R. R. A. Morton",
title = "The Use of Analog Techniques in Binary Arithmetic
Units",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "1",
pages = "29--35",
month = feb,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264051",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038346",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Ross:1965:RTE,
author = "D. R. Ross",
title = "Reducing Truncation Errors Using Cascading
Accumulators",
journal = j-CACM,
volume = "8",
number = "1",
pages = "32--33",
month = jan,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sun Sep 18 22:55:00 1994",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "When accumulating a large number of quantities as in
numerical integration, the sum itself may become much
larger than the individual addends. This results in
truncation error. Much of this error can be eliminated
using cascading accumulators as noted in a recent
article by Wolfe. A simpler and slightly more flexible
algorithm is presented which deals also with the case
of negative addends.",
acknowledgement = ack-nhfb,
checked = "19940304",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "accurate floating-point summation",
sjb = "Refers to \cite{Wolfe:cacm:196,Wilhelm:1977:GMPb}.",
}
@Article{Schreiber:1965:BRB,
author = "Alvin L. Schreiber",
title = "Book Review: {{\booktitle{A Binary Multiplication}}
(W. C. McGee)}",
journal = j-SIAM-REVIEW,
volume = "7",
number = "1",
pages = "134--136",
month = "????",
year = "1965",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1007016",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:05:20 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/7/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1965",
}
@Article{Smith:1965:ASO,
author = "Francis J. Smith",
title = "An Algorithm for Summing Orthogonal Polynomial Series
and their Derivatives with Applications to
Curve-Fitting and Interpolation",
journal = j-MATH-COMPUT,
volume = "19",
number = "89",
pages = "33--36",
month = apr,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Specker:1965:CAL,
author = "W. H. Specker",
title = "A Class of Algorithms for $ \ln x $, $ \exp x $, $
\sin x $, $ \cos x $, $ \tan^{-1} x $, and $ \cot^{-1}
x $",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "1",
pages = "85--86",
month = feb,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264066",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:21 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038361",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Swarztrauber:1965:LED,
author = "P. N. Swarztrauber",
title = "Letter to the {Editor}: On the Double-Precision Square
Root Routine",
journal = j-CACM,
volume = "8",
number = "4",
pages = "202",
month = apr,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Aug 31 14:02:19 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions; floating-point
arithmetic",
}
@Article{Sweeney:1965:AFP,
author = "D. W. Sweeney",
title = "An analysis of floating-point addition",
journal = j-IBM-SYS-J,
volume = "4",
number = "1",
pages = "31--42",
year = "1965",
CODEN = "IBMSA7",
DOI = "https://doi.org/10.1147/sj.41.0031",
ISSN = "0018-8670",
bibdate = "Thu Sep 15 18:42:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmsysj.bib",
note = "Reprinted in
\cite[pp.~317--328]{Swartzlander:1990:CAa}.",
URL = "http://www.research.ibm.com/journal/sj/041/ibmsjIVRID.pdf",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
fjournal = "IBM Systems Journal",
remark = "Page 34, containing a critical table, was originally
missing from the PDF file, and this was finally
corrected by IBM in November 2008.",
xxmonth = "(none)",
}
@Article{Winograd:1965:TRP,
author = "Shmuel Winograd",
title = "On the Time Required to Perform Addition",
journal = j-J-ACM,
volume = "12",
number = "2",
pages = "277--285",
month = apr,
year = "1965",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Multi.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Arango:1966:FCP,
author = "H. Arango and J. Santos",
title = "A Fast Carry-Propagation Circuit for Base $3$ Signed
Non redundant Arithmetic",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-15",
number = "2",
pages = "254--255",
month = apr,
year = "1966",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1966.264311",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 05:46:31 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038725",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Brooker:1966:MFA,
author = "R. A. Brooker and J. S. Rohl and S. R. Clark",
title = "The main features of {Atlas Autocode}",
journal = j-COMP-J,
volume = "8",
number = "4",
pages = "303--310",
month = jan,
year = "1966",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:56:10 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See comment \cite{Clark:1966:CMP}.",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/080303.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/303.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/304.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/305.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/306.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/307.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/308.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/309.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/310.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@MastersThesis{Chang:1966:DHR,
author = "Henry Kwan-cheung Chang",
title = "Design of a high rate floating point digital
accumulator",
type = "Thesis ({M.S. in Engineering})",
school = "University of California, Davis",
address = "Davis, CA, USA",
pages = "60",
year = "1966",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Dissertations, Academic --- California ---
Engineering.",
}
@Article{Chartres:1966:ACP,
author = "Bruce A. Chartres",
title = "Automatic Controlled Precision Calculations",
journal = j-J-ACM,
volume = "13",
number = "3",
pages = "386--403",
month = jul,
year = "1966",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Fri Nov 28 16:23:06 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Recent developments in computer design and error
analysis have made feasible the use of variable
precision arithmetic and the preparation of programs
that automatically determine their own precision
requirements. Such programs enable the user to specify
the accuracy he wants, and yield answers guaranteed to
lie within the bounds prescribed. A class of such
programs, called ``contracting error programs'', is
defined in which the precision is determined by
prescribing error bounds on the data. A variant of
interval arithmetic is defined which enables a limited
class of algorithms to be programmed as contracting
error programs. A contracting error program for the
solution of simultaneous linear equations is described,
demonstrating the application of the idea to a wider
class of problems.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Clark:1966:CMP,
author = "S. R. Clark and W. F. Lunnon",
title = "Correspondence: Multiple precision arithmetic (real
and complex)",
journal = j-COMP-J,
volume = "9",
number = "2",
pages = "174--174",
month = aug,
year = "1966",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:56:14 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Brooker:1966:MFA}.",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_02/tiff/174.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Clark:1966:MPA,
author = "S. R. Clark and W. F. Lunnon",
title = "Multiple precision arithmetic in {Atlas Autocode}",
journal = j-COMP-J,
volume = "9",
number = "2",
pages = "174--174",
month = aug,
year = "1966",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/9.2.174",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:36 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/9/2.toc;
https://www.math.utah.edu/pub/tex/bib/compj1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/9/2/174.full.pdf+html",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Fike:1966:SAS,
author = "C. T. Fike",
title = "Starting Approximations for Square Root Calculation on
{IBM System\slash 360}",
journal = j-CACM,
volume = "9",
number = "4",
pages = "297--299",
month = apr,
year = "1966",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/365278.365556",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See letter \cite{Fike:1967:LER}.",
abstract = "Several starting approximations for square root
calculation by Newton's method are presented in a form
to facilitate their use in IBM System/360 square root
routines. These approximations include several for the
range [1/16, 1], which is the interval of primary
interest on IBM System/360.",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions; IBM S/360",
}
@Article{Filippi:1966:BEE,
author = "S. Filippi",
title = "{Die Berechnung einiger elementarer transzendenter
Funktionen mit Hilfe des Richardson-Algorithmus}
\toenglish {The Computation of Some Elementary
Transcendental Functions by Means of the Richardson
Algorithm} \endtoenglish",
journal = j-COMPUTING,
volume = "1",
number = "??",
pages = "127--132",
month = "????",
year = "1966",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Flehinger:1966:PRI,
author = "B. J. Flehinger",
title = "On the Probability that a Random Integer Has Initial
Digit `{A}'",
journal = j-AMER-MATH-MONTHLY,
volume = "73",
number = "??",
pages = "1056--1061",
year = "1966",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Wed Feb 14 18:53:58 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
remark = "Probably November or December issue; missing from
amermathmonthly1960.bib.",
}
@Article{Flynn:1966:VHS,
author = "M. J. Flynn",
title = "Very high-speed computing systems",
journal = j-PROC-IEEE,
volume = "54",
number = "12",
pages = "1901--1909",
year = "1966",
CODEN = "IEEPAD",
DOI = "https://doi.org/10.1109/proc.1966.5273",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Wed Dec 13 08:39:04 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
keywords = "floating-point arithmetic; Goldschmidt division",
}
@Article{Garner:1966:ECA,
author = "Harvey L. Garner",
title = "Error Codes for Arithmetic Operations",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-15",
number = "5",
pages = "763--770",
month = oct,
year = "1966",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1966.264566",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 05:46:38 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038884",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Grau:1966:BRB,
author = "A. A. Grau",
title = "Book Review: {{\booktitle{Rounding Errors in Algebraic
Processes}} (J. H. Wilkinson)}",
journal = j-SIAM-REVIEW,
volume = "8",
number = "3",
pages = "397--398",
month = "????",
year = "1966",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1008087",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:05:37 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/8/3;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "July 1966",
}
@Article{Gregory:1966:DAU,
author = "Robert T. Gregory",
title = "On the Design of the Arithmetic Unit of a
Fixed-Word-Length Computer from the Standpoint of
Computational Accuracy",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-15",
number = "2",
pages = "255--257",
month = apr,
year = "1966",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1966.264312",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 05:46:31 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038726",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Book{Greve:1966:HLR,
author = "J. Greve and H. Gumin and E. Hochsteller",
title = "{Herrn von Leibniz' Rechnung mit Null und Ein}.
({German}) [{Mister von Leibniz'} calculation with zero
and one]",
publisher = "{Siemens AG}",
address = "Berlin and M{\"u}nchen, West Germany",
pages = "59",
year = "1966",
bibdate = "Fri Mar 17 08:31:51 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Gottfried Wilhelm Freiherr von Leibnitz",
language = "German",
}
@InProceedings{Harding:1966:ISF,
author = "L. J. {Harding, Jr.}",
editor = "????",
booktitle = "{SHARE} {XXVII}, Toronto, Canada, August 1966",
title = "Idiosyncracies of {System\slash 360} Floating-Point",
publisher = "????",
address = "????",
pages = "??--??",
year = "1966",
LCCN = "????",
bibdate = "Wed Feb 14 19:04:14 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{Harding:1966:MSF,
author = "L. J. {Harding, Jr.}",
title = "Modifications of {System\slash 360} Floating-Point",
number = "SSD 157, C4470",
howpublished = "SHARE Secretarial Distribution",
pages = "11--27",
month = "????",
year = "1966",
bibdate = "Wed Feb 14 19:05:45 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Henrici:1966:TPM,
author = "Peter Henrici",
title = "Test of probabilistic models for the propagation of
roundoff errors",
journal = j-CACM,
volume = "9",
number = "6",
pages = "409--410",
month = jun,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:07 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Hull:1966:TPM,
author = "T. E. Hull and J. R. Swenson",
title = "Tests of Probabilistic Models for Propagation of
Roundoff Errors",
journal = j-CACM,
volume = "9",
number = "2",
pages = "108--113",
month = feb,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.80",
MRnumber = "32\#3297",
bibdate = "Fri Nov 25 18:20:04 MST 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/gvl.bib;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In any prolonged computation it is generally assumed
that the accumulated effect of roundoff errors is in
some sense statistical. The purpose of this paper is to
give precise descriptions of certain probabilistic
models for roundoff error, and then to describe a
series of experiments for testing the validity of these
models. It is concluded that the models are in general
very good. Discrepancies are both rare and mild. The
test techniques can also be used to experiment with
various types of special arithmetic.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "decimal floating-point arithmetic; rounding errors",
}
@Manual{IBM:1966:ISM,
key = "IBM",
title = "{IBM System\slash 360 Model 91}: Functional
Characteristics",
publisher = pub-IBM,
address = pub-IBM:adr,
year = "1966",
bibdate = "Fri Aug 20 09:34:43 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "File No. S360-01, Form A22-6907-2.",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Book{Isaacson:1966:ANM,
author = "Eugene Isaacson and Herbert Bishop Keller",
title = "Analysis of numerical methods",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xv + 541",
year = "1966",
LCCN = "QA297 .I8",
bibdate = "Fri Aug 20 09:37:14 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}. Reprinted in
\cite{Isaacson:1994:ANM}.",
subject = "Numerical analysis",
}
@Misc{Kahan:1966:ISS,
author = "W. Kahan",
title = "{7094 II} System Support for Numerical Analysis",
howpublished = "SHARE Secretary Distribution 159, C4537",
pages = "1--54",
year = "1966",
bibdate = "Wed Nov 07 08:39:33 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@InCollection{Kogbetliantz:1966:GEF,
author = "E. G. Kogbetliantz",
title = "Generation of Elementary Functions",
crossref = "Ralston:1966:MMD",
pages = "7--35",
year = "1966",
bibdate = "Sat Dec 09 14:09:27 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Kuki:1966:EGS,
author = "H. Kuki and E. Hanson and J. J. Ortega and J. C.
Butcher and P. G. Anderson",
title = "Evaluation Guidelines {SHARE Numerical Analysis
Project (N.A.P.)}",
journal = "{SHARE Secretary Distribution}",
volume = "SSD 150, part II",
number = "C4304",
pages = "1--42",
year = "1966",
bibdate = "Fri Aug 20 09:45:16 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Lam:1966:COG,
author = "Lay-yong Lam",
title = "On the {Chinese} origin of the {Galley} method of
arithmetical division",
journal = j-BRITISH-J-HIST-SCI,
volume = "3",
number = "part 1, 9",
pages = "66--69",
year = "1966",
CODEN = "BJHSAT",
DOI = "https://doi.org/10.1017/S0007087400000200",
ISSN = "0007-0874 (print), 1474-001X (electronic)",
ISSN-L = "0007-0874",
MRclass = "01.10",
MRnumber = "0204243 (34 \#4087)",
MRreviewer = "I. N. Veselovski{\u\i}",
bibdate = "Wed Sep 22 18:01:23 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
ZMnumber = "0143.24202",
acknowledgement = ack-nhfb,
fjournal = "British Journal for the History of Science",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BJH",
keywords = "history",
}
@Article{Mancino:1966:MPF,
author = "O. G. Mancino",
title = "Multiple precision floating-point conversion from
decimal-to-binary and vice versa",
journal = j-CACM,
volume = "9",
number = "5",
pages = "347--348",
month = may,
year = "1966",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355592.365635",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:06 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Decimal-to-binary and binary-to-decimal floating-point
conversion is often performed by using a table of the
powers $ 10^i $ ($i$ a positive integer) for converting
from base $ 10$ to base $2$, and by using a table of
the coefficients of a polynomial approximation of $
10^x (0 \leq x < 1)$ for converting from base $2$ to
base $ 10$. These tables occupy a large storage region
in the case of a nonsingle precision conversion. This
paper shows that a single small table suffices for a
floating-point conversion from decimal to binary, and
vice versa, in any useful precision.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point arithmetic; Multiple precision
arithmetic; number base conversion",
}
@Unpublished{Mazor:1966:FSI,
author = "Stan Mazor",
title = "{Fairchild Symbol II} Decimal Floating Point Unit",
year = "1966",
bibdate = "Wed Nov 22 21:18:53 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Cited in \cite[p. 106]{Cowlishaw:2003:DFP}.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Book{Moore:1966:IA,
author = "Ramon E. Moore",
title = "Interval analysis",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xi + 145",
year = "1966",
LCCN = "QA297 .M63",
bibdate = "Sat Feb 14 08:15:54 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Nickel:1966:NFA,
author = "K. Nickel",
title = "{{\"U}ber die Notwendigkeit einer Fehlerschranken-
Arithmetik f{\"u}r Rechenautomaten}",
journal = j-NUM-MATH,
volume = "9",
pages = "69--79",
year = "1966",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-jr,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Book{Parker:1966:SNS,
author = "Francis D. Parker",
title = "The structure of number systems",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xi + 137",
year = "1966",
LCCN = "QA241 .P3; QA241 .P239",
bibdate = "Fri Nov 9 19:10:47 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
series = "Teachers' mathematics reference series",
acknowledgement = ack-nhfb,
subject = "Number theory",
}
@Book{Richards:1966:EDS,
author = "R. K. (Richard Kohler) Richards",
title = "Electronic Digital Systems",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "ix + 637",
year = "1966",
LCCN = "TK7888.3 .R52",
bibdate = "Mon Oct 24 05:33:53 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1921--",
remark = "According to \cite[pp. 168--170]{Smiley:2010:MWI},
this was the first book to draw attention to the
pre-World War II work by John Atanasoff (1903--1995)
and Clifford Berry (1918--1963) at Iowa State College
of Agricultural and Mechanic Arts (renamed on 4 July
1959 to Iowa State University of Science and
Technology), and to name their computer the ABC.
Richards is quoted with ``The ancestry of all
electronic digital systems appears to be traceable to a
computer which will be called the Atanasoff--Berry
Computer.'' The book provided important evidence in the
priority dispute and courtroom battles over who
invented the computer (Atanasoff and Berry versus
Mauchly and Eckert). Berry died in unresolved
circumstances: suicide or murder?",
subject = "Electronic digital computers",
tableofcontents = "1: History and Introduction / 1 \\
2: Theory of Digital Systems / 50 \\
3: The Stored-Program Concept / 109 \\
4: Automatic Programming / 293 \\
5: Digital Data Transmission / 362 \\
6: Combined Analog and Digital Techniques / 451 \\
7: Telephone and Message Switching Systems / 481 \\
8: The Relationship between Thinking and Digital
Systems / 519 \\
9: Miscellaneous Digital Systems / 541 \\
10: Digital System Reliability / 571 \\
11: The Automatic Design of Digital Systems / 610 \\
Index / 631",
}
@Article{Saidan:1966:EEA,
author = "A. S. Saidan",
title = "The Earliest Extant {Arabic} Arithmetic:
{{\booktitle{Kitab al-Fusul fi al Hisab al-Hindi}}} of
{Abu al-Hasan, Ahmad ibn Ibrahim al-Uqlidisi}",
journal = j-ISIS,
volume = "57",
number = "4",
pages = "475--490",
month = "Winter",
year = "1966",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:22:16 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i211145;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1960.bib",
URL = "http://www.jstor.org/stable/228518",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Article{Smith:1966:CP,
author = "John Smith",
title = "The Challenge of {Pi}",
journal = j-IEEE-SPECTRUM,
volume = "3",
number = "10",
pages = "5--5",
month = oct,
year = "1966",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1966.5217340",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Wed Jan 15 08:45:04 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib;
https://www.math.utah.edu/pub/tex/bib/pi.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "Computer errors; Digital arithmetic; Educational
institutions; Hardware; Physics computing; Power
engineering computing; Programming profession;
Registers; Testing; Upper bound",
remark = "Report of a computation of $ \pi $ to 17,935 places
using base-1,000,000 arithmetic. A footnote reports
``The AIL result to 17,940 places was identical with
the reference to 17,935 places. Reference: D. Shanks
and J. W. Wrench, Jr., `Calculation of Pi to 100,000
Decimals', Mathematics of Computation, January 1962,
Vol. 16, No. 77, pp. 67--99.''",
}
@Article{Spielberg:1966:CEU,
author = "K. Spielberg",
title = "Computation of $ e^x $ with the use of large tables",
journal = j-IBM-SYS-J,
volume = "5",
number = "2",
pages = "102--114",
year = "1966",
CODEN = "IBMSA7",
ISSN = "0018-8670",
bibdate = "Thu Sep 15 18:43:03 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Systems Journal",
xxmonth = "(none)",
}
@Article{Tienari:1966:SPM,
author = "M. Tienari and V. Suokonautio",
title = "A Set of Procedures Making Real Arithmetic of
Unlimited Accuracy Possible Within {Algol 60}",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "6",
number = "4",
pages = "332--338",
month = jul,
year = "1966",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01966093",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon Sep 12 08:07:38 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=6&issue=4&spage=332",
acknowledgement = ack-nj,
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{vanWijngaarden:1966:NAI,
author = "A. {van Wijngaarden}",
title = "Numerical Analysis as an Independent Science",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "6",
number = "1",
pages = "66--81",
month = mar,
year = "1966",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01939551",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:09 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=6&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=6&issue=1&spage=66",
abstract = "The paper describes how a number of well-known
mathematical concepts ought to be modified in order to
make sense within the scope of numerical analysis. It
is also shown how obvious difficulties can be overcome
in a logical way. All algorithms suggested are given as
ALGOL procedures.",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Watson:1966:SCC,
author = "R. W. Watson and C. W. Hastings",
title = "Self-Checked Computation using Residue Arithmetic",
journal = j-PROC-IEEE,
volume = "54",
number = "12",
pages = "1920--1931",
month = dec,
year = "1966",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Fri Nov 09 19:37:52 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}
@Article{Whitney:1966:PCR,
author = "D. E. Whitney",
title = "Propagation and control of roundoff error in the
matrix exponential method",
journal = j-PROC-IEEE,
volume = "54",
number = "10",
pages = "1483--1484",
month = oct,
year = "1966",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}
@TechReport{Wiegel:1966:MBA,
author = "R. E. Wiegel",
title = "Methods of Binary Addition",
type = "Technical report",
number = "195",
institution = "Department of Computer Science, University of
Illinois",
address = "Urbana, IL, USA",
month = feb,
year = "1966",
bibdate = "Fri Nov 09 19:40:18 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Adams:1967:SCP,
author = "Duane A. Adams",
title = "A stopping criterion for polynomial root finding",
journal = j-CACM,
volume = "10",
number = "10",
pages = "655--658",
month = oct,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.50",
MRnumber = "39\#2314",
bibdate = "Fri Nov 25 18:20:15 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "When searching for the root of a polynomial, it is
generally difficult to know just when to accept a
number as an adequate approximation to the root. In
this paper an algorithm is presented which allows one
to terminate the iteration process on the basis of
calculated bounds for the roundoff error which occurs
in evaluating the polynomial. This stopping criterion
has been tested on numerous examples and has been found
to serve as a satisfactory means for accepting a
complex number as a zero of a real polynomial.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Anderson:1967:ISMb,
author = "S. F. Anderson and J. G. Earle and R. E. Goldschmidt
and D. M. Powers",
title = "The {IBM System\slash 360 Model 91}: Floating-point
execution unit",
journal = j-IBM-JRD,
volume = "11",
number = "1",
pages = "34--53",
month = jan,
year = "1967",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.111.0034",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Sep 11 15:36:09 MDT 2012",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392016",
abstract = "The principal requirement for the Model 91
floating-point execution unit was that it be designed
to support the instruction-issuing rate of the
processor. The chosen solution was to develop separate,
instruction-oriented algorithms for the add, multiply,
and divide functions. Linked together by the
floating-point instruction unit, the multiple execution
units provide concurrent instruction execution at the
burst rate of one instruction per cycle.",
acknowledgement = ack-nhfb # "\slash " # ack-nj,
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@TechReport{Clark:1967:PSF,
author = "N. A. Clark and W. J. Cody and K. E. Hillstrom and E.
A. Thieleker",
title = "Performance Statistics of the {FORTRAN IV (H)} Library
for the {IBM System\slash 360}",
type = "Technical Report",
number = "ANL-7231",
institution = inst-ANL,
address = inst-ANL:adr,
year = "1967",
bibdate = "Fri Aug 20 08:47:24 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in SHARE Secretary Distribution, SDD 169,
C4473, pp. 12 46.",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Cody:1967:CFI,
author = "W. J. Cody",
title = "Critique of the {FORTRAN IV (H)} Library for the {IBM
System\slash 360}",
journal = "{SHARE Secretary Distribution}",
volume = "SSD 169",
number = "C4473",
pages = "4--11",
year = "1967",
bibdate = "Fri Aug 20 08:52:04 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@InProceedings{Cody:1967:IMD,
author = "W. J. Cody",
title = "The influence of machine design on numerical
algorithms",
crossref = "AFIPS:1967:ACP",
pages = "305--309",
year = "1967",
bibdate = "Sat Sep 24 00:18:32 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Cody:1967:LEA,
author = "William J. {Cody, Jr.}",
title = "Letter to the {Editor}: Another Aspect of Economical
Polynomials",
journal = j-CACM,
volume = "10",
number = "9",
pages = "531--531",
month = sep,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363566.363577",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Nov 17 10:20:03 1994",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Fike:1967:MEP}.",
abstract = "In his paper ``Methods of Evaluating Polynomial
Approximations in Function Evaluation Routines'' [Comm.
ACM 10, (March 1967)], C. T. Fike fails to discuss one
very important aspect of the ``economical'' methods for
polynomials. Since these evaluation methods involve a
decreased number of arithmetic operations over the
usual Horner's method (or at least replace a
multiplication by an addition) the implication is that
they are faster to execute. Dr. Fike points out that
these methods can be poorly conditioned for particular
polynomials, thus requiring extended precision or
fixed-point arithmetic to maintain accuracy and costing
more in time than Horner's method. But even if we
assume the methods are well conditioned, the need to
store away and retrieve intermediate results in some
machines with only one floating-point arithmetic
register can wipe out the time savings effected by a
reduction in the number of arithmetic operations. On
many of today's high-performance computers the time
required to store away and retrieve a result is about
the same as the time required for a floating-point
addition. It is no longer sufficient to estimate the
efficiency of a method by a count of arithmetic
operations alone.",
acknowledgement = ack-wjc # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point arithmetic",
}
@Article{Crisansan-Zverca:1967:PED,
author = "Mariana Cri{\c{s}}an-Zverca",
title = "Pseudo-operations of an electronic digital machine
with floating point. ({Romanian})",
journal = j-STUD-CERCET-MAT,
volume = "19",
pages = "1413--1424",
year = "1967",
ISSN = "0039-4068, 0567-6401",
MRclass = "68.00",
MRnumber = "40\#3753",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Studii {\c{s}}i cercet{\u{a}}ri Matematice",
}
@Article{Curry:1967:ART,
author = "E. Curry",
title = "The analysis of round-off and truncation errors in a
hybrid control system",
journal = j-IEEE-TRANS-AUTOMAT-CONTR,
volume = "12",
number = "5",
pages = "601--604",
month = oct,
year = "1967",
CODEN = "IETAA9",
ISSN = "0018-9286 (print), 1558-2523 (electronic)",
ISSN-L = "0018-9286",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Automatic Control",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
summary = "The round-off and truncation errors of a
digital-analog (hybrid) servo system are studied in
terms of the least upper bound and second moment, or
variance. The study was applied to the azimuth function
of a guided missile launcher system and a \ldots{}",
}
@Article{DeRegt:1967:NRA,
author = "M. P. DeRegt",
title = "Negative radix arithmetic",
journal = j-COMP-DESIGN,
volume = "6",
number = "??",
pages = "52--63",
month = may,
year = "1967",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Thu Nov 06 06:07:24 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Design",
keywords = "negative base",
}
@Article{Ferrari:1967:DMU,
author = "Domenico Ferrari",
title = "A Division Method Using a Parallel Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-16",
number = "2",
pages = "224--226",
month = apr,
year = "1967",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1967.264580",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
note = "See correction \cite{Ferrari:1969:CDM}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039036",
abstract = "The use of a parallel multiplier for performing
high-speed binary division requires that an algorithm
be devised that obtains the quotient by means of
multiplications and additions. Furthermore, its
hardware implementation must be as simple and as fast
as possible. A suitable algorithm, which applies to a
first approximation to the reciprocal of the divisor,
has already been proposed [1]. A similar algorithm is
presented in this paper. The comparison between the two
methods for equal numbers of multiplications shows that
the latter is more accurate. Conversely, a given
accuracy can often be obtained with a higher speed. The
generation of a piecewise-linear initial approximation
is also discussed.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Fike:1967:LER,
author = "C. T. Fike",
title = "Letter to the {Editor}: {A} rational approximation
optimal by {Moursund}'s criterion",
journal = j-CACM,
volume = "10",
number = "11",
pages = "683--684",
month = nov,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363790.363795",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:16 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Moursund:1967:OSV,Fike:1966:SAS}",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "elementary function; square root",
remark = "Gives a starting value for $ \sqrt {x} $ ($x$ on $ [1
/ 16, 1]$) of $ R*(x) = 1.68212586 - 1.28977371 / (x +
0.84106293)$, with an error of $ 2^{-12.496}$.",
}
@Article{Fike:1967:MEP,
author = "C. T. Fike",
title = "Methods of Evaluating Polynomial Approximations in
Function Evaluation Routines",
journal = j-CACM,
volume = "10",
number = "3",
pages = "175--178",
month = mar,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363162.363200",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:12 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See remark on efficiency \cite{Cody:1967:LEA}.",
abstract = "The method of nested multiplication is commonly used
in function evaluation routines to evaluate
approximation polynomials. New polynomial evaluation
methods have been developed in recent years which
require fewer multiplications than nested
multiplication and may therefore be preferable for use
in function evaluation routines. Although some of these
methods do not appear to be practically useful because
of rounding-error difficulties, several methods of
evaluating low-degree polynomials have been found to be
satisfactory. Three such methods are described and
illustrated.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Fike:1967:RAO,
author = "C. T. Fike",
title = "A Rational Approximation Optimal by {Moursund}'s
Criterion (letter to the editor)",
journal = j-CACM,
volume = "10",
number = "11",
pages = "683--684",
month = nov,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Filho:1967:AGF,
author = "A. M. S. Filho and G. Schwachheim",
title = "Algorithm 309: Gamma Function with Arbitrary
Precision",
journal = j-CACM,
volume = "10",
number = "8",
pages = "511--512",
month = aug,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Book{Forsythe:1967:CSL,
author = "George E. Forsythe and Cleve B. Moler",
title = "Computer Solution of Linear Algebraic Systems",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xi + 148",
year = "1967",
LCCN = "QA297 .F57 1967",
MRclass = "65.35",
MRnumber = "MR0219223 (36 \#2306)",
MRreviewer = "N. Gastinel",
bibdate = "Tue May 25 08:52:32 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
ZMnumber = "0154.40401",
acknowledgement = ack-nhfb,
keywords = "numerical analysis; software",
remark = "Translated to Russian (1969), Japanese (1969), and
German (1971). Cited in \cite{Sterbenz:1974:FPC}.",
subject = "numerical analysis; data processing; matrices",
tableofcontents = "Reader's background and purpose of book \\
Vector and matrix norms \\
Diagonal form of a matrix under orthogonal equivalence
\\
Proof of diagonal-form theorem \\
Types of computational problems in linear algebra \\
Types of matrices encountered impractical problems \\
Sources of computational problems of linear algebra \\
Condition of a linear system \\
Gaussian elimination and LU decomposition \\
Need for interchanging rows \\
Scaling equations and unknowns \\
The Crout and Doolittle variants \\
Iterative improvement \\
Computing the determinant \\
Nearly singular matrices \\
Algol 60 program \\
Fortran, extended Algol, and PL/1 programs \\
Matrix inversion \\
An example: Hilbert matrices \\
Floating-point round-off analysis \\
Rounding error in Gaussian elimination \\
Convergence of iterative improvement \\
Positive definite matrices; band matrices \\
Iterative methods for solving linear systems \\
Nonlinear systems of equations",
}
@Article{Freeman:1967:CMS,
author = "Herbert Freeman",
title = "Calculation of Mean Shift for a Binary Multiplier
Using $2$, $3$, or $4$ Bits at a Time",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-16",
number = "6",
pages = "864--866",
month = dec,
year = "1967",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1967.264752",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:06 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039205",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Freiman:1967:CDU,
author = "C. V. Freiman and others",
title = "Composite Division Unit",
journal = j-IBM-TDB,
volume = "9",
number = "8",
pages = "994--995",
month = jan,
year = "1967",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Tue Jan 08 22:40:53 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Article{Friedland:1967:AAV,
author = "Paul Friedland",
title = "{Algorithm 312}: {Absolute} Value and Square Root of a
Complex Number",
journal = j-CACM,
volume = "10",
number = "10",
pages = "665--665",
month = oct,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363717.363780",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:15 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\abs(z)$; $\sqrt(z)$; elementary functions",
}
@Article{Goldberg:1967:BED,
author = "I. Bennett Goldberg",
title = "$ 27 $ Bits Are Not Enough For $8$-Digit Accuracy",
journal = j-CACM,
volume = "10",
number = "2",
pages = "105--106",
month = feb,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363067.363112",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:11 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "From the inequality $ 10^8 < 2^{27} $, we are likely
to conclude that we can represent 8-digit decimal
floating-point numbers accurately by 27-bit [binary]
floating-point numbers. However, we need 28 significant
bits to represent some 8-digit numbers accurately. In
general, we can show that if $ 10^p < 2^{q - 1} $, then
$q$ significant bits are always enough for $p$-digit
decimal accuracy. Finally, we can define a compact
27-bit floating-point representation that will give 28
significant bits, for numbers of practical
importance.",
acknowledgement = ack-nj # " and " # ack-mfc # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "decimal floating-point arithmetic",
received = "August 1966 (revised October 1966)",
}
@Book{Gschwind:1967:DDC,
author = "H. W. Gschwind",
title = "Design of Digital Computers: An Introduction",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 530",
year = "1967",
LCCN = "TK7888.3 .G72",
bibdate = "Fri Nov 09 18:56:39 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{Hertz:1967:CHF,
author = "Theodore M. Hertz",
title = "Computer Having Floating Point Multiplication",
howpublished = "US Patent 3,304,417.",
day = "14",
month = feb,
year = "1967",
bibdate = "Sat Mar 24 06:05:12 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Filed 1 October 1962.",
URL = "https://patentimages.storage.googleapis.com/47/86/c8/897ec6540ff584/US3304417.pdf;
https://patents.google.com/patent/US3304417",
abstract = "Prior art digital computers utilized fixed point
arithmetic processes in executing computer operations.
In performing fixed point arithmetic processes a
computer assumes the binary point (analogous to a
decimal point) to be between the sign of a number and
the most significant digit of the number. Thus the
number is considered to have an absolute value of less
than one. As explained in patent application filed
September 24, 1962, Serial No. 225,676, now abandoned,
for a ``Computer Having Floating Point Addition and
Floating Point Subtraction'' invented by me, in order
to execute fixed point addition and subtraction
operations, numbers to be operated upon by a computer
must first be appropriately scaled prior to computation
in order to obtain the scaling of the numbers is
accomplished prior to entering them into the computer
or by shifting them through programming afterwards.
Fixed point multiplication needs to have numbers scale
prior to performing computations with them. In
multiplication, shifting of the result through
programming is desirable in order to prevent loss of
significant portions which should be retained for use
in later computations. Particularly is it true where
after a multiplication operation has been performed,
the product must be added or subtracted from or with
other numbers, in which case scaling would first have
to be done before the additional computation could be
made.",
acknowledgement = ack-nhfb,
}
@Article{Howell:1967:MPA,
author = "K. M. Howell",
title = "Multiple precision arithmetic techniques",
journal = j-COMP-J,
volume = "9",
number = "4",
pages = "383--387",
month = feb,
year = "1967",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:56:19 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/090383.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/383.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/384.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/385.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/386.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/387.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Jarden:1967:EAL,
author = "Dov Jarden",
title = "Existence of Arbitrarily Long Sequences of Consecutive
Members in Arithmetic Progressions Divisible by
Arbitrarily Many Different Primes",
journal = j-FIB-QUART,
volume = "5",
number = "3",
pages = "280--??",
month = oct,
year = "1967",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:04:54 MDT 2011",
bibsource = "http://www.fq.math.ca/5-3.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/5-3/jarden1.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Krishnamurthy:1967:NRD,
author = "E. V. Krishnamurthy and S. K. Nandi",
title = "On the Normalization Requirement of Divisor in
Divide-and-Correct Methods",
journal = j-CACM,
volume = "10",
number = "12",
pages = "809--813",
month = dec,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Kuki:1967:CAE,
author = "H. Kuki",
title = "Comments on the {ANL} Evaluation of the {OS\slash 360
FORTRAN} Math Function Library",
journal = "{SHARE Secretary Distribution}",
volume = "SSD 169",
number = "C4773",
pages = "47--53",
year = "1967",
bibdate = "Fri Aug 20 09:42:04 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Lewis:1967:CFP,
author = "H. R. {Lewis, Jr.} and E. J. {Stovall, Jr.}",
title = "Comments on a Floating-Point Version of {Nordsieck}'s
Scheme for the Numerical Integration of Differential
Equations",
journal = j-MATH-COMPUT,
volume = "21",
number = "98",
pages = "157--161",
month = apr,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Long:1967:LAS,
author = "C. T. Long and J. H. Jordan",
title = "A Limited Arithmetic on Simple Continued Fractions",
journal = j-FIB-QUART,
volume = "5",
number = "2",
pages = "113--128",
month = apr,
year = "1967",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:04:52 MDT 2011",
bibsource = "http://www.fq.math.ca/5-2.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/5-2/long.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Mandelbaum:1967:CLS,
author = "David Mandelbaum",
title = "A Comparison of Linear Sequential Circuits and
Arithmetic Sequences",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-16",
number = "2",
pages = "151--157",
month = apr,
year = "1967",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1967.264810",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:01 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039022",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Massell:1967:RAP,
author = "E. Massell",
title = "{R67-41} An Analog Photoresistive Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-16",
number = "3",
pages = "380--380",
month = jun,
year = "1967",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1967.264730",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:03 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
note = "See comment \cite{Azgapetian:1968:CAP}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039094",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@InProceedings{Matula:1967:BCM,
author = "David W. Matula",
booktitle = "{Proceedings of the AFIPS 1967 Spring Joint Computer
Conference}",
title = "Base Conversion Mappings",
volume = "30",
publisher = pub-AFIPS,
address = pub-AFIPS:adr,
pages = "311--318",
year = "1967",
bibdate = "Wed Feb 14 19:18:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Book{McCalla:1967:INM,
author = "Thomas Richard McCalla",
title = "Introduction to Numerical Methods and {Fortran}
Programming",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xiii + 359",
month = jan,
year = "1967",
ISBN = "0-471-58125-9",
ISBN-13 = "978-0-471-58125-3",
LCCN = "QA297 .M25",
bibdate = "Sat Sep 27 17:58:26 MDT 1997",
bibsource = "http://www.amazon.com/exec/obidos/ISBN=0471581259/wholesaleproductA/;
http://www.cbooks.com/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$27.95",
URL = "http://www.cbooks.com/sqlnut/SP/search/gtsumt?source=&isbn=0471581259",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.; FORTRAN
(Computer program language); Numerical analysis.",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{McKeeman:1967:RER,
author = "W. M. McKeeman",
title = "Representation Error for Real Numbers in Binary
Computer Arithmetic",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-16",
number = "5",
pages = "682--683",
month = oct,
year = "1967",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1967.264781",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:05 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039164",
abstract = "Real numbers can be represented in a binary computer
by the form $ i \cdot B^e $ where $i$ is the integer
part, $B$ the base, and $e$ the exponent. The accuracy
of the representation will depend upon the number of
bits allocated to the integer part and exponent part as
well as what base is chosen. If $ L(i) $ and $ L(e) $
are the number of bits allocated to the magnitudes of
the integer and exponent parts and we define $ I =
2^{L(i)} $ and $ E = 2^{L(e)} $, the exponent range is
given by $ B^{\pm E} $, the maximum relative
representation error is given by $ B / 2 I $, and the
average relative representation error is given by $ (B
- 1) / (4 I \ln B) $. The formulas provide quantitative
comparison for the effectiveness of alternative formats
for real number representations.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
remark = "McKeeman discusses the maximum and average relative
errors in binary (with and without a hidden bit),
octal, and hexadecimal bases for floating-point
arithmetic with a 48-bit computer word. Errors are
smallest with binary and a hidden bit.",
}
@Article{Menzel:1967:AUA,
author = "M. Menzel and N. Metropolis",
title = "Algorithms in unnormalized arithmetic. {II}.
{Unrestricted} polynomial evaluation",
journal = j-NUM-MATH,
volume = "10",
number = "5",
pages = "451--462",
month = nov,
year = "1967",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF02162878",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.80",
MRnumber = "MR0255093 (40 \#8300)",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0225.65059",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Book{Minsky:1967:CFI,
author = "Marvin Lee Minsky",
title = "Computation: Finite and Infinite Machines",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xvii + 317",
year = "1967",
LCCN = "QA267 .M55",
bibdate = "Thu Oct 17 06:05:56 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
author-dates = "1927--2016",
tableofcontents = "Physical machines and their abstract counterparts
\\
Part 1: Finite-state machines \\
Neural networks. Automata made up of parts \\
The memories of events in finite-state machines \\
Part 2: Infinite machines \\
Computability, effective procedures, and algorithms.
Infinite machines \\
Turing machines \\
Universal Turing machines \\
Limitations of effective computability: some problems
not solvable by instruction-obeying machines \\
The computable real numbers \\
The relations between Turing machines and recursive
functions \\
Models similar to digital computers \\
Part 3: Symbol-manipulation systems and computability
\\
The symbol-manipulation systems of post \\
Post's normal-form theorem \\
Very simple bases for computability \\
Solutions to selected problems",
}
@Article{Moler:1967:IRF,
author = "C. B. Moler",
title = "Iterative Refinement in Floating Point",
journal = j-J-ACM,
volume = "14",
number = "2",
pages = "316--321",
month = apr,
year = "1967",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Tue Nov 1 09:43:17 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "ir, nla, lud, iterative refinement",
}
@Article{Mosteller:1967:DSR,
author = "Frederick Mosteller and Cleo Youtz and Douglas Zahn",
title = "The Distribution of Sums of Rounded Percentages",
journal = j-DEMOGRAPHY,
volume = "4",
number = "2",
pages = "850--858",
month = jun,
year = "1967",
CODEN = "????",
ISSN = "0070-3370 (print), 1533-7790 (electronic)",
ISSN-L = "0070-3370",
bibdate = "Thu Nov 24 08:03:16 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Diaconis:1979:RP} for further work.",
URL = "http://muse.jhu.edu/journals/dem/;
http://www.biomedsearch.com/nih/Distribution-Sums-Rounded-Percentages/21318695.html;
http://www.jstor.org/stable/2060324",
abstract = "When percentages are computed for counts in several
categories or for several positive measurements0 each
taken as a fraction of their sum, the rounded
percentages often fail to add to 100 percent. We
investigate how frequently this failure occurs and what
the distributions of sums of rounded percentages are
for (1) an empirical set of data, (2) the multinomial
distribution in small samples, (3) spacings between
points dropped on an interval --- the broken-stick
model; and (4) for simulation for several categories.
The several methods produce similar distributions.We
find that the probability that the sum of rounded
percentages adds to exactly 100 percent is certain for
two categories, about three-fourths for three
categories, about two-thirds for four categories, and
about [Formula: see text] for larger numbers of
categories, c, on the average when categories are not
improbable.",
acknowledgement = ack-nhfb,
fjournal = "Demography",
pubmedid = "21318695",
}
@Article{Moursund:1967:OSV,
author = "David G. Moursund",
title = "Optimal starting values for {Newton--Raphson}
calculation of $ \sqrt {x} $",
journal = j-CACM,
volume = "10",
number = "7",
pages = "430--432",
month = jul,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363427.363454",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.25",
MRnumber = "39\#2297",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See letter \cite{Fike:1967:LER}.",
abstract = "The problem of obtaining starting values for the
Newton-Raphson calculation of $ \sqrt {x} $ on a
digital computer is considered. It is shown that the
conventionally used best uniform approximations to $
\sqrt {x} $ do not provide optimal starting values. The
problem of obtaining optimal starting values is stated,
and several basic results are proved. A table of
optimal polynomial starting values is given.",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions",
remark = "Title of article has incorrect $ \sqrt (x^{1 / 2}) $:
the article discusses computation of {\tt sqrt(x)}.",
}
@Article{Nandi:1967:STD,
author = "Salil K. Nandi and E. V. Krishnamurthy",
title = "A simple technique for digital division",
journal = j-CACM,
volume = "10",
number = "5",
pages = "299--301",
month = may,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:13 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Sandberg:1967:FPR,
author = "I. W. Sandberg",
title = "Floating-Point-Roundoff Accumulation in Digital-Filter
Realizations",
journal = j-BELL-SYST-TECH-J,
volume = "46",
number = "8",
pages = "1775--1791",
month = oct,
year = "1967",
CODEN = "BSTJAN",
ISSN = "0005-8580",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1967/BSTJ.1967.4608.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol46/bstj46-8-1775.pdf",
abstract = "In this paper, several results are presented
concerning the effects of roundoff in the
floating-point realization of a general discrete filter
governed ideally by a stable difference equation of the
form\par
$$ w_n = \sum_{k = 0}^M b_k x_{n - k} - \sum {k = 1}^N
a_k w_{n - k}, \qquad n \geq N \qquad (1) $$ \par
in which $ \{ w_n \} $ and $ \{ x_n \} $ are output and
input sequences, respectively.\par
In particular, for a large class of filters it is
proved that there is a function $ f(K) $ with $ f(K)
\to 0 $ as $ K \to \infty $ and a constant $c$, both
dependent on the $ b_k $, the $ a_k $, the order in
which the products on the right side of (1) are summed
in the machine, and $t$, the number of bits allotted to
the mantissa, such that\par
$$ \langle e \rangle_K \leq c \langle y \rangle_K +
f(K) $$ \par
for all $ K \geq N $, in which, with the computed
output sequence of the realized filter,\par
$$ \langle y \rangle_K = \left (\frac {1}{K + 1}
\sum_{n = 0}^K |y_n|^2 \right)^{1 / 2} $$ \par
and\par
$$ \langle e \rangle_K = \left (\frac {1}{K + 1}
\sum_{n = 0}^K |w_n - y_n|^2 \right)^{1 / 2} $$
\par
Bounds on $ f(K) $ and $c$ are given that are not
difficult to evaluate, and which, in many realistic
cases, are informative. For example, for the
second-order bandpass filter:\par
$$ w_n = x_n - a_1 w_{n - 1} - a_2 w_{n - 2}, \qquad n
\geq 2 \qquad (2) $$ \par
with $ a_1 $ and $ a_2 $ chosen so that its poles arc
at approximately $ \pm 45^\circ $ and at distance
approximately (but not less than) $ 0.001 $ from the
unit circle, we find that $c$, an upper bound on the
``asymptotic output error-to-signal ratio'', is not
greater than $ 0.58 \times 10^{-4} $, assuming that $ t
= 27 $, that the terms on the right side of (2) are
summed in the machine in the order indicated (from
right to left), and that the $ x_n $ in (2) are machine
numbers. If the $ x_n $ are not machine numbers, and
hence must be quantized before processing, then $ c
\leq 0.76 \times 10^{-4} $.\par
In addition to error bounds, an inequality is derived
which, if satisfied, rules out certain types of
generally undesirable behavior such as self-sustained
output limit cycles due to roundoff effects. This
inequality is satisfied for the example described
above.",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Sasaki:1967:ASR,
author = "Akio Sasaki",
title = "Addition and Subtraction in the Residue Number
System",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-16",
number = "2",
pages = "157--164",
month = apr,
year = "1967",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1967.264811",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:01 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039023;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4039015",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
keywords = "residue arithmetic; residue number system",
summary = "Improved residue expression and new arithmetic
algorithms for addition and subtraction are proposed.
In the proposed system positive and negative integers
of any magnitude can be handled regardless of the
particular choice of the set of relatively \ldots{}",
}
@Book{Szabo:1967:RAA,
author = "Nicholas S. Szab{\'o} and Richard I. Tanaka",
title = "Residue arithmetic and its applications to computer
technology",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xvi + 236",
year = "1967",
LCCN = "QA247.35 .S95",
bibdate = "Fri Jun 24 16:02:00 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "McGraw-Hill series in information processing and
computers",
acknowledgement = ack-nhfb,
remark = "Based on the authors' Report on residue (modular)
arithmetic survey.",
subject = "Modular arithmetic; Algorithms; Computer programming",
}
@Article{Tomasulo:1967:EAE,
author = "R. M. Tomasulo",
title = "An Efficient Algorithm for Exploiting Multiple
Arithmetic Units",
journal = j-IBM-JRD,
volume = "11",
number = "1",
pages = "25--33",
month = jan,
year = "1967",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Fri Aug 26 10:27:10 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Book{Wilkinson:1967:BZW,
author = "J. H. Wilkinson",
title = "Bledy Zaokragle{\'n} w Procesach Algebraicznych.
({Polish}) [{Rounding} errors in algebraic Processes]",
publisher = "PWW",
address = "Warszawa, Poland",
pages = "????",
year = "1967",
bibdate = "Thu Aug 25 09:28:02 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Polish translation of \cite{Wilkinson:1963:REA}",
acknowledgement = ack-nhfb,
language = "Polish",
}
@Article{Winograd:1967:TRP,
author = "Shmuel Winograd",
title = "On the Time Required to Perform Multiplication",
journal = j-J-ACM,
volume = "14",
number = "4",
pages = "793--802",
month = oct,
year = "1967",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/321420.321438",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Sat Feb 8 10:29:30 2020",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Multi.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Yarbrough:1967:PCC,
author = "Lynn Yarbrough",
title = "Precision calculations of $e$ and $ \pi $ constants",
journal = j-CACM,
volume = "10",
number = "9",
pages = "537--537",
month = sep,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363566.363578",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:15 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point arithmetic; number base conversion",
remark = "Gives decimal, octal, and hexadecimal values of $e$
and $ \pi $ to 100 digits, and notes ``The difficulty
arises because assemblers and compilers are hardly ever
designed to convert decimal constants to a precision of
more than a dozen or so digits. Thus, if calculations
to greater precision are to be done, constants usually
must be input in octal or other binary-derived
representation.''. Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Atkins:1968:HRD,
author = "D. E. Atkins",
title = "Higher-radix division using estimates of the divisor
and partial remainders",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "10",
pages = "925--934",
month = oct,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.226439",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Azen:1968:DMS,
author = "S. Azen and S. Derr",
title = "On the Distribution of the Most Significant
Hexadecimal Digit",
type = "Technical Report",
number = "RM 5496 PR",
institution = "Rand Report",
address = "Santa Monica, CA, USA",
year = "1968",
bibdate = "Wed Feb 14 17:22:53 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Azgapetian:1968:CAP,
author = "V. Azgapetian",
title = "Comment on {``An Analog Photoresistive Multiplier''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "2",
pages = "188--188",
month = feb,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.229083",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 17:40:47 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
note = "See \cite{Massell:1967:RAP}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687312",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Brennan:1968:FTA,
author = "J. F. Brennan",
title = "The Fastest Time of Addition and Multiplication",
journal = "IBM Research Reports",
volume = "4",
number = "1",
pages = "??--??",
month = "????",
year = "1968",
bibdate = "Fri Nov 09 10:43:37 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Dean:1968:GRB,
author = "K. J. Dean",
title = "Generator for the reciprocals of binary numbers",
journal = j-PROC-IEE,
volume = "115",
number = "6",
pages = "787",
month = jun,
year = "1968",
CODEN = "PIEEAH",
DOI = "https://doi.org/10.1049/piee.1968.0142",
ISSN = "0020-3270 (print), 2053-7891 (electronic)",
ISSN-L = "0020-3270",
bibdate = "Thu Apr 10 13:07:02 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Institution of Electrical
Engineers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5247218",
}
@Article{Dietmeyer:1968:GPI,
author = "D. L. Dietmeyer and J. R. Duley",
title = "Generating prime implicants via ternary encoding and
decimal arithmetic",
journal = j-CACM,
volume = "11",
number = "7",
pages = "520--523",
month = jul,
year = "1968",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363397.363565",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Aug 07 17:25:16 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Decimal arithmetic, ternary encoding of cubes, and
topological considerations are used in an algorithm to
obtain the extremals and prime implicants of Boolean
functions. The algorithm, which has been programmed in
the FORTRAN language, generally requires less memory
than other minimization procedures, and treats DON'T
CARE terms in an efficient manner.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "cubical complexes; extremal; minimization; prime
implicants; switching function; ternary encoding",
}
@Article{Elliott:1968:EAA,
author = "David Elliott",
title = "Error analysis of an algorithm for summing certain
finite series",
journal = j-J-AUSTRALIAN-MATH-SOC,
volume = "8",
number = "2",
pages = "213--221",
month = may,
year = "1968",
CODEN = "JAUMAX",
DOI = "https://doi.org/10.1017/s1446788700005267",
ISSN = "0004-9735 (print), 2059-9234 (electronic)",
ISSN-L = "0004-9735",
MRclass = "65.25",
MRnumber = "0230452",
MRreviewer = "U. C. Guha",
bibdate = "Fri Feb 9 15:20:35 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Australian Mathematical Society",
remark = "Analysis of Clenshaw algorithm for Chebyshev summation
\cite{Clenshaw:1955:NSC}, and report of region of
instability of that procedure",
}
@Book{Fike:1968:CEM,
author = "C. T. Fike",
title = "Computer Evaluation of Mathematical Functions",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xii + 227",
year = "1968",
LCCN = "QA297 .F5",
bibdate = "Thu Sep 1 10:12:51 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Fraser:1968:AUA,
author = "M. Fraser and N. Metropolis",
title = "Algorithms in unnormalized arithmetic. {III}. {Matrix}
inversion",
journal = j-NUM-MATH,
volume = "12",
number = "5",
pages = "416--428",
month = dec,
year = "1968",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.80",
MRnumber = "MR0255094 (40 \#8301)",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0184.37503",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Harman:1968:ADI,
author = "M. G. Harman",
title = "An Attempt to Design an Improved Multiplication
System",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "11",
pages = "1090--1090",
month = nov,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.226864",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 17:40:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687268",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Hart:1968:CAa,
author = "John F. Hart and E. W. Cheney and Charles L. Lawson
and Hans J. Maehly and Charles K. Mesztenyi and John R.
Rice and Henry G. {Thatcher, Jr.} and Christoph
Witzgall",
title = "Computer Approximations",
publisher = pub-R-E-KRIEGER,
address = pub-R-E-KRIEGER:adr,
pages = "x + 343",
year = "1968",
ISBN = "0-88275-642-7",
ISBN-13 = "978-0-88275-642-4",
LCCN = "QA 297 C64 1978",
bibdate = "Tue Dec 14 22:55:11 1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
note = "Reprinted 1978 with corrections.",
acknowledgement = ack-nhfb,
shorttableofcontents = "1: The Design of a Function Subroutine / 1 \\
2: General Methods of Computing Functions / 10 \\
3: Least Maximum Approximations / 42 \\
4: The Choice and Application of Approximations / 58
\\
5: Description and Use of the Tables / 82 \\
6: Function Notes / 89 \\
7: Tables of Coefficients / 155 \\
Appendix A: Conversion Algorithms / 307 \\
Appendix B: Bibliography of Approximations / 313 \\
Appendix C: Decimal and Octal Constants / 333 \\
References / 336 \\
Index / 341",
tableofcontents = "1: The Design of a Function Subroutine / 1 \\
1.1 Introduction / 1 \\
1.2 General Considerations in Writing a Function
Subroutine / 2 \\
1.3 Relation of the Function Subroutine to the Computer
System / 3 \\
1.4 The Three Main Types of Function Subroutine / 4 \\
1.5 Special Programming Techniques / 7 \\
1.6 Subroutine Errors / 7 \\
1.7 Final Steps / 9 \\
2: General Methods of Computing Functions / 10 \\
2.1 Introduction / 10 \\
2.2 Application of Infinite Expansions / 11 \\
2.3 Recurrence and Difference Relations / 23 \\
2.4 Iterative Techniques / 27 \\
2.5 Integral Representations / 28 \\
2.6 Differential Equations / 29 \\
2.7 Tabular Data / 32 \\
2.8 Convergence Acceleration / 33 \\
3: Least Maximum Approximations / 42 \\
3.1 Introduction / 42 \\
3.2 Properties of Least Maximum Approximations / 43 \\
3.3 Nearly Least Maximum Approximations / 46 \\
3.4 Rational Approximation / 51 \\
3.5 Segmented Approximation / 54 \\
3.6 Computation of the Tables / 55 \\
4: The Choice and Application of Approximations / 58
\\
4.1 Introduction / 5 8 \\
4.2 Domain Considerations / 58 \\
4.3 Machine Considerations / 62 \\
4.4 Conditioning of Approximations / 65 \\
4.5 Polynomial Forms / 67 \\
4.6 Rational Forms / 73 \\
4.7 Transformation Algorithms / 78 \\
5: Description and Use of the Tables / 82 \\
5.1 Introduction / 22 \\
5.2 Function Notes / 82 \\
5.3 Accuracy of the Coefficients / 83 \\
5.4 How to Use the Tables / 86 \\
5.5 Preparation of the Tables / 88 \\
6: Function Notes / 89 \\
6.1 Square Root, Cube Root / 89 \\
6.2 Exponential and Hyperbolic Functions / 96 \\
6.3 The Logarithm Function / 105 \\
6.4 Trigonometric Functions / 112 \\
6.5 The Inverse Trigonometric Functions / 120 \\
6.6 The Gamma Function and Its Logarithm / 130 \\
6.7 The Error Function / 136 \\
6.8 Bessel Functions / 141 \\
6.9 Complete Elliptic Integrals / 150 \\
7: Tables of Coefficients / 155 \\
Appendix A: Conversion Algorithms / 307 \\
Appendix B: Bibliography of Approximations / 313 \\
Appendix C: Decimal and Octal Constants / 333 \\
References / 336 \\
Index / 341",
}
@Book{Hart:1968:CAb,
author = "John F. Hart and E. W. Cheney and Charles L. Lawson
and Hans J. Maehly and Charles K. Mesztenyi and John R.
Rice and Henry G. {Thatcher, Jr.} and Christoph
Witzgall",
title = "Computer Approximations",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "x + 343",
year = "1968",
ISBN = "0-471-35630-1",
ISBN-13 = "978-0-471-35630-1",
LCCN = "QA297 .C64",
bibdate = "Sat Jan 14 14:53:06 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "The SIAM series in applied mathematics",
acknowledgement = ack-nhfb,
}
@Book{IBM:1968:ISP,
author = "{IBM Corporation}",
title = "{IBM System}\slash 360 Principles of Operation",
publisher = pub-IBM,
address = pub-IBM:adr,
edition = "Eighth",
pages = "175",
year = "1968",
LCCN = "QA76.8.I12 I59 1968",
bibdate = "Wed Sep 14 23:12:39 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{Kahan:1968:ISS,
author = "W. Kahan",
title = "{7094-II} system support for numerical analysis",
howpublished = "SHARE Secretarial Distribution SSD-159.",
year = "1968",
bibdate = "Mon Sep 16 16:14:28 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaneko:1968:PSA,
author = "T. Kaneko and B. Liu",
title = "Round-off error of floating-point digital filters",
crossref = "Anonymous:1968:PSA",
pages = "219--227",
year = "1968",
MRclass = "65.80",
MRnumber = "41\#7878",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Matula:1968:BCT,
author = "David W. Matula",
title = "The Base Conversion Theorem",
journal = j-PROC-AM-MATH-SOC,
volume = "19",
number = "3",
pages = "716--723",
month = jun,
year = "1968",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.1090/s0002-9939-1968-0234908-9",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
bibdate = "Fri Apr 21 07:26:39 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A demonstration that, in converting numbers from base
$ \beta $ to base $ \nu $, where $ \beta^i \neq \nu^j $
for any positive integers $ i, j $, a one-to-one
mapping exists only if $ \nu^{m - 1} \geq \beta^n - 1
$. Here $m$ is the number of digits in base $ \nu $ and
$n$ that in base $ \beta $.\par
The implications of this result are discussed in the
author's earlier paper [Proc. Amer. Fed. Information
Processing Soc. 30 (1967), 311--318].",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
received = "9 February 1967",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Matula:1968:C,
author = "David W. Matula",
title = "In-and-out conversions",
journal = j-CACM,
volume = "11",
number = "1",
pages = "47--50",
month = jan,
year = "1968",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/362851.362887",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.80",
MRnumber = "39\#2360",
bibdate = "Fri Nov 25 18:20:17 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Goldberg:1967:BED,Matula:1968:BCT}",
abstract = "By an in-and-out conversion we mean that a
floating-point number in one base is converted into a
floating-point number in another base and then
converted back to a floating-point number in the
original base. For all combinations of rounding and
truncation conversions the question is considered of
how many significant digits are needed in the
intermediate base to allow such in-and-out conversions
to return the original number (when possible), or at
least significant digit.",
acknowledgement = ack-nhfb # "\slash " # ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point numbers; number base conversion;
rounding error; significance; truncation error",
received = "April 1967 (revised August 1967)",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Metropolis:1968:ANA,
author = "N. Metropolis",
title = "Algorithms in un-normalized arithmetic: Polynomial
evaluation and matrix decomposition",
journal = "Colloques internationaux, Centre National de la
Recherche Scientifique, Paris",
volume = "165",
pages = "293--303",
year = "1968",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0207.15804",
acknowledgement = ack-nhfb,
classmath = "*65H05 (Single nonlinear equations (numerical
methods)) 65F05 (Direct methods for linear systems)",
}
@Article{Nathan:1968:IVS,
author = "A. Nathan and J. Molcho",
title = "Improved Voltage Selector and Cascade Multiplier
Circuits",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "4",
pages = "380--382",
month = apr,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.229386",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 17:40:48 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687350",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Nickel:1968:EBC,
author = "K. Nickel",
booktitle = "Proceedings of the {IFIP} Congress",
title = "Error Bounds and Computer Arithmetic",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "54--60",
year = "1968",
LCCN = "????",
bibdate = "Fri Aug 20 10:09:47 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Nievergelt:1968:CCP,
author = "J. Nievergelt",
title = "Computers and computing --- Past present Future",
journal = j-IEEE-SPECTRUM,
volume = "5",
number = "1",
pages = "57--61",
month = jan,
year = "1968",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1968.5215633",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Wed Jan 15 09:30:58 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "Computer science; Concurrent computing; Digital
arithmetic; Hardware; History; Instruments;
Maintenance; Manufacturing; Programming; Relays",
}
@Article{Padegs:1968:SAS,
author = "A. Padegs",
title = "Structural aspects of the {SYSTEM\slash 360 Model 85},
Part {III}: Extensions to floating-point architecture",
journal = j-IBM-SYS-J,
volume = "7",
number = "1",
pages = "22--29",
year = "1968",
CODEN = "IBMSA7",
ISSN = "0018-8670",
bibdate = "Tue Mar 19 17:38:46 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Systems Journal",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Phillips:1968:EME,
author = "G. M. Phillips",
title = "Estimate of the maximum error in best polynomial
approximations",
journal = j-COMP-J,
volume = "11",
pages = "110--111",
year = "1968",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Thu Sep 15 18:39:47 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
xxmonth = "(none)",
xxnumber = "(none)",
}
@Article{Rao:1968:ECL,
author = "T. R. N. Rao",
title = "Error-Checking Logic for Arithmetic-Type Operations of
a Processor",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "9",
pages = "845--849",
month = sep,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.229144",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 17:40:50 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687471",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Ross:1968:UMF,
author = "Richard D. Ross",
title = "{University of Mississippi} floating point subroutines
({UMFS})",
institution = "Computer Center, University of Mississippi",
address = "University",
pages = "31",
year = "1968",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic data processing.",
remark = "Cover title.",
}
@Article{Sasaki:1968:BIA,
author = "A. Sasaki",
title = "The Basis for Implementation of Additive Operations in
the Residue Number System",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "11",
pages = "1066--1073",
month = nov,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/TC.1968.226466",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 17:40:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687264;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35582",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "A new residue number system algebra has been
previously proposed by the author. The algebra has
solved an essential theoretical barrier in the residue
number system and has enabled one to pursue additive
operations in the residue \ldots{}",
}
@Article{Schmookler:1968:HSB,
author = "M. S. Schmookler",
title = "High Speed Binary to Decimal Conversion",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
pages = "506--508",
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.226913",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 28 19:09:15 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This note describes several methods of performing
fast, efficient, binary-to-decimal conversion. With a
modest amount of circuitry, an order of magnitude speed
improvement can is obtained. This achievement offers a
unique advantage to general-purpose computers requiring
special hardware to translate between binary and
decimal numbering systems.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "decimal floating-point arithmetic",
}
@Book{Scott:1968:OET,
author = "Th{\'e}odore G. Scott",
title = "Ordinateurs {\'e}lectroniques, techniques de
programmation: Computer programming techniques",
publisher = "Tournai, Ed. Gamma",
address = "Paris, France",
pages = "662",
year = "1968",
bibdate = "Thu May 09 09:52:34 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Cinq volumes. Version fran{\c{c}}aise de Juliette
Charbonneau-Kohiyama.",
acknowledgement = ack-nhfb,
contents = "1. Pr{\'e}sentation du Tutac. Etude du registre - base
et de ses fonctions. Le registre base. - 2. Les sous
programmes. L'entr{\'e}e. La sorite. - 3. La bande
magn{\'e}tique. La d{\'e}tection des erreurs. - 4. Les
calculs en virgule flottante. L'{\'e}dition des
programmes. - 5. La programmation symbolique. Le
language Cobol. Fortran et Algol",
}
@Manual{Smith:1968:CC,
author = "Smith, Robert E. (Robert Elijah)",
title = "Competence course",
organization = "Control Data Corp.",
address = "Minneapolis, MN, USA",
pages = "vi + 296",
year = "1968",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.; FORTRAN (Computer program
language)",
remark = "``Computer programming using FORTRAN and card inputs
without key punching!'' Cover title: Competence course,
FORTRAN computer programming. At head of title: School
computer-use plan.",
}
@Book{Stuart:1968:FP,
author = "Fredric Stuart",
title = "{Fortran} programming",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xix + 353",
year = "1968",
ISBN = "0-471-83477-7",
ISBN-13 = "978-0-471-83477-9",
LCCN = "QA76.5 .S8",
bibdate = "Sat Jan 27 13:40:57 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
{Fortran} (Computer program language)",
remark = "Cited in \cite{Sterbenz:1974:FPC}, but given year
1969.",
}
@Article{Tung:1968:DAS,
author = "Chin Tung",
title = "A Division Algorithm for Signed-Digit Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "9",
pages = "887--889",
month = sep,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.229150",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 17:40:50 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687477",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Urabe:1968:RED,
author = "Minoru Urabe",
title = "Roundoff Error Distribution in Fixed-Point
Multiplication and a Remark about the Rounding Rule",
journal = j-SIAM-J-NUMER-ANAL,
volume = "5",
number = "2",
pages = "202--210",
month = jun,
year = "1968",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@TechReport{Veltkamp:1968:APV,
author = "G. W. Veltkamp",
title = "{ALGOL} procedures voor het berekenen van een inwendig
product in dubbele precisie. ({Dutch}) [{ALGOL}
procedures for calculating an inner product in double
precision]",
type = "Technical report",
number = "22",
institution = "RC-Informatie, Technische Hogeschool Eindhoven",
address = "Eindhoven, The Netherlands",
year = "1968",
bibdate = "Tue Dec 26 14:53:03 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Dutch",
}
@Article{Vitenko:1968:OAA,
author = "{\=I}. V. V{\=\i}ten'{k}o",
title = "Optimal algorithms for addition and multiplication on
machines with floating point. ({Russian})",
journal = "{\v{Z}}. Vy{\v{c}}isl. Mat. i Mat. Fiz",
volume = "8",
pages = "1076--1084",
year = "1968",
MRnumber = "40\#2250",
bibdate = "Sat Dec 16 16:45:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Russian",
reviewer = "J. Kuntzmann",
}
@TechReport{Yohe:1968:CPA,
author = "J. M. Yohe",
title = "Computer Programming for Accuracy",
type = "{MRC} Technical Summary Report",
number = "866",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
month = apr,
year = "1968",
bibdate = "Sun Dec 30 21:42:55 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In most computations, it is tacitly assumed that the
results produced by the program are 'accurate enough'.
This assumption is not always valid. In this report, we
discuss several possible sources of error in digital
computation, and we list several steps which can be
taken to guard against some types of error and
determine an upper bound for the effects of other
types. We illustrate these techniques with our
experience in writing a program to locate zeros of the
Riemann zeta function.",
acknowledgement = ack-nhfb,
}
@Article{Anonymous:1969:VPD,
author = "Anonymous",
title = "Video Probability Distributions",
journal = j-IEEE-SPECTRUM,
volume = "6",
number = "4",
pages = "5--5",
month = apr,
year = "1969",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1969.5214042",
ISSN = "1939-9340",
ISSN-L = "0018-9235",
bibdate = "Wed Jan 15 11:58:06 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "Arithmetic; Circuit noise; Detectors; Distribution
functions; Gaussian noise; Probability distribution;
Signal to noise ratio; Tail; Testing; Voltage",
}
@InProceedings{Babuska:1969:NSM,
author = "Ivo Babu{\v{s}}ka",
title = "Numerical stability in mathematical analysis",
crossref = "Morrell:1969:IPP",
pages = "11--23",
year = "1969",
bibdate = "Tue Nov 22 05:36:22 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}
@Article{Banerji:1969:SDR,
author = "D. K. Banerji and J. A. Brzozowski",
title = "Sign Detection in Residue Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-18",
number = "4",
pages = "313--320",
month = apr,
year = "1969",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1969.222658",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 16:55:18 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671251;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35034",
abstract = "This paper is concerned with the sign detection
problem in residue number systems. The proposed
solution is applicable only to nonredundant systems. It
is shown that under rather general conditions an
explicit, closed formula for the sign function can be
obtained. In a special case, when one of the moduli is
$2$, the sign function becomes an EXCLUSIVE-OR
function. A sign detection algorithm is proposed and
methods of implementing the algorithm are presented.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
}
@Manual{BrinchHansen:1969:RCR,
author = "Per {Brinch Hansen}",
title = "{RC-4000 Computer} Reference Manual",
number = "RCSL No: 55-D1",
organization = "A/S Regnecentralen",
address = "Copenhagen, Denmark",
pages = "85",
month = jun,
year = "1969",
bibdate = "Sat Mar 09 14:14:25 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bitsavers.org/pdf/regnecentralen/RC_4000_Reference_Manual_Jun69.pdf;
https://www.math.utah.edu/~beebe/RC-4000",
acknowledgement = ack-nhfb,
remark = "The RC-4000 has a 24-bit word, and supplies 12-bit and
24-bit integer arithmetic, and 48-bit floating-point
arithmetic. The latter has a signed 36-bit normalized
two's-complement binary fraction stored at the left of
a double word, followed by a 12-bit two's-complement
signed exponent. The representable range is therefore
[-0x1p-2049, +0x1p2047), or about [-1.547e-617,
1.615e+161]. The sign, and zero value, can be
determined by examining only the first word. Its
floating-point arithmetic can exactly represent 35-bit
integer arithmetic.",
tableofcontents = "1. RC 4000 Specifications / 9 \\
2. Design Considerations / 11 \\
2.1. Word Length / 11 \\
2.2. Register Structure / 11 \\
2.3. Address Modification / 11 \\
2.4. Monitor Control / 12 \\
2.5. Input/Output Control / 13 \\
3. Data and Instruction Formats / 15 \\
3.1. Data Formats / 15 \\
3.2. Storage Addressing / 15 \\
3.3. Working Registers / 16 \\
3.4. Instruction Format / 17 \\
3.5. Address Modify Instruction / 18 \\
4. Integer Arithmetic / 19 \\
4.1. Number Representation / 19 \\
4.2. Byte Arithmetic / 19 \\
4.3. Multiplication and Division / 20 \\
4.4. Overflow and Carry Indication / 21 \\
5. Floating-Point Arithmetic / 22 \\
5.1. Number Representation / 22 \\
5.2. Arithmetic Operations / 23 \\
5.3. Normalization and Rounding / 23 \\
5.4. Precision Modes / 24 \\
5.5. Underflow, Overflow, and Non-Normalized Operands /
25 \\
5.6. Number Conversion / 26 \\
5.7. Exact Arithmetic with Floating-Point Instructions
/ 26 \\
6. Protection System / 28 \\
6.1. Storage Protection / 28 \\
6.2. Privileged Instructions / 29 \\
6.3. Summary of Protection System / 29 \\
6.4. An Example of Protected Areas / 30 \\
7. Interruption System / 32 \\
7.1. Interruption Logic / 32 \\
7.2. Interruption Conditions / 33 \\
8. Low-Speed Data Channel / 35 \\
8.1. Main Characteristics / 35 \\
8.2. Input/Output Instruction / 35 \\
8.3. Channel Operation / 36 \\
8.4. Disconnected and Busy Indication / 37 \\
8.5. Device Commands / 37 \\
8.6. Read / 37 \\
8.7. Sense / 37 \\
8.8. Write / 38 \\
8.9. Control / 39 \\
8.10. Summary of Low-Speed Channel / 39 \\
9. High-Speed Data Channel / 41 \\
10. Standard Peripheral Devices / 43 \\
10.1. Console Devices / 43 \\
10.2. Interval Timer / 43 \\
11. Operator Control Panel / 44 \\
11.1. Indicators and Control Keys / 44 \\
11.2. Machine Errors / 44 \\
11.3. Reset Control / 44 \\
11.4. Start Control / 45 \\
11.5. Autoload Control / 45 \\
11.6. Local/Remote Indication / 46 \\
12. Technical Control Panel / 47 \\
12.1. Operating Modes / 47 \\
12.2. Instruction Step Keys / 47 \\
12.3. Register Setting and Display / 47 \\
12.4. Microinstruction Selection and Display / 48 \\
12.5. Parity Control / 48 \\
13. Instruction Set / 49 \\
14. Definition of Instructions / 51 \\
14.1. Algol Notation / 51 \\
14.2. Register Structure / 51 \\
14.3. Elementary Operations / 54 \\
14.4. Control Panel Functions / 55 \\
14.5. Instruction Fetch Cycle / 55 \\
14.6. Protection Procedures / 56 \\
14.7. Arithmetic Procedures / 57 \\
14.8. Instruction Execution / 58 \\
Appendix / 79 \\
A.1. Reserved Storage Locations / 79 \\
A.2. Numeric Instruction Codes / 80 \\
A.3. Instruction Execution Times / 81 \\
Index / 83",
}
@Article{Brown:1969:CB,
author = "W. S. Brown and P. L. Richman",
title = "The Choice of Base",
journal = j-CACM,
volume = "12",
number = "10",
pages = "560--561",
month = oct,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00",
MRnumber = "43\#5755",
bibdate = "Mon Mar 24 21:38:51 MST 1997",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A digital computer is considered, whose memory words
are composed of $N$ $r$-state devices plus two sign
bits (two state devices). The choice of base $ \beta $
for the internal representation floating-point numbers
on such a computer is discussed. It is shown that in a
certain sense $ \beta = r $ is best.",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Bell Telephone Labs. Inc., Murray Hill, NJ, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "accuracy; base choice; digital arithmetic;
floating-point; number representations",
}
@InProceedings{Clark:1969:SCE,
author = "N. W. Clark and W. J. Cody",
title = "Self-contained exponentiation",
crossref = "AFIPS:1969:ACPb",
volume = "35",
pages = "701--706",
year = "1969",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Cody:1969:PTF,
author = "W. J. Cody",
title = "Performance testing of function subroutines",
crossref = "AFIPS:1969:ACPa",
volume = "34",
pages = "759--763",
year = "1969",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Duke:1969:DFP,
author = "K. A. Duke",
title = "Decimal Floating Point Processor",
journal = j-IBM-TDB,
volume = "11-69",
pages = "862--862",
month = nov,
year = "1969",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Fri Nov 28 11:29:48 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
keywords = "decimal floating-point arithmetic",
remark = "Decimal arithmetic with unnormalized binary integers
of unspecified length for coefficient and exponent.",
}
@MastersThesis{Duncan:1969:FFA,
author = "Daniel D. A. Duncan",
title = "{FLOP}: a floating-point arithmetic package",
type = "Thesis ({M.S.})",
school = "University of Southwestern Louisiana",
address = "Lafayette, LA, USA",
pages = "108",
year = "1969",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Algorithms.; Arithmetic --- Foundations.; FLOP
(Computer program language).; Transformations
(Mathematics).",
}
@Article{Dunworth:1969:ECB,
author = "A. Dunworth and J. I. Roche",
title = "The Error Characteristics of the Binary Rate
Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-18",
number = "8",
pages = "741--745",
month = aug,
year = "1969",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1969.222757",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 16:55:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671350",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Ehrman:1969:SFP,
author = "J. R. Ehrman",
title = "A Study of Floating-Point Conversions in Some
{OS\slash 360} Components",
number = "SDD 196, C5207",
institution = "SHARE Secretary Distribution",
address = "????",
pages = "1--6",
year = "1969",
bibdate = "Wed Feb 14 18:50:19 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Fenstad:1969:NSM,
author = "Jens Erik Fenstad",
title = "Non-standard models for arithmetic and analysis",
journal = j-LECT-NOTES-MATH,
volume = "118",
pages = "30--47",
year = "1969",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0060250",
ISBN = "3-540-04907-X (print), 3-540-36246-0 (e-book)",
ISBN-13 = "978-3-540-04907-4 (print), 978-3-540-36246-3
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
bibdate = "Thu May 8 17:39:14 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lnm1960.bib",
URL = "http://link.springer.com/chapter/10.1007/BFb0060250/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/BFb0060247",
book-URL = "http://www.springerlink.com/content/978-3-540-36246-3",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
}
@Article{Fenwick:1969:BMO,
author = "P. M. Fenwick",
title = "Binary Multiplication with Overlapped Addition
Cycles",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-18",
number = "1",
pages = "71--74",
month = jan,
year = "1969",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1969.222527",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 16:55:17 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671120",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Ferrari:1969:CDM,
author = "D. Ferrari",
title = "Correction to {``A Division Method Using a Parallel
Multiplier''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-18",
number = "10",
pages = "960--960",
month = oct,
year = "1969",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1969.222555",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 16:55:21 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
note = "See \cite{Ferrari:1967:DMU}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671148",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Field:1969:OFP,
author = "J. A. Field",
title = "Optimizing floating-point arithmetic via post addition
shift probabilities",
crossref = "AFIPS:1969:ACPa",
pages = "597--??",
year = "1969",
bibdate = "Tue Oct 09 07:54:02 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Flores:1969:BRB,
author = "Ivan Flores",
title = "Book Review: {{\booktitle{Residue Arithmetic and Its
Application to Computer Technology}} (Nicholas S. Szabo
and Richard I. Tanaka)}",
journal = j-SIAM-REVIEW,
volume = "11",
number = "1",
pages = "103--104",
month = "????",
year = "1969",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1011027",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:06:04 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/11/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1969",
}
@Book{Froberg:1969:INA,
author = "Carl Erik Fr{\"o}berg",
title = "Introduction to numerical analysis",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Second",
pages = "xii + 433",
year = "1969",
LCCN = "QA297 .F6813 1969",
bibdate = "Fri Aug 20 09:03:07 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Translation of Swedish original {\em L{\"a}robok i
numerisk analys}. Cited in \cite{Sterbenz:1974:FPC}.",
subject = "Numerical analysis",
}
@PhdThesis{Glaser:1969:HMN,
author = "Anton Glaser",
title = "History of Modern Numeration Systems",
type = "{Educat.D.} thesis",
school = "Temple University",
address = "Philadelphia, PA, USA",
pages = "261",
year = "1969",
bibdate = "Fri Mar 17 08:18:07 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See subsequent books
\cite{Glaser:1971:HBO,Glaser:1981:HBO}.",
URL = "https://www.proquest.com/pqdtglobal/docview/302503306/A48758ED17C34A1APQ/1",
acknowledgement = ack-nhfb,
remark = "ProQuest dissertation number 7016666.",
}
@Article{Hammersley:1969:NAP,
author = "P. Hammersley",
title = "Note on {Algorithm 34}: Procedures for the Basic
Arithmetical Operations in Multi-Length Working",
journal = j-COMP-J,
volume = "12",
number = "1",
pages = "102--103",
month = feb,
year = "1969",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:51:33 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_01/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_01/tiff/102.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_01/tiff/103.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Holzwarth:1969:VBB,
author = "A. Holzwarth",
title = "{Ein Verfahren zur Bestimmung bester
Tscheb\-y\-scheff- Ap\-prox\-i\-ma\-tion\-en der
Quadratwurzelfunktion} \toenglish {A Method for
Determination of Best Chebyshev Approximations to the
Square Root Function} \endtoenglish",
journal = j-COMPUTING,
volume = "4",
number = "2",
pages = "168--177",
year = "1969",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
affiliation = "T{\"u}bingen, West Germany",
classification = "C4130",
description = "Chebyshev approximation; numerical analysis",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
language = "German",
}
@Article{Howell:1969:ASLa,
author = "Jo Ann Howell and Robert T. Gregory",
title = "An algorithm for solving linear algebraic equations
using residue arithmetic. {I}",
journal = j-BIT,
volume = "9",
pages = "200--224",
year = "1969",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65.35",
MRnumber = "MR0261775 (41 \#6388a)",
bibdate = "Thu Nov 8 14:50:15 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Howell:1969:ASLb,
author = "Jo Ann Howell and Robert T. Gregory",
title = "An algorithm for solving linear algebraic equations
using residue arithmetic. {II}",
journal = j-BIT,
volume = "9",
pages = "324--337",
year = "1969",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65.35",
MRnumber = "MR0261776 (41 \#6388b)",
MRreviewer = "J. Legras",
bibdate = "Thu Nov 8 14:50:18 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@MastersThesis{Huey:1969:DFP,
author = "Ben Milton Huey",
title = "Design of a floating point processor for the {PDP-9}
computer",
type = "Thesis ({M.S. - Electrical Engineering})",
school = "University of Arizona",
address = "Tucson, AZ, USA",
pages = "175",
year = "1969",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer storage devices.; Hybrid computers.",
}
@Article{Huttenhoff:1969:AUC,
author = "J. H. Huttenhoff and R. R. Shively",
title = "Arithmetic Unit of a Computing Element in a Global,
Highly Parallel Computer",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-18",
number = "8",
pages = "695--698",
month = aug,
year = "1969",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1969.222751",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 16:55:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671344",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{King:1969:LEN,
author = "Richard F. King and David L. Phillips",
title = "The Logarithmic Error and {Newton}'s Method for the
Square Root",
journal = j-CACM,
volume = "12",
number = "2",
pages = "87--88",
month = feb,
year = "1969",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/362848.362861",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.50",
MRnumber = "44\#2333",
bibdate = "Fri Nov 25 18:20:24 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The problem of obtaining optimal starting values for
the calculation of the square root using Newton's
method is considered. It has been pointed out elsewhere
that if relative error is used as the measure of
goodness of fit, optimal results are not obtained when
the initial approximation is a best fit. It is shown
here that if, instead, the so-called logarithmic error
is used, then a best initial fit is optimal for both
types of error. Moreover, use of the logarithmic error
appears to simplify the problem of determining the
optimal initial approximation.",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C4120 (Functional analysis)",
corpsource = "Argonne Nat. Lab., Argonne, IL, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions; function evaluation;
iterative methods",
}
@Article{Kirsch:1969:ACA,
author = "Arnold Kirsch",
title = "An analysis of commercial arithmetic",
journal = j-EDUC-STUD-MATH,
volume = "1",
number = "3",
pages = "300--311",
month = jan,
year = "1969",
CODEN = "EDSMAN",
DOI = "https://doi.org/10.1007/BF00558315",
ISSN = "0013-1954 (print), 1573-0816 (electronic)",
ISSN-L = "0013-1954",
bibdate = "Sat Jan 14 17:12:11 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/educstudmath.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer.com/accesspage/article/10.1007/BF00558315",
acknowledgement = ack-nhfb,
fjournal = "Educational Studies in Mathematics",
journal-URL = "http://link.springer.com/journal/10649",
}
@MastersThesis{Knight:1969:FPS,
author = "Douglas Wayne Knight",
title = "A floating point software package in {BCD} format for
small, fixed word length, digital computers",
type = "Thesis ({M.S.})",
school = "Arizona State University, Electrical Engineering",
address = "Tempe, AZ, USA",
pages = "151",
year = "1969",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Knuth:1969:SA,
author = "Donald E. Knuth",
title = "Seminumerical Algorithms",
volume = "2",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xi + 624",
year = "1969",
ISBN = "0-201-03802-1",
ISBN-13 = "978-0-201-03802-6",
LCCN = "QA76.5 .K57",
MRclass = "68.00 (65.00)",
MRnumber = "44 \#3531",
MRreviewer = "M. Muller",
bibdate = "Wed Dec 15 15:47:38 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/cryptography.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\$19.75",
series = "The Art of Computer Programming",
acknowledgement = ack-nhfb,
remark = "Benford's Law is discussed on pp. 219--229. Cited in
\cite{Sterbenz:1974:FPC}.",
tableofcontents = "3: Random Numbers \\
3.1. Introduction / 1 \\
3.2. Generating Uniform Random Numbers / 9 \\
3.2.1. The Linear Congruential Method / 9 \\
3.2.1.1. Choice of modulus / 11 \\
3.2.1.2. Choice of multiplier / 15 \\
3.2.1.3. Potency / 21 \\
3.2.2. Other Methods / 25 \\
3.3. Statistical Tests / 34 \\
3.3.1. General Test Procedures for Studying Random Data
/ 35 \\
3.3.2. Empirical Tests / 54 \\
*3.3.3. Theoretical Tests / 69 \\
3.3.4. The Spectral Test / 82 \\
3.4. Other Types of Random Quantities / 100 \\
3.4.1. Numerical Distributions / 101 \\
3.4.2. Random Sampling and Shuffling / 121 \\
*3.5. What is a Random Sequence? / 127 \\
3.6. Summary / 155 \\
4: Arithmetic \\
4.1. Positional Number Systems / 162 \\
4.2. Floating-Point Arithmetic / 180 \\
4.2.1. Single-Precision Calculations / 180 \\
4.2.2. Accuracy of Floating-Point Arithmetic / 195 \\
*4.2.3. Double-Precision Calculations / 210 \\
4.2.4. Statistical Distribution / 218 \\
4.3. Multiple-Precision Arithmetic / 229 \\
4.3.1. The Classical Algorithms / 229 \\
*4.3.2. Modular Arithmetic / 248 \\
*4.3.3. How Fast Can We Multiply? / 258 \\
4.4. Radix Conversion / 280 \\
4.5. Rational Arithmetic / 290 \\
4.5.1. Fractions / 290 \\
4.5.2. The Greatest Common Divisor / 293 \\
*4.5.3. Analysis of Euclid's Algorithm / 316 \\
4.5.4. Factoring into Primes / 339 \\
4.6. Polynomial Arithmetic / 360 \\
4.6.1. Division of Polynomials / 363 \\
*4.6.2. Factorization of Polynomials / 381 \\
4.6.3. Evaluation of Powers / 398 \\
4.6.4. Evaluation of Polynomials / 422 \\
*4.7. Manipulation of Power Series / 444 \\
Answers to Exercises / 452 \\
Appendix A: MIX / 565 \\
1. Description of MIX / 565 \\
2. The MIX Assembly Language / 584 \\
Appendix B: Tables of Numerical Quantities / 596 \\
1. Fundamental Constants (decimal) / 596 \\
2. Fundamental Constants (octal) / 597 \\
3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
Numbers / 598 \\
Appendix C: Index to Notations / 600 \\
Index and Glossary / 605",
xxyear = "{\noopsort{1968c}}1969",
}
@Book{Knuth:ACP69-2,
author = "Donald E. Knuth",
title = "Seminumerical Algorithms",
volume = "2",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xi + 624",
year = "1969",
ISBN = "0-201-03802-1",
ISBN-13 = "978-0-201-03802-6",
LCCN = "QA76.5 .K57",
MRclass = "68.00 (65.00)",
MRnumber = "44 \#3531",
MRreviewer = "M. Muller",
bibdate = "Wed Dec 15 15:47:38 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/cryptography.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\$19.75",
series = "The Art of Computer Programming",
acknowledgement = ack-nhfb,
remark = "Benford's Law is discussed on pp. 219--229.",
tableofcontents = "3: Random Numbers \\
3.1. Introduction / 1 \\
3.2. Generating Uniform Random Numbers / 9 \\
3.2.1. The Linear Congruential Method / 9 \\
3.2.1.1. Choice of modulus / 11 \\
3.2.1.2. Choice of multiplier / 15 \\
3.2.1.3. Potency / 21 \\
3.2.2. Other Methods / 25 \\
3.3. Statistical Tests / 34 \\
3.3.1. General Test Procedures for Studying Random Data
/ 35 \\
3.3.2. Empirical Tests / 54 \\
*3.3.3. Theoretical Tests / 69 \\
3.3.4. The Spectral Test / 82 \\
3.4. Other Types of Random Quantities / 100 \\
3.4.1. Numerical Distributions / 101 \\
3.4.2. Random Sampling and Shuffling / 121 \\
*3.5. What is a Random Sequence? / 127 \\
3.6. Summary / 155 \\
4: Arithmetic \\
4.1. Positional Number Systems / 162 \\
4.2. Floating-Point Arithmetic / 180 \\
4.2.1. Single-Precision Calculations / 180 \\
4.2.2. Accuracy of Floating-Point Arithmetic / 195 \\
*4.2.3. Double-Precision Calculations / 210 \\
4.2.4. Statistical Distribution / 218 \\
4.3. Multiple-Precision Arithmetic / 229 \\
4.3.1. The Classical Algorithms / 229 \\
*4.3.2. Modular Arithmetic / 248 \\
*4.3.3. How Fast Can We Multiply? / 258 \\
4.4. Radix Conversion / 280 \\
4.5. Rational Arithmetic / 290 \\
4.5.1. Fractions / 290 \\
4.5.2. The Greatest Common Divisor / 293 \\
*4.5.3. Analysis of Euclid's Algorithm / 316 \\
4.5.4. Factoring into Primes / 339 \\
4.6. Polynomial Arithmetic / 360 \\
4.6.1. Division of Polynomials / 363 \\
*4.6.2. Factorization of Polynomials / 381 \\
4.6.3. Evaluation of Powers / 398 \\
4.6.4. Evaluation of Polynomials / 422 \\
*4.7. Manipulation of Power Series / 444 \\
Answers to Exercises / 452 \\
Appendix A: MIX / 565 \\
1. Description of MIX / 565 \\
2. The MIX Assembly Language / 584 \\
Appendix B: Tables of Numerical Quantities / 596 \\
1. Fundamental Constants (decimal) / 596 \\
2. Fundamental Constants (octal) / 597 \\
3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
Numbers / 598 \\
Appendix C: Index to Notations / 600 \\
Index and Glossary / 605",
xxyear = "{\noopsort{1968c}}1969",
}
@Article{Linhardt:1969:DDT,
author = "R. J. Linhardt and H. S. Miller",
title = "Digit-by-Digit Transcendental-Function Computation",
journal = j-RCA-REV,
volume = "30",
number = "2",
pages = "209--247",
month = jun,
year = "1969",
CODEN = "RCARCI",
ISSN = "0033-6831",
bibdate = "Fri Sep 16 10:31:06 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "RCA review",
}
@Article{Liu:1969:EAD,
author = "B. Liu and T. Kaneko",
title = "Error analysis of digital filters realized with
floating-point arithmetic",
journal = j-PROC-IEEE,
volume = "57",
number = "10",
pages = "1735--1747",
month = oct,
year = "1969",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See correction \cite{Liu:1970:CEA}.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "This paper calculates the error at the output of a
digital filter using floating-point arithmetic
operations due to roundoff accumulation and input
quantization. Expressions are derived for the mean
square error for each of the three canonical forms
\ldots{}",
}
@InProceedings{Matula:1969:TAM,
author = "David W. Matula",
title = "Towards an Abstract Mathematical Theory of
Floating-Point Arithmetic",
crossref = "AFIPS:1969:ACPa",
pages = "765--772",
year = "1969",
bibdate = "Fri Oct 19 23:01:32 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Posnov:1969:FPR,
author = "N. N. Posnov and M. K. Buza and V. K. Kravcov",
title = "The floating point in a residue class number system.
({Russian})",
journal = "Vestnik Beloruss. Gos. Univ. Ser. I",
volume = "3",
pages = "21--27",
year = "1969",
MRclass = "10A10",
MRnumber = "45 3303e",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Russian",
reviewer = "J. B. Roberts",
}
@Book{Rice:1969:AFV,
author = "John R. Rice",
title = "The Approximation of Functions",
volume = "2",
publisher = pub-AW,
address = pub-AW:adr,
pages = "various",
year = "1969",
LCCN = "QA221 .R5 V.1-2",
bibdate = "Fri Dec 08 13:02:54 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@TechReport{Rigby:1969:DFP,
author = "G. W. Rigby",
title = "To draw a floating point number on the graph
plotter({PRP 2})",
type = "Group Research report",
institution = "British Steel Corporation",
address = "London, UK",
year = "1969",
bibdate = "Thu May 09 08:32:48 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Rosen:1969:ECH,
author = "Saul Rosen",
title = "Electronic Computers: a Historical Survey",
journal = j-COMP-SURV,
volume = "1",
number = "1",
pages = "7--36",
month = mar,
year = "1969",
CODEN = "CMSVAN",
DOI = "https://doi.org/10.1145/356540.356543",
ISSN = "0010-4892",
ISSN-L = "0360-0300",
bibdate = "Mon Sep 19 18:18:44 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The first large scale electronic computers were built
in connection with university projects sponsored by
government military and research organizations. Many
established companies, as well as new companies,
entered the computer field during the first generation,
1947-1959, in which the vacuum tube was almost
universally used as the active component in the
implementation of computer logic. The second generation
was characterized by the transistorized computers that
began to appear in 1959. Some of the computers built
then and since are considered super computers; they
attempt to go to the limit of current technology in
terms of size, speed, and logical complexity. From 1965
onward, most new computers belong to a third
generation, which features integrated circuit
technology and multiprocessor multiprogramming
systems.",
acknowledgement = ack-nhfb,
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
keywords = "computer history; electronic computers; magnetic drum
computers; super computers; time-sharing;
transistorized computers; university computer projects;
vacuum tube computers",
}
@Article{S:1969:BRQ,
author = "D. S.",
title = "Book Review: {{\em Square Roots of Integers $2$ to $
15 $ in Various Bases $2$ to $ 10 $: $ 88062 $ Binary
Digits or Equivalent} by W. A. Beyer, N. Metropolis,
and J. R. Neergaard}",
journal = j-MATH-COMPUT,
volume = "23",
number = "107",
pages = "679--679",
month = jul,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Mar 20 13:34:21 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0025-5718%28196907%2923%3A107%3C679%3ASROI2T%3E2.0.CO%3B2-C",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Shea:1969:NDN,
author = "Dale D. Shea",
title = "On the Number of Divisions Needed in Finding the
Greatest Common Divisor",
journal = j-FIB-QUART,
volume = "7",
number = "4",
pages = "337--340",
month = nov,
year = "1969",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:19 MDT 2011",
bibsource = "http://www.fq.math.ca/7-4.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/7-4/shea.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Sterbenz:1969:OSA,
author = "P. H. Sterbenz and C. T. Fike",
title = "Optimal Starting Approximations for {Newton}'s
Method",
journal = j-MATH-COMPUT,
volume = "23",
number = "106",
pages = "313--318",
month = apr,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nj # " and " # ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Svoboda:1969:DAS,
author = "A. Svoboda",
title = "Decimal Adder with Signed Digit Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-18",
number = "3",
pages = "212--215",
month = mar,
year = "1969",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1969.222633",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jun 24 20:44:42 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "decimal floating-point arithmetic",
}
@Article{Troelstra:1969:EA,
author = "A. S. Troelstra",
title = "Elementary arithmetic",
journal = j-LECT-NOTES-MATH,
volume = "95",
pages = "12--13",
year = "1969",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0080646",
ISBN = "3-540-04614-3 (print), 3-540-36130-8 (e-book)",
ISBN-13 = "978-3-540-04614-1 (print), 978-3-540-36130-5
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
bibdate = "Thu May 8 17:39:14 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lnm1960.bib",
URL = "http://link.springer.com/chapter/10.1007/BFb0080646",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/BFb0080643",
book-URL = "http://www.springerlink.com/content/978-3-540-36130-5",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
}
@Article{Turner:1969:CSI,
author = "L. Richard Turner",
title = "Comment on Some {IBM} Software",
journal = "{SHARE Secretary Distribution}",
volume = "SSD 199",
number = "C5279",
pages = "40--43",
year = "1969",
bibdate = "Fri Aug 20 10:23:55 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Turner:1969:DSC,
author = "L. Richard Turner",
title = "Difficulty in {\tt sin\slash cos} Routine",
journal = j-SIGNUM,
volume = "4",
number = "3",
pages = "13--13",
month = oct,
year = "1969",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Feb 15 15:23:23 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@TechReport{Turner:1969:IOC,
author = "L. R. Turner",
title = "Input-Output Conversion in {System\slash 360}",
number = "SSD 194, C5173",
institution = "SHARE Secretary Distribution",
address = "????",
pages = "1--8",
year = "1969",
bibdate = "Thu Feb 15 15:21:42 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Usow:1969:SSC,
author = "Karl H. Usow",
title = "{SIGNUM} subroutine certification committee",
journal = j-SIGNUM,
volume = "4",
number = "3",
pages = "15--18",
month = oct,
year = "1969",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Mon Mar 5 17:26:29 MST 2007",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@TechReport{Veltkamp:1969:APV,
author = "G. W. Veltkamp",
title = "{ALGOL} procedures voor het rekenen in dubbele lengte.
({Dutch}) [{ALGOL} procedures for double-length
arithmetic]",
type = "Technical report",
number = "21",
institution = "RC-Informatie, Technische Hogeschool Eindhoven",
address = "Eindhoven, The Netherlands",
year = "1969",
bibdate = "Tue Dec 26 14:53:03 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Dutch",
}
@Article{Weinstein:1969:CCR,
author = "C. Weinstein and A. V. Oppenheim",
title = "Correction to {``A comparison of roundoff noise in
floating point and fixed point digital filter
realizations''}",
journal = j-PROC-IEEE,
volume = "57",
number = "8",
pages = "1466--1466",
month = aug,
year = "1969",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Weinstein:1969:CRN}.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}
@Article{Weinstein:1969:CRN,
author = "C. Weinstein and A. V. Oppenheim",
title = "A comparison of roundoff noise in floating point and
fixed point digital filter realizations",
journal = j-PROC-IEEE,
volume = "57",
number = "6",
pages = "1181--1183",
month = jun,
year = "1969",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See correction \cite{Weinstein:1969:CCR}.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "A statistical model for roundoff noise in floating
point digital filters, proposed by Kaneko and Liu, is
tested experimentally for first- and second-order
digital filters. Good agreement between theory and
experiment is obtained. The model is used to \ldots{}",
}
@Article{Weinstein:1969:RNF,
author = "C. Weinstein",
title = "Roundoff noise in floating point fast {Fourier}
transform computation",
journal = j-IEEE-TRANS-AUDIO-ELECTROACOUST,
volume = "17",
number = "3",
pages = "209--215",
month = sep,
year = "1969",
CODEN = "ITADAS",
ISSN = "0018-9278 (print), 1558-2582 (electronic)",
ISSN-L = "0018-9278",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Audio and Electroacoustics",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8337",
summary = "A statistical model for roundoff errors is used to
predict output noise-to-signal ratio when a fast
Fourier transform is computed using floating point
arithmetic. The result, derived for the case of white
input signal, is that the ratio of mean-square
\ldots{}",
}
@Article{Whipple:1969:CHR,
author = "W. L. Whipple",
title = "Comments on {``Higher-Radix Division Using Estimates
of the Divisor and Partial Remainders''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-18",
number = "2",
pages = "183--183",
month = feb,
year = "1969",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1969.222623",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 16:55:18 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
note = "See \cite{Atkins:1968:HRD}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671216",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Young:1969:SCN,
author = "David M. Young and Alvis E. McDonald",
title = "On the surveillance and control of number range and
accuracy in numerical computation (with discussion)",
crossref = "Morrell:1970:IPP",
pages = "145--152",
year = "1969",
MRclass = "65.80",
MRnumber = "40\#8303",
bibdate = "Thu Jan 18 13:48:21 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}, but given year
1968.",
}
@Article{Atkins:1970:DAU,
author = "D. E. Atkins",
title = "Design of the Arithmetic Units of {ILLIAC III}: Use of
Redundancy and Higher Radix Methods",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "720--723",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223022",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Oct 09 19:03:30 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Atkins.pdf",
abstract = "In keeping with the experimental nature of the
Illinois Pattern Recognition Computer (ILLIAC III), the
arithmetic units are intended to be a practical testing
ground for recent theoretical work in computer
arithmetic. This paper describes the use of redundant
number systems and the design of a structure with which
multiplication and division are executed radix 256. The
heart of the unit is the stored-sign subtracter, a
recently discovered member of the family of borrow-save
subtracters and carry-save adders. A cascade of these
subtracters, controlled by a multiplier recoder,
provides multiplication. The same structure, controlled
by a ``model division'' (a quotient recoder), performs
division.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "arithmetic unit; computer arithmetic; division; higher
radix arithmetic; ILLIAC III; multiplication; redundant
number systems; signed-digit subtracter; stored-sign
subtracter; stored-sign subtracter. Arithmetic unit",
remark = "Despite statements elsewhere that the ILLIAC III used
base 256, that is incorrect. The original manuals for
the machine clearly show an IBM System/360-style
base-16 encoding. This paper reveals the source of the
confusion: the multiplier uses a Wallace recoding
scheme, first defined for radix 4, but extended for the
ILLIAC III to radix 256. Thus, multiplication is done 8
bits at a time. Division is done 4 bits at a time.",
}
@Article{Avizienis:1970:UAB,
author = "Algirdas Avi{\v{z}}ienis and Chin Tung",
title = "A Universal Arithmetic Building Element ({ABE}) and
Design Methods for Arithmetic Processors",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "733--745",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223023",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Avizienis.pdf",
abstract = "The advent of large-scale integration of logic
circuits requires the definition of digital computer
structure in terms of large functional arrays of logic
of very few types. This paper describes a
single-package arithmetic processor called the
arithmetic building element (ABE). The ABE accepts
operands in either conventional or signed-digit radix-r
representation and produces signed-digit results, which
the ABE can reconvert to conventional form. Radix 16 is
chosen for illustrations. Arrays of ABE's may be
arranged to implement unit-time parallel addition,
all-combinational multiplication, and more complex
functions which are presently computed by subroutines.
To facilitate such arithmetic design, a graph model is
developed which permits a translation of the given
arithmetical algorithm into an interconnection diagram
of ABE's. The design procedure is illustrated by an
array for polynomial evaluation. Speed, cost, and
roundoff error of the array are considered. A computer
program has been written for the automatic translation
of the algorithm graph to an interconnection graph, and
for the evaluation of the cost and speed for a given
polynomial degree and a given precision requirement.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1",
}
@Article{Behringer:1970:BFI,
author = "F. A. Behringer",
title = "{Eine bedingte Form der Integral-Ungleichun von
Gronwal, leichte Verallgemeinerung eins
Stabilit{\"a}tsatzes von Perron und {\"u}berlauffreie
Skalierung von Analogrechenschaltungen}. ({German})
[{A} conditional version of the integral inequality of
{Gronwall}, a slight generalization of a stability
theorem of {Perron}, and overflow-free scaling of
analogue computer set-ups]",
journal = j-COMPUTING,
volume = "5",
number = "4",
pages = "333--348",
year = "1970",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:51 MST 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-ec # " and " # ack-nhfb,
affiliation = "Tech. Hochschule, M{\"u}nchen, West Germany",
classification = "C5460",
description = "analogue computer methods; differential equations",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
language = "German",
}
@Article{Beyer:1970:GST,
author = "W. A. Beyer and N. Metropolis and J. R. Neergaard",
title = "The Generalized Serial Test Applied to Expansions of
Some Irrational Square Roots in Various Bases",
journal = j-MATH-COMPUT,
volume = "24",
number = "111",
pages = "745--747",
month = jul,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.15",
MRnumber = "MR0273773 (42 \#8649)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
URL = "http://links.jstor.org/sici?sici=0025-5718%28197007%2924%3A111%3C745%3ATGSTAT%3E2.0.CO%3B2-2",
ZMnumber = "0227.10044",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Beyer:1970:SSD,
author = "W. A. Beyer and N. Metropolis and J. R. Neergaard",
title = "Statistical Study of Digits of Some Square Roots of
Integers in Various Bases",
journal = j-MATH-COMPUT,
volume = "24",
number = "110",
pages = "455--473",
month = apr,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "62.70",
MRnumber = "MR0272129 (42 \#7010)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
URL = "http://links.jstor.org/sici?sici=0025-5718%28197004%2924%3A110%3C455%3ASSODOS%3E2.0.CO%3B2-I",
ZMnumber = "0208.19505",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Brent:1970:ABN,
author = "R. Brent",
title = "On the Addition of Binary Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "758--759",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223027",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Brent.pdf",
abstract = "An upper bound is derived for the time required to add
numbers modulo $ 2^n $, using circuit elements with a
limited fan-in and unit delay, and assuming that all
numbers have the usual binary encoding. The upper bound
is within a factor $ (1 + \epsilon) $ of Winograd's
lower bound (which holds for all encodings), where $
\epsilon \rightarrow 0 $ as $ n \rightarrow \infty $,
and only $ O(n \log n) $ circuit elements are
required.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "addition; ARITH-1; binary numbers; computational
complexity; group multiplication; logic circuits;
logical design",
}
@TechReport{deLugish:1970:CAA,
author = "B. G. de Lugish",
title = "A Class of Algorithms for Automatic Evaluation of
Certain Elementary Function in a Binary Computer",
type = "Report",
number = "399",
institution = "Department of Computer Science, University of
Illinois",
pages = "??",
month = jun,
year = "1970",
bibdate = "Fri Sep 02 22:49:20 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Flynn:1970:DFI,
author = "M. J. Flynn",
title = "On Division by Functional Iteration",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "702--706",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223019",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite{Swartzlander:1990:CAa}.",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Flynn.pdf",
abstract = "In order to avoid the time delays associated with
linearly convergent division based on subtraction,
other iterative schemes can be used. These are based on
(1) series expansion of the reciprocal, (2)
multiplicative sequence, or (3) additive sequence
convergent to the quotient. These latter techniques are
based on finding the root of an arbitrary function at
either the quotient or reciprocal value. A
Newton--Raphson iteration or root finding iteration can
be used.
The most useful techniques are quadratically convergent
(i.e., $ \mathrm {error}_{i + 1} = O((\mathrm
{error}_i)^2) $). These techniques generally require
two arithmetic operations (add or multiply) to double
the precision of the quotient.",
acknowledgement = ack-sfo # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1",
}
@Article{Forsythe:1970:PCW,
author = "George E. Forsythe",
title = "Pitfalls in Computation, or Why a Math Book Isn't
Enough",
journal = j-AMER-MATH-MONTHLY,
volume = "77",
number = "9",
pages = "931--956",
month = nov,
year = "1970",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "Contributed Item",
MRnumber = "MR1536090",
bibdate = "Tue Nov 22 09:08:17 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
ZMnumber = "0207.15401",
acknowledgement = ack-nhfb,
classmath = "*65G50 Roundoff error 65Y20 Complexity and performance
of numerical algorithms",
fjournal = "The American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@TechReport{Gardiner:1970:SDA,
author = "V. Gardiner and N. Metropolis",
title = "Significant Digit Arithmetic on a {CDC 6600}",
type = "Technical Report",
number = "LA--4470",
institution = inst-LASL,
address = inst-LASL:adr,
pages = "4",
day = "1",
month = jan,
year = "1970",
bibdate = "Tue Mar 20 11:46:17 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=4093265&query_id=0",
acknowledgement = ack-nhfb,
}
@Article{Good:1970:CIA,
author = "Donald I. Good and Ralph L. London",
title = "Computer Interval Arithmetic: Definition and Proof of
Correct Implementation",
journal = j-J-ACM,
volume = "17",
number = "4",
pages = "603--612",
month = oct,
year = "1970",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Sun Nov 6 11:55:54 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Habibi:1970:FM,
author = "A. Habibi and P. A. Wintz",
title = "Fast Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "2",
pages = "153--157",
month = feb,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222881",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 08:01:30 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671474",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Hall:1970:GPQ,
author = "E. L. Hall and D. D. Lynch and S. J. Dwyer",
title = "Generation of Products and Quotients Using Approximate
Binary Logarithms for Digital Filtering Applications",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "2",
pages = "97--105",
month = feb,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222874",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 08:01:30 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671467",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Hamming:1970:DN,
author = "R. W. Hamming",
title = "On the Distribution of Numbers",
journal = j-BELL-SYST-TECH-J,
volume = "49",
number = "8",
pages = "1609--1625",
month = oct,
year = "1970",
CODEN = "BSTJAN",
DOI = "https://doi.org/10.1002/j.1538-7305.1970.tb04281.x",
ISSN = "0005-8580 (print), 2376-7154 (electronic)",
ISSN-L = "0005-8580",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://bstj.bell-labs.com/oldfiles/year.1970/BSTJ.1970.4908.html;
http://www.alcatel-lucent.com/bstj/vol49-1970/bstj-vol49-issue08.html;
https://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
https://www.math.utah.edu/pub/tex/bib/bstj1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol49/bstj49-8-1609.pdf;
http://www.alcatel-lucent.com/bstj/vol49-1970/articles/bstj49-8-1609.pdf",
abstract = "This paper examines the distribution of the mantissas
of floating-point numbers and shows how the arithmetic
operations of a computer transform various
distributions toward the limiting distribution $$ r(x)
= 1 / (x \ln b) \qquad (1 / b \leq x \leq 1) $$ (where
$b$ is the base of the number system). The paper also
gives a number of applications to hardware, software,
and general computing which show that this distribution
is not merely an amusing curiosity. A brief examination
of the distribution of exponents is included.",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Hansen:1970:APN,
author = "Rodney T. Hansen",
title = "Arithmetic of Pentagonal Numbers",
journal = j-FIB-QUART,
volume = "8",
number = "1",
pages = "83--86",
month = feb,
year = "1970",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:23 MDT 2011",
bibsource = "http://www.fq.math.ca/8-1.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/8-1/hansen.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Harris:1970:NND,
author = "V. C. Harris",
title = "Note on the Number of Divisions Required in Finding
the Greatest Common Divisor",
journal = j-FIB-QUART,
volume = "8",
number = "1",
pages = "104--??",
month = feb,
year = "1970",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:23 MDT 2011",
bibsource = "http://www.fq.math.ca/8-1.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/8-1/harris2.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@MastersThesis{Harvey:1970:SSP,
author = "Michael P. Harvey",
title = "A system study and problem solution in polynomial
evaluation",
type = "Thesis ({M.S.})",
school = "California State College",
address = "Long Beach, CA, USA",
pages = "vi + 119",
year = "1970",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers.; Numerical
calculations.; Polynomials.",
remark = "Title on spine: Automated floating point polynomial
evaluation.",
}
@TechReport{Hillstrom:1970:PSF,
author = "K. E. Hillstrom",
title = "Performance Statistics for the {FORTRAN IV (H)} and
{PL/I} (Version 5) Libraries in the {IBM OS\slash 360
Release 18}",
type = "Report",
number = "ANL-7666",
institution = inst-ANL,
address = inst-ANL:adr,
year = "1970",
bibdate = "Fri Aug 20 09:29:37 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Hornbuckle:1970:LMA,
author = "G. D. Hornbuckle and E. I. Ancona",
title = "The {LX-1} Microprocessor and Its Application to
Real-Time Signal Processing",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "710--720",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223021",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Hornbuckle.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1",
}
@Article{Howell:1970:SLE,
author = "Jo Ann Howell and Robert T. Gregory",
title = "Solving linear equations using residue arithmetic ---
{Algorithm II}",
journal = j-BIT,
volume = "10",
pages = "23--37",
year = "1970",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65.35",
MRnumber = "MR0261777 (41 \#6389)",
MRreviewer = "J. Legras",
bibdate = "Thu Nov 8 14:50:19 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Kailas:1970:AMC,
author = "M. V. Kailas",
title = "Another method of converting from hexadecimal to
decimal",
journal = j-CACM,
volume = "13",
number = "3",
pages = "193--193",
month = mar,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "There is a simple paper-and-pencil method of
converting a hexadecimal number N to decimal.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "digital arithmetic",
}
@Article{Knuth:1970:VNF,
author = "Donald E. Knuth",
title = "{Von Neumann}'s First Computer Program",
journal = j-COMP-SURV,
volume = "2",
number = "4",
pages = "247--260",
month = dec,
year = "1970",
CODEN = "CMSVAN",
DOI = "https://doi.org/10.1145/356580.356581",
ISSN = "0010-4892",
ISSN-L = "0360-0300",
bibdate = "Sat Mar 23 15:03:00 2002",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/compsurv.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/HBP/ACMCS.bib;
https://www.math.utah.edu/pub/tex/bib/compsurv.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite{Aspray:1987:PJN}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
}
@Article{Krishnamurthy:1970:OIS,
author = "E. V. Krishnamurthy",
title = "On Optimal Iterative Schemes For High-Speed Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "3",
pages = "227--231",
month = mar,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222901",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jan 08 23:09:36 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Krishnamurthy:1970:RTT,
author = "E. V. Krishnamurthy",
title = "On Range-Transformation Techniques for Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "2",
pages = "157--160",
month = feb,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222882",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 08:01:30 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671475",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Ling:1970:HSC,
author = "H. Ling",
title = "High-Speed Computer Multiplication Using a
Multiple-Bit Decoding Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "706--709",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223020",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Ling.pdf",
abstract = "This paper presents a method of performing the binary
multiplication beyond the scheme of multiple ADD and
SHIFT. The binary multiplication algorithm will be
discussed first, followed by block decoding method,
logic implementation, hardware consideration, and two
examples which are at the end of the discussion.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1",
}
@Article{Linz:1970:AFP,
author = "Peter Linz",
title = "Accurate Floating-Point Summation",
journal = j-CACM,
volume = "13",
number = "6",
pages = "361--362",
month = jun,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.25",
MRnumber = "44\#3468",
MRreviewer = "R. P. Brent",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "Compendex database;
ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1970.bib;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper describes an alternate method for summing a
set of floating-point numbers. Comparison of the error
bound for this method with that of the standard
summation method shows that it is considerably less
sensitive to propagation of round-off error.",
acknowledgement = ack-nhfb # "\slash " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "New York University, NY, USA",
descriptors = "Simulation; statistics; numeric calculation",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "accurate floating-point summation; computers, data
processing; digital arithmetic; floating point
arithmetic; floating-point addition; mathematics;
numerical methods; round-off error; round-off errors;
round-off propagation; summation",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Liu:1970:CEA,
author = "B. Liu and T. Kaneko",
title = "Correction to {``Error analysis of digital filters
realized with floating-point arithmetic''}",
journal = j-PROC-IEEE,
volume = "58",
number = "3",
pages = "376--376",
month = mar,
year = "1970",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Liu:1969:EAD}.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}
@Article{Long:1970:LAS,
author = "C. T. Long and J. H. Jordan",
title = "A Limited Arithmetic on Simple Continued Fractions ---
{II}",
journal = j-FIB-QUART,
volume = "8",
number = "2",
pages = "135--157",
month = mar,
year = "1970",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:25 MDT 2011",
bibsource = "http://www.fq.math.ca/8-2.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/8-2/long.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@TechReport{Malcolm:1970:AFA,
author = "Michael Malcolm",
title = "An algorithm for floating-point accumulation of sums
with small relative error",
number = "STAN-CS-70-163",
institution = "Computer Science Department, Stanford University",
address = "Stanford, CA, USA",
pages = "21",
year = "1970",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; Algorithms.;
FORTRAN (Computer program language); Numerical
calculations --- Computer programs.",
remark = "Reproduced by National Technical Information Service.
AD 708 691.",
}
@MastersThesis{Marasa:1970:AAE,
author = "John D. Marasa",
title = "Accumulated arithmetic error in floating-point and
alternative logarithmic number systems",
type = "Thesis ({M.S.})",
school = "Washington University, Sever Institute of Technology,
Department of Applied Mathematics and Computer
Science",
address = "St. Louis, MO, USA",
pages = "vii + 88",
year = "1970",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Programming (Mathematics)",
}
@Article{Matula:1970:ECA,
author = "David W. Matula",
title = "The emergence of computational arithmetic as a
component of the computer science curriculum",
journal = j-SIGCSE,
volume = "2",
number = "3",
pages = "41--44",
month = nov,
year = "1970",
CODEN = "SIGSD3",
DOI = "https://doi.org/10.1145/873641.873650",
ISSN = "0097-8418 (print), 2331-3927 (electronic)",
ISSN-L = "0097-8418",
bibdate = "Sun Nov 18 08:53:42 MST 2012",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigcse1970.bib",
acknowledgement = ack-nhfb,
fjournal = "SIGCSE Bulletin (ACM Special Interest Group on
Computer Science Education)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J688",
}
@Article{Matula:1970:FFP,
author = "D. W. Matula",
title = "A Formalization of Floating-Point Numeric Base
Conversion",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "681--692",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223017",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 08:01:35 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671610;
http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Matula.pdf",
abstract = "The process of converting arbitrary real numbers into
a floating-point format is formalized as a mapping of
the reals into a specified subset of real numbers. The
structure of this subset, the set of $n$ significant
digit base $b$ floating-point numbers, is analyzed and
properties of conversion mappings are determined. For a
restricted conversion mapping of the $n$ significant
digit base $b$ numbers to the $m$ significant-digit
base $d$ numbers, the one-to-one, onto, and
order-preserving properties of the mapping are
summarized. Multiple conversions consisting of a
composition of individual conversion mappings are
investigated and some results of the invariant points
of such compound conversions are presented. The
hardware and software implications of these results
with regard to establishing goals and standards for
floating-point formats and conversion procedures are
considered.",
acknowledgement = ack-nj # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1",
}
@Article{Mifsud:1970:MDA,
author = "C. J. Mifsud",
title = "A multiple-precision division algorithm",
journal = j-CACM,
volume = "13",
number = "11",
pages = "666--668",
month = nov,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See addendum \cite{Mifsud:1973:AMP}.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Mitre Corp., McLean, VA, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "digital arithmetic",
}
@Article{Nickel:1970:KBS,
author = "K. Nickel",
title = "{Das Kahan--Babu{\v{s}}kasche Summierungsverfahren in
Triplex-ALGOL 60}. ({German}) [{The
Kahan--Babu{\v{s}}ka} summation method in
{Triplex-ALGOL 60}]",
journal = j-Z-ANGE-MATH-MECH,
volume = "50",
pages = "369--373",
year = "1970",
CODEN = "ZAMMAX",
ISSN = "0044-2267 (print), 1521-4001 (electronic)",
ISSN-L = "0044-2267",
bibdate = "Tue Aug 28 06:12:04 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und
Mechanik}",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
keywords = "accurate floating-point summation",
language = "German",
}
@Article{Ninomiya:1970:BRS,
author = "Ichizo Ninomiya",
title = "Best Rational Starting Approximations and Improved
{Newton} Iteration for the Square Root",
journal = j-MATH-COMPUT,
volume = "24",
number = "110",
pages = "391--404",
month = apr,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb # " and " # ack-nj,
ajournal = "Math. Comput.",
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Nagoya University, Chikua ku, Japan",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "computing procedure; function approximation; iterative
methods; Newton iteration; rational approximation;
square root",
treatment = "T Theoretical or Mathematical",
}
@Article{Oppenheim:1970:RDF,
author = "A. Oppenheim",
title = "Realization of digital filters using
block-floating-point arithmetic",
journal = j-IEEE-TRANS-AUDIO-ELECTROACOUST,
volume = "18",
number = "2",
pages = "130--136",
month = jun,
year = "1970",
CODEN = "ITADAS",
ISSN = "0018-9278 (print), 1558-2582 (electronic)",
ISSN-L = "0018-9278",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Audio and Electroacoustics",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8337",
summary = "Recently, statistical models for the effects of
roundoff noise in fixed-point and floating-point
realizations of digital filters have been proposed and
verified, and a comparison between these realizations
presented. In this paper a structure for \ldots{}",
}
@Article{Phillips:1970:GLE,
author = "David L. Phillips",
title = "Generalized Logarithmic Error and {Newton}'s Method
for the $m$ th Root",
journal = j-MATH-COMPUT,
volume = "24",
number = "110",
pages = "383--389",
month = apr,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nj # " and " # ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Rao:1970:BEC,
author = "T. R. N. Rao",
title = "Biresidue Error-Correcting Codes for Computer
Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "5",
pages = "398--402",
month = may,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222937",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 08:01:32 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671530",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Rao:1970:BLR,
author = "T. R. N. Rao and A. K. Trehan",
title = "Binary Logic for Residue Arithmetic Using Magnitude
Index",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "752--757",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223026",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Rao.pdf",
abstract = "We consider a residue number system using n pairwise
relatively prime moduli $ m_1, \ldots {}, m_n $ to
represent any integer $X$ in the range $ M / 2 \leq X >
M / 2 $, when $ M = \prod m_i $. The moduli $ m_i $ are
chosen to be of the $ 2 - 1 $ type, in order that the
residue arithmetic can be implemented by means of
binary registers and binary logic. Further, for each
residue number $X$, a magnitude index $ P_x $ is
maintained for all arithmetic operations. We
investigate the properties of such a system and derive
the addition, subtraction, multiplication, sign
determination, and overflow detection algorithms. The
proposed organization is found to improve the operation
times for sign detection and overflow detection
operations, while rendering multiplication to be a
difficult operation.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1; base extension; index generation logic;
magnitude index; modular adders; naturalized form;
overflow detection; residue multiplication; residue
number system; scale by 2; sign determination",
}
@Article{Robertson:1970:CBM,
author = "J. E. Robertson",
title = "The Correspondence Between Methods of Digital Division
and Multiplier Recoding Procedures",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "692--701",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223018",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Robertson.pdf",
abstract = "This paper relates previous analyses of the binary SRT
division to the theory of multiplier recoding. Since
each binary quotient digit has three possible values,
the quotient resulting from the SRT division is in
recoded form; in this paper it is shown that the
recoding is a function of the divisor, and the method
for determining the characteristic Boolean function of
the recoding is presented. The relationship between the
division and the recoding is established by scaling the
division in such a way that the scaled ``visor''
becomes a constant. Higher radix results are also
discussed.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1",
}
@TechReport{Rothmaier:1970:BQN,
author = "B. Rothmaier",
title = "{Die Berechnung der Quadratwurzel nebst Schranken auf
Dualmaschinen} \toenglish {The Computation of the
Square Root together with [Interval] Bounds on Binary
Machines} \endtoenglish",
type = "{Interner Bericht}",
number = "Nr. 70/17",
institution = "Institut f{\"u}r Informatik, Universit{\"a}t
Karlsruhe",
pages = "??",
year = "1970",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@TechReport{Rothmaier:1970:DSB,
author = "B. Rothmaier",
title = "{Dokumentation der Standardfunktionen des
Betriebssystems Hydra X8} \toenglish {Documentation} of
the Elementary Functions of the Operating System {Hydra
X8} \endtoenglish",
type = "{Interner Bericht}",
number = "Nr. 70/8",
institution = "Institut f{\"u}r Informatik, Universit{\"a}t
Karlsruhe",
pages = "??",
year = "1970",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Shively:1970:PFI,
author = "Richard R. Shively",
title = "Preface: {First IEEE Conference on Computer
Arithmetic, Minneapolis, Minnesota, June 16, 1969}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "679--680",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223016",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671609;
http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_contents.pdf;
http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Shively.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1",
}
@Article{Sikdar:1970:DMM,
author = "K. Sikdar",
title = "Determination of Multipliers Mapping an Arbitrary
Integer into a Range of Certain Type",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "12",
pages = "1221--1222",
month = dec,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222863",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 08:01:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671456",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Svoboda:1970:ADC,
author = "A. Svoboda",
title = "Adder With Distributed Control",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "749--751",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223025",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Svoboda.pdf",
abstract = "An adder is described for addition of a large number
of binary numbers $ x_j, j = 1, 2, \ldots {}, m $,
where $ x_j = \sum_i x_{j, i} 2^i, x_{j, i} = 0, 1, i =
0, 1, \ldots {}, n - 1 $. The adder's algorithm has two
parts: (1) the bits $ x_{j, i} $ are added
independently for each binary order $ i : s_i = \sum_j
x_{j, i} \leq m $ and the result expressed in the
binary form $ s_i = \sum_k a_{i, k} 2^k, a_{i, k} = 0,
1, k = 0, 1, \ldots {}, p - 1 $ (where $ 2^{p - 1} \leq
m < 2^p $) ; (2) the sum $ y = \sum_j x_j $ is formed
by adding terms $ s_{i, k} {2^{i + k}} $ as
contributions of the bit $ s_{i, k} $ to the total $y$.
A hardware implementation of this algorithm is
suggested where the sum $ s_i $ is obtained by a
sequential circuit which reorders the values $ x_{j,
i}' $ so that their sum $ s_i $, remains unchanged and
so that after the reordering the new values $ x_{j, i}'
$ obey the conditions $ x_{j + 1, i} \leq x_{j, i} $
for every $ j = 1, 2, \ldots {}, m - 1 $. The
implementation with integrated circuits should be quite
rewarding because the control of the circuit is done
with independent control elements distributed all over
the chip.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "adder; adder for large number of numbers; ARITH-1;
distributed control; reordering",
}
@Article{Taub:1970:ECS,
author = "D. M. Taub and C. E. Owen and B. P. Day",
title = "Experimental Computer for Schools",
journal = "Proceedings of the IEE",
volume = "117",
number = "2",
pages = "303--312",
month = feb,
year = "1970",
bibdate = "Fri Nov 28 19:30:38 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The computer is a small desk-top machine designed for
teaching schoolchildren how computers work. It works in
decimal notation and has a powerful instruction set
which includes 3-address floating-point instructions
implemented as `extracode' subroutines. Addressing can
be absolute, relative or indirect. For input it uses a
capacitive touch keyboard, and for output and display a
perfectly normal TV receiver is used. Another
input/output device is an ordinary domestic tape
recorder, used mainly for long term storage of
programs. To make the operation of the machine easy to
follow, it can be made to stop at certain stages in the
processing of an instruction and automaticaly display
the contents of all registers and storage locations
relevant at that time. The paper gives a description of
the machine and a discussion of the factors that hav
influenced its design.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "IBM Schools computer with scaled integer format, six
decimal digits and exponent range of $ [ - 6, 0] $.",
}
@Book{Thornton:1970:DCC,
author = "James E. Thornton",
title = "Design of a Computer: the {Control Data 6600}",
publisher = pub-SF,
address = pub-SF:adr,
pages = "v + 181",
year = "1970",
ISBN = "0-07-057302-6, 0-07-057303-4",
ISBN-13 = "978-0-07-057302-4, 978-0-07-057303-1",
LCCN = "TK7889.C6 T5 1970",
bibdate = "Wed Sep 14 22:45:51 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://archive.computerhistory.org/resources/text/CDC/cdc.6600.thornton.design_of_a_computer_the_control_data_6600.1970.102630394.pdf",
acknowledgement = ack-nhfb,
remark = "See Table V: Nonstandard Floating Point Arithmetic on
page 79 for the rules governing Indefinite, Infinity,
and Negative Zero operands.",
tableofcontents = "I: Introduction / 1 \\
A. Justification for Large Computers / 1 \\
B. Building Blocks / 4 \\
C. The Approach / 5 \\
II: Organization of the 6600 / 9 \\
A. General / 9 \\
B. Peripheral Subsystem / 10 \\
C. Central Processor-CPU / 12 \\
D. Central Storage / 15 \\
E. Extended Core Storage / 17 \\
III: Basic Circuit Properties / 19 \\
A. The Silicon Transistor / 19 \\
B. DCTL Logic Circuits / 21 \\
C. Logic Symbols / 24 \\
D. Transmission Lines / 28 \\
E. Packaging / 32 \\
IV: Central Storage System / 37 \\
A. Storage Module / 37 \\
B. Theory of Interleaved Storage / 44 \\
C. Stunt Box / 47 \\
D. Storage Bus System / 51 \\
E. Extended Core Storage / 53 \\
F. ECS Coupler and Controller / 55 \\
V: Central Processor Functional Units / 57 \\
A. Boolean Unit / 59 \\
B. Fixed Add Unit / 63 \\
C. Data Trunks / 69 \\
D. Shift Unit / 71 \\
E. Add Unit / 77 \\
F. Multiply Unit / 88 \\
G. Divide Unit / 101 \\
H. Increment Unit / 105 \\
I. Branch Unit / 111 \\
J. ECS Coupler-Controller / 114 \\
VI: Central Processor Control / 117 \\
A. Exchange Jump / 117 \\
B. Instruction Fetch / 120 \\
C. Instruction Issue / 123 \\
D. Scoreboard / 125 \\
Register Entry/Exit Control / 134 \\
F. Summary / 137 \\
VII: Peripheral Subsystem / 141 A. Peripheral
Processors / 141 \\
B. Dead Start / 154 \\
C. Disk Storage / 157 \\
VIII: Systems Operation / 163 \\
A. Files / 163 \\
B. Tables / 165 \\
C. Circular Buffer for 1/0 / 166 \\
D. Job Processing / 167 \\
E. System Monitor MTR / 168 \\
F. Control Points / 169 \\
G. Summary / 171 \\
Appendix / 173 \\
Index / 177",
}
@Article{Tienari:1970:SMR,
author = "Martti Tienari",
title = "A Statistical Model of Roundoff Error for Varying
Length Floating-Point Arithmetic",
journal = j-BIT,
volume = "10",
number = "3",
pages = "355--365",
month = sep,
year = "1970",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01934204",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "68.00 (65.00)",
MRnumber = "42\#7108",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=10&issue=3&spage=355",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
reviewer = "R. W. Hamming",
}
@Article{Tung:1970:SDD,
author = "Chin Tung",
title = "Signed-Digit Division Using Combinational Arithmetic
Nets",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "746--748",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223024",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Tung.pdf",
abstract = "To meet the challenge created by the advent of large-
scale integration, a unique microelectronic arithmetic
building element and combinational arithmetic nets,
composed of the building elements, have been studied
and proposed for arithmetic processor design. A fast
division algorithm, particularly suitable for floating-
point arithmetic, has also been developed for
signed-digit arithmetic. This algorithm is
characterized by the need of preprocessing the divisor
and then exact generation of quotient digits. This
paper describes the implementation of this division
algorithm with the arithmetic building element and
combinational arithmetic nets. The intention here is to
explore the feasibility of applying large-scale
integration technology to arithmetic processors.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1; arithmetic building element; combinational
arithmetic net; division; large-scale integration;
microelectronic block; signed-digit number system",
}
@Article{Usow:1970:CB,
author = "K. H. Usow",
title = "Certification Bibliography",
journal = j-SIGNUM,
volume = "5",
number = "2",
pages = "14--15",
month = mar,
year = "1970",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Fri Aug 20 10:26:49 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Waksman:1970:WAI,
author = "A. Waksman",
title = "On {Winograd}'s Algorithm for Inner Products",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "4",
pages = "360--361",
month = apr,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222926",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Oct 09 18:54:12 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This correspondence demonstrates an improvement on
Winograd's algorithm for inner products as applied to
the multiplication of two matrices.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "fast matrix multiplication; product of matrices;
sufficient number of arithmetical operations",
}
@Article{Wilson:1970:OSA,
author = "M. Wayne Wilson",
title = "Optimal Starting Approximations for Generating Square
Root for Slow or No Divide",
journal = j-CACM,
volume = "13",
number = "9",
pages = "559--560",
month = sep,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.50",
MRnumber = "44\#2338",
MRreviewer = "J. E. {Dennis, Jr.}",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "On computing machines with slow or no division, it is
preferable to use an iterative scheme for the square
root different from the classical Heron scheme. The
problem of optimal initial approximants is considered,
and some optimal polynomial initial approximations are
tabulated.",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "IBM, Houston, TX, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "CACMA; digital arithmetic; ele; iterative methods;
mathematics; numerical methods; optimisation",
}
@TechReport{Yohe:1970:ACB,
author = "J. M. Yohe",
title = "Accurate Conversion Between Number Bases",
type = "{MRC} Technical Summary Report",
number = "1109",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
month = oct,
year = "1970",
bibdate = "Sun Dec 30 21:39:41 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The author presents and proves algorithms for taking a
number expressed in base gamma and finding, for a
predetermined floating point representation in base
beta, its least upper bound, greatest lower bound, and
closest approximation.",
acknowledgement = ack-nhfb,
}
@TechReport{Yohe:1970:BPF,
author = "J. M. Yohe",
title = "Best possible floating point arithmetic",
type = "{MRC} Technical Summary Report",
number = "1054",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
pages = "ii + 27",
month = mar,
year = "1970",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The report presents an algorithm for floating point
arithmetic, using single-length arithmetic registers,
which yields the most accurate approximation which can
be expressed in the given floating point format, the
greatest lower bound, or the least upper bound for the
result of the operation, whichever is specified by the
programmer. This makes the algorithm particularly
useful for implementation of interval arithmetic.",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.",
remark = "March 1970. Sponsored by Army Research Office, Durham,
N.C.",
}
@Article{Yong:1970:GBA,
author = "Lam Lay Yong",
title = "The Geometrical Basis of the {Ancient Chinese}
Square-Root Method",
journal = j-ISIS,
volume = "61",
number = "1",
pages = "92--102",
month = "Spring",
year = "1970",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:28:39 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302287;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1970.bib",
URL = "http://www.jstor.org/stable/229151",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Article{Zohar:1970:NRC,
author = "S. Zohar",
title = "Negative Radix Conversion",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "3",
pages = "222--226",
month = mar,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222900",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 08:01:31 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See comments \cite{Pawlak:1971:ACN,Wadel:1971:CNR}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671493",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
}
@Book{Zuse:1970:CML,
author = "Konrad Zuse",
title = "{Der Computer, mein Lebenswerk}",
publisher = "Verlag moderne Industrie",
address = "M{\"u}nchen, Germany",
pages = "221",
year = "1970",
LCCN = "QA76.2.Z8 A3",
bibdate = "Mon Nov 4 07:46:57 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "computer engineers --- Germany --- biography;
computers --- Germany --- history; Zuse, Konrad",
}
@Article{Abdelmalek:1971:REA,
author = "Nabih N. Abdelmalek",
title = "Round-off Error Analysis for {Gram--Schmidt} Method
and Solution of Linear Least Squares Problems",
journal = j-BIT,
volume = "11",
number = "4",
pages = "345--367",
month = dec,
year = "1971",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01939404",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:12 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=11&issue=4;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=11&issue=4&spage=345",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Alway:1971:GFA,
author = "G. G. Alway",
title = "A general factorising algorithm",
journal = j-COMP-J,
volume = "14",
number = "2",
pages = "166--168",
month = may,
year = "1971",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:51:53 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/140166.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/tiff/166.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/tiff/167.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/tiff/168.tif",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Nat. Phys. Lab., Teddington, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "computer algorithm; digital arithmetic; general
factorising algorithm; primality of large numbers",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Banerji:1971:RAC,
author = "D. K. Banerji",
title = "Residue arithmetic in computer design",
institution = "University of Waterloo",
address = "Waterloo, ON, Canada",
year = "1971",
bibdate = "Thu Nov 18 09:13:45 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://books.google.com/books?id=YNVcPgAACAAJ",
acknowledgement = ack-nhfb,
}
@Article{Bataille:1971:GCW,
author = "M. Bataille",
title = "The {Gamma 60}: The computer that was ahead of its
time",
journal = j-HONEYWELL-COMP-J,
volume = "5",
number = "3",
pages = "99--105",
month = "????",
year = "1971",
CODEN = "HNCJA3",
ISSN = "0046-7847",
bibdate = "Thu Nov 25 09:37:15 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Honeywell Computer Journal",
keywords = "decimal floating-point arithmetic",
remark = "The Gamma 60 decimal floating-point system provides 11
to 19 decimal digits with an exponent range of $ \pm 40
$.",
}
@Book{Bell:1971:CSR,
editor = "C. Gordon Bell and Allen Newell",
booktitle = "Computer Structures: Readings and Examples",
title = "Computer Structures: Readings and Examples",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xix + 668",
year = "1971",
ISBN = "0-07-004357-4",
ISBN-13 = "978-0-07-004357-2",
LCCN = "TK7888.3 .B4",
bibdate = "Tue Aug 15 18:20:34 MDT 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkes-maurice-v.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
acknowledgement = ack-nhfb,
shorttableofcontents = "Part 1 The Structure of Computers \\
Chapter 1 Introduction \\
Chapter 2 The PMS and ISP Descriptive Systems \\
Chapter 3 The Computer Space \\
Part 2 The Instruction-set Processor: Main-line
computers \\
Section 1 Processors with One Address per Instruction
\\
Chapter 4 Preliminary Discussion of the Logical Design
of an Electronic Computing Instrument \\
Chapter 5 The DEC PDP-8 \\
Chapter 6 The Whirlwind I Computer \\
Chapter 7 Some Aspects of the Logical Design of a
Control Computer: A Case Study \\
Chapter 8 The UNIVAC System \\
Section 2 Processors with a General-Register State \\
Chapter 9 The Design Philosophy of Pegasus, A
Quantity-production Computer \\
Chapter 10 An 8-bit-character Computer \\
Part 3 The Instruction-Set Processor Level: Variations
in the Processor \\
Section 1 Processors with Greater than One Address per
Instruction \\
Chapter 11 The Pilot ACE \\
Chapter 12 ZEBRA, A Simple Binary Computer \\
Chapter 13 UNIVAC Scientific (1103A) Instruction Logic
\\
Chapter 14 Instruction Logic of the MIDAC \\
Chapter 15 Instruction Logic of the Soviet Strela
(Arrow) \\
Section 2 Processors Constrained by a Cyclic, Primary
Memory \\
Chapter 16 The LGP-30 and LGP-21 \\
Chapter 17 IBM 650 Instruction Logic \\
Section 3 Processors for Variable-length-string Data
\\
Chapter 18 The IBM 1401 \\
Section 4 Desk Calculator Computers: Keyboard
Programmable Processors with Small Memories \\
Chapter 19 The OLIVETTI Programma 101 Desk Calculator
\\
Chapter 20 The HP Model 9100A Computing Calculator \\
Section 5 Processors with Stack Memories (Zero
Addresses per Instruction) \\
Chapter 21 Design of an Arithmetic Unit Incorporating a
Nesting Store \\
Chapter 22 Design of the B 5000 System \\
Section 6 Processors with Multiprogramming Ability \\
Chapter 23 One-level Storage System \\
Chapter 24 A User Machine in a Time-sharing System \\
Part 4 The Instruction-set Processor Level:
Special-function Processors \\
Section 1 Processors to Control Terminals and Secondary
Memories (Input-output Processors) \\
Chapter 25 The DEC 338 Display Processor \\
Section 2 Processors for Array Data \\
Chapter 26 NOVA: A List-oriented Computer \\
Chapter 27 The ILLIAC IV Computer \\
Section 3 Processors Defined by a Microprogram \\
Chapter 28 Microprogramming and the Design of the
Control Circuits in an Electronic Computer \\
Chapter 29 The Design of a General-Purpose
Microprogram-controlled Computer with Elementary
Structure \\
Section 4 Processors Based on a Programming Language
\\
Chapter 30 A Command Structure for Complex Information
Processing \\
Chapter 31 System Design of a FORTRAN Machine \\
Chapter 32 A Microprogrammed Implementation of EULER on
IBM System/360 Model 30 \\
Part 5 The PMS Level \\
Section 1 Computers with One Central Processor \\
Section 2 Computers with One Central Processor and
Multiple Input/Output Processors \\
Chapter 33 The IBM 1800 \\
Chapter 34 The Engineering Design of the Stretch
Computer \\
Chapter 35 PILOT, The NBS Multicomputer System \\
Section 3 Computers for Multiprocessing and Parallel
Processing \\
Chapter 36 D825 --- A Multiple-computer System for
Command and Control \\
Chapter 37 A Survey of Problems and Preliminary Results
Concerning Parallel Processing and Parallel Processors
\\
Section 4 Network Computers and Computer Networks \\
Chapter 38 The RW-400: A New Polymorphic Data System
\\
Chapter 39 Parallel Operation in the Control Data 6600
\\
Chapter 40 Computer Network Examples / 504 \\
Part 6 Computer Families \\
Section 1 The IBM 701--7094 II Sequence, a Family by
Evolution \\
Chapter 41 The IBM 7094 I, 11 / 517 \\
Section 2 The SDS 910--9300 Series, a Planned Family\\
Chapter 42 The SDS 910-9300 Series \\
Section 3 The IBM System/360 --- A Series of Planned
Machines Which Span a Wide Performance Range \\
Chapter 43 The Structure of System/360, Part I ---
Outline of the Logical Structure System Implementations
\\
Chapter 44 The Structure of System/360, Part II ---
System Implementations \\
Appendix PMS and ISP Notations",
subject-dates = "John von Neumann (28 December 1903--8 February 1957);
James H. Wilkinson (27 September 1919--5 October 1986);
Sir Maurice Vincent Wilkes (26 June 1913--29 November
2010)",
tableofcontents = "[NB: Bracketed chapter entries are subject cross
references] \\
Preface / v \\
Contributors / xiii \\
Acknowledgments / x \\
\\
Part 1 The Structure of Computers \\
\\
Chapter 1 Introduction / 3 \\
Chapter 2 The PMS and ISP Descriptive Systems / 15 \\
Chapter 3 The Computer Space / 37 \\
\\
Part 2 The Instruction-set Processor: Main-line
computers \\
\\
Section 1 Processors with One Address per Instruction /
89 \\
\\
Chapter 4 Preliminary Discussion of the Logical Design
of an Electronic Computing Instrument --- Arthur W.
Burks, Herman H. Goldstine, and John von Neumann / 92
\\
Chapter 5 The DEC PDP-8 / 120 \\
Chapter 6 The Whirlwind I Computer --- R. R. Everett /
137 \\
[Chapter 33 The IBM 1800] \\
Chapter 7 Some Aspects of the Logical Design of a
Control Computer: A Case Study --- R. L. Alonso, H.
Blair-Smith, and A. L. Hopkins / 146 \\
[Chapter 42 The SDS 910-9300 Series] \\
[Chapter 16 The LGP-30 and LGP-21] \\
[Chapter 17 IBM 650 Instruction Logic ---John W. Carr
III] \\
[Chapter 41 The IBM 7094 I, II] \\
Chapter 8 The UNIVAC System --- J. Presper Eckert, Jr,
James B. Weiner, H. Frazer Welsh, and Herbert F.
Mitchell / 157 \\
[Chapter 23 One-level Storage System --- T. Kilburn, D.
B. G. Edwards, M. J. Lanigan, and F. H. Summer] \\
[Chapter 34 The Engineering Design of the Stretch
Computer --- Erich Bloch] \\
\\
Section 2 Processors with a General-Register State \\
\\
Chapter 9 The Design Philosophy of Pegasus, A
Quantity-production Computer --- W. S. Elliott, C. E.
Owen, C. H. Devonald, and B. G. Maudsley / 171 \\
[Chapter 43 The Structure of System/360, Part I ---
Outline of the Logical Structure --- G. A. Blaauw and
F. P. Brooks, Jr.] \\
Chapter 10 An 8-bit-character Computer / 184 \\
[Chapter 39 Parallel Operation in the Control Data 6600
--- James E. Thornton] \\
\\
Part 3 The Instruction-Set Processor Level: Variations
in the Processor \\
\\
Section 1 Processors with Greater than One Address per
Instruction / 191 \\
\\
Chapter 11 The Pilot ACE --- J. H. Wilkinson / 193 \\
Chapter 12 ZEBRA, A Simple Binary Computer --- W. L.
van der Poel / 200 \\
Chapter 13 UNIVAC Scientific (1103A) Instruction Logic
--- John W. Carr III / 205 \\
[Chapter 38 The RW-400: A New Polymorphic Data System
--- R. E. Porter] \\
Chapter 14 Instruction Logic of the MIDAC --- John W.
Carr III / 209 \\
Chapter 15 Instruction Logic of the Soviet Strela
(Arrow) ---John W. Carr III / 213 \\
\\
Section 2 Processors Constrained by a Cyclic, Primary
Memory / 216 \\
\\
[Chapter 19 The OLIVETTI Programma 101 Desk Calculator]
\\
[Chapter 12 ZEBRA, A Simple Binary Computer --- W. L.
van der Poel] \\
Chapter 16 The LGP-30 and LGP-21 / 217 \\
[Chapter 11 The Pilot ACE --- J. H. Wilkinson] \\
[Chapter 8 The UNIVAC System --- J. Presper Eckert,
Jr., James R. Weiner, H. Frazer Welsh, and Herbert F.
Mitchell] \\
[Chapter 9 The Design Philosophy of Pegasus, A
Quantity-production Computer --- W. S. Elliott, C. E.
Owen, C. H. Devonald, and B. G. Maudsley] \\
Chapter 17 IBM 650 Instruction Logic --- John W. Carr
III / 220 \\
[Chapter 26 NOVA: A List-oriented Computer --- Joseph
E. Wirsching] \\
\\
Section 3 Processors for Variable-length-string Data /
224 \\
\\
Chapter 18 The IBM 1401 / 228 \\
[Chapter 10 An 8-bit-character Computer] \\
\\
Section 4 Desk Calculator Computers: Keyboard
Programmable Processors with Small Memories / 235 \\
\\
Chapter 19 The OLIVETTI Programma 101 Desk Calculator /
237 \\
Chapter 20 The HP Model 9100A Computing Calculator ---
Richard E. Monnier, Thomas E. Osborne, and David S.
Cochran / 243 \\
\\
Section 5 Processors with Stack Memories (Zero
Addresses per Instruction) / 257 \\
\\
Chapter 21 Design of an Arithmetic Unit Incorporating a
Nesting Store --- R. H. Allmark and J. R. Lucking / 262
\\
Chapter 22 Design of the B 5000 System --- William
Lonergan and Paul King / 267 \\
[Chapter 36 D825 --- A Multiple-computer System for
Command and Control --- James P. Anderson, Samuel A.
Hoffman, Joseph Shifman, and Robert J. Williams] \\
[Chapter 30 A Command Structure for Complex Information
Processing --- J. C. Shaw, A. Newell, H. A. Simon, T.
O. Ellis] \\
[Chapter 32 Microprogrammed Implementation of EULER on
IBM System/360 Model 30 --- Helmut Weber] \\
\\
Section 6 Processors with Multiprogramming Ability /
274 \\
\\
Chapter 23 One-level Storage System --- T. Kilburn, D.
B. G. Edwards, M. J. Lanigan, and F. H. Sumner / 276
\\
[Chapter 21 Design of the B 5000 System --- William
Lonergan and Paul King] \\
Chapter 24 A User Machine in a Time-sharing System ---
B. W. Lampson, W. W. Lichtenberger, and M. W. Pirtle /
291 \\
\\
Part 4 The Instruction-set Processor Level:
Special-function Processors \\
\\
Section 1 Processors to Control Terminals and Secondary
Memories (Input-output Processors) / 303 \\
\\
[Chapter 41 The IBM 7094 I, II] \\
[Chapter 43 The Structure of System/360, Part I ---
Outline of the Logical Structure ---- G. A. Blaauw and
F. P. Brooks, Jr.] \\
[Chapter 33 The IBM 1800] \\
Chapter 25 The DEC 338 Display Processor / 305 \\
\\
Section 2 Processors for Array Data / 315 \\
\\
Chapter 26 NOVA: A List-oriented Computer --- Joseph E.
Wirsching / 316 \\
Chapter 27 The ILLIAC IV Computer --- George H. Barnes,
Richard M. Brown, Maso Kato, David J. Kuck, Daniel L.
Slotnick, and Richard E. Stokes / 320 \\
\\
Section 3 Processors Defined by a Microprogram / 334
\\
\\
Chapter 28 Microprogramming and the Design of the
Control Circuits in an Electronic Computer --- M. V.
Wilkes and J. B. Stringer / 335 \\
Chapter 29 The Design of a General-Purpose
Microprogram-controlled Computer with Elementary
Structure --- Thomas W. Kampe / 341 \\
[Chapter 20 The HP Model 9100A Computing Calculator
---Richard E. Monnier, Thomas E. Osborne, and David S.
Cochran] \\
[Chapter 32 A Microprogrammed Implementation of EULER
on IBM System/360 Model 30 --- Helmut Weber] \\
\\
Section 4 Processors Based on a Programming Language /
348 \\
\\
Chapter 30 A Command Structure for Complex Information
Processing --- J. C. Shaw, A.Newell, H. A. Simon, and
T.O. Ellis / 349 \\
\\
Chapter 31 System Design of a FORTRAN Machine ---
Theodore R. Bashkow, Azra Sasson, and Arnold Kronfeld /
363 \\
Chapter 32 A Microprogrammed Implementation of EULER on
IBM System/360 Model 30 --- Helmut Weber / 382 \\
\\
Part 5 The PMS Level \\
\\
Section 1 Computers with One Central Processor / 395
\\
\\
[Chapter 6 The Whirlwind I Computer --- R. R. Everett]
\\
[Chapter 42 The SDS 910-9300 Series] \\
\\
Section 2 Computers with One Central Processor and
Multiple Input/Output Processors / 396 \\
\\
[Chapter 5 The DEC PDP-8] \\
Chapter 33 The IBM 1800 / 399 \\
[Chapter 41 The IBM 7094 I, II] \\
[Chapter 43 The Structure of System/360, Part I ---
Outline of the Logical Structure -- G. A. Blaauw and F.
P. Brooks, Jr.] \\
Chapter 34 The Engineering Design of the Stretch
Computer -- Erich Bloch / 421 \\
Chapter 35 PILOT, The NBS Multicomputer System --- A.
L. Leiner, W. A. Notz, J. L. Smith, and A. Weinberger /
440 \\
\\
Section 3 Computers for Multiprocessing and Parallel
Processing / 446 \\
\\
Chapter 36 D825 --- A Multiple-computer System for
Command and Control --- James P. Anderson, Samuel A.
Hoffman, Joseph Shifman, and Robert J. Williams / 447
\\
[Chapter 22 Design of the B 5000 System ---- William
Lonergan and Paul King] \\
Chapter 37 A Survey of Problems and Preliminary Results
Concerning Parallel Processing and Parallel Processors
--- M. Lehman / 456 \\
\\
Section 4 Network Computers and Computer Networks / 470
\\
\\
Chapter 38 The RW-400: A New Polymorphic Data System
--- R. E. Porter / 477 \\
Chapter 39 Parallel Operation in the Control Data 6600
--- James E. Thornton / 489 \\
Chapter 40 Computer Network Examples / 504 \\
\\
Part 6 Computer Families \\
\\
Section 1 The IBM 701--7094 II Sequence, a Family by
Evolution / 515 \\
\\
Chapter 41 The IBM 7094 I, 11 / 517 \\
\\
Section 2 The SDS 910--9300 Series, a Planned Family /
542 \\
\\
Chapter 42 The SDS 910-9300 Series / 543 \\
\\
Section 3 The IBM System/360 --- A Series of Planned
Machines Which Span a Wide Performance Range / 561 \\
\\
Chapter 43 The Structure of System/360, Part I ---
Outline of the Logical Structure --- G. A. Blaauw and
F. P. Brooks, Jr. / 588 \\
Chapter 44 The Structure of System/360, Part II ---
System Implementations --- W. Y. Stevens / 602 \\
\\
Appendix PMS and ISP Notations / 607 \\
\\
General Conventions / 607 \\
\\
1 Basic Semantics / 608 \\
2 Metanotation / 608 \\
3 Basic Syntax / 609 \\
4 Commands: Assignments, Abbreviation, Variables, Forms
/ 609 \\
5 Indefinite Expressions / 610 \\
6 Lists and Sets / 611 \\
7 Definite Expressions / 611 \\
8 Attributes / 612 \\
9 Null Symbol and Optional Expression / 613 \\
10 Names / 613 \\
11 Numbers / 614 \\
12 Quantities, Dimensions, and Units / 615 \\
13 Boolean and Relations / 615 \\
\\
PMS Conventions / 615 \\
\\
1 Dimensions / 616 \\
2 General Units / 616 \\
3 Information Units / 616 \\
4 Component / 617 \\
5 Link (L) / 619 \\
6 Memory (M) / 620 \\
7 Switch (S) / 623 \\
8 Control (K) / 624 \\
9 Transducer (T) / 625 \\
10 Data-operations (D) / 626 \\
11 Processor (P) / 626 \\
12 Computer (C) / 628 \\
\\
ISP Conventions / 628 \\
\\
1 Data-types / 629 \\
2 Instruction / 631 \\
3 Operations / 632 \\
4 Processors / 635 \\
\\
Bibliography / 638 \\
Name Index / 653 \\
Machine and Organization Index / 656 \\
Subject Index / 661",
}
@Article{Berg:1971:SAO,
author = "R. O. Berg and L. L. Kinney",
title = "Serial Adders with Overflow Correction",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "6",
pages = "668--671",
month = jun,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223321",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:16 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671914",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Caprani:1971:ILR,
author = "Ole Caprani",
title = "Implementation of a Low Round-Off Summation Method",
journal = j-BIT,
volume = "11",
number = "3",
pages = "271--275",
month = sep,
year = "1971",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01931808",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Sat Nov 14 09:14:57 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=11&issue=3&spage=271",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "accurate floating-point summation; floating-point
arithmetic; rounding errors",
}
@Misc{Chen:1971:BAU,
author = "Tien Chi Chen",
title = "Binary arithmetic unit implementing a multiplicative
iteration for the exponential, logarithm, quotient and
square root functions",
howpublished = "United States Patent 3,631,230",
day = "28",
month = dec,
year = "1971",
bibdate = "Tue Jan 08 21:54:11 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.freepatentsonline.com/3631230.html",
abstract = "Apparatus and a method is described for efficiently
achieving arithmetic evaluations for functions such as
exponential, logarithm, quotient, and square root with
a minimum use of multiplications or divisions.
Basically, use is made of the fact that $ x(1 \pm
2^{-m}) $ can be evaluated by a shift followed by an
add. A pair of numbers $ (x_k, y_k) $ can represent a
function $ x : f(x) = g(x_k, y_k) $, such that $ g(l,
y_n) = y_n $ for logarithm, quotient and square root.
Then, multiplication by shifting is applied to $ x_k $
with suitable adjustments on $ y_k $, until $ x_k $ is
close to unity, at which time $ y_k $ represents the
desired answer. The exponential is computed by
essentially reversing the logarithm procedure. A
termination algorithm further improves accuracy. The
apparatus involves two registers for $ x_k $ and $ y_k
$, a local memory, an adder and a shift register.",
acknowledgement = ack-nhfb,
}
@Article{Chen:1971:BMS,
author = "Tien Chi Chen",
title = "A Binary Multiplication Scheme Based on Squaring",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "6",
pages = "678--680",
month = jun,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223325",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:16 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671918",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Misc{Chen:1971:DNC,
author = "Tien Chi Chen",
title = "Decimal Number Compression",
howpublished = "Internal IBM memo to Dr. Irving T. Ho.",
pages = "4",
day = "29",
month = mar,
year = "1971",
bibdate = "Fri Nov 28 16:24:59 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The fact that four bits can represent 16 different
states, but a decimal digit exploits only 10 of then
(0--9) has been a valid criticism against decimal
arithmetic.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Chen:1971:EAA,
author = "Tien Chi Chen",
title = "Efficient Arithmetic Apparatus and Method",
journal = j-IBM-TDB,
volume = "14",
number = "1",
pages = "328--330",
month = jun,
year = "1971",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Tue Jan 08 22:33:33 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
}
@InCollection{Clark:1971:SCP,
author = "N. W. Clark and W. J. Cody and H. Kuki",
title = "Self-Contained Power Routines",
crossref = "Rice:1971:MS",
pages = "399--415",
year = "1971",
bibdate = "Thu Sep 15 18:56:49 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Cody:1971:DHC,
author = "W. J. Cody",
title = "Desirable Hardware Characteristics for Scientific
Computation",
journal = j-SIGNUM,
volume = "6",
number = "1",
pages = "16--31",
month = jan,
year = "1971",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/1052614.1052616",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:49:57 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
xxtitle = "Hardware characteristics (pages missing from print)",
}
@InCollection{Cody:1971:SEF,
author = "W. J. Cody",
title = "Software for the Elementary Functions",
crossref = "Rice:1971:MS",
pages = "171--186",
year = "1971",
bibdate = "Thu Sep 15 18:56:47 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Dekker:1971:FPT,
author = "Theodorus J. Dekker",
title = "A Floating-Point Technique for Extending the Available
Precision",
journal = j-NUM-MATH,
volume = "18",
number = "3",
pages = "224--242",
month = jun,
year = "1971",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01397083",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "68A55",
MRnumber = "MR0299007 (45 \#8056)",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib;
Parallel/par.lin.alg.bib",
URL = "http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN362160546_0018",
abstract = "A technique is described for expressing multilength
floating-point arithmetic in terms of singlelength
floating point arithmetic, i.e. the arithmetic for an
available (say: single or double precision)
floating-point number system. The basic algorithms are
exact addition and multiplication of two singlelength
floating-point numbers, delivering the result as a
doublelength floating-point number. A straight-forward
application of the technique yields a set of algorithms
for doublelength arithmetic which are given as ALGOL 60
procedures.",
acknowledgement = ack-nhfb # " and " # ack-nj,
classification = "C5230 (Digital arithmetic methods)",
corpsource = "Math. Centre, Amsterdam, Netherlands",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "accurate floating-point summation; ALGOL 60
procedures; available precision; digital arithmetic;
double precision; multilength; single; single length
floating point arithmetic; subroutines",
remark = "Report MR 118/70, Computation Department, Mathematical
Centre, Amsterdam. Part of this research was done while
the author was visiting Bell Telephone Laboratories,
Murray Hill, New Jersey.",
treatment = "T Theoretical or Mathematical",
}
@Article{DeLong:1971:UPA,
author = "Howard DeLong",
title = "Unsolved Problems in Arithmetic",
journal = j-SCI-AMER,
volume = "224",
number = "3",
pages = "50--60",
month = mar,
year = "1971",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican0371-50",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Wed May 22 12:00:01 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciam1970.bib",
URL = "http://www.nature.com/scientificamerican/journal/v224/n3/pdf/scientificamerican0371-50.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@Article{Dutka:1971:SRD,
author = "Jacques Dutka",
title = "The Square Root of $2$ to $ 1, 000, 000 $ Decimals",
journal = j-MATH-COMPUT,
volume = "25",
number = "116",
pages = "927--930",
month = oct,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Gentleman:1971:OMC,
author = "W. Morven Gentleman",
title = "Optimal multiplication chains for computing a power of
a symbolic polynomial",
journal = j-SIGSAM,
volume = "??",
number = "18",
pages = "23--30",
month = apr,
year = "1971",
CODEN = "SIGSBZ",
DOI = "https://doi.org/10.1145/1093425.1093426",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Tue Jun 17 19:14:25 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper shows that in a certain model of symbolic
manipulation of algebraic formulae, the simple method
of computing a power of a symbolic polynomial by
repeated multiplication by the original polynomial is,
in essence, the optimal method.",
acknowledgement = ack-nhfb,
fjournal = "SIGSAM Bulletin",
issue = "18",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@TechReport{Ghest:1971:TCD,
author = "R. C. Ghest",
title = "A Two's Complement Digital Multiplier, the {Am25S05}",
type = "Technical report",
institution = "Advanced Micro Devices",
address = "Sunnyvale, CA, USA",
pages = "????",
year = "1971",
bibdate = "Fri Nov 09 18:50:36 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Ginsberg:1971:NID,
author = "Myron Ginsberg",
booktitle = "Proceedings of the First Annual Rocky Mountain
Symposium on Microprocessors",
title = "Numerical influences on the design of floating-point
arithmetic for microcomputers",
publisher = "????",
address = "????",
pages = "24--72",
year = "1971",
bibdate = "Fri Nov 09 18:52:22 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Glaser:1971:HBO,
author = "Anton Glaser",
title = "History of Binary and Other Nondecimal Numeration",
publisher = "Anton Glaser",
address = "Southampton, PA, USA",
pages = "ix + 196",
year = "1971",
ISBN = "0-9600324-1-X",
ISBN-13 = "978-0-9600324-1-9",
LCCN = "QA141.2 .G55",
bibdate = "Fri Mar 17 08:12:27 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "See also revised edition \cite{Glaser:1981:HBO}.",
acknowledgement = ack-nhfb,
author-dates = "1924--",
remark = "Based on the author's thesis, Temple University, with
title: History of modern numeration systems.",
subject = "Numeration; History",
tableofcontents = "Before Leibniz \\
Leibniz (1646--1716) \\
The rest of the 1700s \\
The nineteenth century \\
The twentieth century up to the computer age \\
Applications to computers \\
Contemporary literature",
}
@Article{Golub:1971:CAC,
author = "G. H. Golub and L. B. Smith",
title = "{Chebyshev} Approximation of Continuous Functions by a
{Chebyshev} System of Functions",
journal = j-CACM,
volume = "14",
number = "11",
pages = "737--746",
month = nov,
year = "1971",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Aug 15 09:54:14 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "ACM Algorithm 414.",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@TechReport{Haavie:1971:SMA,
author = "T. H{\aa}vie",
title = "Some Methods for Automatic Integration and their
Implementation on the {CERN CDC 65\slash 6600}
Computers",
type = "Report",
number = "CERN 71-26",
institution = "CERN",
address = "Geneva, Switzerland",
day = "1",
month = dec,
year = "1971",
bibdate = "Thu Jan 04 13:15:46 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://cds.cern.ch/record/190218/files/CERN-71-26.pdf",
abstract = "Two schemes for automatic integration using modified
Romberg and Clenshaw--Curtis quadratures are discussed.
The experience gained testing FORTRAN routines, using
both rounded and unrounded arithmetic, on a set of 20
test examples are reported.",
acknowledgement = ack-nhfb,
keywords = "automatic integration; CDC arithmetic; Clenshaw\slash
Curtis; Romberg; rounding corrections",
onlinedate = "iv + 43",
remark = "The report gives results, and recommendations, for
default (unrounded) and rounded arithmetic computation
in the peculiar arithmetic of the CDC 6000\slash 7000
family computers, for single precision (48-bit
significand, about 14 decimal digits) and double
precision (96-bit significand, almost 29 decimal
digits). Unlike Wirth's compiler work
\cite{Wirth:1972:PCG}, it does not get down to
instruction set details, or discuss the problems of
integer arithmetic.",
}
@Article{Honey:1971:CCD,
author = "D. W. Honey",
title = "Correspondence: Calculation of a double-length square
root from a double length number using single precision
techniques",
journal = j-COMP-J,
volume = "14",
number = "4",
pages = "443--443",
month = nov,
year = "1971",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:51:58 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/140443.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/tiff/443.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Kagan:1971:FPS,
author = "Claude A. R. Kagan",
title = "Floating point sub-language of a string language",
journal = j-SIGPLAN,
volume = "6",
number = "10",
pages = "20--22",
month = nov,
year = "1971",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/1317448.1317449",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sat Dec 2 08:35:10 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigplan1970.bib",
URL = "https://dl.acm.org/citation.cfm?id=1317449",
abstract = "The facilities for floating point computation within
the framework of a string language currently operating
on the PDP-10 at the Western Electric Company
Engineering Research Center are considered to be a
sublanguage. This sublanguage is accessed through use
of the * (asterisk) as a function marker in lieu of the
colon, and such use causes execution of all of the
available arithmetic functions as well as a family of
additional functions whose names are the same as those
used in Fortran. The list of functions that will
execute in this sublanguage is displayed through
execution of ** (LF), expression.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@InProceedings{Kahan:1971:SEA,
author = "W. M. Kahan",
title = "A Survey of Error Analysis",
crossref = "Freiman:1971:PIC",
pages = "1214--1239",
year = "1971",
MRclass = "65G05",
MRnumber = "MR0458845 (56 \#17045)",
bibdate = "Tue Aug 28 05:24:53 2001",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Information Processing 71",
URL = "http://dblp.uni-trier.de/db/conf/ifip/ifip71-2.html#Kahan71",
acknowledgement = ack-jr # " and " # ack-nhfb,
keywords = "accurate floating-point summation",
remark = "This paper contains the modified compensating
summation algorithm wherein `e = (temp - s) + y' is
replaced by `f = 0; if (sign(temp) == sign(y)) {f =
(0.46*s - s) + s} e = ((temp - f) - (s - f)) + y',
cited in e.g.,
\cite{Dalhquist:1974:NM,Higham:1993:AFP}.",
}
@Article{Kan:1971:EAD,
author = "E. Kan and J. Aggarwal",
title = "Error analysis of digital filter employing
floating-point arithmetic",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "18",
number = "6",
pages = "678--686",
month = nov,
year = "1971",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See correction \cite{Kan:1973:CEA}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "The error accumulation in a digital filter employing
floating-point arithmetic is studied. Sources of errors
are considered to originate from (1) roundoff in the
arithmetic operations, (2) quantization of both the
input and the initial states, and (3) \ldots{}",
}
@Article{Kingsbury:1971:DFU,
author = "N. G. Kingsbury and P. J. W. Rayner",
title = "Digital filtering using logarithmic arithmetic",
journal = j-ELECT-LETTERS,
volume = "7",
number = "2",
pages = "56--58",
day = "28",
month = jan,
year = "1971",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:19710039",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Mon May 30 07:32:20 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}
@Article{Krishnamurthy:1971:CTW,
author = "E. V. Krishnamurthy",
title = "Complementary Two-Way Algorithms for Negative Radix
Conversions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "5",
pages = "543--550",
month = may,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223288",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:14 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671881",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
}
@Article{Krishnamurthy:1971:EIR,
author = "E. V. Krishnamurthy",
title = "Economical Iterative and Range-Transformation Schemes
for Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "4",
pages = "470--472",
month = apr,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223270",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:14 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671863",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kuki:1971:FEP,
author = "H. Kuki and J. Ascoly",
title = "{FORTRAN} extended-precision library",
journal = j-IBM-SYS-J,
volume = "10",
number = "1",
pages = "39--61",
year = "1971",
CODEN = "IBMSA7",
ISSN = "0018-8670",
bibdate = "Thu Sep 15 18:51:32 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Systems Journal",
xxmonth = "(none)",
}
@InCollection{Kuki:1971:MFS,
author = "H. Kuki",
title = "Mathematical Function Subprograms for Basic System
Libraries\emdash Objectives, Constraints, and
Trade-Off",
crossref = "Rice:1971:MS",
pages = "187--199",
year = "1971",
bibdate = "Fri Sep 16 16:27:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Kulisch:1971:AAR,
author = "U. Kulisch",
title = "An axiomatic approach to rounded computations",
journal = j-NUM-MATH,
volume = "18",
number = "1",
pages = "1--17",
month = feb,
year = "1971",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01398455",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 16:12:48 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The present paper is intended to give an axiomatic
approach to rounded computations. A rounding is defined
as a monotone mapping of an ordered set into a subset,
which in general is called a lower respectively an
upper screen. The first chapter deals with roundings in
ordered sets. In the second chapter further properties
of roundings in linearly ordered sets are studied. The
third chapter deals with the two most important
applications, the approximation of the real arithmetic
on a finite screen and the approximation of the real
interval arithmetic on an upper screen. Beyond these
examples various further applications are possible.",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Kupka:1971:SRA,
author = "I. Kupka",
title = "Simulation of real arithmetic and real functions in
finite sets",
journal = j-NUM-MATH,
volume = "17",
number = "2",
pages = "143--152",
year = "1971",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C1220 (Simulation, modelling and identification);
C4110 (Error analysis in numerical methods)",
corpsource = "Univ. Hamburg, West Germany",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "error estimation; errors; estimation theory; finite
set; floating point arithmetic; real functions;
simulation",
language = "German",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Lindsay:1971:RAF,
author = "D. S. Lindsay",
title = "A rounded arithmetic {FORTRAN} compiler for {CDC 6000}
machines",
type = "Report",
number = "????",
institution = inst-BERKELEY-CS,
address = inst-BERKELEY-CS:adr,
pages = "????",
month = dec,
year = "1971",
bibdate = "Thu Jan 04 13:08:56 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "rounding corrections",
remark = "No copy of this report seems to be available online;
it is cited in \cite[p. 34]{Wirth:1972:PCG}. See the
remarks in that entry about the challenges of the CDC
arithmetic system.",
}
@Article{Majithia:1971:CAN,
author = "J. C. Majithia and R. Kitai",
title = "A Cellular Array for the Nonrestoring Extraction of
Square Roots",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "12",
pages = "1617--1618",
month = dec,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223191",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671784",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Majithia:1971:IAM,
author = "J. C. Majithia and R. Kitai",
title = "An Iterative Array for Multiplication of Signed Binary
Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "2",
pages = "214--216",
month = feb,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223216",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:12 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671809",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Malcolm:1971:AFP,
author = "Michael A. Malcolm",
title = "On Accurate Floating-Point Summation",
journal = j-CACM,
volume = "14",
number = "11",
pages = "731--736",
month = nov,
year = "1971",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/362854.362889",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65G05 (68-XX)",
MRnumber = "47 4434",
MRreviewer = "P. Brock",
bibdate = "Mon Jan 22 07:01:06 MST 2001",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm14.html#Malcolm71;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Stanford University, CA, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "accurate floating-point summation; digital arithmetic;
error analysis",
oldlabel = "Malcolm71",
treatment = "P Practical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Malcolm71",
}
@TechReport{Malcolm:1971:ARP,
author = "Michael A. Malcolm",
title = "Algorithm to reveal properties of floating-point
arithmetic",
institution = "Stanford University",
address = "Stanford, Ca.",
pages = "8",
year = "1971",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "AD-727 104",
acknowledgement = ack-nhfb,
keywords = "Algorithms.; Floating-point arithmetic.",
remark = "``STAN-CS-71-211.''",
}
@Article{Morris:1971:TFP,
author = "R. Morris",
title = "Tapered Floating Point: a New Floating-Point
Representation",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "12",
pages = "1578--1579",
month = dec,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223174",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671767",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Mullet:1971:NME,
author = "Gary M. Mullet and Tracy W. Murray",
title = "A New Method for Examining Rounding Error in
Least-Squares Regression Computer Programs",
journal = j-J-AM-STAT-ASSOC,
volume = "66",
number = "335",
pages = "496--498",
month = sep,
year = "1971",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:44 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314211;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib",
URL = "http://www.jstor.org/stable/2283514",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Nicoud:1971:IAR,
author = "Jean-Daniel Nicoud",
title = "Iterative Arrays for Radix Conversion",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "12",
pages = "1479--1489",
month = dec,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223160",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Oct 10 13:44:30 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The general study of the conversion of a number from
the radix p to the radix q number system leads to four
different algorithms for integers, and to four similar
ones for fractions. Most transform algorithms can be
implemented by iterative arrays of cells characterized
by simple equations. Such arrays are very attractive
with present-time large-scale integration technology.
Two kinds of cells, that is, two iterative arrays, are
sufficient for the near instantaneous conversion of
fixed-point numbers from radix p to radix q, or vice
versa. For the important special case of binary-decimal
conversion, the structure of the cells is studied, and
different realizations using the BCD code are
described. One of them is specially suited for an LSI
realization in MOS technology. The advantages of other
codes are discussed. In particular, the use of the
biquinary code allows the realization of the fastest
cells, with only one gate delay for each line of
cells.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "base conversion; binary-decimal conversion; cellular
arrays; code conversion; iterative arrays; large-scale
integration; MOS technology; number systems; radix
conversion algorithms",
}
@Article{Paker:1971:BFP,
author = "Y. Paker",
title = "A Binary Floating-Point Resistor",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "1",
pages = "7--11",
month = jan,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223074",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:11 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671667",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Paus:1971:FPA,
author = "Dag Paus",
title = "Floating point arithmetikk til {Nord-2B}",
type = "Hovedoppgave i fysikk",
institution = "Universitetet i Oslo",
address = "Oslo, Norway",
pages = "156",
year = "1971",
bibdate = "Thu May 09 08:11:14 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Norwegian",
}
@Article{Pawlak:1971:ACN,
author = "Z. Pawlak",
title = "Another Comment on {``Negative Radix Conversion''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "5",
pages = "587--587",
month = may,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223301",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:15 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Wadel:1971:CNR,Zohar:1970:NRC}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671894",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
}
@Article{Pezaris:1971:BBA,
author = "S. D. Pezaris",
title = "A 40ns 17-bit by 17-bit array multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "4",
pages = "442--447 (??)",
month = apr,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223261",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:12:55 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Pezaris:1971:NBB,
author = "S. D. Pezaris",
title = "A 40-ns 17-Bit by 17-Bit Array Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "4",
pages = "442--447",
month = apr,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223261",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:14 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671854",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Rhyne:1971:SPN,
author = "V. T. Rhyne",
title = "A Simple Postcorrection for Nonrestoring Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "2",
pages = "213--214",
month = feb,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223215",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:12 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671808",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@PhdThesis{Rothmaier:1971:BEF,
author = "B. Rothmaier",
title = "{Die Berechnung der elementaren Funktionen mit
beliebiger Genauigkeit} \toenglish {The Computation of
Elementary Functions with Arbitrary Accuracy}
\endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "??",
year = "1971",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Sarkar:1971:EPP,
author = "B. P. Sarkar and E. V. Krishnamurthy",
title = "Economic Pseudodivision Processes for Obtaining Square
Root, Logarithm, and Arctan",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "12",
pages = "1589--1593",
month = dec,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223178",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:22 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671771",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Schmookler:1971:HSD,
author = "Martin S. Schmookler and Arnold Weinberger",
title = "High speed decimal addition",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "8",
pages = "862--867",
month = aug,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223362",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 28 19:10:32 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Parallel decimal arithmetic capability is becoming
increasingly attractive with new applications of
computers in a multiprogramming environment. The direct
production of decimal sums offers a significant
improvement in addition over methods requiring decimal
correction. These techniques are illustrated in the
eight-digit adder which appears in the System/360 Model
195.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "decimal floating-point arithmetic",
}
@Article{Schonhage:1971:SMG,
author = "A. Sch{\"o}nhage and V. Strassen",
title = "{Schnelle Multiplikation gro{\ss}er Zahlen}.
({German}) [{Fast} multiplication of large numbers]",
journal = j-COMPUTING,
volume = "7",
number = "3--4",
pages = "281--292",
year = "1971",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Thu Jan 04 08:42:36 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
note = "Check pages??",
acknowledgement = ack-ec # " and " # ack-nhfb,
affiliation = "University, Konstanz, West Germany",
classification = "C5230",
description = "digital arithmetic",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
keywords = "algorithm; binary numbers; logical nets; multitape
Turing machines; product",
language = "German",
}
@Article{Shepherd:1971:RSL,
author = "B. J. Shepherd",
title = "Right Shift for Low-Cost Multiply and Divide",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "12",
pages = "1586--1589",
month = dec,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223177",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671770",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Stein:1971:IMA,
author = "Marvin L. Stein and William D. Munro",
title = "Introduction to machine arithmetic",
publisher = pub-AW,
address = pub-AW:adr,
pages = "viii + 295",
year = "1971",
LCCN = "QA76.5 .S752",
bibdate = "Fri Nov 9 19:20:08 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
subject = "Electronic digital computers; Arithmetic",
}
@Article{Stein:1971:SMA,
author = "M. L. Stein and W. D. Munro",
title = "Scaling Machine Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "6",
pages = "675--678",
month = jun,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223324",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:16 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671917",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Wadel:1971:CNR,
author = "L. B. Wadel",
title = "Comment on {``Negative Radix Conversion''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "5",
pages = "587--587",
month = may,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223300",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:15 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Pawlak:1971:ACN,Zohar:1970:NRC}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671893",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
}
@Article{Walker:1971:BS,
author = "R. J. Walker",
title = "Binary Summation",
journal = j-CACM,
volume = "14",
number = "6",
pages = "417--417",
month = jun,
year = "1971",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:27:52 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm14.html#Walker71;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Cornell University, Ithaca, NY, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "binary summation; digital arithmetic; floating point;
roundoff errors; space; storage",
oldlabel = "Walker71",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Walker71",
}
@InProceedings{Walther:1971:UAE,
author = "J. S. Walther",
title = "A unified algorithm for elementary functions",
crossref = "AFIPS:1971:ACP",
volume = "38",
pages = "379--385",
year = "1971",
bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Wlodarski:1971:FLN,
author = "J. Wlodarski",
title = "{Fibonacci} and {Lucas} Numbers Tend to Obey
{Benford's Law}",
journal = j-FIB-QUART,
volume = "9",
number = "1",
pages = "87--88",
month = feb,
year = "1971",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:33 MDT 2011",
bibsource = "http://www.fq.math.ca/9-1.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/9-1/wlodarski2.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@InProceedings{Yohe:1971:R,
author = "J. M. Yohe",
booktitle = "Proceedings of the 1971 Army Numerical Analysis and
Computers Conference",
title = "Rounding",
publisher = "US Army Research Office",
address = "Durham, NC, USA",
pages = "213--223",
year = "1971",
LCCN = "????",
bibdate = "Sun Dec 30 21:37:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "ARO-D Report 71-4",
acknowledgement = ack-nhfb,
}
@MastersThesis{Abdelmagid:1972:DFP,
author = "Mohamed Nabil Fouad Abdelmagid",
title = "Design of a floating point arithmetic unit",
type = "Thesis ({M.S.})",
school = "Illinois Institute of Technology",
address = "Chicago, IL.",
pages = "v + 60",
year = "1972",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Ahmad:1972:ISH,
author = "M. Ahmad",
title = "Iterative schemes for high speed division",
journal = j-COMP-J,
volume = "15",
number = "4",
pages = "333--336",
month = nov,
year = "1972",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:52:07 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/150333.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/333.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/334.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/335.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/336.tif",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Univ. Manchester, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "digital arithmetic; digital computers; high speed
division; iterative methods; iterative schemes;
multiplicative",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Bandyopadhyay:1972:IAM,
author = "S. Bandyopadhyay and S. Basu and A. K. Choudhury",
title = "An Iterative Array for Multiplication of Signed Binary
Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "8",
pages = "921--922",
month = aug,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009055",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:46 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009055",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Banerji:1972:TAR,
author = "D. K. Banerji and J. A. Brzozowski",
title = "On Translation Algorithms in Residue Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "12",
pages = "1281--1285",
month = dec,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1972.223499",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:48 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672092;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35066",
abstract = "This paper considers translation problems in residue
number systems. The conversion from a fixed-base
representation to a residue representation can be done
using residue adders only; we show that relatively
simple combinational logic can be used to replace one
level of residue addition. In the reverse translation
problem, we examine the conditions under which base
extension can be used to compute the fixed-base digits
from a residue code number, and we study the efficiency
of the algorithm.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "base extension; input translation; modular arithmetic;
output translation; residue arithmetic; residue number
systems",
}
@Article{Brakefield:1972:OFP,
author = "James C. Brakefield",
title = "An optimal floating point format",
journal = j-COMP-ARCH-NEWS,
volume = "1",
number = "4",
pages = "16--17",
month = oct,
year = "1972",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 12 09:41:08 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{Chen:1972:ACE,
author = "Tien Chi Chen",
title = "Automatic Computation of Exponentials, Logarithms,
Ratios and Square Roots",
journal = j-IBM-JRD,
volume = "16",
number = "4",
pages = "380--388",
month = jul,
year = "1972",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "65D20",
MRnumber = "49 \#1738",
bibdate = "Tue Mar 25 14:26:59 MST 1997",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.research.ibm.com/journal/rd/164/chen.pdf",
abstract = "It is shown how a relatively simple device can
evaluate exponentials, logarithms, ratios and square
roots for fraction arguments, employing only shifts,
adds, high-speed table lookups, and bit counting. The
scheme is based on the cotransformation of a number
pair $ (x, y) $ such that the $ F(x, y) = f(x_0) $ is
invariant; when $x$ is driven towards a known value $
x_w $, $y$ is driven towards the result. For an $N$-bit
fraction about $ N / 4 $ iterations are required, each
involving two or three adds; then a termination
algorithm, based on an add and an abbreviated multiply,
completes the process, for a total cost of about one
conventional multiply time. Convergence, errors and
simulation using APL are discussed.",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "IBM, San Jose, CA, USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "adds; APL; bit counting; convergence;
cotransformation; digital arithmetic; errors;
exponentials; high speed table; iteration; logarithms;
lookups; ratios; shifts; simulation; square roots;
termination algorithm",
reviewer = "F. Gotze",
treatment = "P Practical",
}
@Article{Chiang:1972:NAB,
author = "A. C. L. Chiang and I. S. Reed",
title = "Notes on the Arithmetic {BN} Modulo {A} Codes",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "8",
pages = "891--894",
month = aug,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009046",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:46 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009046",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Chien:1972:ECH,
author = "R. T. Chien and Se June Hong",
title = "Error Correction in High-Speed Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "5",
pages = "433--438",
month = may,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1972.223538",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672131",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Chinal:1972:SCP,
author = "J. P. Chinal",
title = "Some Comments on Postcorrections for Nonrestoring
Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "12",
pages = "1385--1394",
month = dec,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1972.223511",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:49 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672104",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{DeMori:1972:PSS,
author = "R. {De Mori} and A. Serra",
title = "A Parallel Structure for Signed-Number Multiplication
and Addition",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "12",
pages = "1453--1454",
month = dec,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1972.223525",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:49 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672118",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Fenwick:1972:BRD,
author = "Peter M. Fenwick",
title = "A Binary Representation for Decimal Numbers",
journal = j-AUSTRALIAN-COMP-J,
volume = "4",
number = "4",
pages = "146--149",
month = nov,
year = "1972",
CODEN = "ACMJB2",
ISSN = "0004-8917",
bibdate = "Fri Nov 28 11:31:38 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Australian Computer Journal",
keywords = "decimal floating-point arithmetic",
}
@Article{Fettweis:1972:CBM,
author = "A. Fettweis",
title = "On the connection between multiplier word length
limitation and roundoff noise in digital filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "19",
number = "5",
pages = "486--491",
month = sep,
year = "1972",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "It is shown that for digital filters there exists a
direct and an indirect connection between the
generation of roundoff noise by a multiplier and the
effect that the coefficient word length limitation of
this multiplier has upon the response \ldots{}",
}
@Article{Franklin:1972:ZDA,
author = "J. W. Franklin",
title = "Zoned Decimal Arithmetic",
journal = j-IBM-TDB,
volume = "15",
number = "7",
pages = "2123--2124",
month = dec,
year = "1972",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
keywords = "decimal floating-point arithmetic",
}
@Book{Goldstine:1972:CPN,
author = "Herman H. Goldstine",
title = "The Computer: {From Pascal} to {von Neumann}",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "xii + 378",
year = "1972",
ISBN = "0-691-02367-0; 0-691-08104-2",
ISBN-13 = "978-0-691-02367-0; 978-0-691-08104-5",
bibdate = "Mon Jun 06 19:17:03 2005",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/Matrix.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/sparse.linear.systems.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/TUBScsd/1972.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Second printing, 1973. Paperback edition 1980. Fifth
printing, 1993 with new preface. Reprint 2000 by Books
on Demand, Ann Arbor, MI, USA.",
acknowledgement = ack-nhfb,
descriptor = "Computer, ENIAC, Entwicklung, Geschichte, Pascal, Von
Neumann",
kwds = "book, history, computer",
}
@TechReport{Gosper:1972:HCF,
author = "R. W. Gosper",
title = "{HAKMEM} 101: Continued Fractions",
type = "Memo",
number = "AIM 239",
institution = "MIT AI Laboratory",
address = "Cambridge, MA, USA",
pages = "37--44",
year = "1972",
bibdate = "Fri Nov 30 06:37:23 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.inwap.com/pdp10/hbaker/hakmem/cf.html#item101a",
acknowledgement = ack-nhfb,
remark = "From the document: ``The familiar transcendental
functions of rational arguments also have simple
continued fractions, but these are generally not
regular and cannot be reconstructed from numerical
values by a simple algorithm, since nonregular
representations aren't unique. The point is, however,
that numbers like e, pi, sqrt(2), sin .5, sqrt(7)
arctan sqrt(7), etc. can be expressed to unlimited
precision by simple programs which produce the terms on
demand.'' Also: ``Rational number arithmetic often
loses because numerators and denominators grow so large
as to require icky multiprecision. Algorithms for
arithmetic on continued fractions seem generally
unknown. The next items describe how to arithmetically
combine continued fractions to produce new ones, one
term at a time.'' and ``Continued fractions let us
perform numerical calculations a little at a time
without ever introducing any error, such as roundoff or
truncation. As if this weren't enough, the calculations
provide automatic error analysis, and obviate most
forms of successive approximation.''",
}
@Article{Gregory:1972:CFP,
author = "James Gregory",
title = "A Comparison of Floating Point Summation Methods",
journal = j-CACM,
volume = "15",
number = "9",
pages = "838--838",
month = sep,
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:46:23 MST 2001",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Gregory72;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Argonne Nat. Lab., IL, USA",
descriptors = "Simulation; statistics; numeric calculation",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "accurate floating-point summation; comparison; digital
arithmetic; error; error propagation; floating point
summation methods; truncation",
oldlabel = "Gregory72",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Gregory72",
}
@Article{Gregory:1972:URA,
author = "Robert Todd Gregory",
title = "The use of residue arithmetic with automatic digital
computers",
journal = "Delta (Waukesha)",
volume = "3",
number = "2",
pages = "1--27",
year = "1972\slash 1973",
MRclass = "68A10",
MRnumber = "MR0321348 (47 \#9881)",
MRreviewer = "A. D. Booth",
bibdate = "Thu Nov 8 14:50:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Hallin:1972:PAF,
author = "T. G. Hallin and M. J. Flynn",
title = "Pipelining of Arithmetic Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "8",
pages = "880--886",
month = aug,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009044",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 18:57:52 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Heising:1972:MM,
author = "W. Heising and M. O. Rabin and Shmuel Winograd",
title = "Multiplication Method",
journal = j-IBM-TDB,
volume = "15",
number = "4",
pages = "1147--1148",
month = sep,
year = "1972",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Manual{IBM:1972:ISR,
author = "{International Business Machines Corporation}",
title = "{IBM System\slash 360} reference data: direct
evaluation of floating point numbers in hexadecimal:
debugging aid",
organization = "IBM Corporation",
address = "White Plains, NY, USA",
pages = "18",
year = "1972",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "IBM 360 (Computer)",
remark = "``GX20-1787-0.''",
}
@Article{Kamal:1972:HSM,
author = "A. A. Kamal and M. A. N. Ghannam",
title = "High-Speed Multiplication Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "9",
pages = "1017--1021",
month = sep,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009082",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:46 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009082",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Liu:1972:REF,
author = "B. Liu and M. {Van Valkenburg}",
title = "On roundoff error of fixed-point digital filters using
sign-magnitude truncation",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "19",
pages = "536--537",
month = sep,
year = "1972",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "This correspondence gives the statistical mean squared
error at the output of a digital filter due to roundoff
accumulation when fixed-point arithmetic with
sign-magnitude truncation is \ldots{}",
}
@Article{Loevenbruck:1972:CNR,
author = "A. P. Loevenbruck",
title = "Conversion of Number Representations",
journal = j-IBM-TDB,
volume = "15",
number = "7",
pages = "2148--2151",
month = dec,
year = "1972",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Article{Majithia:1972:CAE,
author = "J. C. Majithia",
title = "Cellular Array for Extraction of Squares and Square
Roots of Binary Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "9",
pages = "1023--1024",
month = sep,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009084",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:46 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009084",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Malcolm:1972:ARP,
author = "Michael A. Malcolm",
title = "Algorithms to Reveal Properties of Floating-Point
Arithmetic",
journal = j-CACM,
volume = "15",
number = "11",
pages = "949--951",
month = nov,
year = "1972",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355606.361870",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:14:16 1994",
bibsource = "Compendex database;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Malcolm72;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Gentleman:1974:MAR}.",
abstract = "Two algorithms are presented in the form of Fortran
subroutines. Each subroutine computes the radix and
number of digits of the floating-point numbers and
whether rounding or chopping is done by the machine on
which it is run. The methods are shown to work on any
``reasonable'' floating-point computer.",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
classification = "723",
corpsource = "Stanford University, CA, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "chopping; computer programming; computer programming
languages --- Fortran; digital arithmetic; digits;
floating point arithmetic; Fortran subroutines;
mathematical techniques --- Digital Arithmetic; number
of; properties; radix; rounding",
oldlabel = "Malcolm72",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Malcolm72",
}
@Article{Mandelbaum:1972:ECR,
author = "David Mandelbaum",
title = "Error correction in residue arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
pages = "538--545",
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009006",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "94A10 (94A20)",
MRnumber = "MR0345709 (49 \#10440)",
MRreviewer = "P. Deussen",
bibdate = "Thu Nov 8 14:50:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Manos:1972:CCA,
author = "Paul Manos and L. Richard Turner",
title = "Constrained {Chebyshev} approximations to some
elementary functions suitable for evaluation with
floating-point arithmetic",
type = "{NASA} Technical Note",
number = "TN D-6698",
institution = "NASA",
address = "Washington, DC, USA",
pages = "iii + 68",
month = mar,
year = "1972",
bibdate = "Mon May 22 11:27:24 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720010958_1972010958.pdf",
acknowledgement = ack-nhfb,
}
@MastersThesis{Maple:1972:FPA,
author = "Christopher Marion Maple",
title = "A floating point analog to digital and digital to
analog converter",
type = "Thesis ({B.S.})",
school = "Massachusetts Institute of Technology. Dept. of
Electrical Engineering",
address = "Cambridge, MA, USA",
pages = "18",
year = "1972",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Marino:1972:NAA,
author = "D. Marino",
title = "New Algorithms for the Approximate Evaluation in
Hardware of Binary Logarithms and Elementary
Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "21",
number = "12",
pages = "1416--1421",
month = dec,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1972.223516",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 08 08:05:51 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Matula:1972:NTF,
author = "David W. Matula",
title = "Number Theoretic Foundations of Finite Precision
Arithmetic",
crossref = "Zaremba:1972:ANT",
pages = "479--489",
year = "1972",
bibdate = "Fri Oct 19 22:58:55 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "base conversion; finite-precision rational arithmetic;
number theory; overflow; radix conversion; tape
updating problem",
}
@TechReport{Metropolis:1972:ABCa,
author = "N. Metropolis",
title = "Analyzed Binary Computing",
type = "Technical Report",
number = "LA-DC--72-783; CONF-720916--2",
institution = inst-LASL,
address = inst-LASL:adr,
pages = "4",
day = "12",
month = sep,
year = "1972",
bibdate = "Tue Mar 20 11:25:24 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=4647144&query_id=0",
acknowledgement = ack-nhfb,
}
@InProceedings{Metropolis:1972:ABCb,
author = "N. Metropolis",
title = "Analyzed Binary Computing",
crossref = "IEEE:1972:IAD",
pages = "81--84",
year = "1972",
bibdate = "Wed Mar 21 09:24:37 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A single format for the representation of numbers in a
computer is proposed to accommodate both exact and
inexact quantities. A consistent set of rules is
described for addition (subtraction), multiplication
and division of such quantities, both within their
separate types, as well as in combination. Error
correlation aside, the propagation of inherent errors
is monitored in operations with at least one imprecise
value. A definitive algorithm must, of course take into
account any correlations of inherent errors; these
correlations must be recognized and incorporated into
the algorithm by the numerical analyst, not by the
logical designer of the computer.",
acknowledgement = ack-nhfb,
}
@InProceedings{Metropolis:1972:ABCc,
author = "Nicholas C. Metropolis",
title = "Analyzed binary computing",
crossref = "IEEE:1972:ITS",
pages = "1--14",
year = "1972",
DOI = "https://doi.org/10.1109/ARITH.1972.6153912",
bibdate = "Tue Mar 5 08:31:37 MST 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6153912",
acknowledgement = ack-nhfb,
journal-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6148543",
}
@MastersThesis{Miller:1972:DFD,
author = "Peter Edwin Miller",
title = "The design of a floating-point, double-precision
arithmetic unit for the {Digital Equipment
Corporation}'s {PDP-9} computer",
type = "Thesis ({M.S.})",
school = "Ohio State University",
address = "Columbus, OH, USA",
pages = "83",
year = "1972",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Arithmetic --- Computer programs; PDP-9 (Computer)",
}
@InProceedings{Neely:1972:CSN,
author = "Peter M. Neely",
title = "On conventions for systems of numerical
representation",
crossref = "ACM:1972:PAA",
pages = "644--561",
year = "1972",
bibdate = "Fri Nov 28 11:28:06 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Present conventions for numeric representation are
considered inadequate to serve the needs of applied
computing. Thus an augmented digital number system is
proposed for use in programming languages and in
digital computers. Special symbols are proposed for
numbers too large, too small or too close to zero to be
represented in the normal digital number system, or
which are undefined. Properties of mappings among and
between digital number systems are used to justify the
augments chosen. Finally a suggestion is made for a new
floating point word format that will serve all the
above needs and will greatly extend the exponent range
of floating point numbers.",
acknowledgement = ack-nhfb,
}
@Article{Oberman:1972:FRM,
author = "R. M. M. Oberman",
title = "A Flexible Rate Multiplier Circuit with Uniform Pulse
Distribution Outputs",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "8",
pages = "896--899",
month = aug,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009048",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:46 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009048",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Paris:1972:MA,
author = "J. B. Paris",
title = "On models of arithmetic",
journal = j-LECT-NOTES-MATH,
volume = "255",
pages = "251--280",
year = "1972",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0059548",
ISBN = "3-540-05744-7 (print), 3-540-37162-1 (e-book)",
ISBN-13 = "978-3-540-05744-4 (print), 978-3-540-37162-5
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
MRclass = "02H05 (02H13)",
MRnumber = "0392552 (52 \#13369)",
MRreviewer = "W. Marek",
bibdate = "Fri May 9 19:07:09 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lnm1970.bib",
URL = "http://link.springer.com/chapter/10.1007/BFb0059548/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/BFb0059533",
book-URL = "http://www.springerlink.com/content/978-3-540-37162-5",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
}
@Article{Pettus:1972:IDC,
author = "C. Pettus",
title = "Indeterminate $ 0 \div 0 $ check in {APL}",
journal = j-SIGPLAN,
volume = "7",
number = "4",
pages = "40--41",
month = apr,
year = "1972",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Thu May 25 06:58:23 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "One unique feature of the APL system is the definition
$ (0 \div 0) = 1 $. Although there is obvious merit in
this decision, in real analysis $ (0 \div 0) $ is
indeterminate. If one wishes to be alerted to the fact
that a denominator is zero and does not want the result
$1$ if the numerator is also zero, one can replace the
expression $ X \div Y $ with $ X \times \div Y $. Then
if $X$ and $Y$ are both zero, a Domain Error will be
reported instead of yielding.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "floating-point arithmetic; zero divide",
}
@Article{Phillips:1972:ICF,
author = "C. Phillips",
title = "Instabilities caused by floating-point arithmetic
quantization",
journal = j-IEEE-TRANS-AUTOMAT-CONTR,
volume = "17",
number = "2",
pages = "242--243",
month = apr,
year = "1972",
CODEN = "IETAA9",
ISSN = "0018-9286 (print), 1558-2523 (electronic)",
ISSN-L = "0018-9286",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Automatic Control",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
summary = "It is shown that an otherwise stable digital control
system may become unstable due to signal quantization
if the controller operates on floating-point
arithmetic. Sufficient conditions for instability are
developed \ldots{}",
}
@Article{Pichat:1972:CSA,
author = "M. Pichat",
title = "Correction d'une Somme en Arithm{\'e}tique {\`a}
Virgule Flottante. ({French}) {[Correction of a Sum in
Floating-Point Arithmetic]}",
journal = j-NUM-MATH,
volume = "19",
number = "5",
pages = "400--406",
year = "1972",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sat Sep 17 18:30:51 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "From Douglas Priest:
(\path=Douglas.Priest@eng.sun.com=) writing in Usenet
newsgroup sci.math.num-analysis on 13 Sep 1994 16:04:56
GMT: ``\ldots{} An iterative algorithm for computing a
protracted sum to working precision by repeatedly
applying the sum-and-roundoff method.''",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
corpsource = "Conservatoire Nat. Arts M{\'e}tiers, Paris, France",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "accurate floating-point summation; correct rounding;
correction; digital arithmetic; floating point
arithmetic; rounding off law; sum; truncature with
guard digit",
language = "French",
treatment = "T Theoretical or Mathematical",
xxmonth = "(none)",
xxnumber = "(none)",
}
@Article{Ramamoorthy:1972:SPI,
author = "C. V. Ramamoorthy and James R. Goodman and K. H. Kim",
title = "Some Properties of Iterative Square-Rooting Methods
Using High-Speed Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "8",
pages = "837--847",
month = aug,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009039",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:45 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009039",
acknowledgement = ack-nj # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Randell:1972:ATO,
author = "Brian Randell",
title = "On {Alan Turing} and the origins of digital
computers",
type = "Technical report",
number = "33",
institution = "University of Newcastle upon Tyne, Computing
Laboratory",
address = "Newcastle upon Tyne, UK",
pages = "36",
year = "1972",
LCCN = "TK7888.3 .R35",
bibdate = "Wed Oct 13 09:24:25 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "University of Newcastle upon Tyne. Computing
Laboratory. Technical report series",
acknowledgement = ack-nhfb,
subject = "Von Neumann, John; Turing, Alan Mathison; Electronic
digital computers; History",
subject-dates = "1903--1957 (John von Neumann); 1912--1954 (Alan
Turing)",
}
@TechReport{Randell:1972:ODC,
author = "Brian Randell",
title = "The origins of digital computers: a bibliography",
type = "Technical report",
number = "38",
institution = "Computing Laboratory, University of Newcastle upon
Tyne",
address = "Newcastle upon Tyne, UK",
pages = "iii + 59",
year = "1972",
LCCN = "TK7888.3 .R35",
bibdate = "Wed Oct 13 09:24:25 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "University of Newcastle upon Tyne, Computing
laboratory. Technical report series",
acknowledgement = ack-nhfb,
subject = "Electronic digital computers; History; Bibliography",
}
@Article{Richman:1972:AEA,
author = "Paul L. Richman",
title = "Automatic Error Analysis for Determining Precision",
journal = j-CACM,
volume = "15",
number = "9",
pages = "813--817",
month = sep,
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65G05",
MRnumber = "47 2808",
bibdate = "Mon Jan 22 07:15:56 MST 2001",
bibsource = "Compendex database;
http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Richman72;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The problem considered is that of evaluating a
rational expression to within any desired tolerance on
a computer which performs variable-precision
floating-point arithmetic operations. An automatic
error analysis technique is given for determining,
directly from the results of a trial low-precision
interval arithmetic calculation, just how much
precision and data accuracy are required to achieve a
desired final accuracy. The technique given generalize
easily to the evaluation of many nonrational
expressions.",
acknowledgement = ack-nhfb,
classcodes = "B0290B (Error analysis in numerical methods); C4110
(Error analysis in numerical methods); C5230 (Digital
arithmetic methods)",
classification = "921",
corpsource = "Bell Telephone Labs. Inc., Denver, CO, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "automatic error analysis; control; digital arithmetic;
error analysis; floating point arithmetic; interval
arithmetic; mathematical techniques; precision;
precision control",
oldlabel = "Richman72",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Richman72",
}
@PhdThesis{Ripley:1972:PFP,
author = "Jerald Lester Ripley",
title = "On proofs of floating-point program correctness and a
measure of their relative efficiency",
type = "Thesis ({Ph.D.})",
school = "University of Oklahoma",
address = "????",
pages = "vi + 105",
year = "1972",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Numerical calculations.",
}
@Article{Rohl:1972:NCA,
author = "J. S. Rohl and J. A. Linn",
title = "A Note on Compiling Arithmetic Expressions",
journal = j-COMP-J,
volume = "15",
number = "1",
pages = "13--14",
month = feb,
year = "1972",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/15.1.13",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:49 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/15/1.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_01/;
https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/15/1/13.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_01/150013.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_01/tiff/13.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_01/tiff/14.tif",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques); C6150C (Compilers, interpreters
and other processors)",
corpsource = "Univ. Manchester, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "arithmetic expressions; compilers; compiling; data
handling; digital arithmetic; minimisation;
minimization; program; single accumulator; storing;
temporary",
treatment = "T Theoretical or Mathematical",
}
@Article{Samet:1972:CDL,
author = "P. A. Samet and D. W. Honey",
title = "Calculation of a Double-Length Square Root from
Double-Length Number using Single Precision
Techniques",
journal = j-COMP-J,
volume = "15",
number = "2",
pages = "116--116",
month = may,
year = "1972",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/15.2.116",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:49 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/15/2.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/15/2/116.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/tiff/116.tif",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Univ. Coll., London, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "digital arithmetic; double length; precision
techniques; single; square root",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Schulenberg:1972:RSS,
author = "Craig Schulenberg and James E. Kernan",
title = "Results of space shuttle computer floating-point
precision study",
type = "Report",
number = "E-2637",
institution = "M.I.T. Charles Stark Draper Laboratory",
address = "Cambridge",
pages = "various",
year = "1972",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic data processing --- Space trajectories.;
Reusable space vehicles.",
remark = "At head of title: Apollo guidance, navigation and
control.",
}
@Article{Schurmann:1972:MEA,
author = "A. Schurmann",
title = "On the minimum error in addition processes of positive
floating-point numbers",
journal = j-ZASTOS-MAT,
volume = "13",
pages = "351--366",
year = "1972--1973",
CODEN = "ZAMTAK",
MRclass = "65G05",
MRnumber = "48 3242",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Zastosowania Matematyki",
reviewer = "A. D. Booth",
}
@Article{Shaham:1972:NDA,
author = "Z. Shaham and Z. Riesel",
title = "A Note on Division Algorithms Based on
Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "5",
pages = "513--514",
month = may,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1972.223557",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672150",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Stallings:1972:CPM,
author = "W. T. Stallings and T. L. Boullion",
title = "Computation of Pseudoinverse Matrices Using Residue
Arithmetic",
journal = j-SIAM-REVIEW,
volume = "14",
number = "1",
pages = "152--163",
month = "????",
year = "1972",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1014005",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:06:35 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/14/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1972",
}
@Article{Stefanelli:1972:SHS,
author = "R. Stefanelli",
title = "A Suggestion for a High-Speed Parallel Binary
Divider",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "1",
pages = "42--55",
month = jan,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1972.223430",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jan 08 22:42:31 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "family of four procedures to compute the inverse $ 1 /
X $ of a given binary number $X$ normalized between 0.5
and 1 is described. The quotient is obtained in
redundant binary form, i.e., in a base 2 code in which
digits can assume any positive or negative integer
value. All methods here described can be implemented by
combinatorial networks; the dividers realized in this
way are very fast because all carry propagations take
place at the same time.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InCollection{Tung:1972:A,
author = "C. Tung",
title = "Arithmetic",
crossref = "Cardenas:1972:CS",
pages = "??--??",
year = "1972",
bibdate = "Sat May 18 14:39:14 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Urabae:1972:CEA,
author = "Minoru Urabae",
title = "Component-wise error analysis of iterative methods
practiced on a floating-point system",
type = "{MRC} Technical Summary Report",
number = "1268",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
pages = "57",
year = "1972",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Error analysis (Mathematics); Floating-point
arithmetic.; Iterative methods (Mathematics)",
remark = "``Received August 11, 1972.'' Sponsored by Army
Research Office, Durham, N.C.",
}
@Article{Varian:1972:LEB,
author = "Hal R. Varian",
title = "Letter to the {Editor}: {Benford's Law}",
journal = j-AMER-STAT,
volume = "26",
number = "3",
pages = "65--66",
month = jun,
year = "1972",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Fri Mar 30 11:34:37 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/amstat.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0003-1305%28197206%2926%3A3%3C62%3ALTTE%3E2.0.CO%3B2-Q",
abstract = "Around 1938 the physicist Frank Benford observed a
rather strange fact: tables of logarithms in libraries
tend to be dirtier at the beginning than at the end.
This indicated to Benford that people had more occasion
to calculate with numbers beginning with 1 or 2 than
with 8 or 9.\par
Benford also found that the frequency of the digit p
being the first digit of a decimal number was very
closely approximated by $ \log (p + 1) - \log p $
[i.e., $ \log (1 + 1 / p) $ ]. This has become known as
Benford's law.",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@TechReport{Wirth:1972:PCG,
author = "Niklaus Wirth",
title = "On ``{Pascal}'', Code Generation, and the {CDC 6000}
Computer",
type = "Report",
number = "STAN-CS-72-257",
institution = inst-STAN-CS,
address = inst-STAN-CS:adr,
pages = "i + 38",
month = feb,
year = "1972",
bibdate = "Thu Jan 04 12:57:12 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "``PASCAL'' is a general purpose programming language
with characteristics similar to ALGOL 60, but with an
enriched set of program- and data structuring
facilities. It has been implemented on the CDC 6000
computer. This paper discusses selected topics of code
generation, in particular the selection of instruction
sequences to represent simple operations on arithmetic,
Boolean, and powerset operands. Methods to implement
recursive procedures are briefly described, and it is
hinted that the more sophisticated solutions are not
necessarily also the best. The CDC 6000 architecture
appears as a frequent source of pitfalls and nuisances,
and its main trouble spots are scrutinized and
discussed.",
acknowledgement = ack-nhfb,
author-dates = "15 February 1934--1 January 2024",
remark = "This report contains an interesting discussion of the
problems for compiler writers with a hardware
arithmetic design that subsumes integer arithmetic
inside one's complement floating-point arithmetic, and
is unable to detect integer overflow. The CDC 6000 and
7000, and Burroughs 5000 and 6000 families, share some
of these difficulties.",
}
@Book{Young:1972:SNM,
author = "David M. Young and Robert Todd Gregory",
title = "A Survey of Numerical Mathematics",
publisher = pub-AW,
address = pub-AW:adr,
pages = "x + 492 (A1--A18 and B1--B14 and I1--I19)",
year = "1972",
ISBN = "0-201-08773-1, 0-486-65691-8 (Dover paperback)",
ISBN-13 = "978-0-201-08773-4, 978-0-486-65691-5 (Dover
paperback)",
LCCN = "QA297 .Y63 1972",
MRclass = "65-02",
MRnumber = "53 11954a",
bibdate = "Wed Jan 17 10:57:04 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "D. Greenspan",
tableofcontents = "1: Numerical Analysis as a Subject Area \\
1.1 Introduction \\
1.2 Some pitfalls in computation \\
1.3 Mathematical and computer aspects of an algorithm
\\
1.4 Numerical instability of algorithms and
ill-conditioned problems \\
1.5 Typical problems of interest to the numerical
analyst \\
1.6 Iterative methods \\
2: Elementary Operations with Automatic Digital
Computers \\
2.1 Introduction \\
2.2 Binary arithmetic \\
2.3 Conversion from base $D$ to base $B$ representation
\\
2.4 Representation of integers on a binary computer \\
2.5 Floating-point representations \\
2.6 Computer-representable numbers \\
2.7 Floating-point arithmetic operations \\
2.8 Fortran analysis of a floating-point number \\
2.9 Calculation of elementary functions \\
3: Surveillance of Number Ranges \\
3.1 Introduction \\
3.2 Allowable number ranges \\
3.3 Basic real arithmetic operations \\
3.4 The quadratic equation \\
3.5 Complex arithmetic operations \\
4: Solution of Equations \\
4.1 Introduction \\
4.2 Attainable accuracy \\
4.3 Graphical methods \\
4.4 The method of bisection \\
4.5 The method of false position \\
4.6 The secant method \\
4.7 General properties of iterative methods \\
4.8 Generation of iterative methods \\
4.9 The Newton method \\
4.10 Muller's method \\
4.11 Orders of convergence of iterative methods \\
4.12 Acceleration of the convergence \\
4.13 Systems of nonlinear equations \\
5: Roots of Polynomial Equations \\
5.1 Introduction \\
5.2 General properties of polynomials \\
5.3 The Newton method and related methods \\
5.4 Muller's method and Cauchy's method \\
5.5 Location of the roots \\
5.6 Root acceptance and refinement \\
5.7 Matrix related methods: the modified Bernoulli
method \\
5.8 Matrix related methods: the IP method \\
5.9 Polyalgorithms \\
5.10 Other methods \\
6: Interpolation and Approximation \\
6.1 Introduction \\
6.2 Linear interpolation \\
6.3 Convergence and accuracy of linear interpolation
\\
6.4 Lagrangian interpolation \\
6.5 Convergence and accuracy of Lagrangian
interpolation \\
6.6 Interpolation with equal intervals \\
6.7 Hermite interpolation \\
6.8 Limitations on polynomial interpolation: smooth
interpolation \\
6.9 Inverse interpolation \\
6.10 Approximation by polynomials \\
6.11 Least squares approximation by polynomials \\
6.12 Rational approximation \\
6.13 Trigonometric interpolation and approximation \\
6.14 Interpolation in two variables \\
7: Numerical Differentiation and Quadrature \\
7.1 Introduction \\
7.2 The method of undetermined weights \\
7.3 Numerical differentiation \\
7.4 Numerical quadrature --- equal intervals \\
7.5 The Euler--MacLaurin formula \\
7.6 Romberg integration \\
7.7 Error determination \\
7.8 Numerical quadrature --- unequal intervals \\
8: Ordinary Differential Equations \\
8.1 Introduction \\
8.2 Existence and uniqueness \\
8.3 Analytic methods \\
8.4 Integral equation formulation --- the Picard method
of successive approximations \\
8.5 The Euler method \\
8.6 Methods based on numerical quadrature \\
8.7 Error estimation for predictor-corrector methods
\\
8.8 A numerical example \\
8.9 Runge--Kutta methods \\
8.10 Methods based on numerical differentiation \\
8.11 Higher-order equations and systems of first-order
equations \\
8.12 The use of high-speed computers \\
Appendix A \\
Appendix B \\
Appendix C \\
Bibliography \\
Index",
}
@Article{Aird:1973:SUM,
author = "T. Aird and D. Dodson and E. Houstis and J. Rice",
title = "Statistics on the Use of Mathematical Subroutines from
a Computer Center Library",
journal = j-SIGNUM,
volume = "8",
number = "4",
pages = "8--9",
month = oct,
year = "1973",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Sep 1 10:14:44 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@MastersThesis{Anjoorian:1973:EME,
author = "Harry Anjoorian",
title = "An example of microprogrammed extended-precision
floating-point arithmetic",
type = "Thesis ({M.A.})",
school = "California State University, Chico",
address = "Chico, CA, USA",
pages = "ix + 94",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units.; Electronic
digital computers --- Design and construction.",
}
@Article{Atkins:1973:PCA,
author = "David E. {Atkins, III} and Harvey L. Garner",
title = "Preface: Computer Arithmetic: An Introduction and
Overview [{Second IEEE Symposium on Computer
Arithmetic, May 15--16, 1972, University of
Maryland}]",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "549--551",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009104",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009104;
http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Atkins.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Article{Avizienis:1973:AAE,
author = "Algirdas Avi{\v{z}}ienis",
title = "Arithmetic Algorithms for Error-Coded Operands",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "567--572",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009108",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Avizienis.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Book{Barna:1973:ICD,
author = "Arpad Barna and Dan I. Porat",
title = "Integrated Circuits in Digital Electronics",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xi + 483",
year = "1973",
ISBN = "0-471-05050-4",
ISBN-13 = "978-0-471-05050-6",
LCCN = "TK7868.D5 B43",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@Article{Barsi:1973:ECP,
author = "F. Barsi and P. Maestrini",
title = "Error Correcting Properties of Redundant Residue
Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "3",
pages = "307--315",
month = mar,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1973.223711",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:18 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672304;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35074",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "The error correcting properties of the redundant
residue number systems (RNS) are investigated through a
more natural a approach than was previously known. The
necessary and sufficient condition for the correction
of a given error affecting a single \ldots{}",
}
@Article{Baugh:1973:TCP,
author = "C. R. Baugh and B. A. Wooley",
title = "A Two's Complement Parallel Array Multiplication
Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "12",
pages = "1045--1047",
month = dec,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1973.223648",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:37 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See comments
\cite{Blankenship:1974:CTC,Kroft:1974:CTC}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672241",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Besslich:1973:MDS,
author = "P. W. Besslich and S. Raman",
title = "Multiplication, Division and Square Root Extraction
Methods for Electronic Desk Calculators",
journal = "Journal of the Institution of Telecommunication
Engineers (India)",
volume = "19",
number = "4",
month = apr,
year = "1973",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Brent:1973:PAV,
author = "Richard P. Brent",
title = "On the Precision Attainable with Various
Floating-Point Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "601--607",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009113",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:14:15 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Brent.pdf",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Article{Brent:1973:PEA,
author = "R. Brent and D. Kuck and K. Maruyama",
title = "The Parallel Evaluation of Arithmetic Expressions
Without Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "5",
pages = "532--534",
month = may,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1973.223757",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:23 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672350",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Cappa:1973:AIA,
author = "M. Cappa and V. C. Hamacher",
title = "An Augmented Iterative Array for High-Speed Binary
Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "2",
pages = "172--175",
month = feb,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1973.223680",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:15 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See comments \cite{Gardiner:1974:CAI}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672273",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Cody:1973:SDN,
author = "William J. {Cody, Jr.}",
title = "Static and Dynamic Numerical Characteristics of
Floating-Point Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "598--601",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009112",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:14:15 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Cody.pdf",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Article{Dorr:1973:REC,
author = "Fred W. Dorr and Cleve B. Moler",
title = "Roundoff error on the {CDC 6600\slash 7600}
computers",
journal = j-SIGNUM,
volume = "8",
number = "2",
pages = "24--26",
month = apr,
year = "1973",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:49:59 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Univ. California, Los Alamos, NM, USA",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "arithmetic; CDC 6600/7600 computers; computer; digital
arithmetic; program; roundoff error",
treatment = "P Practical; X Experimental",
}
@Article{Du:1973:CSS,
author = "Min-Wen Du and C. Dennis Weiss",
title = "Circuit Structure and Switching Function
Verification",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "618--625",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009116",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Du.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Article{Ercegovac:1973:REC,
author = "Milo{\v{s}} D. Ercegovac",
title = "Radix-16 Evaluation of Certain Elementary Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "561--566",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009107",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:15:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Ercegovac.pdf",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@TechReport{Erkio:1973:EAV,
author = "Hannu Erkio",
title = "An extension of {ALGOL} with variable precision
floating-point arithmetic",
type = "Series {A}. Report",
number = "1973/2",
institution = "University of Helsinki, Department of Computer
Science",
address = "Helsinki",
pages = "ii + 20",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ALGOL (Computer program language); Floating-point
arithmetic",
}
@Article{Fettweis:1973:RNA,
author = "A. Fettweis",
title = "Roundoff noise and attenuation sensitivity in digital
filters with fixed-point arithmetic",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "20",
number = "2",
pages = "174--175",
month = mar,
year = "1973",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "A general expression is established which relates the
output roundoff noise generated by a fixed-point
multiplier in a digital filter to the sensitivity of
the filter attenuation with respect to the
corresponding multiplier coefficient. It confirms
\ldots{}",
}
@Article{Gelenbe:1973:UAE,
author = "Erol Gelenbe",
title = "A Unified Approach to the Evaluation of a Class of
Replacement Algorithms",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "611--618",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009115",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Gelenbe.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Article{Green:1973:NTF,
author = "D. H. Green and R. G. Kelsch",
title = "Nonlinear Ternary Feedback Shift Registers",
journal = j-COMP-J,
volume = "16",
number = "4",
pages = "360--367",
month = nov,
year = "1973",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:52:16 MDT 2000",
bibsource = "Compendex database;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/160360.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/360.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/361.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/362.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/363.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/364.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/365.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/366.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/367.tif",
acknowledgement = ack-nhfb,
classcodes = "B1260 (Pulse circuits); B1265 (Digital electronics);
C5120 (Logic and switching circuits); C5230 (Digital
arithmetic methods)",
classification = "722",
corpsource = "Univ. Manchester Inst. Sci. Technol., UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "arithmetic; coding theory; communications; computers,
digital; digital arithmetic; digital computers;
feedback shift registers; functions; nonlinear;
polynomial domain representation; shift registers;
ternary",
treatment = "T Theoretical or Mathematical",
}
@Book{Hamming:1973:NMS,
author = "R. W. (Richard Wesley) Hamming",
title = "Numerical methods for scientists and engineers",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
edition = "Second",
pages = "ix + 721",
year = "1973",
ISBN = "0-07-025887-2",
ISBN-13 = "978-0-07-025887-7",
LCCN = "QA297 .H28 1973",
bibdate = "Fri Aug 20 09:12:08 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "International series in pure and applied mathematics",
acknowledgement = ack-nhfb,
subject = "Numerical analysis; Data processing",
}
@Article{Hwang:1973:RRS,
author = "W. G. Hwang and John Todd",
title = "A recurrence relation for the square root",
journal = j-J-APPROX-THEORY,
volume = "9",
pages = "299--306",
year = "1973",
CODEN = "JAXTAZ",
DOI = "https://doi.org/10.1016/0021-9045(73)90075-0",
ISSN = "0021-9045,1096-0430",
ISSN-L = "0021-9045",
MRclass = "65H05",
MRnumber = "373270",
MRreviewer = "L. Fox",
bibdate = "Sat Oct 21 14:25:01 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0271.65032",
acknowledgement = ack-nhfb,
author-dates = "John Todd (16 May 1911--21 June 2007)",
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
received = "19 April 1971",
ZBmath = "3426800",
}
@Article{Jacobsohn:1973:CDA,
author = "David H. Jacobsohn",
title = "A Combinatoric Division Algorithm for Fixed-Integer
Divisors",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "608--610",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009114",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Jacobsohn.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@TechReport{Kahan:1973:IAL,
author = "W. Kahan",
title = "Implementation of algorithms (lecture notes by {W. S.
Haugeland} and {D. Hough})",
type = "Technical report",
number = "20",
institution = "Department of Computer Science",
address = "Berkeley, CA, USA",
year = "1973",
bibdate = "Tue Aug 28 05:28:07 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
remark = "This paper contains the modified compensating
summation algorithm wherein `e = (temp - s) + y' is
replaced by `f = 0; if (sign(temp) == sign(y)) {f =
(0.46*s - s) + s} e = ((temp - f) - (s - f)) + y',
cited in e.g.,
\cite{Dalhquist:1974:NM,Higham:1993:AFP}. Kahan remarks
``The mysterious constant 0.46, which could perhaps be
any number between 0.25 and 0.50, and the fact that the
proof requires a consideration of known machines
designs, indicate that this algorithm is not an advance
in computer science.''",
}
@Article{Kan:1973:CEA,
author = "E. Kan and J. Aggarwal",
title = "Correction to {``Error Analysis of Digital Filters
Employing Floating-Point Arithmetic''}",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "20",
number = "5",
pages = "617--618",
month = sep,
year = "1973",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Kan:1971:EAD}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
}
@Article{Kanani:1973:NCS,
author = "Dhirubhai V. Kanani and Kenneth H. O'Keefe",
title = "A Note on Conditional-Sum Addition for Base $ - 2 $
Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "626--626",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009117",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:26 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009117;
http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Kanani.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2; negative base",
}
@Article{Kaneko:1973:LCO,
author = "T. Kaneko",
title = "Limit-cycle oscillations in floating-point digital
filters",
journal = j-IEEE-TRANS-AUDIO-ELECTROACOUST,
volume = "21",
number = "2",
pages = "100--106",
month = apr,
year = "1973",
CODEN = "ITADAS",
ISSN = "0018-9278 (print), 1558-2582 (electronic)",
ISSN-L = "0018-9278",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Audio and Electroacoustics",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8337",
summary = "In a digital filter realized with fixed-point
arithmetic, there is a peculiar phenomenon known as
limit-cycle oscillation, which is due to roundoff
errors. For floating-point arithmetic, it has been
conjectured that its amplitude is negligibly small,
\ldots{}",
}
@Article{Kaneko:1973:LRE,
author = "Toyohisa Kaneko and Bede Liu",
title = "On Local Roundoff Errors in Floating-Point
Arithmetic",
journal = j-J-ACM,
volume = "20",
number = "3",
pages = "391--398",
month = jul,
year = "1973",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/321765.321771",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "65G05",
MRnumber = "49 8318",
bibdate = "Tue Oct 09 10:18:49 2007",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A bound on the relative error in floating-point
addition using a single-precision accumulator with
guard digits is derived. It is shown that even with a
single guard digit, the accuracy can be almost as good
as that using a double-precision accumulator. A
statistical model for the roundoff error in
double-precision multiplication and addition is also
derived. The model is confirmed by experimental
measurements.",
acknowledgement = ack-nhfb # " and " # ack-nj,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
reviewer = "V. V. Ivanov",
}
@TechReport{Kent:1973:PDS,
author = "Jan G. Kent",
title = "Procedures for the description and simulation of
floating point instructions",
type = "Report",
number = "426",
institution = "Norwegian Computing Center",
address = "Oslo, Norway",
month = sep,
year = "1973",
bibdate = "Sat Jan 09 06:27:20 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Kent:1973:TDA,
author = "Jan G. Kent",
title = "Theoretical definition, analysis and comparison of
floating point instructions",
type = "Report",
number = "425",
institution = "Norwegian Computing Center",
address = "Oslo, Norway",
month = sep,
year = "1973",
bibdate = "Sat Jan 09 06:27:20 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Kielbasinski:1973:SAC,
author = "Andrzej Kie{\l}basi{\'n}ski",
title = "Summation algorithm with corrections and some of its
applications",
journal = j-MATH-STOS,
volume = "1",
pages = "22--41",
year = "1973",
bibdate = "Tue Aug 28 06:06:57 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "In Polish.",
acknowledgement = ack-nhfb,
fjournal = "Math. Stos.",
keywords = "accurate floating-point summation",
remark = "The author's name is correct [verified by a Polish
colleague who knows the author]: some references have
it incorrectly as Kie{\l}baszi{\'n}ski.",
}
@Article{Kinoshita:1973:GDS,
author = "E. Kinoshita and H. Kosako and Y. Kojima",
title = "General Division in the Symmetric Residue Number
System",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "2",
pages = "134--142",
month = feb,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1973.223674",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672267;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35073",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "In the residue number system, the arithmetic
operations of addition, subtraction, and multiplication
are executed in the same period of time without the
need for interpositional carry. There is a hope for
high-speed operation if residue arithmetic \ldots{}",
}
@Article{Kreifelts:1973:OBF,
author = "T. Kreifelts",
title = "{Optimale Basiswahl f{\"u}r eine
Gleitkomma-Arithmetik} \toenglish {Optimal Choice of
Basis for a Floating-Point Arithmetic} \endtoenglish",
journal = j-COMPUTING,
volume = "11",
number = "??",
pages = "353--363",
month = "????",
year = "1973",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Kreifelts:1973:OBG,
author = "Thomas Kreifelts",
title = "{Optimale Basiswahl f{\"u}r eine
Gleitkomma-Arithmetik}. ({German}) [{Optimal} Choice of
Basis for a Floating-Point Arithmetic]",
journal = j-COMPUTING,
volume = "11",
number = "4",
pages = "353--363",
month = dec,
year = "1973",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:51 MST 2001",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
note = "See correction \cite{Kreifelts:1975:OBF}.",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "Inst. Numerische Datenverarbeitung, Bonn, West
Germany",
classification = "723; 921; C5230",
description = "digital arithmetic",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Comput (Vienna/NY)",
keywords = "base; computer programming; correct rounding; floating
point arithmetic; mathematical techniques; optimal
choice; rounding errors",
language = "German",
}
@Article{Kuki:1973:SSA,
author = "H. Kuki and W. J. Cody",
title = "A Statistical Study of the Accuracy of Floating Point
Number Systems",
journal = j-CACM,
volume = "16",
number = "4",
pages = "223--230",
month = apr,
year = "1973",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68A20 (65G05)",
MRnumber = "51 2344",
MRreviewer = "I. Kaufmann",
bibdate = "Wed Aug 31 13:47:33 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents the statistical results of tests
of the accuracy of certain arithmetic systems in
evaluating sums, products and inner products, and
analytic error estimates for some of the computations.
The arithmetic systems studied are 6-digit hexadecimal
and 22-digit binary floating point number
representations combined with the usual chop and round
modes of arithmetic with various numbers of guard
digits, and with a modified round mode with guard
digits. In a certain sense, arithmetic systems
differing only in their use of binary or hexadecimal
number representations are shown to be approximately
statistically equivalent in accuracy. Further, the
usual round mode with guard digits is shown to be
statistically superior in accuracy to the usual chop
mode in all cases save one. The modified round mode is
found to be superior to the chop mode in all cases.",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
classification = "723",
corpsource = "Univ. Chicago, IL, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "accuracy; arithmetic; computer programming; digital
arithmetic; error analysis; floating point arithmetic;
floating point number systems; guard digits; number
representation; rounding; statistical study",
oldlabel = "KukiC73",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/KukiC73",
}
@Article{Larson:1973:HSM,
author = "R. H. Larson",
title = "High Speed Multiply Using Four Input Carry Save
Adder",
journal = j-IBM-TDB,
volume = "??",
number = "??",
pages = "2053--2054",
month = dec,
year = "1973",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Fri Jun 24 20:46:32 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Article{Larson:1973:MSM,
author = "R. H. Larson",
title = "Medium Speed Multiply",
journal = j-IBM-TDB,
volume = "??",
number = "??",
pages = "2055--2055",
month = dec,
year = "1973",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Fri Jun 24 20:42:28 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
}
@PhdThesis{Lee:1973:SFP,
author = "Keng Ho Lee",
title = "Survey of floating-point software arithmetics and
basic library mathematical functions",
type = "Thesis ({Ph.D.})",
school = "Glasgow University",
address = "Glasgow, Scotland",
year = "1973",
bibdate = "Thu May 09 08:34:15 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Majithia:1973:NBL,
author = "J. C. Majithia and D. Levan",
title = "A note on base-2 logarithm computations",
journal = j-PROC-IEEE,
volume = "61",
number = "10",
pages = "1519--1520",
month = oct,
year = "1973",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 18:05:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "The well-known methods of iteration used suitably can
yield a more accurate and rapidly convergent
computation for the values of many functions. One
typical example is the base-2 logarithm-antilogarithm
computation. Some recently proposed techniques
\ldots{}",
}
@TechReport{Malcolm:1973:MAP,
author = "Michael A. Malcolm",
title = "A machine-independent {ALGOL} procedure for accurate
floating-point summation",
type = "Technical report",
number = "STAN-CS-73-374",
institution = "Stanford University, Computer Science Department",
address = "Stanford, CA, USA",
pages = "6",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ALGOL (Computer program language)",
}
@PhdThesis{Malcolm:1973:PAF,
author = "Michael A. Malcolm",
title = "Part {I}: On accurate floating-point summation; Part
{II}: Computation of nonlinear spline functions",
type = "Thesis ({Ph.D.})",
school = "Department of Computer Science, Stanford University",
address = "Stanford, CA, USA",
pages = "ix + 129",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; Interpolation;
spline theory",
}
@Article{Marasa:1973:SSC,
author = "John D. Marasa and David W. Matula",
title = "A simulated study of correlated error propagation in
various finite-precision arithmetics",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "587--597",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009111",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon May 20 05:07:23 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Marasa.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Article{Metropolis:1973:ABC,
author = "Nicholas C. Metropolis",
title = "Analyzed Binary Computing",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "573--576",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009109",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Mar 21 09:24:37 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A single format for the representation of numbers in a
computer is proposed to accommodate both exact and
inexact quantities. A consistent set of rules is
described for addition (subtraction), multiplication,
and division of such quantities, both within their
separate types, as well as in combination. Error
correlation aside, the propagation of inherent errors
is monitored in operations with at least one imprecise
value. A definitive algorithm must, of course take into
account any correlations of inherent errors; these
correlations must be recognized and incorporated into
the algorithm by the numerical analyst, not by the
logical designer of the computer.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2; control of propagated errors; floating-point
representation; representation error; significant digit
arithmetic",
}
@Article{Metropolis:1973:SAC,
author = "N. Metropolis and Gian-Carlo Rota and S. Tanny",
title = "Significance arithmetic: the carrying algorithm",
journal = j-J-COMB-THEORY-A,
volume = "14",
pages = "386--421",
month = may,
year = "1973",
CODEN = "JCBTA7",
ISSN = "0097-3165 (print), 1096-0899 (electronic)",
ISSN-L = "0097-3165",
MRclass = "10A30 (02E10)",
MRnumber = "MR0321857 (48 \#222)",
MRreviewer = "R. L. Goodstein",
bibdate = "Thu Nov 8 14:50:22 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0259.00001",
abstract = "It has been remarked that, in mathematics, a
notational deficiency is often a symptom of conceptual
obscurity. The starting point of this work is one such
deficiency. In ordinary binary arithmetic, a number
ending in a string of ones, such as $ 0.0110111 \ldots
{} $ is equal to the number obtained by replacing the
digit zero next to the string of ones by the digit one,
and the string of succeeding ones by zeros; in the
example, $ 0.0111000 $",
acknowledgement = ack-nhfb,
fjournal = "Journal of Combinatorial Theory. Series A",
journal-URL = "http://www.sciencedirect.com/science/journal/00973165",
}
@Article{Mifsud:1973:AMP,
author = "Charles J. Mifsud and Michael J. Bohlen",
title = "Addendum to a Multiple-Precision Division Algorithm",
journal = j-CACM,
volume = "16",
number = "10",
pages = "628--??",
year = "1973",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:04:18 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#MifsudB73;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Mifsud:1970:MDA}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "MifsudB73",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/MifsudB73",
}
@Article{Newbery:1973:EAF,
author = "A. C. R. Newbery",
title = "Error Analysis for {Fourier} Series Evaluation",
journal = j-MATH-COMPUT,
volume = "27",
number = "123",
pages = "639--644",
month = jul,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "B0290B (Error analysis in numerical methods); C4110
(Error analysis in numerical methods)",
corpsource = "Univ. Kentucky, Lexington, KY, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "error analysis; evaluation; floating point; Fourier
series evaluation; numerical methods; polynomials;
recursive method; series (mathematics); trigonometric
polynomials",
treatment = "T Theoretical or Mathematical",
}
@Article{OKeefe:1973:RBE,
author = "Kenneth H. O'Keefe and John L. Wright",
title = "Remarks on Base Extension for Modular Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "9",
pages = "833--835",
month = sep,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009173",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:31 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009173",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@MastersThesis{Parker:1973:DHF,
author = "Tony Edwin Parker",
title = "Design of a hardware floating point processor for the
{PDP-8s}",
type = "Thesis ({B.S.})",
school = "Massachusetts Institute of Technology. Dept. of
Electrical Engineering",
address = "Cambridge, MA, USA",
pages = "19",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Paterson:1973:NNM,
author = "Michael S. Paterson and Larry J. Stockmeyer",
title = "On the Number of Nonscalar Multiplications Necessary
to Evaluate Polynomials",
journal = j-SIAM-J-COMPUT,
volume = "2",
number = "1",
pages = "60--66",
month = mar,
year = "1973",
CODEN = "SMJCAT",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
bibdate = "Mon Nov 29 10:57:40 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/2/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Theory/Matrix.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
kwds = "na, polynomial, complexity",
xxnote = "Cited in \cite{govl:89}.",
}
@Article{Pittnauer:1973:AA,
author = "E. Pittnauer",
title = "{Eine Aussage {\"u}ber Alternanten} \toenglish {??}
\endtoenglish",
journal = j-NUM-MATH,
volume = "23",
number = "??",
pages = "427--432",
month = "????",
year = "1973",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Pittnauer:1973:NPK,
author = "E. Pittnauer",
title = "{Numerische Polynomapproximation mit Knotenpolynomen}
\toenglish {Numerical Polynomial Approximations with
Knot Polynomials} \endtoenglish",
journal = j-NUM-MATH,
volume = "21",
number = "3",
pages = "256--263",
year = "1973",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
xxmonth = "(none)",
}
@Book{Randell:1973:ODC,
editor = "Brian Randell",
title = "The origins of digital computers: selected papers",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 464",
year = "1973",
ISBN = "0-387-06169-X, 3-540-06169-X",
ISBN-13 = "978-0-387-06169-6, 978-3-540-06169-4",
LCCN = "TK7888.3 .R36",
bibdate = "Wed Oct 13 09:24:25 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "See also later editions
\cite{Randell:1975:ODC,Randell:1982:ODC}.",
}
@Article{Richman:1973:VPE,
author = "Paul L. Richman",
title = "Variable-Precision Exponentiation",
journal = j-CACM,
volume = "16",
number = "1",
pages = "38--40",
month = jan,
year = "1973",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65D20",
MRnumber = "51 4631",
MRreviewer = "V. V. Ivanov",
bibdate = "Mon Jan 22 07:15:57 MST 2001",
bibsource = "Compendex database;
http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Richman73;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A previous paper presented an efficient algorithm,
called the Recomputation Algorithm, for evaluating a
rational expression to within any desired tolerance on
a computer which performs variable-precision arithmetic
operations. The Recomputation Algorithm can be applied
to expressions involving any variable-precision
operations having $ O(10^( - p) + \sum_i|E_i|) $ error
bounds, where $p$ denotes the operation's precision and
$ E_i $ denotes the error in the operation's $i$-th
argument. \par
This paper presents an efficient variable-precision
exponential operation with an error bound of the above
order. Other operations such as log, sin, and cos,
which have simple series expansions, can be handled
similarly.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
classification = "723; 921",
corpsource = "Bell Telephone Labs. Inc., Denver, CO, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "computer programming; digital arithmetic; error
analysis; exponential function; exponentiation;
interval arithmetic; mathematical programming; variable
precision; variable-precision",
oldlabel = "Richman73",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Richman73",
}
@Article{Robertson:1973:SIC,
author = "James E. Robertson and Kishor S. Trivedi",
title = "The status of investigations into computer hardware
design based on the use of continued fractions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "555--560",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009106",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 8 14:50:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Robertson.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2; continued fractions",
}
@Article{Roy:1973:ARC,
author = "P. K. Sinha Roy and C. L. Sheng",
title = "Author's Reply to Comments on {``Decomposition Method
of Determining Maximum Compatibles''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "627--627",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009119",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Sureshchander:1973:CDM}.",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Sureshchander.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@MastersThesis{Rubinfield:1973:FM,
author = "Louis P. Rubinfield",
title = "A floating-point macromodule",
type = "Thesis ({M.S.})",
school = "Washington University, Department of Electrical
Engineering",
address = "St. Louis, MO, USA",
pages = "vii + 111",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Design and
construction.",
}
@Article{Sankar:1973:AAN,
author = "P. V. Sankar and S. Chakrabarti and E. V.
Krishnamurthy",
title = "Arithmetic Algorithms in a Negative Base",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "2",
pages = "120--125",
month = feb,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1973.223671",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:14 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672264",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
}
@Article{Sankar:1973:DDA,
author = "P. V. Sankar and S. Chakrabarti and E. V.
Krishnamurthy",
title = "Deterministic Division Algorithm in a Negative Base",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "2",
pages = "125--128",
month = feb,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1973.223672",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:14 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672265",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
}
@Article{Schatte:1973:VMG,
author = "Peter Schatte",
title = "{Zur Verteilung der Mantisse in der
Gleitkommadarstellung einer Zufallsgr{\"o}{\ss}e}.
({German}) [Distribution of the mantissa in the
floating-point representation of a random variable]",
journal = j-Z-ANGE-MATH-MECH,
volume = "53",
number = "??",
pages = "553--565",
month = "????",
year = "1973",
CODEN = "ZAMMAX",
ISSN = "0044-2267 (print), 1521-4001 (electronic)",
ISSN-L = "0044-2267",
bibdate = "Mon Nov 14 16:35:28 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und
Mechanik}",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
language = "German",
}
@Article{Schmid:1973:BLIa,
author = "H. Schmid",
title = "{BCD} logic {I}: {BCD} -- logic of many uses",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "13",
pages = "90--95",
month = jun,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872 (print), 1944-9550 (electronic)",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 08 08:17:30 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
}
@Article{Schmid:1973:BLIb,
author = "H. Schmid",
title = "{BCD} logic {II}: {BCD} multiplication",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "14",
pages = "62--69",
month = jul,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872 (print), 1944-9550 (electronic)",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
}
@Article{Schmid:1973:BLIc,
author = "H. Schmid",
title = "{BCD} logic {III}: {BCD} division",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "15",
pages = "86--92",
month = jul,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872 (print), 1944-9550 (electronic)",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
}
@Article{Schmid:1973:BLId,
author = "H. Schmid",
title = "{BCD} logic {IV}: {BCD} decimal-point location",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "16",
pages = "80--84",
month = aug,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872 (print), 1944-9550 (electronic)",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
keywords = "decimal floating-point arithmetic",
}
@Article{Schmid:1973:BLVa,
author = "H. Schmid",
title = "{BCD} logic {V}: {BCD} square root",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "17",
pages = "62--69",
month = aug,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872 (print), 1944-9550 (electronic)",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
}
@Article{Schmid:1973:BLVb,
author = "H. Schmid",
title = "{BCD} logic {VI}: {BCD} logarithms and exponentials",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "18",
pages = "118--123",
month = sep,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872 (print), 1944-9550 (electronic)",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
}
@Article{Schmid:1973:BLVc,
author = "H. Schmid",
title = "{BCD} logic {VII}: {BCD} trig and hyperbolic
functions",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "19",
pages = "68--73",
month = sep,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872 (print), 1944-9550 (electronic)",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
}
@Article{Sentance:1973:FAB,
author = "W. A. Sentance",
title = "A Further Analysis of {Benford's Law}",
journal = j-FIB-QUART,
volume = "11",
number = "5",
pages = "490--494",
month = dec,
year = "1973",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:58:46 MDT 2011",
bibsource = "http://www.fq.math.ca/11-5.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/11-5/sentance.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Shea:1973:NDN,
author = "Dale D. Shea",
title = "On the Number of Divisions Needed in Finding the
Greatest Common Divisor",
journal = j-FIB-QUART,
volume = "11",
number = "5",
pages = "508--510",
month = dec,
year = "1973",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:58:46 MDT 2011",
bibsource = "http://www.fq.math.ca/11-5.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/11-5/shea.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Singh:1973:MOA,
author = "S. Singh and R. Waxman",
title = "Multiple Operand Addition and Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "2",
pages = "113--120",
month = feb,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1973.223670",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:14 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672263",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Sites:1973:FPS,
author = "Richard L. Sites",
title = "Floating point significance interrupt proposal",
journal = j-COMP-ARCH-NEWS,
volume = "2",
number = "1",
pages = "10--12",
month = jan,
year = "1973",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 12 09:40:28 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The purpose of this proposal is to aid numerical
analysts in observing the significance of results in
floating-point calculations. This proposal is not a
cure-all, but it does attempt to a first, high-payoff
step in understanding and analyzing floating-point
algorithms. This proposal is specifically for IBM
360/370 architecture, but the ideas are applicable to
all machines.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
remark = "The author observes that register clearing by
subtraction is common, and is one of the reasons that
``all IBM language processors execute with significance
masked off.'' He proposes suppressing the significance
interrupt in subtractions when both operands are
equal.",
}
@Article{Sjoding:1973:NVR,
author = "T. Sjoding",
title = "Noise variance for rounded two's complement product
quantization",
journal = j-IEEE-TRANS-AUDIO-ELECTROACOUST,
volume = "21",
number = "4",
pages = "378--380",
month = aug,
year = "1973",
CODEN = "ITADAS",
ISSN = "0018-9278 (print), 1558-2582 (electronic)",
ISSN-L = "0018-9278",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Audio and Electroacoustics",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8337",
summary = "The Halyo-McAlpine discrete model for product
quantization is reconstructed using an error variable
set having an even number of members. It is shown in
this case that the noise variance associated with a
continuous model becomes an upper rather \ldots{}",
}
@Article{Spira:1973:CTA,
author = "Philip M. Spira",
title = "Computation Times of Arithmetic and {Boolean}
functions in $ (d, r) $ circuits",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "552--555",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009105",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Spira.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Book{Stone:1973:DMS,
author = "Harold S. Stone",
title = "Discrete mathematical structures and their
applications",
publisher = "Science Research Associates",
address = "Chicago, IL, USA",
pages = "401",
year = "1973",
LCCN = "QA162 .S877d; QA162 .S77",
bibdate = "Fri Nov 9 19:24:02 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
series = "The SRA computer science series",
acknowledgement = ack-nhfb,
subject = "Algebra, Abstract; Group theory; Machine theory",
tableofcontents = "Foundations of discrete mathematics. \\
Groups. \\
The P\'olya theory of enumeration. \\
Applications of group theory to computer design. \\
Group codes. \\
Semigroups. \\
Finite-state machines. \\
Rings and fields. \\
Linear -finite-state machines. \\
Boolean algebra with applications to computer design.",
}
@Article{Sureshchander:1973:CDM,
author = "Sureshchander",
title = "Comments on {``Decomposition Method of Determining
Maximum Compatibles''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "627--627",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009118",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Roy:1973:ARC}.",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Sureshchander.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
xxnote = "Author has only a single name",
}
@Article{Swartzlander:1973:QSM,
author = "E. E. {Swartzlander, Jr.}",
title = "The Quasi-Serial Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "4",
pages = "317--321",
month = apr,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1973.223717",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672310",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@PhdThesis{Tanny:1973:SSA,
author = "Stephen Michael Tanny",
title = "Studies in Significance Arithmetic",
type = "{Ph.D.} thesis",
school = "Massachusetts Institute of Technology",
address = "Cambridge, MA, USA",
pages = "195",
year = "1973",
bibdate = "Tue Oct 22 06:18:19 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://search.proquest.com/pqdtglobal/docview/302720894",
acknowledgement = ack-nhfb,
remark = "Full text is not available in ProQuest.",
}
@Article{Urabe:1973:CEA,
author = "Minoru Urabe",
title = "Component-wise error analysis of iterative methods
practiced on a floating-point system",
journal = j-MEM-FAC-SCI-KYUSHU-UNIV-A,
volume = "27",
pages = "23--64",
year = "1973",
CODEN = "MFKAAF",
ISSN = "0373-6385 (print), 1883-2172 (electronic)",
ISSN-L = "0373-6385",
MRclass = "65H10",
MRnumber = "48 1457",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Memoirs of the Faculty of Science, Kyushu Imperial
University. Series A, Mathematics = Kyushu Teikoku
Daigaku Rigakubu kiyo",
reviewer = "D. C. Handscomb",
}
@PhdThesis{Wiatrowski:1973:DFP,
author = "Claude A. Wiatrowski",
title = "Design of a floating-point processor for digital
simulation",
type = "Thesis ({Ph.D.} - Electrical Engineering)",
school = "University of Arizona",
address = "Tucson, AZ, USA",
pages = "107",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units.; Computer storage
devices.",
}
@Article{Yau:1973:ECR,
author = "S. S.-S. Yau and Yu-Cheng Liu",
title = "Error Correction in Redundant Residue Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "1",
pages = "5--11",
month = jan,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1973.223594",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:11 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672187;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35069",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "Two error-correcting algorithms for redundant residue
number systems are presented, one for single
residue-error correction and the other for burst
residue-error correction. Neither algorithm requires
table lookup, and hence their implementation \ldots{}",
}
@TechReport{Yohe:1973:FFPa,
author = "J. M. Yohe",
title = "Foundations of floating point computer arithmetic",
type = "{MRC} Technical Summary Report",
number = "1302",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
pages = "25",
month = jan,
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A formal structure, within which computer arithmetic
operations may be defined, is described. Several
floating point arithmetic schemes are defined within
this context. The structure described in the paper
includes, as a sub-structure, the significance spaces
of Matula.",
acknowledgement = ack-nhfb,
keywords = "Computers.; Floating-point arithmetic.",
remark = "January 1973. Sponsored by Army Research Office,
Durham, NC, USA.",
}
@Article{Yohe:1973:IBS,
author = "J. M. Yohe",
title = "Interval Bounds for Square Roots and Cube Roots",
journal = j-COMPUTING,
volume = "11",
number = "1",
pages = "51--57",
year = "1973",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:51 MST 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-jr # " and " # ack-nhfb,
affiliation = "Univ. Wisconsin, Madison, WI, USA",
classification = "C5230",
description = "digital arithmetic; error analysis",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
keywords = "binary computers; cube roots; error analysis; interval
bounds; machine representable number; optimal upward
directed rounding; smallest machine representable
interval; square roots",
}
@Article{Yohe:1973:RFP,
author = "J. Michael Yohe",
title = "Roundings in Floating-Point Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "577--586",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009110",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:25 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009110;
http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Yohe.pdf",
abstract = "In this paper we discuss directed roundings and
indicate how hardware might be designed to produce
proper upward directed, downward directed, and certain
commonly used symmetric roundings. Algorithms for the
four binary arithmetic operations and for rounding are
presented, together with proofs of their correctness;
appropriate formulas for a priori error analysis of
these algorithms are presented. Some of the basic
applications of directed roundings are surveyed.",
acknowledgement = ack-jr # "\slash " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2; correct rounding; floating-point arithmetic",
}
@Book{Zacher:1973:HDG,
author = "H. J. Zacher",
title = "{Die Hauptschriften zur Dyadik von G. W. Leibniz: Ein
Beitr. zur Geschichte des bin{\"a}ren Zahlen-systems}.
({German}) [{The} main writings on the dyadic by {G. W.
Leibniz}: a contribution to the history of the binary
number system]",
publisher = "V. Klostermann",
address = "Frankfurt am Main, West Germany",
pages = "viii + 384",
year = "1973",
LCCN = "QA141.4.Z3; QA141.4.Z3 1973",
bibdate = "Fri Mar 17 09:19:21 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Ver{\"o}ffentlichungen des Leibniz-Archivs",
acknowledgement = ack-nhfb,
language = "German",
remark = "Selected original texts and correspondence in French,
German or Latin.",
subject = "Leibniz, Gottfried Wilhelm; Freiherr von; Yi jing;
Freiherr von,; Binary system (Mathematics); History;
Sources; Syst{\'e}me binaire (Math{\'e}matiques);
Histoire; Binary system (Mathematics)",
}
@Article{Zohar:1973:DCR,
author = "Shalhav Zohar",
title = "{A/D} Conversion for Radix ($ - 2$)",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "7",
pages = "698--701",
month = jul,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009137",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:28 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009137",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
}
@Article{Agrawal:1974:NCL,
author = "D. P. Agrawal",
title = "Negabinary carry-look-ahead adder and fast
multiplier",
journal = j-ELECT-LETTERS,
volume = "10",
number = "??",
pages = "312--313",
month = jul,
year = "1974",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Thu Nov 06 06:16:38 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "negative base",
}
@Article{Banerji:1974:NIM,
author = "D. K. Banerji",
title = "A Novel Implementation Method for Addition and
Subtraction in Residue Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "1",
pages = "106--109",
month = jan,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1974.223790",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:29 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672383;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35077",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "This correspondence describes an implementation scheme
for the operations of addition and subtraction in the
residue number systems. The method is based on the
property that the set of residues modulo m form a
finite group under addition and \ldots{}",
}
@Article{Banerji:1974:URA,
author = "D. K. Banerji",
title = "On the Use of Residue Arithmetic for Computation",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "12",
pages = "1315--1317",
month = dec,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.223855",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:38 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672448",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Barsi:1974:EDC,
author = "F. Barsi and P. Maestrini",
title = "Error Detection and Correction by Product Codes in
Residue Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "9",
pages = "915--924",
month = sep,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1974.224055",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:35 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672648;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35088",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "The arithmetic error detecting and correcting
capabilities of product (AN) codes in residue number
systems (RNS) are described. The redundancy necessary
and sufficient to allow single residue digit error
detection or correction is determined, under \ldots{}",
}
@Article{Bauer:1974:CGR,
author = "F. L. Bauer",
title = "Computational Graphs and Rounding Error",
journal = j-SIAM-J-NUMER-ANAL,
volume = "11",
number = "1",
pages = "87--96",
month = mar,
year = "1974",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0711010",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65G05",
MRnumber = "356482",
MRreviewer = "L. B. Rall",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
JSTOR database; Theory/auto.diff.bib",
note = "In memoriam George Forsythe.",
URL = "https://www.jstor.org/stable/2156433",
ZMID = "03527739",
ZMnumber = "0337.65028",
acknowledgement = ack-nhfb,
author-dates = "Friedrich (``Fritz'') Ludwig Bauer (10 June 1924--26
March 2015)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
referred = "[Char91a]; [Irim91a].",
}
@Article{Blankenship:1974:CTC,
author = "P. E. Blankenship",
title = "Comments on {``A Two's Complement Parallel Array
Multiplication Algorithm''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "12",
pages = "1327--1327",
month = dec,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.223862",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:38 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Baugh:1973:TCP,Kroft:1974:CTC}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672455",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Boyes:1974:BNS,
author = "J. D. Boyes",
title = "Binary Noise Sources Incorporating Modulo-{$N$}
Dividers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "5",
pages = "550--552",
month = may,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.223980",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:33 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672573",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Brent:1974:FEP,
author = "Barry Brent",
title = "Functional Equations with Prime Roots from Arithmetic
Expressions for {$ G_\alpha $}",
journal = j-FIB-QUART,
volume = "12",
number = "2",
pages = "199--207",
month = apr,
year = "1974",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:58:50 MDT 2011",
bibsource = "http://www.fq.math.ca/12-2.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/12-2/brent1.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Brown:1974:BDE,
author = "D. A. H. Brown",
title = "Biquinary Decimal Error Detection Codes with One, Two
and Three Check Digits",
journal = j-COMP-J,
volume = "17",
number = "3",
pages = "201--204",
month = aug,
year = "1974",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compendex database;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/201.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/202.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/203.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/204.tif",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
classification = "722; 723",
corpsource = "Royal Radar Establ., Malvern, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "biquinary decimal error detection codes; check digits;
computer systems, digital; computers --- Debugging;
decimal floating-point arithmetic; digital arithmetic;
error detection codes; polynomial coding",
treatment = "T Theoretical or Mathematical",
}
@Article{Brown:1974:SEC,
author = "D. A. H. Brown",
title = "Some Error Correcting Codes for Certain Transposition
and Transcription Errors in Decimal Integers",
journal = j-COMP-J,
volume = "17",
number = "1",
pages = "9--12",
month = feb,
year = "1974",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Nov 28 16:12:29 2003",
bibsource = "Compendex database;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/10.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/11.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/12.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/9.tif",
acknowledgement = ack-mfc # " and " # ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques)",
classification = "731",
corpsource = "Royal Radar Establ., Malvern, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "algorithm; block; codes, symbolic; cyclic; decimal
floating-point arithmetic; decimal integers; digital
arithmetic; error correcting codes; error correction
codes; modulus 11; transcription; transposition",
treatment = "P Practical",
}
@Article{Carta:1974:HLR,
author = "David G. Carta",
title = "Help!!: {The} Lost Reference: ({A} Modified {Newton}
Method for Square Roots)",
journal = j-SIGNUM,
volume = "9",
number = "4",
pages = "9--9",
month = oct,
year = "1974",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/1206085.1206086",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Jun 17 18:47:00 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Around 1970 I saw a journal article describing a
modified Newton iteration for square roots. It involved
changing the usual factor of 0.5 in $ x_{n + 1} = 0.5
(x_n + a / x_n) $ to $ c_n $ where $ c_n \rightarrow
0.5 $, thereby increasing the asymptotic rate of
convergence from $ e_{n + 1} = 0.5 e_n^2 $ to $ e_{n +
1} = 0.25 e_n^2 $.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@Article{Catlin:1974:MR,
author = "Paul A. Catlin",
title = "On the Multiplication of Recurrences",
journal = j-FIB-QUART,
volume = "12",
number = "4",
pages = "365--367",
month = dec,
year = "1974",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:58:54 MDT 2011",
bibsource = "http://www.fq.math.ca/12-4.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/12-4/catlin2.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Chakrabarti:1974:DCA,
author = "S. Chakrabarti",
title = "Divide-and-Correct Algorithm for Division in a
Negative Base",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "9",
pages = "981--983",
month = sep,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.224066",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:35 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672659",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Chan:1974:REM,
author = "O. Chan and E. Jury",
title = "Roundoff error in multidimensional generalized
discrete transforms",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "21",
number = "1",
pages = "100--108",
month = jan,
year = "1974",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "The analysis of rounding error in the one-dimensional
fast Fourier transform (FFT) is extended to a class of
generalized orthogonal transforms [1] with a common
fast algorithm similar to the FFT algorithm. This class
includes the BInary FOurier \ldots{}",
}
@Book{Dahlquist:1974:NM,
author = "Germund Dahlquist and {\AA}ke Bj{\"o}rck and Ned
Anderson",
title = "Numerical Methods",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xviii + 573",
year = "1974",
ISBN = "0-13-627315-7",
ISBN-13 = "978-0-13-627315-8",
LCCN = "QA297 .D131 1969",
bibdate = "Tue Dec 14 22:44:59 1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
note = "Translated by Ned Anderson.",
series = "Prentice-Hall Series in Automatic Computation",
acknowledgement = ack-nhfb,
shorttableofcontents = "1: Some General Principles of Numerical
Calculation / 1 \\
2: How to Obtain and Estimate Accuracy in Numerical
Calculations / 21 \\
3: Numerical Uses of Series / 60 \\
4: Approximation of Functions / 81 \\
5: Numerical Linear Algebra / 137 \\
6: Nonlinear Equations / 218 \\
7: Finite Differences with Applications to Numerical
Integration, Differentiation, and Interpolation / 255
\\
8: Differential Equations / 330 \\
9: Fourier Methods / 405 \\
10: Optimization / 422 \\
11: The Monte Carlo Method and Simulation / 448 \\
12: Solutions to Problems / 465 \\
13: Bibliography and Published Algorithms / 536 \\
Index by Subject to Algorithms, 1960--1970 / 548 \\
Appendix Tables / 563 \\
Index / 565",
tableofcontents = "Preface / xvii \\
Conventions / xix \\
1: Some General Principles of Numerical Calculation / 1
\\
1.1. Introduction / 1 \\
1.2. Some Common Ideas and Concepts in Numerical
Methods / 2 \\
1.3. Numerical Problems and Algorithms / 13 \\
1.3.1. Definitions / 13 \\
1.3.2. Recursive Formulas; Homer's Rule / 14 \\
1.3.3. An Example of Numerical Instability / 16 \\
2: How to Obtain and Estimate Accuracy in Numerical
Calculations / 21 \\
2.1. Basic Concepts in Error Estimation / 21 \\
2.1.1. Introduction / 21 \\
2.1.2. Sources of Error / 22 \\
2.1.3. Absolute and Relative Errors / 23 \\
2.1.4. Rounding and Chopping / 24 \\
2.2 Propagation of Errors / 26 \\
2.2.1. Simple Examples of Error Analysis / 26 \\
2.2.2. The General Formula for Error Propagation;
Maximum Error and Standard Error / 29 \\
2.2.3. On the Practical Application of Error Estimation
/ 34 \\
2.2.4. The Use of Experimental Perturbations / 36 \\
2.2.5. Automatic Control of Accuracy / 37 \\
2.3. Number Systems; Floating and Fixed Representation
/ 42 \\
2.3.1. The Position System / 42 \\
2.3.2. Floating and Fixed Representation / 43 \\
2.3.3. Floating Decimal Point / 44 \\
2.3.4. Fixed Decimal Point / 46 \\
2.3.5. Round-off Errors in Computation with Floating
Arithmetic Operations / 46 \\
2.4. Backward Error Analysis; Condition Numbers / 51
\\
2.4.1. Backward Error Analysis / 51 \\
2.4.2. Condition Numbers for Problems and Algorithms /
53 \\
2.4.3. Geometrical Illustration of Error Analysis / 56
\\
3: Numerical Uses of Series / 60 \\
3.1. Elementary Uses of Series / 60 \\
3.1.1. Simple Examples / 60 \\
3.1.2. Estimating the Remainder / 62 \\
3.1.3. Power Series / 65 \\
3.2. Acceleration of Convergence / 71 \\
3.2.1. Slowly Converging Alternating Series / 71 \\
3.2.2. Slowly Converging Series with Positive Terms /
73 \\
3.2.3. Other Simple Ways to Accelerate Convergence / 74
\\
3.2.4. Ill-Conditioned Series / 75 \\
3.2.5. Numerical Use of Divergent Series / 77 \\
4: Approximation of Functions / 81 \\
4.1. Basic Concepts in Approximation / 81 \\
4.1.1. Introduction / 81 \\
4.1.2. The Idea of a Function Space / 84 \\
4.1.3. Norms and Seminorms / 85 \\
4.1.4. Approximation of Functions as a Geometric
Problem in Function Space / 87 \\
4.2. The Approximation of Functions by the Method of
Least Squares / 88 \\
4.2.t. Statement of the Problems / 88 \\
4.2.2. Orthogonal Systems / 89 \\
4.2.3. Solution of the Approximation Problem / 92 \\
4.3. Polynomials / 97 \\
4.3.1. Basic Terminology; the Weierstrass Approximation
Theorem / 97 \\
4.3.2. Triangle Families of Polynomials / 98 \\
4.3.3. A Triangle Family and Its Application to
Interpolation / 99 \\
4.3.4. Equidistant Interpolation and the Runge
Phenomenon / 101 \\
4.4. Orthogonal Polynomials and Applications / 104 \\
4.4.1. Tchebycheff Polynomials / 104 \\
4.4.2. Tchebycheff Interpolation and Smoothing / 106
\\
4.4.3. General Theory of Orthogonal Polynomials / 108
\\
4.4.4. Legendre Polynomials and Gram Polynomials / 113
\\
4.5. Complementary Observations on Polynomial
Approximation / 117 \\
4.5.1. Summary of the Use of Polynomials / 117 \\
4.5.2. Some Inequalities for $E_n(f)$ with Applications
to the Computation of Linear Functionals / 120 \\
4.5.3. Approximation in the Maximum Norm / 124 \\
4.5.4. Economization of Power Series; Standard
Functions / 125 \\
4.5.5. Some Statistical Aspects of the Method of Least
Squares / 126 \\
4.6. Spline Functions / 131 \\
5: Numerical Linear Algebra / 137 \\
5,1. Introduction / 137 \\
5.2. Basic Concepts of Linear Algebra / 138 \\
5.2.1. Fundamental Definitions / 138 \\
5.2.2. Partitioned Matrices / 140 \\
5.2.3. Linear Vector Spaces / 141 \\
5.2.4. Eigenvalues and Similarity Transformations / 142
\\
5.2.5. Singular-Value Decomposition and Pseudo-Inverse
/ 143 \\
5.3. Direct Methods for Solving Systems of Linear
Equations / 146 \\
5.3.1. Triangular Systems / 146 \\
5.3.2. Gaussian Elimination / 147 \\
5.3.3. Pivoting Strategies / 150 \\
5.3.4. $L U$-Decomposition / 152 \\
5.3.5. Compact Schemes for Gaussian Elimination / 157
\\
5.3.6. Inverse Matrices / 159 \\
5.4. Special Matrices / 162 \\
5.4.1. Symmetric Positive-Definite Matrices / 162 \\
5.4.2. Band Matrices / 165 \\
5.4.3. Large-Scale Linear Systems / 168 \\
5.4.4. Other Sparse Matrices / 169 \\
5.5. Error Analysis for Linear Systems / 174 \\
5.5.1. An Ill-Conditioned Example / 174 \\
5.5.2. Vector and Matrix Norms / 175 \\
5.5.3. Perturbation Analysis / 176 \\
5.5.4. Rounding Errors in Gaussian Elimination / 177
\\
5.5.5. Scaling of Linear Systems / 181 \\
5.5.6. Iterative Improvement of a Solution / 183 \\
5.6. Iterative Methods / 188 \\
5.7. Overdetermined Linear Systems / 196 \\
5.7.1. The Normal Equations / 197 \\
5.7.2. Orthogonalization Methods / 201 \\
5.7.3. Improvement of Least-Squares Solutions / 204 \\
5.7.4. Least-Squares Problems with Linear Constraints /
205 \\
5.8. Computation of Eigenvalues and Eigenvectors / 208
\\
5.8.1. The Power Method / 209 \\
5.8.2. Methods Based on Similarity Transformations /
211 \\
5.8.3. Eigenvalues by Equation Solving / 215 \\
5.8.4. The $Q R$-Algorithm / 216 \\
6: Nonlinear Equations / 218 \\
6.1. Introduction / 218 \\
6.2. Initial Approximations; Starting Methods / 219 \\
6.2.1. Introduction / 219 \\
6.2.2. The Bisection Method / 220 \\
6.3. Newton--Raphson's Method / 222 \\
6.4. The Secant Method / 227 \\
6.4.1. Description of the Method / 227 \\
6.4.2. Error Analysis for the Secant Method / 228 \\
6.4.3. Regula Falsi / 230 \\
6.4.4. Other Related Methods / 230 \\
6.5. General Theory of Iteration Methods / 233 \\
6.6. Error Estimation and Attainable Accuracy in
Iteration Methods / 238 \\
6.6.1. Error Estimation / 238 \\
6.6.2. Attainable Accuracy; Termination Criteria / 240
\\
6.7. Multiple Roots / 242 \\
6.8. Algebraic Equations / 243 \\
6.8.1. Introduction / 243 \\
6.8.2. Deflation / 245 \\
6.8.3. Ill-Conditioned Algebraic Equations / 246 \\
6.9. Systems of Nonlinear Equations / 248 \\
6.9.1. Iteration / 249 \\
6.9.2. Newton--Raphson's Method and Some Modifications
/ 249 \\
6.9.3. Other Methods / 251 \\
7: Finite Differences with Applications to Numerical
Integration, Differentiation, and Interpolation / 255
\\
7.1. Difference Operators and Their Simplest Properties
/ 255 \\
7.2. Simple Methods for Deriving Approximation Formulas
and Error Estimates / 263 \\
7.2.1. Statement of the Problems and Some Typical
Examples / 263 \\
7.2.2, Repeated Richardson Extrapolation / 269 \\
7.3. Interpolation / 275 \\
7.3.1. Introduction / 275 \\
7.3.2. When is Linear Interpolation Sufficient? / 276
\\
7.3.3. Newton's General Interpolation Formula / 277 \\
7.3.4. Formulas for Equidistant Interpolation / 279 \\
7.3.5. Complementary Remarks on Interpolation / 282 \\
7.3.6. Lagrange's Interpolation Formula / 284 \\
7.3.7. Hermite Interpolation / 285 \\
7.3.8. Inverse Interpolation / 286 \\
7.4. Numerical Integration / 290 \\
7.4.1. The Rectangle Rule, Trapezoidal Rule, and
Romberg's Method / 291 \\
7.4.2. The Truncation Error of the Trapezoidal Rule /
293 \\
7.4.3. Some Difficulties and Possibilities in Numerical
Integration / 294 \\
7.4.4. The Euler--Maclaurin Summation Formula / 297 \\
7.4.5. Uses of the Euler--Maclaurin Formula / 300 \\
7.4.6. Other Methods for Numerical Integration / 302
\\
7.5. Numerical Differentiation / 307 \\
7.6. The Calculus of Operators / 311 \\
7.6.1. Operator Algebra / 311 \\
7.6.2. Operator Series with Applications / 312 \\
7.7. Functions of Several Variables / 318 \\
7.7.1. Working with One Variable at a Time / 319 \\
7.7.2. Rectangular Grids / 319 \\
7.7.3. Irregular Triangular Grids / 322 \\
8: Differential Equations / 330 \\
8.1. Theoretical Background / 330 \\
8.1.1. Initial-Value Problems for Ordinary Differential
Equations / 330 \\
8.1.2. Error Propagation / 333 \\
8.1.3. Other Differential Equation Problems / 337 \\
8.2. Euler's Method, with Repeated Richardson
Extrapolation / 338 \\
8.3. Other Methods for Initial-Value Problems in
Ordinary Differential Equations / 342 \\
8.3.1. The Modified Midpoint Method / 342 \\
8.3.2. The Power-Series Method / 345 \\
8.3.3. Runge--Kutta Methods / 346 \\
8.3.4. Implicit Methods / 347 \\
8.3.5. Stiff Problems / 349 \\
8.3.6. Control of Step Size / 350 \\
8.3.7. A Finite-Difference Method for a Second-Order
Equation / 352 \\
8.4. Orientation on Boundary and Eigenvalue Problems
for Ordinary Differential Equations / 359 \\
8.4.1. Introduction / 359 \\
8.4.2. The Shooting Method / 359 \\
8.4.3. The Band Matrix Method / 361 \\
8.4.4. Numerical Example of an Eigenvalue Problem / 363
\\
8.5. Difference Equations / 367 \\
8.5.1. Homogeneous Linear Difference Equations with
Constant Coefficients / 368 \\
8.5.2. General Linear Difference Equations / 370 \\
8.5.3. Analysis of a Numerical Method with the Help of
a Test Problem / 372 \\
8.5.4. Linear Multistep Methods / 375 \\
8.6. Partial Differential Equations / 383 \\
8.6.1. Introduction / 383 \\
8.6.2. An Example of an Initial-Value Problem / 384 \\
8.6.3. An Example of a Boundary-Value Problem / 389 \\
8.6.4. Methods of Undetermined Coefficients and
Variational Methods / 392 \\
8.6.5. Finite-Element Methods / 395 \\
8.6.6. Integral Equations / 397 \\
9: Fourier Methods / 405 \\
9.1. Introduction / 405 \\
9.2. Basic Formulas and Theorems in Fourier Analysis /
406 \\
9.2.1. Functions of One Variable / 406 \\
9.2.2. Functions of Several Variables / 411 \\
9.3. Fast Fourier Analysis / 413 \\
9.3.1. An Important Special Case / 413 \\
9.3.2. Fast Fourier Analysis, General Case / 414 \\
9.4. Periodic Continuation of a Nonperiodic Function /
417 \\
9.5. The Fourier Integral Theorem / 419 \\
10: Optimization / 422 \\
10.1. Statement of the Problem, Definitions, and Normal
Form / 422 \\
10.2. The Simplex Method / 426 \\
10.3. Duality / 435 \\
10.4. The Transportation Problem and Some Other
Optimization Problems / 436 \\
10.5. Nonlinear Optimization Problems / 438 \\
10.5.1. Basic Concepts and Introductory Examples / 438
\\
10.5.2. Line Search / 440 \\
10.5.3. Algorithms for Unconstrained Optimization / 441
\\
10.5.4. Overdetermined Nonlinear Systems / 443 \\
10.5.5. Constrained Optimization / 444 \\
11: The Monte Carlo Method and Simulation / 448 \\
11.1. Introduction / 448 \\
11.2. Random Digits and Random Numbers / 449 \\
11.3. Applications; Reduction of Variance / 455 \\
11.4. Pseudorandom Numbers / 463 \\
12: Solutions to Problems / 465 \\
13: Bibliography and Published Algorithms / 536 \\
13.1. Introduction / 536 \\
13.2. General Literature in Numerical Analysis / 536
\\
13.3. Tables, Collections of Formulas, and Problems /
539 \\
13.4. Error Analysis and Approximation of Functions /
540 \\
13.5. Linear Algebra and Nonlinear Systems of Equations
/ 541 \\
13.6. Interpolation, Numerical Integration, and
Numerical Treatment of Differential Equations / 543 \\
13.7. Optimization; Simulation / 545 \\
13.8. Reviews, Abstracts and Other Periodicals / 547
\\
13.9. Survey of Published Algorithms / 548 \\
Index by Subject to Algorithms, 1960--1970 / 548 \\
Appendix Tables / 563 \\
Index / 565",
}
@Article{Davis:1974:USN,
author = "R. L. Davis",
title = "Uniform Shift Networks",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "3",
pages = "317--322",
month = mar,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224214",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 10:48:43 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Fateman:1974:PMP,
author = "Richard J. Fateman",
title = "Polynomial Multiplication, Powers, and asymptotic
Analysis: {Some} Comments",
journal = j-SIAM-J-COMPUT,
volume = "3",
number = "3",
pages = "196--213",
month = "????",
year = "1974",
CODEN = "SMJCAT",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
bibdate = "Mon Nov 29 10:57:57 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/3/3;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Theory/auto.diff.bib; Theory/Comp.Alg.1.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
referred = "[Bren78a].",
}
@Article{Fettweis:1974:PFP,
author = "A. Fettweis",
title = "On properties of floating-point roundoff noise",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "22",
number = "2",
pages = "149--151",
month = apr,
year = "1974",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "The probability density and related properties of the
relative error due to rounding after floating-point
arithmetic operations can be computed from the
distributions of the mantissa and its absolute error.
Various results obtained, in particular, \ldots{}",
}
@Article{Fischer:1974:FLI,
author = "Michael J. Fischer and Larry J. Stockmeyer",
title = "Fast on-line integer multiplication",
journal = j-J-COMP-SYS-SCI,
volume = "9",
number = "3",
pages = "317--331",
month = dec,
year = "1974",
CODEN = "JCSSBM",
DOI = "https://doi.org/10.1016/S0022-0000(74)80047-4",
ISSN = "0022-0000 (print), 1090-2724 (electronic)",
ISSN-L = "0022-0000",
bibdate = "Tue Jan 29 15:25:28 MST 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcompsyssci.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022000074800474",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computer and System Sciences",
journal-URL = "http://www.sciencedirect.com/science/journal/00220000",
}
@MastersThesis{Fischer:1974:FPP,
author = "David Michael Fischer",
title = "Floating point processor for teleoperator studies",
type = "Thesis ({M.S.})",
school = "Massachusetts Institute of Technology. Dept. of
Mechanical Engineering",
address = "Cambridge, MA, USA",
pages = "35 + 14",
year = "1974",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Gardiner:1974:CAI,
author = "A. B. Gardiner",
title = "Comments on {``An Augmented Iterative Array for High
Speed Division''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "3",
pages = "326--327",
month = mar,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.223931",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:31 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Cappa:1973:AIA}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672524",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Gentleman:1974:MAR,
author = "W. Morven Gentleman and Scott B. Marovich",
title = "More on Algorithms that Reveal Properties of Floating
Point Arithmetic Units",
journal = j-CACM,
volume = "17",
number = "5",
pages = "276--277",
month = may,
year = "1974",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/360980.361003",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:43:47 MST 2001",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#GentlemanM74;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Malcolm:1972:ARP}.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Univ. Waterloo, Ont., Canada",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "algorithms; base of the arithmetic; digital
arithmetic; floating point arithmetic units; high
level; languages; trailing digits",
oldlabel = "GentlemanM74",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/GentlemanM74",
}
@Book{Hildebrand:1974:INA,
author = "Francis Begnaud Hildebrand",
title = "Introduction to numerical analysis",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
edition = "Second",
pages = "xiii + 669",
year = "1974",
ISBN = "0-07-028761-9",
ISBN-13 = "978-0-07-028761-7",
LCCN = "QA297 .H54 1974",
bibdate = "Fri Aug 20 09:19:58 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "International series in pure and applied mathematics",
acknowledgement = ack-nhfb,
remark = "Reprinted in \cite{Hildebrand:1987:INA}.",
subject = "Numerical analysis",
}
@Article{Hill:1974:RFF,
author = "Bruce M. Hill",
title = "The rank-frequency form of {Zipf}'s law",
journal = j-J-AM-STAT-ASSOC,
volume = "69",
number = "348",
pages = "1017--1026",
month = dec,
year = "1974",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
MRclass = "62E15",
MRnumber = "0426242 (54 \#14188)",
MRreviewer = "S. M. Samuels",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
ZMnumber = "Zbl 0301.60011",
acknowledgement = ack-nhfb,
classification = "B0240 (Probability and statistics); C1140
(Probability and statistics)",
corpsource = "Department of Statistics, University of Michigan, Ann
Arbor, MI, USA",
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
keywords = "Bose--Einstein allocation; distribution; random
processes; rank frequency form; statistics; Zipf's
law",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Hull:1974:LFM,
author = "T. E. Hull and J. J. Hofbauer",
title = "Language facilities for multiple precision floating
point computation, with examples, and the description
of a preprocessor",
type = "Technical report",
number = "63",
institution = "University of Toronto, Department of Computer
Science",
address = "Toronto, ON, Canada",
pages = "vi + 84",
year = "1974",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic; Electronic digital
computers --- Programming",
}
@Article{Kinoshita:1974:FPA,
author = "Eisuke Kinoshita and Hideo Kosako and Yoshiaki
Kojima",
title = "Floating-Point Arithmetic Algorithms in the Symmetric
Residue Number System",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "1",
pages = "9--20",
month = jan,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1974.223772",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "68A10",
MRnumber = "50 9042",
bibdate = "Tue Jul 12 11:27:29 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672365;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35077",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
reviewer = "M. S. Cheema",
summary = "The residue number system is an integer number system
and is inconvenient to represent numbers with
fractional parts. In the symmetric residue system, a
new representation of floating-point numbers and
arithmetic algorithms for its addition, \ldots{}",
}
@Article{Kroft:1974:CTC,
author = "D. Kroft",
title = "Comments on {``A Two's Complement Parallel Array
Multiplication Algorithm''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "12",
pages = "1327--1328",
month = dec,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.223863",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:38 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Baugh:1973:TCP,Blankenship:1974:CTC}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672456",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Kulisch:1974:PCC,
author = "U. Kulisch",
title = "Formalization and implementation of floating-point
arithmetics",
crossref = "Panagiotopoulos:1974:PCC",
pages = "328--369",
year = "1974",
MRclass = "65G05",
MRnumber = "57 14392",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "R. H. Bartels",
}
@Article{Ling:1974:CSA,
author = "Robert F. Ling",
title = "Comparison of several algorithms for computing sample
means and variances",
journal = j-J-AM-STAT-ASSOC,
volume = "69",
number = "348",
pages = "859--866",
month = dec,
year = "1974",
CODEN = "JSTNAL",
DOI = "https://doi.org/10.1080/01621459.1974.10480219",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:46 MST 2012",
bibsource = "Distributed/QLD.bib; Distributed/QLD/1974.bib;
http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314230;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib;
Theory/Matrix.bib",
URL = "http://www.jstor.org/stable/2286154;
https://www.tandfonline.com/doi/abs/10.1080/01621459.1974.10480219;
https://www.tandfonline.com/doi/pdf/10.1080/01621459.1974.10480219",
acknowledgement = ack-nhfb,
country = "USA",
date = "13/05/93",
descriptors = "Simulation; statistics; numeric calculation",
enum = "7605",
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
keywords = "mean; standard deviation; stat; updating; variance",
location = "SEL: Wi",
remark = "This is an early paper on the numerical difficulties
associated with two important statistical algorithms.
See also entry \cite{McCullough:2019:WTS} in
fparith.bib that shows that even after 45 years, some
statistics code in database software remains poor.",
revision = "16/01/94",
xxtitle = "Comparison of Several Algorithms for Computing Means
and Variances",
}
@Article{Linnainmaa:1974:ASK,
author = "Seppo Linnainmaa",
title = "Analysis of Some Known Methods of Improving the
Accuracy of Floating-Point Sums",
journal = j-BIT,
volume = "14",
number = "2",
pages = "167--202",
month = jun,
year = "1974",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01932946",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65G05",
MRnumber = "MR0483373 (58 \#3381)",
bibdate = "Fri Dec 08 13:05:19 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=14&issue=2&spage=167",
acknowledgement = ack-nj,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "accurate floating-point summation; floating-point
arithmetic; rounding errors",
reviewer = "H. Ratschek",
}
@InCollection{Metropolis:1974:SAA,
author = "N. Metropolis and Gian-Carlo Rota",
booktitle = "Studies in numerical analysis (papers in honour of
{Cornelius Lanczos} on the occasion of his 80th
birthday)",
title = "Significance arithmetic---on the algebra of binary
strings",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "241--251",
year = "1974",
MRclass = "02F43 (68A15)",
MRnumber = "MR0354335 (50 \#6815)",
MRreviewer = "Stephen Tanny",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0311.65031",
acknowledgement = ack-nhfb,
}
@InProceedings{Miller:1974:CCN,
author = "Webb Miller",
title = "Computational complexity and numerical stability",
crossref = "ACM:1974:CRS",
pages = "317--322",
year = "1974",
bibdate = "Wed Nov 24 12:46:29 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Manual{Moon:1974:MRM,
author = "David A. Moon",
title = "{MacLISP} Reference Manual",
organization = "MIT Project MAC",
address = "Cambridge, MA, USA",
month = apr,
year = "1974",
bibdate = "Wed Jan 29 16:47:55 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "From \cite{Steele:2004:RHP}: ``In early 1971, he
[White] began to analyze the machine-language algorithm
used in the implementation of MacLisp (described in
this report) to convert PDP-10 floating-point numbers
into decimal notation.''",
}
@Article{Neumaier:1974:REV,
author = "A. Neumaier",
title = "{Rundungsfehleranalyse Einiger Verfahren Zur Summation
Endlicher Summen}. ({German}) [{Rounding} error
analysis of a method for summation of finite sums]",
journal = j-Z-ANGE-MATH-MECH,
volume = "54",
pages = "39--51",
year = "1974",
CODEN = "ZAMMAX",
ISSN = "0044-2267 (print), 1521-4001 (electronic)",
ISSN-L = "0044-2267",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-jr,
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und
Mechanik}",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
keywords = "accurate floating-point summation",
language = "German",
}
@Article{Newbery:1974:EAP,
author = "A. C. R. Newbery",
title = "Error Analysis for Polynomial Evaluation",
journal = j-MATH-COMPUT,
volume = "28",
number = "127",
pages = "789--793",
month = jul,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "B0290B (Error analysis in numerical methods); B0290D
(Functional analysis); C4110 (Error analysis in
numerical methods); C4120 (Functional analysis)",
corpsource = "Univ. Kentucky, Lexington, KY, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "analysis; Chebyshev; computable error bound; error
analysis; floating point error; function evaluation;
Horner's scheme; polynomial evaluation; polynomials",
treatment = "T Theoretical or Mathematical",
}
@MastersThesis{Prezas:1974:FPA,
author = "Pericles Panos Prezas",
title = "Floating point arithmetic unit",
type = "Thesis ({M.S.})",
publisher = "The author",
school = "Illinois Institute of Technology",
address = "Chicago, IL.",
pages = "ix + 77",
year = "1974",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Rauscher:1974:MUX,
author = "Tomlinson G. Rauscher",
title = "Microprogramming the {AN\slash UYK-17(XB-1)(V)} signal
processing element signal processing arithmetic unit",
journal = j-SIGMICRO,
volume = "5",
number = "2",
pages = "29--63",
month = apr,
year = "1974",
CODEN = "SIGMDJ",
DOI = "https://doi.org/10.1145/1217157.1217160",
ISSN = "0163-5751, 1050-916X",
ISSN-L = "0163-5751",
bibdate = "Fri Apr 16 10:27:17 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
URL = "https://dl.acm.org/doi/10.1145/1217157.1217160",
abstract = "The AN/UYK-17(XB-1)(V) Signal Processing Element (SPE)
is a high performance computer system being developed
at the Naval Research Laboratory for radar, sonar, and
communication applications. To perform signal
processing tasks efficiently, the SPE comprises
multiple functional units that execute different
processes in parallel. Due to the inherent parallelism
in signal processing tasks, horizontal microprograms
are used to control the functional units [references 5
and 6]. This report overviews the SPE, describes the
Signal Processing Arithmetic Unit (SPAU) in detail,
discusses ANIMIL --- the microprogramming language for
representing SPAU microprograms, and illustrates the
use of the ANIMIL translator with a simple
microprogram. Companion documents describe the SPAU
simulator program (reference 3) and the formal syntax
and semantics of the ANIMIL language (reference 4).",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMICRO Newsletter",
journal-URL = "https://dl.acm.org/loi/sigmicro",
}
@Article{Renner:1974:RRN,
author = "K. Renner and S. Gupta",
title = "Reduction of roundoff noise in wave digital filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "21",
number = "2",
pages = "305--310",
month = mar,
year = "1974",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "Roundoff noise generated by arithmetic operations in a
digital-filter computational sequence is undesirable in
that it serves to distort the true signal at the
output. Furthermore, coefficient wordlength is directly
related to the generated noise. \ldots{}",
}
@Book{Scaife:1974:SNA,
editor = "B. K. P. Scaife",
title = "Studies in numerical analysis",
publisher = "The Royal Irish Academy",
address = "Dublin, Ireland",
pages = "xxii + 333",
year = "1974",
MRclass = "65-06",
MRnumber = "MR0347039 (49 \#11759)",
bibdate = "Thu Nov 8 19:02:54 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Papers in honour of Cornelius Lanczos on the occasion
of his 80th birthday",
acknowledgement = ack-nhfb,
}
@Book{Schmid:1974:DC,
author = "Hermann Schmid",
title = "Decimal Computation",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xi + 266",
year = "1974",
ISBN = "0-471-76180-X",
ISBN-13 = "978-0-471-76180-8",
LCCN = "QA75 .S34",
bibdate = "Thu Sep 1 10:14:05 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted \cite{Schmid:1983:DC}.",
acknowledgement = ack-nj,
keywords = "decimal floating-point arithmetic",
}
@Article{Sites:1974:SBD,
author = "R. L. Sites",
title = "Serial Binary Division by Ten",
journal = j-IEEE-TRANS-COMPUT,
volume = "23",
number = "12",
pages = "1299--1301",
month = dec,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.223849",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Aug 07 18:02:35 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A technique is presented for dividing a positive
binary integer by ten, in which the bits of the input
are presented serially, low-order bit first. A complete
division by ten is performed in two word times
(comparable to the time needed for two serial
additions). The technique can be useful in serial
conversions from binary to decimal, or in scaling
binary numbers by powers of 10.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "decimal arithmetic",
}
@Book{Sterbenz:1974:FPC,
author = "Pat H. Sterbenz",
title = "Floating Point Computation",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xiv + 316",
year = "1974",
ISBN = "0-13-322495-3",
ISBN-13 = "978-0-13-322495-5",
LCCN = "QA76.8.I12 S771 1974",
MRclass = "68A05 (65G05)",
MRnumber = "50 1556",
bibdate = "Sat May 29 08:01:36 1999",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
series = "Prentice-Hall Series in Automatic Computation.",
acknowledgement = ack-nj # " and " # ack-nhfb,
keywords = "Compiling (Electronic computers); Computation by
computer systems --- Floating point representation;
Floating-point arithmetic; IBM 360 (Computer) ---
Programming",
remark = "From p. 116: ``There is general agreement that the
mantissas of floating-point numbers are not uniformly
distributed. [See Hamming (1962)
[\cite{Hamming:1962:NMS}], Pinkham (1961)
[Pinkham:1961:DFS], or Knuth (1969) [Knuth:1969:SNM].]
Instead, it is customary to assume that they are
distributed logarithmically, that is, that the
probability density function is
$$ (3.12.9) f(m) = \frac {1}{m \ln r}, \qquad r^{-1}
\leq m \leq 1. $$
This assumption is based on the following observations:
First, this distribution reproduces itself under
multiplication, but a uniform distribution does not.
[See Hamming (1962) [\cite{Hamming:1962:NMS}] and
Exercise 20.] A second justification is based on the
fact that many of the numbers that arise in computation
represent measurable quantities such as lengths,
forces, etc., and it is reasonable to believe that the
distribution of the mantissas of such quantities is
independent of the units in which they are measured.
Pinkham (1961) shows that this leads to the conclusion
that the distribution of mantissas must be
logarithmic.''",
reviewer = "F. J. Murray",
tableofcontents = "Preface / ix \\
1. Floating-Point Number Systems / 1 \\
1.1 Fixed-Point Calculation / 1 \\
1.2 Floating-Decimal Representation of Numbers / 4 \\
1.3 Floating-Decimal Arithmetic / 6 \\
1.4 Floating-Point Number Systems / 9 \\
1.5 FP(r, p, c) and FP(r, p, R) / 12 \\
1.6 Laws of Algebra / 14 \\
1.7 Inequalities in FP(r,p, c) / 21 \\
1.8 FP(r, p, clq) / 22 \\
1.9 The Solution of a * x = b in FP(r,p, c) / 29 \\
1.10 Division / 33 \\
Exercises / 35 \\
2. Floating-Point Overflow and Underflow / 39 \\
2.1 Bounds for Exponents / 39 \\
2.2 $\Omega$-Zero Fixup / 41 \\
2.3 Interrupt / 44 \\
2.4 Messages and Tests / 46 \\
2.5 ON OVERFLOW and ON UNDERFLOW in PL/I / 49 \\
2.6 Example / 50 \\
2.7 Counting Mode / 57 \\
2.8 Gradual Underflow / 59 \\
2.9 Imprecise Interrupt / 61 \\
2.10 Changing the Treatment of Spill / 62 \\
2.11 Virtual Overflow and Underflow / 64 \\
2.12 Division by Zero and Indeterminant Forms / 66 \\
Exercises / 67 \\
3. Error Analysis / 71 \\
3.1 Significant Digits / 71 \\
3.2 Relative Error / 73 \\
3.3 Relative Error in FP(r,p, clq) / 75 \\
3.4 Approximate Laws of Algebra / 80 \\
3.5 Propagation of Rounding Error / 87 \\
3.6 X**N / 92 \\
3.7 Condition / 98 \\
3.8 Error Analysis of a Program / 103 \\
3.9 Backward Error Analysis / 105 \\
3.10 Examples / 107 \\
3.11 Changing the Problem / 109 \\
3.12 Statistical Error Analysis / 113 \\
Exercises / 117 \\
4. Example / 123 \\
4.1 Quadrature / 123 \\
4.2 Power Series / 130 \\
4.3 Exact Sums and Differences in FP(r, p, clq) / 137
\\
4.4 Dismantling Floating-Point Numbers / 143 \\
Exercises / 146 \\
5. Double-Precision Calculation / 154 \\
5.1 Programs Using Double-Precision Arithmetic / 155
\\
5.2 Implicit Typing of Names / 162 \\
5.3 Routines to Perform Double-Precision Arithmetic /
163 \\
5.4 Double-Precision Multiplication / 165 \\
5.5 Double-Precision Addition and Subtraction / 168 \\
5.6 Double-Precision Division / 171 \\
5.7 Writing Double-Precision Programs Without Language
Support / 178 \\
5.8 Uses of Double-Precision / 180 \\
5.9 Higher-Precision Arithmetic / 185 \\
Exercises / 186 \\
6. Rounding / 189 \\
6.1 General Considerations / 189 \\
6.2 Uses of Rounding / 191 \\
6.3 Implementation of Rounding / 192 \\
6.4 Bias Removal / 194 \\
6.5 Other ``Rounding'' Procedures / 197 \\
Exercises / 198 \\
7. Automatic Analysis of Error / 201 \\
7.1 Introduction / 201 \\
7.2 Significance Arithmetic / 202 \\
7.3 Noisy Mode / 205 \\
7.4 Interval Arithmetic / 207 \\
7.5 Rerunning the Program in Higher-Precision / 213 \\
Exercises / 222 \\
8. Radix Conversion / 224 \\
8.1 Equivalent Number of Digits / 224 \\
8.2 Properties of Conversion Transformations / 228 \\
8.3 Conversion Techniques / 232 \\
Exercises / 238 \\
9/ Carefully Written Programs / 240 \\
9.1 Introduction / 240 \\
9.2 Average Problem / 240 \\
9.3 Quadratic Equation / 246 \\
Exercises / 252 \\
10. Checking and Testing / 255 \\
10.1 Range Checking / 255 \\
10.2 Mathematical Checks / 256 \\
10.3 Testing / 259 \\
Exercises / 261 \\
11. Language Features for Floating-Point Computation /
263 \\
11.1 Introduction / 263 \\
11.2 Predictability, Controllability, Observability /
264 \\
11.3 Ease of Programming / 265 \\
11.4 Machine Independence / 267 \\
Exercises / 269 \\
12. Floating-Point Hardware / 271 \\
12.1 Choice of Radix / 271 \\
12.2 The Representation of Floating-Point Numbers / 273
\\
12.3 FP(r, p, c) and FP(r, p, R) / 277 \\
12.4 Unnormalized Numbers and Unnormalized Arithmetic /
278 \\
Exercises / 282 \\
13. Complex Numbers / 285 \\
13.1 Programs Using Complex Numbers / 285 \\
13.2 Relative Error / 286 \\
13.3 Complex Arithmetic / 287 \\
Exercises / 297 \\
Bibliography / 301 \\
Glossary of Symbols / 309 \\
Index / 311",
}
@Article{Suter:1974:MAA,
author = "B. W. Suter",
title = "The Modular Arithmetic of Arbitrarily Long Sequences
of Digits",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "12",
pages = "1301--1303",
month = dec,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.223850",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:38 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672443",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Syslo:1974:RAP,
author = "M. M. Syslo",
title = "Remarks on addition processes of positive
floating-point numbers",
journal = j-ZASTOS-MAT,
volume = "14",
pages = "415--417",
year = "1974",
CODEN = "ZAMTAK",
MRclass = "65G05",
MRnumber = "50 8953",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Zastosowania Matematyki",
reviewer = "Sven-{\AA}ke Gustafson",
}
@PhdThesis{Thompson:1974:IUF,
author = "Jackie Lloyd Thompson",
title = "An implementation of user-oriented floating point
arithmetic",
type = "Dissertation ({Ph.D.} in {Computing Science})",
school = "Texas A\&M University",
address = "College Station, TX, USA",
pages = "150",
year = "1974",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Tsao:1974:DSD,
author = "Nai Kuan Tsao",
title = "On the Distributions of Significant Digits and
Roundoff Errors",
journal = j-CACM,
volume = "17",
number = "5",
pages = "269--271",
month = may,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65G05",
MRnumber = "49 6595",
MRreviewer = "N. N. Abdelmalek",
bibdate = "Mon Jan 22 07:26:38 MST 2001",
bibsource = "Compendex database;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Tsao74;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Generalized logarithmic law is derived for the
distribution of the first $t$ significant digits of a
random digital integer. This result is then used to
determine the distribution of the roundoff errors in
floating-point operations, which is a mixture of
uniform and reciprocal distributions.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
classification = "921",
corpsource = "Aerospace Res. Labs., Wright-Patterson AFB, OH, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "Benford's Law; digital arithmetic; digital integer;
distributions; error analysis; floating point
operations; Law of Anomalous Numbers; logarithmic law;
mathematical techniques; mean value; random;
reciprocal; roundoff errors; significant digits;
uniform distribution; variance; Zipf's Law",
oldlabel = "Tsao74",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Tsao74",
}
@Article{Tsao:1974:SPE,
author = "Nai-Kuan Tsao",
title = "Some a Posteriori Error Bounds in Floating-Point
Computations",
journal = j-J-ACM,
volume = "21",
number = "1",
pages = "6--17",
month = jan,
year = "1974",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "65G05",
MRnumber = "49 8319",
bibdate = "Fri Dec 08 13:06:33 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
reviewer = "N. N. Abdelmalek",
}
@Article{Walker:1974:FGU,
author = "A. J. Walker",
title = "Fast generation of uniformly distributed pseudorandom
numbers with floating-point representation",
journal = j-ELECT-LETTERS,
volume = "10",
number = "25--26",
pages = "533--534",
day = "12",
month = dec,
year = "1974",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:19740423",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Fri Dec 30 16:39:46 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4245313",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}
@Article{Agrawal:1975:AAN,
author = "D. P. Agrawal",
title = "Arithmetic Algorithms in a Negative Base",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "10",
pages = "998--1000",
month = oct,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224109",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672702",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Agrawal:1975:OAL,
author = "Dharma P. Agrawal",
title = "Optimum Array-Like Structures for High-Speed
Arithmetic",
crossref = "IEEE:1975:SCA",
pages = "208--219",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Agrawal.pdf",
abstract = "Array-like structures for high-speed multiplication,
division, square and square-root operations have been
described in this paper. In these designs the division
and square-rooting time have been made to approach to
that of multiplication operation. These structures are
optimum from speed and versatility point of view. Most
of the cellular arrays described in the literature are
adequately slow. The time delay is particularly
significant in the division and square-rooting
operations due to the ripple effect of the carries.
Though the carry-save technique has been widely
utilized for multiplication operation, it has been only
recently employed by Cappa et al. in the design of a
nonrestoring divider array. This requires sign-bit
detection that makes the array non-uniform. Such an
array has been named as an array-like structure. The
carry-save method has been extended here for restoring
division operation. Due to sign-detection and overflow
correction requirements, the restoring method is
slightly complex. But the main advantage of such
restoring array is in its simple extension for
multiplication operation. The array for the two
operations, when pipelined, will have more computing
power than all other multiplier-divider arrays.
Suggestions have also been included for further speed
improvement.\par
The technique applied for division operation is as well
applicable for the square-rooting and an array-like
structure for square-square-rooting operations has also
been given. For performing any one of the four
operations, the only manipulation to be done is to
combine the two arrays; one for multiplication-division
and another for square-square-rooting. Possible.
methods of combining the two arrays have been indicated
and their relative advantages and disadvantages have
been mentioned. Finally, a generalized pipeline
array-like structure with complete internal details and
for 4-bit operation, has been shown. Due consideration
has also been given to the possibility of
large-scale-integration of different arrays presented
in this paper.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Atkins:1975:HRN,
author = "Daniel E. Atkins",
title = "Higher Radix, Non-restoring Division: History and
recent Developments",
crossref = "IEEE:1975:SCA",
pages = "158--167",
year = "1975",
bibdate = "Wed Nov 14 17:43:08 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Atkins.pdf",
abstract = "This paper reviews work related to the theory and
application of higher-radix. non-restoring division as
originally defined by Robertson in 1958.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Atkins:1975:IRR,
author = "D. E. Atkins",
title = "Introduction to the Role of Redundancy in Computer
Arithmetic",
journal = j-COMPUTER,
volume = "8",
number = "6",
pages = "74--77",
month = jun,
year = "1975",
CODEN = "CPTRB4",
DOI = "https://doi.org/10.1109/C-M.1975.219001",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Sat May 7 16:08:43 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computer1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@InProceedings{Avizienis:1975:RNR,
author = "Algirdas Avi{\v{z}}ienis",
title = "Redundancy in Number Representations as an Aspect of
Computational Complexity of Arithmetic Functions",
crossref = "IEEE:1975:SCA",
pages = "87--89",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Avizienis.pdf",
abstract = "Recent research has led to the derivation of bounds
for the time required to perform arithmetic operations
by means of logical elements with a limited number of
inputs [1--4]. The model of a $ (d, r) $ logical
circuit $C$ employed in these studies consists of a set
of $ (d, r) $ logical elements and a rule of
interconnection with designated sets of input and
output lines. The $ (d, r) $ logical element has $r$
input lines and one output line; these lines can assume
one of $d$ distinct states. The $ (d, r) $ logical
element has a unit time delay; that is, the state of
the output line at the time $ t + 1 $ is a function of
the states of the input lines at time $t$.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Baker:1975:MER,
author = "P. W. Baker",
title = "More Efficient Radix-2 Algorithms for Some Elementary
Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "11",
pages = "1049--1054",
month = nov,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224132",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:15:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Banerji:1975:CLS,
author = "D. K. Banerji",
title = "On Combinational Logic for Sign Detection in Residue
Number Systems",
crossref = "IEEE:1975:SCA",
pages = "113--116",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Banerji.pdf",
abstract = "This paper is concerned with the algebraic sign
detection of a number in a residue number system. The
proposed solution is applicable only to nonredundant
systems. The method utilizes a systematic decomposition
of the sign function $S$ that is based on some special
properties of $S$. Starting with the canonical
sum-of-products expression for $S$, we transform the
expression to a form whose realization is simpler than
the canonical form realization and, if possible, also
simpler than the minimal sum-of-products realization.
In some cases, the proposed method yields savings as
high as 85\% compared to the minimal sum-of-products
realization for $S$.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Basu:1975:SPN,
author = "D. Basu and T. Jayashree",
title = "On a Simple Postcorrection for Nonrestoring Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "10",
pages = "1019--1020",
month = oct,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224116",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672709",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Benedek:1975:DLB,
author = "M. Benedek",
title = "Developing Large Binary to {BCD} Conversion
Structures",
crossref = "IEEE:1975:SCA",
pages = "188--196",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Benedek.pdf",
abstract = "Static binary to BCD conversion has been described in
many papers during the last decade, but none of the
methods presented were practical for the conversion of
large number of binary bits.\par
In this paper it is intended to further develop static
conversions by the expansion of the original BIDEC
method (Ref. 1). There are quite a few static
conversion schemes published which use other methods of
conversion. The static method, developed from the
BIDEC, lends itself best for the expansion to larger
structures as in its original ``correct and shift''
form there were no basic limitations on the size of the
binary words to be converted. with the appearance of
large bipolar ROMs and the even larger but somewhat
slower MOS ROMs there is a renewed interest in large
structures for fast binary to BCD conversions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Bivins:1975:SAA,
author = "R. L. Bivins and N. Metropolis",
title = "Significance Arithmetic: Application to a Partial
Differential Equation",
crossref = "IEEE:1975:SCA",
pages = "64--66",
year = "1975",
DOI = "https://doi.org/10.1109/ARITH.1975.6156973",
bibdate = "Mon Mar 19 18:17:32 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Also available as Los Alamos Technical Report
LA-UR-75-1763 CONF-751103-1.",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Bivins.pdf",
abstract = "The methods of significance arithmetic are applied to
the numerical solution of a nonlinear partial
differential equation. The authors approach permits the
use of initial values having imprecision considerably
greater than that of rounding error; moreover, the
intermediate and final quantities are monitored so that
at any stage the precision of such quantities is
available. An algorithm is found that represents
faithfully the solution to a difference equation
approximation to Burger's equation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3; significance arithmetic",
}
@InProceedings{Bohlender:1975:FPC,
author = "G. Bohlender",
title = "Floating-Point Computation of Functions with Maximum
Accuracy",
crossref = "IEEE:1975:SCA",
pages = "14--23",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Bohlender.pdf",
abstract = "Algorithms are given which compute multiple sums and
products and arbitrary roots of floating-point numbers
with maximum accuracy. The summation algorithm can be
applied to compute scalar products, matrix products,
etc. For all these functions, simple error formulas and
the smallest floating-point intervals containing the
exact result can be obtained.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@TechReport{Brent:1975:FMP,
author = "R. P. Brent",
title = "A {Fortran} Multiple-Precision Arithmetic Package",
type = "Technical report",
institution = "Department of Computer Science, Australian National
University",
address = "Canberra, Australia",
year = "1975",
bibdate = "Fri Jan 06 07:38:05 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic; multiple-precision
arithmetic",
}
@TechReport{Brent:1975:MZM,
author = "R. P. (Richard P.) Brent",
title = "Multiple-precision zero-finding methods and the
complexity of elementary function evaluation",
institution = "Department of Computer Science, Carnegie-Mellon
University",
address = "Pittsburgh, PA, USA",
pages = "26",
year = "1975",
bibdate = "Sat Jan 11 10:14:06 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Iterative methods (Mathematics)",
searchkey = "ti:elementary n1 function",
}
@Article{Brubaker:1975:MUL,
author = "T. A. Brubaker and J. C. Becker",
title = "Multiplication Using Logarithms Implemented with
Read-Only Memory",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "8",
pages = "761--765",
month = aug,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224307",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672900",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Caprani:1975:REF,
author = "Ole Caprani",
title = "Round-off Errors in Floating-Point Summation",
journal = j-BIT,
volume = "15",
number = "1",
pages = "5--9",
month = mar,
year = "1975",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01932993",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65G05",
MRnumber = "58 19088",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "accurate floating-point summation; floating-point
arithmetic; rounding errors",
xxtitle = "Roundoff errors in floating-point summation",
}
@Article{Chen:1975:SER,
author = "Tien Chi Chen and Irving T. Ho",
title = "Storage-Efficient Representation of Decimal Data",
journal = j-CACM,
volume = "18",
number = "1",
pages = "49--52",
month = jan,
year = "1975",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "94A15 (68A20)",
MRnumber = "50 16105",
MRreviewer = "R. N. Goss",
bibdate = "Mon Jan 22 06:30:44 MST 2001",
bibsource = "Compendex database;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#ChenH75;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Collection of articles honoring {Alston S.
Householder}. See comment \cite{Smith:1975:CPC}.",
abstract = "Usually $n$ decimal digits are represented by $ 4 n $
bits in computers. Actually, two BCD digits can be
compressed optimally and reversibly into $7$ bits, and
three digits into $ 10 $ bits, by a very simple
algorithm based on the fixed-length combination of two
variable field-length encodings. In over half of the
cases the compressed code results from the conventional
BCD code by simple removal of redundant $0$ bits. A
long decimal message can be subdivided into three-digit
blocks, and separately compressed; the result differs
from the asymptotic minimum length by only $ 0.34 $
percent. The hardware requirement is small, and the
mappings can be done manually.",
acknowledgement = ack-nhfb,
classcodes = "C6130 (Data handling techniques)",
classification = "722; 921",
corpsource = "IBM San Jose Res. Lab., CA, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "asymptotic minimum; binary coded decimal; codes;
compressed code; data compression; data storage units;
decimal data; decimal floating-point arithmetic; fixed
length combination; hardware; length; length encodings;
mathematical techniques --- Digital Arithmetic;
representation; storage efficient; variable field",
oldlabel = "ChenH75",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/ChenH75",
}
@InProceedings{Chinal:1975:LMA,
author = "Jean P. Chinal",
title = "The Logic of Modulo $ 2^k + 1 $ Adders",
crossref = "IEEE:1975:SCA",
pages = "126--136",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Chinal_2.pdf",
abstract = "The design of modulo $ 2^k + 1 $ adders for arbitrary
$k$ is considered, with the objective of achieving a
logic structure as regular as possible so as to allow a
convenient implementation in large-scale integration
technology (LSI). It is shown how the design problem
can be reduced. to the recursive generation of a
subtract signal and to the merging, in various degrees,
of the corresponding logic with the logic of an
ordinary adder or, alternately, of a so-called {\em
signed-carry adder\/} which is defined and designed
itself in general, with both recursive and explicit
carry schemes. Modulo $ 2^k + 1 $ adder designs are
given, one with conventional adder, another based on
signed-carry adder and a third, derived from the
signed-carry scheme, where subtract signal generation
and carry logic are merged. This last scheme can be set
up with two backward recursion chains and five or six
forward ones. Two more basic variants are finally
indicated for this integrated scheme, aiming at
reducing as much as possible the residual logic
structure irregularity presented by the most
significant position in the word.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Chinal:1975:MA,
author = "Jean P. Chinal",
title = "Mirror Arithmetic",
crossref = "IEEE:1975:SCA",
pages = "98--107",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Chinal_1.pdf",
abstract = "Mirror coding for signed numbers is defined by means
of a set of primitive powers of two $ \{ + 2^n, - 2^{n
- 1}, \ldots {}, - 2^0 \} $ where signs of the usual
set used in 2's complement representation are reversed.
Use of the mirror representation is shown as an
alternate design approach and is illustrated by a
special purpose adder design in mirror code, by an
alternate proof of a basic property of signed-digit
arithmetic and as another interpretation of cells used
in some array multipliers for signed numbers. Lastly,
the concept is used to define a variable mode redundant
coding, allowing simple sign-flipping without
overflow.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Cobb:1975:IPS,
author = "Gary W. Cobb",
title = "The Impact of Parallelism on Software",
crossref = "IEEE:1975:SCA",
pages = "220--222",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Cobb.pdf",
abstract = "There seems to be a tug-of-war raging between computer
procurement technical evaluation committees, computer
designers and scholars of computer science and
numerical analysis over the issue of parallelism in
computations. Caught in the middle seems to be the user
community and the compiler writers. For the scope of
this paper, the term ``user community'' will be assumed
to be Fortran programmers who are involved in solving
problems that require large computer resources, e.g.,
plasma research, weather prediction, ray tracing,
seismic analysis, econometric modeling, weapons
research, reactor calculation, etc.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{DeMori:1975:MMM,
author = "Renato {De Mori} and Michele Elia and Angelo Serra",
title = "Minimization Methods for Macrocellular Arithmetic
Networks",
crossref = "IEEE:1975:SCA",
pages = "232--240",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_DeMori.pdf",
abstract = "This paper presents a new method to study arithmetic
combinatorial circuits. Using polynomial associated to
the input-output sequences and to the system, it is
possible to solve the problem of minimization of the
number of the component blocks. Particularly, the
important case of the multiple outputs elementary units
can be treated.\par
Applications of the introduced procedures to multiplier
and to fast networks for performing convolution are
presented.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Deverell:1975:PIA,
author = "J. Deverell",
title = "Pipeline Iterative Arithmetic Arrays",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "3",
pages = "317--322",
month = mar,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224214",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 18:46:50 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Elias:1975:UCS,
author = "P. Elias",
title = "Universal codeword sets and representations of the
integers",
journal = j-IEEE-TRANS-INF-THEORY,
volume = "21",
number = "2",
pages = "194--203",
month = mar,
year = "1975",
CODEN = "IETTAW",
DOI = "https://doi.org/10.1109/tit.1975.1055349",
ISSN = "0018-9448 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
bibdate = "Fri Dec 15 15:10:16 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Information Theory",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
}
@PhdThesis{Ercegovac:1975:GMEa,
author = "Milo{\v{s}} Dragutin Ercegovac",
title = "A General Method for Evaluation of Functions and
Computations in a Digital Computer",
type = "{Ph.D.} Thesis",
school = "Department of Computer Science, University of Illinois
at Urbana-Champaign",
address = "Urbana-Champaign, IL, USA",
pages = "viii + 109",
month = jul,
year = "1975",
bibdate = "Mon Feb 10 07:18:12 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://search.proquest.com/pqdtglobal/docview/302756306",
acknowledgement = ack-nhfb,
advisor = "James E. Robertson",
}
@InProceedings{Ercegovac:1975:GMEb,
author = "Milo{\v{s}} D. Ercegovac",
title = "A General Method for Evaluation of Functions in a
Digital Computer",
crossref = "IEEE:1975:SCA",
pages = "147--157",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Ercegovac.pdf",
abstract = "This paper presents a recently discovered general
computational method, amenable for efficient
implementation in digital computing systems. The method
provides a unique, simple and fast algorithm for
solving many computational problems, such as the
evaluation of polynomials, rational functions and
arithmetic expressions, or solving a class of systems
of linear equations, or performing the basic
arithmetics. In particular, the method is well suited
for fast evaluation of commonly used mathematical
functions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@MastersThesis{Fawcett:1975:MCR,
author = "B. K. Fawcett",
title = "Maximal Clocking Rates for Pipelined Digital Systems",
type = "{M.S.} thesis",
school = "Department of Electrical Engineering, University of
Illinois at Urbana-Champaign",
address = "Urbana-Champaign, IL, USA",
year = "1975",
bibdate = "Fri Nov 09 10:50:56 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Foster:1975:CNM,
author = "Caxton Foster and Edward Riseman and Fred Stockton and
Conrad Wogrin",
title = "{CHARGOGGAGGOGGMANCHAUGAGOGGCHAUBUNAGUNGAMAUG}: a
Novel Multiply-by-Three Circuit",
crossref = "IEEE:1975:SCA",
pages = "185--187",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Foster.pdf",
abstract = "Recently, while considering the connection of a 48 bit
word computer to a 16 bit computer, we felt the need
for a fast and inexpensive device that would multiply a
binary address by a factor of three. Since $ 3 N = N +
2 N $, there is an obvious solution of providing a
normal adder circuit and presenting one set of inputs
with $N$ and the other with $N$-shifted left one place.
But, there is a great deal of redundancy here since
knowing one input we have complete knowledge of the
other.\par
Seeking to take advantage of this redundancy, we have
spent some twenty man hours and have saved one gate per
stage over a conventional full adder. Since the
ultimate circuit is to be a ``one-of'' this is scarcely
economic, but it has been fun. Before going further,
the interested reader may enjoy puzzling over the
problem for himself. We make no pretense of minimality,
but we have a circuit with 6 gates per stage and a
propagation delay of one gate per stage.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
remark = "Footnote to title: The title of this paper refers to
the Indian name of a lake in Massachusetts which
reputedly means ``You fish on your side, I fish on my
side, nobody fish in the middle.'",
}
@InProceedings{Gabrielian:1975:FSN,
author = "Armen Gabrielian",
title = "Formal Systems of Numerals",
crossref = "IEEE:1975:SCA",
pages = "76--81",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Gabrielian.pdf",
abstract = "A new system of numerals is introduced for
representing numbers in base $ 2^N $, for $ N \leq 8 $.
The new notation greatly simplifies arithmetical
operations on numbers. For example, for $ N = 3 (4) $
one obtains a notation for octal (hexadecimal) numbers
in which one can perform addition and multiplication
much more easily than in the standard notation. For $ N
= 8 $ one obtains a practical way of representing
numbers to the base 256. A simplification of the
decimal notation is also presented.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{George:1975:ARR,
author = "James E. George",
title = "Algorithms to Reveal the Representation of Characters,
Integers, and Floating-Point Numbers",
journal = j-TOMS,
volume = "1",
number = "3",
pages = "210--216",
month = sep,
year = "1975",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355644.355647",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Aug 26 23:44:16 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Gibson:1975:SCT,
author = "J. A. Gibson and R. W. Gibbard",
title = "Synthesis and Comparison of Two's Complement Parallel
Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "10",
pages = "1020--1027",
month = oct,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224117",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672710",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Ginsberg:1975:DUFa,
author = "Myron Ginsberg and Dennis J. Frailey",
title = "The design and use of a floating-point (software)
simulator for testing the arithmetic behavior of
mathematical software",
type = "Technical report",
number = "CP 74028",
institution = "Department of Computer Science, Institute of
Technology, Southern Methodist University",
address = "Dallas",
edition = "Revised Oct. 1975.",
pages = "26",
year = "1975",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units --- Testing.;
Computer programs --- Testing.; Floating-point
arithmetic.",
}
@InProceedings{Ginsberg:1975:DUFb,
author = "Myron Ginsberg and Dennis J. Frailey",
title = "The Design and Use of a Floating-Point (Software)
Simulator for Testing the Arithmetic Behavior of
Mathematical Software",
crossref = "IEEE:1975:SCA",
pages = "56--63",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Ginsberg.pdf",
abstract = "An important aspect of any evaluative procedure for
developing high quality mathematical software is
testing the effects of arithmetic behavior on
algorithmic implementations. This paper describes a
proposed design approach and various applications of a
high-level language floating-point simulator which has
two inputs: the program to be tested and a description
of the floating-point arithmetic under which the
routine is to be executed. A brief discussion of the
motivation for this approach is given along with a
review of existing efforts to study the influences of
computer arithmetic on the accuracy and reliability of
mathematical. software. An overview of the simulator's
structure is presented as well as suggestions for
experiments to assist in determining the effects of
floating-point behavior across several different
computer architectures. Present and future uses of the
simulator are also indicated.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Goodman:1975:REP,
author = "R. Goodman and A. Feldstein",
title = "Round-Off Error in Products",
journal = j-COMPUTING,
volume = "15",
number = "3",
pages = "263--273",
month = sep,
year = "1975",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/BF02242373",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:52 MST 2001",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "Department of Math., University of Miami, Coral
Gables, FL, USA",
classification = "921; C5230",
description = "digital arithmetic",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Comput (Vienna/NY)",
keywords = "digit by digit deviation; floating point numbers;
fraction; logarithmic distribution; mathematical
techniques; mean; multiplication; products; roundoff
errors; variance",
}
@InProceedings{Goyal:1975:DAE,
author = "Lakshmi N. Goyal",
title = "Design of an Arithmetic Element for Serial Processing
in an Iterative Structure",
crossref = "IEEE:1975:SCA",
pages = "223--231",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Goyal.pdf",
abstract = "This paper describes the arithmetic and logic design
of the digit processing logic of an arithmetic element.
The arithmetic element is used in an iterative
structure and arithmetic processing takes place
serially on a digit by digit basis with the most
significant digit first. Starting from the arithmetic
specification of the digit processing logic, the
arithmetic design (namely, the choice of number system,
number representation and the digit algorithm) is
developed. Algebraic and logic designs of the logic
necessary to execute the digit algorithm and its
implication for LSI implementation are discussed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Grant:1975:TAS,
author = "J. A. Grant and G. D. Hitchins",
title = "Two Algorithms for the Solution of Polynomial
Equations to Limiting Machine Precision",
journal = j-COMP-J,
volume = "18",
number = "3",
pages = "258--264",
month = aug,
year = "1975",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/18.3.258",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:56 MST 2012",
bibsource = "Compendex database;
http://comjnl.oxfordjournals.org/content/18/3.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/;
https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/18/3/258.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/258.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/259.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/260.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/261.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/262.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/263.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/264.tif",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
classification = "723; 921",
corpsource = "Department of Math., University of Bradford, Bradford,
UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "algorithms; complex coefficients; computer programming
--- Subroutines; limiting machine; mathematical
techniques; polynomial equations; polynomials;
precision; real coefficients",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Gregory:1975:BCR,
author = "Robert Todd Gregory and David W. Matula",
title = "Base Conversion in Residue Number Systems",
crossref = "IEEE:1975:SCA",
pages = "117--125",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Gregory.pdf",
abstract = "We are concerned in this paper with the representation
of an integer in a (multiple-modulus) residue number
system and, in particular, with an algorithm for
changing the base vector of the residue number system.
Szabo and Tanaka [1, p.47] describe such an algorithm
when each modulus of the second base vector is
relatively prime to each modulus of the first base
vector. However, we show that a much simpler algorithm
exists if we allow the moduli of the second base vector
to have factors in common with the moduli of the first
base vector (even though the moduli of the second base
vector are pairwise relatively prime among
themselves).",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Hunter:1975:QMP,
author = "G. Hunter",
title = "A quantitative measure of precision",
journal = j-COMP-J,
volume = "18",
number = "3",
pages = "231--233",
month = aug,
year = "1975",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compendex database;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/231.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/232.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/233.tif",
abstract = "The precision $ z_b $ of a real number is defined
quantitatively in terms of the fractional error in the
number, and the base of the arithmetic in which it is
represented. The definition is an extension of the
traditional rough measure of precision as the number of
signification digits in the number. In binary
arithmetic the integral part of $ z_b $ is the number
of binary digits required to store the number.
Conversion of the precision from one base to another
(such as binary/decimal) is discussed, and applied to
consideration of the intrinsic precision of
input/output routines and floating point arithmetic.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
classification = "723; 921",
corpsource = "York University, Department of Chem., Downsview, Ont.,
Canada",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "binary arithmetic; digital arithmetic; digits;
floating; fractional error; input/output routines;
mathematical techniques; point arithmetic; precision;
real number; significant",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Kehl:1975:MMA,
author = "T. H. Kehl and Kenneth Burkhardt",
title = "A Minicomputer Microprogrammable, Arithmetic
Processor",
crossref = "IEEE:1975:SCA",
pages = "174--178",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kehl.pdf",
abstract = "Except for a few notable examples, all computers have
been designed as ``adder-central'' architectures.
``Adder-central,'' as used here, refers to an
organization which places the Arithmetic Logic Unit
(ALU) at that junction of the system through which all
data must flow --- thus creating a bottleneck. In the
early days, when adders were expensive, cost
considerations precluded more than one ALU. Nowadays
powerful ALU's are available at very low cost and a
designer, even of minicomputers, can consider placing
more than one ALU in a system.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Keir:1975:CNR,
author = "Roy A. Keir",
title = "Compatible number representations",
crossref = "IEEE:1975:SCA",
pages = "82--87",
year = "1975",
bibdate = "Fri Nov 28 11:38:18 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Keir_2.pdf",
abstract = "A compatible number system for mixed fixed-point and
floating-point arithmetic is described in terms of
number formats and opcode sequences (for hardwired or
microcoded control). This inexpensive system can be as
fast as fixed-point arithmetic on integers, is faster
than normalized arithmetic in floating point, gets
answers identical to those of normalized arithmetic,
and automatically satisfies the Algol-60 mixed-mode
rules. The central concept is the avoidance of
meaningless ``normalization'' following arithmetic
operations. Adoption of this system could lead to
simpler compilers.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3; decimal floating-point arithmetic",
}
@InProceedings{Keir:1975:PCR,
author = "Roy A. Keir",
title = "Programmer-controlled roundoff and the selection of a
stable roundoff rule",
crossref = "IEEE:1975:SCA",
pages = "73--76",
year = "1975",
bibdate = "Fri Nov 28 18:11:30 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Keir_1.pdf",
abstract = "The author suggests that every computer with
floating-point addition and subtraction should have PSW
controllable roundoff facilities. Yohe's catalog should
be included. There should also be a stable roundoff
mode using the round-to-off [{\em -odd\/}] or
round-to-even rule based on whether the radix is
divisible by four or only by two.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
keywords = "ARITH-3",
}
@Article{Keir:1975:SSR,
author = "R. A. Keir",
title = "Should the stable rounding rule be radix-dependent?",
journal = j-INFO-PROC-LETT,
volume = "3",
number = "6",
pages = "188--189",
day = "??",
month = jul,
year = "1975",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Tue Nov 17 10:49:43 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
corpsource = "Department of Computer Sci., University of Utah, Salt
Lake City, UT, USA",
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
keywords = "digital arithmetic; drift; floating point addition;
radices; round to even rule; round to odd rule; stable
rounding rule",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Kent:1975:CSU,
author = "Jan G. Kent",
title = "Comparison Sets: a Useful Partitioning of the Space of
Floating-Point Operand Pairs",
crossref = "IEEE:1975:SCA",
pages = "36--39",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kent.pdf",
abstract = "In this paper the definition of comparison sets and a
discussion of their usefulness are presented based on
the research work reported in (14). In addition some
new results concerning the distribution of floating
point (FLP) operand pairs over comparison sets are
given.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Klatte:1975:CPI,
author = "R. Klatte and Ch. Ullrich",
title = "Consequences of a Properly Implemented Computer
Arithmetic for Periodicities of Iterative Methods",
crossref = "IEEE:1975:SCA",
pages = "24--32",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Klatte.pdf",
abstract = "In ordered sets it is possible to show under certain
assumptions two basic theorems concerning the cycle
length of sequences of iterates generated by monotone
operators. These results are applied to different
iterative methods, where the conclusions are valid for
the sequences of iterates produced by the numerical
computations only, if the used computer arithmetic is
properly implemented.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3; cycle, weakly cyclic vector function;
floating-point arithmetic; Rounding invariant
structures",
}
@InProceedings{Kornerup:1975:UND,
author = "Peter Kornerup",
title = "A Unified Numeric Data Type in {Pascal}",
crossref = "IEEE:1975:SCA",
pages = "40--47",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kornerup.pdf",
abstract = "It is proposed to substitute the standard data type
{\em real\/} of a high level language, with a unified
data representation which can include a variety of
interpretations as well as formats, in order to allow
experiments with an environment containing a spectrum
of non-standard arithmetics, as well as
standard.\par
The implementation of a system is described where
syntactic extensions to a language are made to support
a microprogrammed virtual arithmetic unit which can
treat variants such as integers, normalized, and
unnormalized floating point numbers and intervals,
within a unified representation.\par
More specifically Pascal is chosen as the base
language, because it allows the user to define new data
types, and the extension then mainly consists in
substituting the simple (unstructured) data type {\em
real\/} with a skeletal structured type (which will be
called {\em numeric\/}).\par
The system is intended to be implemented on a
microprogrammable processor (called MATHILDA) with a 64
bit wide datapath. The language Pascal has already been
partially implemented based on a stack machine
specifically designed for that language, and realized
by interpretation in microcode. The present compiler
was constructed with the aid of a parser-generator
system, which will allow the language extensions to be
made with a moderate effort.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Kreifelts:1975:OBF,
author = "T. Kreifelts",
title = "{Optimale Basiswahl f{\"u}r eine Gleitkomma-Arithmetik
(Berichtigung)} \toenglish {Optimal Basis Choice for a
Floating-Point Arithmetic (Correction)} \endtoenglish",
journal = j-COMPUTING,
volume = "14",
number = "??",
pages = "313--314",
month = "????",
year = "1975",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@InProceedings{Krishnamurthy:1975:MPU,
author = "E. V. Krishnamurthy",
title = "Matrix Processors Using $p$-{ADIC} Arithmetic for
Exact Linear Computations",
crossref = "IEEE:1975:SCA",
pages = "92--97",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Krishnamurthy.pdf",
abstract = "A unique code (called Hensel's code) is derived for a
rational number, by truncating its infinite $p$-adic
expansion. The four basic arithmetic algorithms for
these codes are described and their application to
rational matrix computations is demonstrated by solving
a system of linear equations exactly, using the
Gaussian elimination procedure.\par
A comparative study of the computational complexity
involved in this arithmetic and the multiple prime
module arithmetic is made with reference to matrix
computations. On this basis, a multiple $p$-adic scheme
is suggested for the design of a highly parallel matrix
processor.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Ku:1975:FPC,
author = "W. Ku and Siu-Ming Ng",
title = "Floating-point coefficient sensitivity and roundoff
noise of recursive digital filters realized in ladder
structures",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "22",
number = "12",
pages = "927--936",
month = dec,
year = "1975",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "Coefficient sensitivity and roundoff error with
floating-point rounding have been investigated for
several digital ladder filter structures. It is found
that in all the cases studied, the ladder structures
first proposed by Fettweis show a much lower \ldots{}",
}
@InProceedings{Kuck:1975:RRN,
author = "D. J. Kuck and D. S. Parker and A. H. Sameh",
title = "{ROM}-Rounding: a New Rounding Scheme",
crossref = "IEEE:1975:SCA",
pages = "67--72",
year = "1975",
bibdate = "Thu Sep 01 12:13:06 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kuck.pdf",
abstract = "ROM-rounding is introduced and is shown to compare
favorably with existing floating-point rounding methods
on design considerations and on performance over a
series of error tests. The error-retarding value of
guard digits, of rounding the aligned operand, and of
rounding in general are discussed.",
acknowledgement = ack-nj,
keywords = "ARITH-3",
}
@Article{Kulisch:1975:FIF,
author = "U. Kulisch",
title = "Formalization and implementation of floating-point
arithmetics",
journal = j-COMPUTING,
volume = "14",
number = "4",
pages = "323--348",
year = "1975",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G05 (68A10)",
MRnumber = "53 14897",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
reviewer = "A. D. Booth",
}
@InProceedings{Kulisch:1975:MFC,
author = "U. Kulisch",
title = "Mathematical Foundation of Computer Arithmetic",
crossref = "IEEE:1975:SCA",
pages = "1--13",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kulisch.pdf",
abstract = "During the last years a number of papers concerning a
mathematical foundation of computer arithmetic have
been written. Some of these papers are still
unpublished. The papers consider the spaces which occur
in numerical computations on computers in dependence of
a properly defined computer arithmetic. The following
treatment gives a summary of the main ideas of these
papers. Many of the proofs had to be sketched or
completely omitted. In such cases the full information
can be found in the references.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Lacroix:1975:PEM,
author = "Arild Lacroix",
title = "Limit cycles in floating point digital filters",
crossref = "Swamy:1975:PEM",
pages = "475--479",
year = "1975",
MRclass = "94A05",
MRnumber = "55 12278",
bibdate = "Fri Dec 08 12:19:10 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "Krzysztof Sapiecha",
}
@Article{Landauro:1975:ODC,
author = "A. Landauro and J. Lienard",
title = "On Overflow Detection and Correction in Digital
Filters",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "12",
pages = "1226--1228",
month = dec,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224168",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:59 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672761",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Lang:1975:DPA,
author = "Allan L. Lang and Bruce D. Shriver",
title = "The Design of a Polymorphic Arithmetic Unit",
crossref = "IEEE:1975:SCA",
pages = "48--55",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Lang.pdf",
abstract = "This paper presents results which stem from a research
effort concerned with the specification and design of
arithmetic units which can execute nonstandard integer
and floating-point arithmetic. An arithmetic unit is
proposed whose characteristics are based on user
specifications and subsequently is termed a Polymorphic
Arithmetic Unit (PAU). The user binds the identity of
the PAU by specifying the contents of various
descriptors and semantic interpretation tables which
the PAU accesses during its execution. This capability
removes several of the restrictions found in
commercially available arithmetic units and potentially
assists in making mathematically software portable.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Laurie:1975:PIR,
author = "D. P. Laurie",
title = "Propagation of Initial Rounding Error in
{Romberg}-Like Quadrature",
journal = j-BIT,
volume = "15",
number = "3",
pages = "277--282",
month = sep,
year = "1975",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01933660",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:14 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=15&issue=3;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=15&issue=3&spage=277",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Lemeire:1975:CEI,
author = "Frans Lemeire",
title = "Computation of Equivalent Inherent Rounding Errors in
the Solution of a Set of Linear Equations",
journal = j-BIT,
volume = "15",
number = "1",
pages = "65--71",
month = mar,
year = "1975",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01932997",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:14 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=15&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=15&issue=1&spage=65",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Linnainmaa:1975:TAS,
author = "Seppo Linnainmaa",
title = "Towards Accurate Statistical Estimation of Rounding
Errors in Floating-Point Computations",
journal = j-BIT,
volume = "15",
number = "2",
pages = "165--173",
month = jun,
year = "1975",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01932690",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65G05",
MRnumber = "58 19090",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=15&issue=2&spage=165",
abstract = "A new method of estimating a posteriori the
statistical characteristics of the rounding errors of
an arbitrary algorithm is presented. This method is
based on a discrete model of the distribution of
rounding errors which makes more accurate estimates
possible. The analysis is given for both rounding and
truncating arithmetic. Finally, some experimental
results are reported.",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@InProceedings{Lipovski:1975:RND,
author = "G. J. Lipovski",
title = "On Residue Number {A/D} and {D/A} Converters",
crossref = "IEEE:1975:SCA",
pages = "197--199",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Lipovski.pdf",
abstract = "A very simple analog to digital converter and digital
to analog converter is described for residue number
digital processing. These simple devices make it
feasible to replace analog components with
comparatively inexpensive digital processors that use
residue, or modulus, arithmetic capable of operating at
very high speeds. Using off-the-shelf integrated
circuits, addition, subtraction or multiplication of
about 15 bits of accuracy can easily be done in as
little as fifty nanoseconds. Any function using these
operations (polynomial expansions, linear filters, Fast
Fourier Transforms) can be economically implemented in
a pipeline or other structure to get very fast systems.
Moreover, a stage in the pipeline can correct for
nonlinearities in the A/D or D/A converters. The simple
devices described herein make residue arithmetic
digital processors extremely attractive for use in fast
analog systems.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3; residue number system",
}
@Article{Liu:1975:REF,
author = "B. Liu and T. Kaneko",
title = "Roundoff error in fast {Fourier} transforms",
journal = j-PROC-IEEE,
volume = "63",
number = "6",
pages = "991--992",
month = jun,
year = "1975",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "The finite word length used in the computer causes
round-off error in the calculation of Fourier
coefficients. When the fast Fourier transform method is
used, the statistical mean-square error has been
previously determined [3] for the case of the
\ldots{}",
}
@Article{Lorez:1975:BGB,
author = "H. Lorez and F. J. Urbanek and H. Will and R. Weiss
and W. Baron and others",
title = "{Buchbesprechungen} ({German}) {Book Reviews}",
journal = j-COMPUTING,
volume = "14",
number = "3",
pages = "315--322",
month = sep,
year = "1975",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Kreifelts:1973:OBG}.",
acknowledgement = ack-nj,
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
language = "German",
}
@Book{Luke:1975:MFT,
author = "Yudell L. Luke",
title = "Mathematical Functions and Their Approximations",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xvii + 568",
year = "1975",
ISBN = "0-12-459950-8, 1-4832-6245-6 (e-book)",
ISBN-13 = "978-0-12-459950-5, 978-1-4832-6245-1 (e-book)",
LCCN = "QA55 .L96 1975",
bibdate = "Fri Jun 30 05:58:16 MDT 2023",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
URL = "https://shop.elsevier.com/books/mathematical-functions-and-their-approximations/luke/978-0-12-459950-5",
acknowledgement = ack-nhfb,
libnote = "Not in my library.",
remark = "An updated version of part of Handbook of mathematical
functions with formulas, graphs, and mathematical
tables, edited by M. Abramowitz and I. A. Stegun.
Includes indexes.",
subject = "Mathematics; Tables; Fonctions (Math{\'e}ematiques);
Math{\'e}ematiques; Calculus; Mathematical Analysis;
Mathematics; Approximation; Funktion; Mathematik;
Spezielle Funktion",
tableofcontents = "Preface / xv \\
\\
I. The Gamma Function and Related Functions \\
\\
1.1 Definitions and Elementary Properties / 1 \\
1.2 Power Series and Other Series Expansions / 1 \\
1.3 Asymptotic Expansions / 7 \\
1.4 Rational Approximations for y (z) / 13 \\
1.5 Inequalities / 17 \\
1.6 Bibliographic and Numerical Data / 20 \\
1.6.1 General References / 20 \\
1.6.2 Description of and References to Tables / 21 \\
1.6.3 Description of and References to Other
Approximations and Expansions / 22 \\
\\
II. The Binomial Function \\
\\
2.1 Power Series / 24 \\
2.2 Expansions in Series of Jacobi and Chebyshev
Polynomials / 24 \\
2.3 Expansions in Series of Bessel Functions / 26 \\
2.4 Pad{\'e} Approximations / 27 \\
24.1 $(1 + 1 / z)^{-c}$ / 27 \\
2.4.2 The Square Root / 28 \\
2.4.3 Pad{\'e} Coefficients / 30 \\
2.4.4 The Function $e^{-w}$ / 31 \\
2.5 Inequalities / 34 \\
\\
III. Elementary Functions \\
\\
3.1 Logarithmic Functions / 36 \\
3.1.1 Power Series / 36 \\
3.1.2 Expansion in Series of Chebyshev Polynomials / 38
\\
3.1.3 Pad{\'e} Approximations / 39 \\
3.1.4 Inequalities / 41 \\
3.2 Exponential Function / 42 \\
3.2.1 Series Expansions / 42 \\
3.2.2 Expansions in Series of Jacobi and Chebyshev
Polynomials and Bessel Functions / 42 \\
3.2.3 Pad{\'e} Approximations / 46 \\
3.2.4 Inequalities / 51 \\
3.3 Circular and Hyperbolic Functions / 52 \\
3.3.1 Power Series / 52 \\
3.3.2 Expansions in Series of Jacobi and Chebyshev
Polynomials and Bessel Functions / 52 \\
3.3.3 Rational and Pad{\'e} Approximations / 57 \\
3.3.4 Inequalities / 60 \\
3.4 Inverse Circular and Hyperbolic Functions / 61 \\
3.4.1 Power Series / 61 \\
3.4.2 Expansions in Series of Chebyshev Polynomials /
63 \\
3.4.3 Pad{\'e} Approximations / 68 \\
3.4.4 Inequalities / 72 \\
3.5 Bibliographic and Numerical Data / 74 \\
3.5.1 Description of and References to Tables / 74 \\
3.5.2 Description of and References to Other
Approximations and Expansions / 74 \\
\\
IV. Incomplete Gamma Functions \\
\\
4.1 Definitions and Series Expansions / 77 \\
4.2 Differential Equations and Difference Equations /
78 \\
4.3 Pad{\'e} Approximations / 79 \\
4.3.1 $_1F_1(1; \nu + 1; -z)$ / 79 \\
4.3.2 $z^{1 - \nu} e^z \Gamma(\nu, z)$ / 82 \\
4.3.3 The Error $T_n(\nu, z)$ for $|{\rm arg} z/k| \leq
\pi$ / 84 \\
4.3.4 The Negative Real Axis and the Zeros of $F_n(\nu,
z)$ / 89 \\
4.4 Inequalities / 95 \\
4.4.1 $H(\nu, z)$ / 95 \\
4.4.2 $\Gamma(\nu, z)$ / 96 \\
4.5 Notes on the Computation of the Incomplete Gamma
Function / 97 \\
4.6 Exponential Integrals / 103 \\
4.6.1 Relation to Incomplete Gamma Function and Other
Properties / 103 \\
4.6.2 Expansions in Series of Chebyshev Polynomials /
104 \\
4.6.3 Rational and Pad Approximations / 106 \\
4.7 Cosine and Sine Integrals / 115 \\
4.7.1 Relation to Exponential Integral and Other
Properties / 115 \\
4.7.2 Expansions in Series of Chebyshev Polynomials /
116 \\
4.8 Error Functions / 119 \\
4.8.1 Relation to Incomplete Gamma Function and Other
Properties / 119 \\
4.8.2 Expansions in Series of Chebyshev Polynomials and
Bessel Functions / 122 \\
4.8.3 Pad{\'e} Approximations / 124 \\
4.8.4 Trapezoidal Rule Approximations / 134 \\
4.8.5 Inequalities / 137 \\
4.9 Fresnel Integrals / 139 \\
4.9.1 Relation to Error Functions and Other Properties
/ 139 \\
4.9.2 Expansions in Series of Chebyshev Polynomials /
140 \\
4.10 Bibliographic and Numerical Data / 143 \\
4.10.1 References / 143 \\
4.10.2 Description of and References to Tables / 143
\\
4.10.3 Description of and References to Other
Approximations and Expansions / 149 \\
\\
V. The Generalized Hypergeometric Function $_pF_g$ and
the $G$-Function \\
\\
5.1 Introduction / 154 \\
5.2 The $_pF_q$ / 155 \\
5.2.1 Power Series / 155 \\
5.2.2 Derivatives and Contiguous Relations / 159 \\
5.2.3 Integral Representations and Integrals Involving
the $_pF_q$ / 160 \\
5.2.4 Evaluation for Special Values of the Variable and
Parameters / 163 \\
5.3 The $G$-Function / 170 \\
5.3.1 Definition and Relation to the $_pF_q$ / 170 \\
5.3.2 Elementary Properties / 176 \\
5.3.3 Analytic Continuation of $G_{p, p}^{m, n}(z)$ /
178 \\
5.4 The Confluence Principle / 179 \\
5.5 Multiplication Theorems / 184 \\
5.6 Integrals Involving $G$-Functions / 186 \\
5.7 Differential Equations / 190 \\
5.7.1 The $_pF_q$ / 190 \\
5.7.2 The $G$-Function / 192 \\
5.8 Series of $G$-Functions / 194 \\
5.8.1 Introduction / 194 \\
5.8.2 Notation / 194 \\
5.8.3 Expansion Theorems / 197 \\
5.9 Asymptotic Expansions / 199 \\
5.9.1 $G_{p, q}^{q, n}(z)$, $n = 0, 1$ / 199 \\
5.9.2 $G_{p, q}^{m, n}(z)$ / 201 \\
5.9.3 $_pF_q(z)$ / 206 \\
5.10 Expansions in Series of Generalized Jacobi,
Generalized Laguerre and Chebyshev Polynomials / 213
\\
5.10.1 Expansions for $G$-Functions / 213 \\
5.10.2 Expansions for $_pF_q$ / 220 \\
5.11 Expansions in Series of Bessel Functions / 223 \\
5.12 Polynomial and Rational Approximations / 224 \\
5.13 Recurrence Formulas for Polynomials and Functions
Occurring in Approximations to Generalized
Hypergeometric Functions / 234 \\
5.13.1 Introduction / 234 \\
5.13.2 Recursion Formulas for Extended Jacobi and
Laguerre Functions / 235 \\
5.13.3 Recursion Formulas for the Numerator and
Denominator Polynomials in the Rational Approximations
for the Generalized Hypergeometric Function / 244 \\
5.13.4 Recursion Formula for Coefficients in the
Expansion of the $G$-Function in Series of Extended
Jacobi Polynomials / 247 \\
5.14 Inequalities / 252 \\
\\
VI. The Gaussian Hypergeometric Function $_2F_1$ \\
\\
6.1 Introduction / 257 \\
6.2 Elementary Properties / 257 \\
6.2.1 Derivatives / 257 \\
6.2.2 Contiguous Relations / 258 \\
6.2.3 Integral Representations / 259 \\
6.3 Differential Equations / 260 \\
6.4 Kummer Solutions and Transformation Formulae / 262
\\
6.5 Analytic Continuation / 263 \\
6.6 The Complete Solution and Wronskians / 265 \\
6.7 Quadratic Transformations / 270 \\
6.8 The $_2F_1$ for Special Values of the Argument /
271 \\
6.9 Expansion in Series of Chebyshev Polynomials / 274
\\
6.10 Pad{\'e} Approximations for $_2F_1(1, \sigma;\rho
+ 1;-1/z)$ / 274 \\
6.11 Inequalities / 278 \\
6.12 Bibliographic and Numerical Data / 279 \\
6.12.1 References / 279 \\
6.12.2 Description of and References to Tables / 279
\\
\\
VII. The Confluent Hypergeometric Function \\
\\
7.1 Introduction / 284 \\
7.2 Integral Representations / 284 \\
7.3 Elementary Relations / 285 \\
7.3.1 Derivatives / 285 \\
7.3.2 Contiguous Relations / 285 \\
7.3.3 Products of Confluent Functions / 286 \\
7.4 Differential Equations / 287 \\
7.5 The Complete Solution and Wronskians / 288 \\
7.6 Asymptotic Expansions / 291 \\
7.7 Expansions in Series of Chebyshev Polynomials / 293
\\
7.8 Expansions in Series of Besse! Functions / 294 \\
7.9 Inequalities / 295 \\
7.10 Other Notations and Related Functions / 295 \\
7.11 Bibliographic and Numerical Data / 296 \\
7.11.1 References / 296 \\
7.11.2 Description of and References to Tables and
Other Approximations / 296 \\
\\
VIII. Identification of the $_pF_q$, and $G$-Functions
with the Special Functions \\
\\
8.1 Introduction / 298 \\
8.2 Named Special Functions Expressed as $_pF_q$'s /
298 \\
8.2.1 Elementary Functions / 298 \\
8.2.2 The Incomplete Gamma Function and Related
Functions / 298 \\
8.2.3 The Gaussian Hypergeometric Function / 298 \\
8.2.4 Legendre Functions / 299 \\
8.2.5 Orthogonal Polynomials / 299 \\
8.2.6 Complete Elliptic Integrals / 299 \\
8.2.7 Confluent Hypergeometric Functions, Whittaker
Functions and Bessel Functions / 300 \\
8.3 Named Functions Expressed in Terms of the
$G$-Function / 300 \\
8.4 The $G$-Function Expressed as a Named Function /
306 \\
\\
IX. Bessel Functions and Their Integrals \\
\\
9.1 Introduction / 311 \\
9.2 Definitions, Connecting Relations and Power Series
/ 311 \\
9.3 Difference--Differential Formulas / 313 \\
9.4 Products of Bessel Functions / 314 \\
9.5 Asymptotic Expansions for Large Variable / 315 \\
9.6 Integrals of Bessel Functions / 315 \\
9.7 Expansions in Series of Chebyshev Polynomials / 316
\\
9.8 Expansions in Series of Bessel Functions / 360 \\
9.9 Rational Approximations / 361 \\
9.9.1 Introduction / 361 \\
9.9.2 $I_\nu(z)$, $z$ Small / 361 \\
9.9.3 $K_\nu(z)$, $z$ Large / 366 \\
9.10 Computation of Bessel Functions by Use of
Recurrence Formulas / 380 \\
9.10.1 Introduction / 380 \\
9.10.2 Backward Recurrence Schemata for Generating
$I_\nu(z)$ / 380 \\
9.10.3 Closed Form Expressions / 382 \\
9.10.4 Expressions for $J_\nu(z)$ / 389 \\
9.10.5 Numerical Examples / 392 \\
9.11 Evaluation of Bessel Functions by Application of
Trapezoidal Type Integration Formulas / 395 \\
9.12 Inequalities / 399 \\
9.13 Bibliographic and Numerical Data / 403 \\
9.13.1 References / 403 \\
9.13.2 Description of and References to Tables / 404
\\
9.13.3 Description of and References to Other
Approximations and Expansions / 410 \\
\\
X. Lommel Functions, Struve Functions, and Associated
Bessel Functions \\
\\
10.1 Definitions, Connecting Relations and Power Series
/ 413 \\
10.2 Asymptotic Expansions / 415 \\
10.3 Expansions in Series of Chebyshev Polynomials and
Bessel Functions / 415 \\
10.4 Rational Approximations for $H_\nu(z) - Y_\nu(z)$
and the Errors in These Approximations / 422 \\
10.5 Bibliographic and Numerical Data / 426 \\
10.5.1 References / 426 \\
10.5.2 Description of and References to Tables / 426
\\
\\
XI. Orthogonal Polynomials \\
\\
11.1 Introduction / 428 \\
11.2 Orthogonal Properties / 428 \\
11.3 Jacobi Polynomials / 436 \\
11.3.1 Expansion Formulae / 436 \\
11.3.2 Difference--Differential Formulae / 439 \\
11.3.3 Integrals / 439 \\
11.3.4 Expansion of $x^\rho$ in Series of Jacobi
Polynomials / 440 \\
11.3.5 Convergence Theorems for the Expansion of
Arbitrary Functions in Series of Jacobi Polynomials /
442 \\
11.3.6 Evaluation and Estimation of the Coefficients in
the Expansion of a Given Function $f(x)$ in Series of
Jacobi Polynomials / 443 \\
11.4 The Chebyshev Polynomials $T_n(x)$ and $U_n(x)$ /
453 \\
11.5 The Chebyshev Polynomials $T_n^*(x)$ and
$U_n^*(x)$ / 459 \\
11.6 Coefficients for Expansion of Integrals of
Functions in Series of Chebyshev Polynomials of the
First Kind / 464 \\
11.6.1 Introduction / 464 \\
11.6.2 Series of Shifted Chebyshev Polynomials / 464
\\
11.6.3 Series of Chebyshev Polynomials of Even Order /
468 \\
11.6.4 Series of Chebyshev Polynomials of Odd Order /
468 \\
11.7 Orthogonality Properties of Chebyshev Polynomials
with Respect to Summation / 469 \\
11.8 A Nesting Procedure for the Computation of
Expansions in Series of Functions Where the Functions
Satisfy a Linear Finite Difference Equation / 475 \\
\\
XII. Computation by Use of Recurrence Formulas \\
\\
12.1 Introduction / 483 \\
12.2 Homogeneous Difference Equations / 483 \\
12.3 Inhomogeneous Difference Equations / 487 \\
\\
XIII. Some Aspects of Rational and Polynomial
Approximations \\
\\
13.1 Introduction / 490 \\
13.2 Approximations in Series of Chebyshev Polynomials
of the First Kind / 490 \\
13.3 The Pad{\'e} Table / 493 \\
13.4 Approximation of Functions Defined by a
Differential Equation --- The $\tau$-Method / 495 \\
13.5 Approximations of Functions Defined by a Series /
499 \\
13.6 Solution of Differential Equations in Series of
Chebyshev Polynomials of the First Kind / 500 \\
\\
XIV. Miscellaneous Topics \\
\\
14.1 Introduction / 505 \\
14.2 Bernoulli Polynomials and Numbers / 505 \\
14.3 $D$ and $\delta$ Operators / 507 \\
14.4 Computation and Check of the Tables / 509 \\
14.5 Mathematical Constants / 512 \\
14.6 Late Bibliography / 516 \\
\\
Bibliography / 517 \\
\\
Notation Index / 545 \\
\\
Subject Index / 551",
}
@Article{Martinson:1975:DMF,
author = "L. Martinson and R. Smith",
title = "Digital matched filtering with pipelined floating
point fast {Fourier} transforms ({FFT}'s)",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "23",
number = "2",
pages = "222--234",
month = apr,
year = "1975",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "A special floating point arithmetic technique for fast
Fourier transform (FFT) processors has been developed.
The implementation of a high-speed pipeline FFT matched
filter using the method employs significantly fewer
components than a fixed-point \ldots{}",
}
@InProceedings{Matula:1975:FSF,
author = "D. W. Matula",
title = "Fixed-Slash and Floating-Slash Arithmetic",
crossref = "IEEE:1975:SCA",
pages = "90--91",
year = "1975",
bibdate = "Wed Nov 14 17:45:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Matula.pdf",
abstract = "A finite precision rational number system provides for
representation of a collection of rational numbers
subject to limitations on numerator and denominator
magnitude. In fixed-point and floating-point radix
number systems, only rationals of the form $ i /
\beta^j $, where $ \beta $ is the base, can be
realized. In contrast, a finite precision rational
number system will allow representation of practically
all simple fractions encountered in applications.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{McDonald:1975:TCQ,
author = "T. G. McDonald and R. K. Guha",
title = "The Two's Complement Quasi-Serial Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "12",
pages = "1233--1235",
month = dec,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224170",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:59 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672763",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Meo:1975:ANT,
author = "A. R. Meo",
title = "Arithmetic Networks and Their Minimization Using a New
Line of Elementary Units",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "3",
pages = "258--280",
month = mar,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224207",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672800",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Miller:1975:SRA,
author = "Webb Miller",
title = "Software for Roundoff Analysis",
journal = j-TOMS,
volume = "1",
number = "2",
pages = "108--128",
month = jun,
year = "1975",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355637.355639",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65G05",
MRnumber = "53 \#9622",
bibdate = "Fri Aug 26 23:44:16 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
reviewer = "James H. Wilkinson",
}
@Article{Nance:1975:IFR,
author = "Richard E. Nance and Claude {Overstreet, Jr.}",
title = "Implementation of {Fortran} Random Number Generators
on Computers with One's Complement Arithmetic",
journal = j-J-STAT-COMPUT-SIMUL,
volume = "4",
number = "3",
pages = "235--243",
month = "????",
year = "1975",
CODEN = "JSCSAJ",
DOI = "https://doi.org/10.1080/00949657508810126",
ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
ISSN-L = "0094-9655",
bibdate = "Thu Jan 05 10:58:18 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/00949657508810126",
abstract = "Random number generators can be programmed in FORTRAN
using several methods on 1's complement machines. We
have presented several methods for the SRU 1107--1108
and CDC 6000 and CYBER series, the two most popular
that utilize 1's complement arithmetic. We believe the
logical mask method to be the most efficient technique
based on execution time on both machines. This method
requires only a little more than one-half the time of
the signed residue method on the SRU 1107--1108 and a
little more than two thirds the time of the unsigned
residue method on the CDC 6000--CYBER. A fast composite
generator in FORTRAN uses the logical mask method
combined with the FLD function to implement the table
approach of MacLaren and Marsaglia (1965). This
generator proves to be more than twice as fast as a
previous one for the SRU 1108, Marsaglia and Bray
(1968)",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Computation and Simulation",
journal-URL = "http://www.tandfonline.com/loi/gscs20",
onlinedate = "20 Mar 2007",
}
@Article{Nelson:1975:PPF,
author = "James M. Nelson and Charles E. Cohn",
title = "Parallel Processing in {FORTRAN} with Floating-Point
Hardware",
journal = j-SPE,
volume = "5",
number = "1",
pages = "65--68",
month = jan # "\slash " # mar,
year = "1975",
CODEN = "SPEXBL",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Sat May 31 13:36:16 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/spe.bib",
acknowledgement = ack-nhfb,
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}
@Article{Newbery:1975:PES,
author = "A. C. R. Newbery",
title = "Polynomial Evaluation Schemes",
journal = j-MATH-COMPUT,
volume = "29",
number = "132",
pages = "1046--1050",
month = oct,
year = "1975",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Department of Computer Sci., University of Kentucky,
Lexington, KY, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "floating; function evaluation; point arithmetic;
polynomial evaluation algorithm; polynomials; round off
error",
treatment = "T Theoretical or Mathematical",
}
@Manual{NSC:1975:IFP,
author = "{National Semiconductor Corporation}",
title = "{IMP-16F\slash 400} floating point firmware technical
description",
type = "Publication - National Semiconductor Corporation no.
4200072A",
organization = "National Semiconductor Corporation",
address = "Santa Clara, CA, USA",
pages = "16",
year = "1975",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Microprocessors --- Handbooks, manuals, etc.;
Microprogramming --- Handbooks, manuals, etc.",
remark = "At head of title: Integrated microprocessor-16.",
}
@Article{OKeefe:1975:NFB,
author = "K. H. O'Keefe",
title = "A Note on Fast Base Extension for Residue Number
Systems with Three Moduli",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "11",
pages = "1132--1133",
month = nov,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1975.224147",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:58 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672740;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35091",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "An algorithm is given for the base-extension (BE)
computation in residue number systems that requires the
standard four steps (for systems with three moduli) but
which saves hardware. Furthermore, for the particular
moduli m-1, m, and m+1 it is \ldots{}",
}
@InCollection{Phillips:1975:BC,
author = "E. William Phillips",
title = "Binary Calculation",
crossref = "Randell:1975:ODC",
pages = "293--304",
year = "1975",
bibdate = "Wed Oct 13 09:51:37 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "The 1936 epigraph credited to this author in
\cite[Chapter 7]{Coonen:1984:CPS} says: ``The ultimate
aim is to persuade all of the civilized world to
abandon the decimal numeration and to use octonal in
its place; to discontinue counting in tens and to count
in eights instead. However, it seems unlikely that the
whole civilized world will be persuaded to complete
this change during the next twelve months, having
previously declined similar invitations.''",
}
@InProceedings{Rao:1975:TIS,
author = "T. R. N. Rao and D. W. Matula",
title = "The {Third IEEE Symposium on Computer Arithmetic}:
Foreword",
crossref = "IEEE:1975:SCA",
pages = "v--v",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_contents.pdf;
http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_foreword.pdf;
http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_preface.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Reiser:1975:EDF,
author = "John F. Reiser and Donald E. Knuth",
title = "Evading the Drift in Floating-Point Addition",
journal = j-INFO-PROC-LETT,
volume = "3",
number = "3",
pages = "84--87",
month = jan,
year = "1975",
CODEN = "IFPLAT",
DOI = "https://doi.org/10.1016/0020-0190(75)90022-8",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Sun Dec 04 12:21:37 1994",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/infoproc1970.bib",
note = "See erratum \cite{Reiser:1975:EED}.",
acknowledgement = ack-nhfb # "\slash " # ack-nj,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
remark = "From p. 87: ``Actually Tannery's and Scarborough's
contradictory arguments [round-up and round-to-even]
are both incorrect; for example, the logarithmic law of
distribution of leading digits [3] [Benford's Law]
implies that the least significant digit of a
floating-point number will be odd slightly less often
than it will be even, assuming that $b$ is even and $ p
> 1$. The real justification for stable rounding is
that it eliminates drift.''",
}
@Article{Reiser:1975:EED,
author = "John F. Reiser and Donald E. Knuth",
title = "Erratum: {``Evading the Drift in Floating-Point
Addition''}",
journal = j-INFO-PROC-LETT,
volume = "3",
number = "5",
pages = "164--164",
month = may,
year = "1975",
CODEN = "IFPLAT",
DOI = "https://doi.org/10.1016/0020-0190(75)90031-9",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Sun Dec 04 12:21:42 1994",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/infoproc1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Reiser:1975:EDF}.",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@Article{Rokne:1975:ACI,
author = "J. Rokne and P. Lancaster",
title = "Algorithm 86. Complex Interval Arithmetic",
journal = j-COMP-J,
volume = "18",
number = "1",
pages = "83--85",
month = feb,
year = "1975",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods); C7310 (Mathematics
computing)",
corpsource = "Univ. Calgary, Alta., Canada",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "algorithm; complex interval arithmetic; digital
arithmetic; floating point; real numbers; subroutines",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Rubinfield:1975:PMB,
author = "L. P. Rubinfield",
title = "A Proof of the Modified {Booth}'s Algorithm for
Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "10",
pages = "1014--1015",
month = oct,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224114",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672707",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Senzig:1975:CA,
author = "Don Senzig",
title = "Calculator Algorithms",
journal = "IEEE Compcon Reader Digest",
pages = "139--141",
year = "1975",
bibdate = "Fri Nov 28 19:19:40 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 75CH0920-9C.",
abstract = "This paper discusses algorithms for generating the
trigonometric, exponential, and hyperbolic functions
and their inverses. No invention is claimed here. The
algorithm for logarithm was used by Briggs in compiling
his table of logarithms in the 1600's. Other earlier
references are [cited]. The development presented here
is, perhaps, more direct than those given in the above
references but leads to the same result.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@Article{Shimizu:1975:REF,
author = "Tatsujiro Shimizu and Tsunemichi Oohashi",
title = "Rounding errors in floating point addition",
journal = "TRU Math.",
volume = "11",
pages = "41--50",
year = "1975",
MRclass = "65G05",
MRnumber = "55 4646",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "R. P. Brent",
}
@InProceedings{Shriver:1975:BCA,
author = "B. D. Shriver and E. K. Reuter",
title = "A Bibliography on Computer Arithmetic",
crossref = "IEEE:1975:SCA",
pages = "241--249",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Biography.pdf",
abstract = "This bibliography on computer arithmetic uses, by and
large, the format and abbreviations employed by
Computing Reviews. It is presented in alphabetical
order only and not by individual topics. The topics
included, however, span the abstract and implementation
problems associated with finite precision computer
arithmetic.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Shriver:1975:UUN,
author = "Bruce D. Shriver and Peter Kornerup",
title = "The {UNRAU} --- a {Unified Numeric Representation
Arithmetic Unit}",
crossref = "IEEE:1975:SCA",
pages = "179--184",
year = "1975",
bibdate = "Wed Nov 14 17:46:23 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Shriver.pdf",
abstract = "A companion paper entitled, ``A Unified Numeric Data
Type in Pascal'', proposes the substitution of the
standard data type {\em real\/} of the language Pascal
with a unified data representation termed {\em
numeric}. The {\em numeric\/} data type can represent a
variety of arithmetic operands such as integers,
normalized floating point numbers, and centered-radius
intervals.\par
This paper describes an arithmetic unit which is
capable of executing the standard arithmetic operations
(addition, subtraction, multiplication, and division)
on pairs of operands specified to be of the {\em
numeric\/} data type. This arithmetic unit, called the
UNRAU --- Unified Numeric Representation Arithmetic
Unit, supports operations on operands externally
represented as 5-tuples $ (t, a, e, f, r) $. The UNRAU
provides for automatic conversion among the various
data types and can also be used to perform an explicit
conversion on a single operand.\par
It is intended to implement the UNRAU on a dynamically
microprogrammable microprocessor to determine what host
facilities are required to efficiently realize such an
arithmetic unit and to experiment with the high level
language support of such a unit.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Smith:1975:CPC,
author = "Alan Jay Smith",
title = "Comments on a paper by {T. C. Chen} and {I. T. Ho}",
journal = j-CACM,
volume = "18",
number = "8",
pages = "463--463",
month = aug,
year = "1975",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:22:40 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#Smith75a;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Chen:1975:SER}.",
acknowledgement = ack-nhfb,
classcodes = "C6130 (Data handling techniques)",
corpsource = "University of California, Berkeley, CA, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "advantages; alternatives; binary coded decimal; codes;
coding; compression of numbers; data handling; decimal
data; decimal floating-point arithmetic; decoding;
deletions; Huffman codes; insertions; permutations;
storage efficient representation; variable length
codes",
oldlabel = "Smith75a",
treatment = "G General Review; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Smith75a",
}
@Article{Smith:1975:SCO,
author = "Cyril Stanley Smith",
title = "A {Seventeenth-Century} Octonary Arithmetic",
journal = j-ISIS,
volume = "66",
number = "3",
pages = "390--394",
month = sep,
year = "1975",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:29:19 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302314;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1970.bib",
URL = "http://www.jstor.org/stable/228846",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Book{Smith:1975:SAP,
author = "Jon M. Smith",
title = "Scientific Analysis on the Pocket Calculator",
publisher = pub-Wiley,
address = pub-Wiley:adr,
pages = "xii + 380",
year = "1975",
ISBN = "0-471-79997-1",
ISBN-13 = "978-0-471-79997-9",
LCCN = "QA75 .S555",
bibdate = "Wed Jun 12 16:56:02 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Part I: Introduction to Pocket Calculator Analysis
\\
1: The Pocket Calculator / 3 \\
2: Difference Tables, Data Analysis, and Function
Evaluation / 53 \\
Part II: Numerical Evaluation of Functions on the
Pocket Calculator \\
3: Elementary Analysis with the Pocket Calculator / 81
\\
4: Numerical Evaluation of Advanced Functions / 114 \\
Part III: Advanced Analysis on the Pocket Calculator
\\
5: Fourier Analysis / 139 \\
6: Numerical Integration / 154 \\
7: Linear Systems Simulation / 180 \\
8: Chebyshev and Rational Polynomial Approximations for
Analytic Substitution / 198 \\
9: Determining the Roots of a Function / 224 \\
10: Statistics and Probability / 242 \\
Part IV: The Programmable Pocket Calculator \\
11: The Programmable Pocket Calculator / 283 \\
12: Optimization / 300 \\
Appendix 1: Some Tricks of the Pocket Calculator Trade
/ 323 \\
Appendix 2: Matrix Analysis on the Pocket Calculator /
333 \\
Appendix 3: Complex Numbers and Functions / 336 \\
Appendix 4: Key Stroke Sequences for Complex Variable
Analysis and Hyperbolic Inverse Functions / 340 \\
Index",
}
@Article{Soule:1975:AAB,
author = "Stephen Soule",
title = "Addition in an Arbitrary Base Without Radix
Conversion",
journal = j-CACM,
volume = "18",
number = "6",
pages = "344--346",
month = jun,
year = "1975",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:23:30 MST 2001",
bibsource = "Compendex database;
ftp://ftp.ira.uka.de/pub/bibliography/Theory/Seiferas/1975.bib;
http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#Soule75;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents a generalization of an old
programming technique; using it, one may add and
subtract numbers represented in any radix, including a
mixed radix, and stored one digit per byte in bytes of
sufficient size. Radix conversion is unnecessary, no
looping is required, and numbers may even be stored in
a display (I/O) format. Applications to Cobol, MIX, and
hexadecimal sums are discussed.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques)",
classification = "723; 921",
corpsource = "University of Calgary, Calgary, Alta., Canada",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "add; addition; arbitrary base; arbitrary radix
arithmetic; Cobol display arithmetic; computer systems
programming; data handling; decimal arithmetic; decimal
floating-point arithmetic; digital arithmetic;
mathematical techniques --- Digital Arithmetic; MIX
arithmetic; mixed radix arithmetic; numbers;
programming; radix conversion; subtract; subtraction;
without radix conversion",
oldlabel = "Soule75",
treatment = "A Application; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Soule75",
}
@InProceedings{Stephenson:1975:CSP,
author = "Charles Stephenson",
title = "Case Study of the Pipelined Arithmetic Unit for the
{TI Advanced Scientific Computer}",
crossref = "IEEE:1975:SCA",
pages = "168--173",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Stephenson.pdf",
abstract = "Many scientific applications today require computers
which are very fast and capable of processing large
amounts of data. Some advances in scientific processing
have been slowed due to the lack of supercomputer
capabilities which are required primarily in the area
of Central Processor speed and the availability of
large amounts of high speed memory. Particularly in the
fields of modeling and simulation, additional speed and
memory capacity are desired to allow increased
resolution of the experiment. Technological
developments: In such things as integrated circuits,
multilayer printed circuit boards, memory speeds, and
others have contributed to the ability of computer
manufacturers to serve this market. In addition to
these developments, however, large advances had to be
realized from the standpoint of the basic computer
architecture. The concept of pipelining has provided an
answer to the large data execution rate required.
Pipelined capabilities in the form of arithmetic units
and special purpose functional units are included in
machines such as the CDC 7600, IBM 360/195, CDC
STAR-100, etc. The Texas Instruments Advanced
Scientific Computer (ASC) uses the pipeline concept
throughout the Central Processor and carries the
concept throughout the Central Processor and carries
the concept further to include vector instructions in
response to the high execution rates required. 3",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Sterbenz:1975:UA,
author = "Pat H. Sterbenz",
title = "Understandable Arithmetic",
crossref = "IEEE:1975:SCA",
pages = "33--35",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Sterbenz.pdf",
abstract = "Since the floating-point operations form the basic
steps in our programs, the programmer has to understand
the results that will be produced by these operations.
This paper discusses operations which have been or
might be implemented in the hardware. The emphasis is
on making the results easy for the user to
understand.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Book{Stone:1975:ICA,
editor = "Harold S. Stone and Tien Chi Chen and Michael J. Flynn
and Samuel H. Fuller and others",
title = "Introduction to computer architecture",
publisher = "Science Research Associates",
address = "Chicago, IL, USA",
pages = "x + 565",
year = "1975",
ISBN = "0-574-18405-8",
ISBN-13 = "978-0-574-18405-4",
LCCN = "QA76.5 .I7; QA76.9.A73 I57; QA76.5 .I63; QA76.9.A73
I57 1975",
bibdate = "Fri Nov 9 19:22:07 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
series = "SRA computer science series",
acknowledgement = ack-nhfb,
subject = "Electronic digital computers",
}
@InProceedings{Svoboda:1975:SCA,
author = "Antonin Svoboda",
title = "Self-Checking Adder for Large Scale Integration",
crossref = "IEEE:1975:SCA",
pages = "108--112",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Svoboda.pdf",
abstract = "The testing of LSI chips is expensive and
unsatisfactory. On the other hand there are cases (as
in space ship computers) where a damaged chip must be
localized and replaced. The use of self-checking chips
seems to be one of several possible solutions of this
problem. The theory of the structure of self-checking
logical circuit is covered by literature at least at
the fundamental form (see References). However, even
when the design principles are supposed to be known,
their application to the actual creation of a
self-checking circuit of an average complexity is and
will remain an art. The reason is quite simple and
fundamental optimization of design criteria
(engineering qualifications, performance and physical
properties of components of the circuits are entities
possessing different physical dimensions --- it is
impossible to qualify, for instance, two circuits A, B
designed for the same task by comparing their speeds
and costs if A is faster than B but B is cheaper than
A) will never be objective and independent of the
talent or whim of the circuit designer.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Swartzlander:1975:SLN,
author = "E. E. {Swartzlander, Jr.} and A. G. Alexopoulos",
title = "The Sign\slash Logarithm Number System",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "12",
pages = "1238--1242",
month = dec,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224172",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:59 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Hongyuan:1986:CSL}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672765",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Toma:1975:CLA,
author = "C. I. Toma",
title = "Cellular Logic Array for High-Speed Signed Binary
Number Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "9",
pages = "932--935",
month = sep,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224340",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672933",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Trivedi:1975:LAD,
author = "Kishor S. Trivedi and Milo{\v{s}} D. Ercegovac",
title = "On-Line Algorithms for Division and Multiplication",
crossref = "IEEE:1975:SCA",
pages = "161--177",
year = "1975",
bibdate = "Fri Dec 08 10:45:59 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Trivedi_2.pdf",
abstract = "In this paper we are considering problems of division
and multiplication in a computational environment in
which all but basic arithmetic operations satisfy
``on-line'' property: to generate $ j^{\mbox {th}} $
digits of the result it is necessary and sufficient to
have argument(s) available up to the $ (j +
\delta)^{\mbox {th}} $ digit, where the index
difference $ \delta $ is a small positive
constant.
Such an environment, due to its potential to perform a
sequence of operations in an overlapped fashion, could
conveniently speed up an arithmetic multiprocessor
structure it could be useful in certain real-time
applications, with inherent on-line properties. The
on-line property implies a left-to-right digit-by-digit
type of algorithm and consequently, a redundant
representation, at least of the results. For addition
and subtraction such algorithms satisfying on-line
property can be easily specified. Multiplication
requires a somewhat more elaborate approach and there
are several possible ways of defining an on-line
algorithm. However, the existence of an on-line
division algorithm is not obvious and its analysis
appears interesting.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Trivedi:1975:UCF,
author = "Kishor S. Trivedi",
title = "On the Use of Continued Fractions for Digital Computer
Arithmetic",
crossref = "IEEE:1975:SCA",
pages = "137--146",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Trivedi_1.pdf",
abstract = "Recently, there has been some interest in the use of
continued fractions for digital hardware calculations.
We require that the coefficients of the continued
fractions be integral powers of two. As a result well
known continued fraction expansions of functions cannot
be used. Methods of expansion of a large number of
functions are presented.\par
We show that the problem of selection of coefficients
of the continued fractions does not have practical
solution in most of the cases we have considered. We
conjecture that the solution of a polynomial equation
is the only problem that can be solved in our
formulation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@MastersThesis{Tzaferos:1975:EBD,
author = "Konstantina Tzaferos",
title = "Error bounds due to index of significance
specifications in floating-point operations with
encoded mantissa lengths",
type = "Thesis ({M.S.})",
school = "California State University, Chico",
address = "Chico, CA, USA",
pages = "vi + 43",
year = "1975",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.",
}
@Manual{Wadsworth:1975:MLP,
author = "Nat Wadsworth",
title = "Machine Language Programming for the 8008 (and Similar
Microcomputers)",
organization = "Scelbi Computer Consulting. Inc.",
address = "1322 Rear --- Boston Post Road, Milford, CT 0646,
USA",
pages = "172 (chapter numbering)",
year = "1975",
bibdate = "Fri Dec 01 15:53:00 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.scelbi.com/files/docs/books/Machine%20Language%20Programming%20For%20The%208008.pdf",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic; multiple-precision
arithmetic",
remark = "Chapter 5 discusses implementation of floating-point
arithmetic in software on the Intel 8008, with
assembly-code routines for each operation.",
}
@Article{Wakerly:1975:DUM,
author = "J. F. Wakerly",
title = "Detection of Unidirectional Multiple Errors Using
Low-Cost Arithmetic Codes",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "2",
pages = "210--212",
month = feb,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224187",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:37 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672780",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Weinberger:1975:HSZ,
author = "Arnold Weinberger",
title = "High-Speed Zero-Sum Detection",
crossref = "IEEE:1975:SCA",
pages = "200--207",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Weinberger.pdf",
abstract = "A common requirement accompanying high-speed parallel
addition is the early detection that the sum is equal
to zero. Normally, this condition is detected from the
sum, generally at least two logic gate levels after the
sum.\par
This paper derives expressions for detecting a zero-sum
condition concurrently with or even earlier than the
determination of the sum digits proper. As a result, a
branch operation based on detecting a zero-sum can be
executed earlier.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Wilkinson:1975:PAA,
author = "J. H. Wilkinson",
title = "The {Pilot ACE at the NPL}",
journal = j-RADIO-ELECTRON-ENG,
volume = "45",
number = "7",
pages = "336--340",
month = jul,
year = "1975",
CODEN = "RDEEA4",
ISSN = "0033-7722",
bibdate = "Mon Nov 1 18:34:26 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "The Radio and Electronic Engineer",
}
@TechReport{Wozniakowski:1975:NSI,
author = "H. Wozniakowski",
title = "Numerical stability of iterations for solution of
nonlinear equations and large linear systems",
institution = "Department of Computer Science, Carnegie-Mellon
University",
address = "Pittsburgh, PA, USA",
pages = "16",
year = "1975",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Differential equations, Nonlinear.; Floating-point
arithmetic.; Iterative methods (Mathematics); Linear
systems.",
}
@Article{Yamashita:1975:EEF,
author = "Shin-ichiro Yamashita",
title = "On the error estimation in floating-point arithmetic",
journal = "Information Processing in Japan",
volume = "15",
pages = "64--69",
year = "1975",
MRclass = "65G05",
MRnumber = "54 4081",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "Artenio De Matteis",
}
@Article{Yuen:1975:FPR,
author = "C. K. Yuen",
title = "On the Floating Point Representation of Complex
Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "8",
pages = "846--848",
month = aug,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224321",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See comments \cite{Bauer:1977:CFP}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672914",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Yuen:1975:NBA,
author = "C. K. Yuen",
title = "A Note on Base $ - 2 $ Arithmetic Logic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "3",
pages = "325--329",
month = mar,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224216",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See comments \cite{Agrawal:1977:CNB}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672809",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
received = "25 January 1974; revised 3 June 1978",
remark-1 = "From page 328: ``[In base $-2$,] the product of two
$n$-bit numbers may have $2 n + 1$ bits.''",
remark-2 = "From page 329: ``In general circumstances, however, it
is at present difficult to see base $-2$ as a strong
competitor against positive base arithmetic. We have
seen that arithmetic operations are usually more
complex, and fast adders are difficult to design. The
range of base $-2$ numbers is not symmetrical: either
there are twice as many positive numbers as negative
ones, or vice versa.''",
remark-3 = "The appendix on page 329 shows a simple algorithm for
converting between numbers with base $b$ and base
$-b$.",
}
@Article{Asai:1976:RRC,
author = "H. Asai",
title = "A recursive radix conversion formula and its
application to multiplication and division",
journal = j-COMPUT-MATH-APPL,
volume = "2",
number = "3--4",
pages = "255--265",
month = "????",
year = "1976",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 18:51:13 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122176900183",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Assmus:1976:NFS,
author = "E. F. {Assmus, Jr.} and H. F. {Mattson, Jr.} and
Howard E. Sachar",
title = "A New Form of the Square Root Bound",
journal = j-SIAM-J-APPL-MATH,
volume = "30",
number = "2",
pages = "352--354",
month = mar,
year = "1976",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classification = "B0250 (Combinatorial mathematics); C1160
(Combinatorial mathematics)",
corpsource = "Department of Math., Lehigh University, Bethlehem, PA,
USA",
fjournal = "SIAM Journal on Applied Mathematics",
journal-URL = "http://epubs.siam.org/siap",
keywords = "combinatorial mathematics; linear codes; square root
bound; sufficient combinatorial conditions",
treatment = "T Theoretical or Mathematical",
}
@Article{Baker:1976:SFB,
author = "P. W. Baker",
title = "Suggestion for a fast binary sine\slash cosine
generator",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "??",
pages = "1134--1137",
month = nov,
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.1674566",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon May 20 05:24:26 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Brent:1976:FMP,
author = "Richard P. Brent",
title = "Fast Multiple-Precision Evaluation of Elementary
Functions",
journal = j-J-ACM,
volume = "23",
number = "2",
pages = "242--251",
month = apr,
year = "1976",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/321941.321944",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "68A20 (68A10)",
MRnumber = "52 \#16111",
MRreviewer = "Amnon Barak",
bibdate = "Wed Jan 15 18:12:53 MST 1997",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Let $ f(x) $ be one of the usual elementary functions
($ \exp $, $ \log $, $ \artan $, $ \sin $, $ \cosh $,
etc.), and let $ M(n) $ be the number of
single-precision operations required to multiply
$n$-bit integers. It is shown that $ f(x) $ can be
evaluated, with relative error $ O(2 - n) $, in $
O(M(n)l o g (n)) $ operations as $ n \rightarrow \infty
$, for any floating-point number $x$ (with an $n$-bit
fraction) in a suitable finite interval. From the
Sch{\"o}nhage--Strassen bound on $ M(n) $, it follows
that an $n$-bit approximation to $ f(x) $ may be
evaluated in $ O(n \log_(n) \log \log (n)) $
operations. Special cases include the evaluation of
constants such as $ \pi $ $e$, and $ e^\pi $. The
algorithms depend on the theory of elliptic integrals,
using the arithmetic-geometric mean iteration and
ascending Landen transformations.",
acknowledgement = ack-nhfb,
classification = "723",
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
journalabr = "J Assoc Comput Mach",
keywords = "computational complexity; computer arithmetic;
computer programming",
}
@InProceedings{Brent:1976:MPZ,
author = "Richard P. Brent",
title = "Multiple-precision zero-finding methods and the
complexity of elementary function evaluation",
crossref = "Traub:1976:ACC",
pages = "151--176",
year = "1976",
MRclass = "68A20",
MRnumber = "54 \#11843",
MRreviewer = "Claus-Peter Schnorr",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Carter:1976:ANT,
author = "Allison Birchard Carter",
title = "Applications of number theory to the avoidance of
round-off in digital computer systems",
type = "Thesis ({M.S.})",
school = "University of Florida",
address = "Gainesville, FL, USA",
pages = "v + 74",
year = "1976",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers.; Floating-point
arithmetic.; Number theory.",
}
@Article{Cohen:1976:EFD,
author = "Daniel I. A. Cohen",
title = "An explanation of the first digit phenomenon",
journal = j-J-COMB-THEORY-A,
volume = "20",
number = "3",
pages = "367--370",
month = may,
year = "1976",
CODEN = "JCBTA7",
ISSN = "0097-3165 (print), 1096-0899 (electronic)",
ISSN-L = "0097-3165",
bibdate = "Thu Feb 15 16:29:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Combinatorial Theory. Series A",
journal-URL = "http://www.sciencedirect.com/science/journal/00973165",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Davies:1976:IPS,
author = "M. Davies and B. Dawson",
title = "The incrementation parameter in square root
iteration",
journal = j-J-INST-MATH-APPL,
volume = "17",
number = "2",
pages = "219--223",
year = "1976",
CODEN = "JMTAA8",
ISSN = "0020-2932",
MRclass = "65H05",
MRnumber = "55 \#9514",
MRreviewer = "Luciano Biasini",
bibdate = "Fri Apr 5 07:38:01 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0319.65039",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Institute of Mathematics and its
Applications",
journal-URL = "http://imamat.oxfordjournals.org/content/by/year",
}
@Book{DEC:1976:DHM,
author = "{Digital Equipment Corporation}",
title = "{DECsystem}-10\slash 20 Hardware Manual",
publisher = pub-DP,
address = pub-DP:adr,
edition = "Fourth",
pages = "various",
month = mar,
year = "1976",
bibdate = "Fri Dec 08 13:03:19 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Also published as Stanford Artificial Intelligence
Laboratory Operating Note 75, November 1976.",
acknowledgement = ack-nhfb,
}
@Misc{DeSandre:1976:FPF,
author = "Giovanni {De Sandre} and Angelo Subrizi and Franco
Bretti",
title = "Fixed point to floating point conversion in an
electronic computer",
howpublished = "US Patent US3961170.",
day = "1",
month = jun,
year = "1976",
bibdate = "Sat Mar 24 06:14:58 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Patent filed 17 April 1974.",
URL = "https://patents.google.com/patent/US3961170A;
https://tinyurl.com/ybz9rrqy",
abstract = "In a digital electronic computer which comprises a
memory including a first and a second register, the
first register is receptive of a number to be converted
from fixed to floating point notation and the second
register is receptive of a significant zero digit with
an associated decimal point. Shifting means including a
register is operable to shift the contents of either
register and aligning means is operable to cause
shifting of the second register until the decimal point
stored therein is aligned with the decimal point in the
first register. Indicating means indicates whether the
number stored in the first register is greater or less
than one and the shifting means next begins shifting
the contents of one or the other of the registers when
the number is indicated greater or less than one
respectively. A control means includes a detecting
means for stopping the shifting means when the decimal
point of the second register becomes aligned with the
location of the next higher order with respect to the
highest significant digit of the first register. The
control means also includes counting means which is
incremented or decremented by one for each shifting
operation in dependence on the direction of shifting.
The resultant numbers in the first and second registers
represent the mantissa and exponent respectively, of
the desired floating point number.",
acknowledgement = ack-nhfb,
}
@Article{Detlefsen:1976:CRN,
author = "Michael Detlefsen and Douglas K. Erlandson and J.
Clark Heston and Charles M. Young",
title = "Computation with {Roman} numerals",
journal = j-ARCH-HIST-EXACT-SCI,
volume = "15",
number = "2",
pages = "141--148",
month = jun,
year = "1976",
CODEN = "AHESAN",
DOI = "https://doi.org/10.1007/BF00348497",
ISSN = "0003-9519 (print), 1432-0657 (electronic)",
ISSN-L = "0003-9519",
MRclass = "00A05 (01A20)",
MRnumber = "0453407 (56 \#11671)",
MRreviewer = "Richard L. Francis",
bibdate = "Fri Feb 4 21:50:12 MST 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=15&issue=2;
https://www.math.utah.edu/pub/tex/bib/archhistexactsci.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=15&issue=2&spage=141",
acknowledgement = ack-nhfb,
fjournal = "Archive for History of Exact Sciences",
journal-URL = "http://link.springer.com/journal/407",
MRtitle = "Computation with {Roman} numerals",
}
@MastersThesis{Dickinson:1976:PAA,
author = "Fred Kenneth Dickinson",
title = "Pseudo-round: an alternative approach for
floating-point representation",
type = "Thesis ({M.S.})",
school = "Southwest Texas State University",
address = "San Marcos, TX, USA",
pages = "vi + 53",
year = "1976",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Numerical calculations ---
Computer programs.",
}
@Article{Fateman:1976:MAP,
author = "R. J. Fateman",
title = "{Macsyma} Arbitrary Precision Floating Point
Arithmetic Package --- Philosophy and an Overview of
its Implementation",
journal = j-SIAM-REVIEW,
volume = "18",
number = "4",
pages = "802--802",
month = "????",
year = "1976",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Feldstein:1976:CED,
author = "Alan Feldstein and Richard Goodman",
title = "Convergence Estimates for the Distribution of Trailing
Digits",
journal = j-J-ACM,
volume = "23",
number = "2",
pages = "287--297",
month = apr,
year = "1976",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/321941.321948",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Wed Jan 15 18:12:53 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An analysis is made of the distribution of trailing
digits (tail end digits) of positive real
floating-point numbers represented in arbitrary base $
\beta $ and randomly chosen from a logarithmic
distribution. The analysis shows that the $n$ th digit
for $ n \geq 2 $ is actually approximately uniformly
distributed. The approximation depends upon both $n$
and the base beta. It becomes better as $n$ increases,
and it is exact in the limit as $ n \rightarrow \infty
$. A table of this distribution is presented for
various $ \beta $ and $n$, along with a table of the
maximum digit by digit deviation $ \Delta $ of the
logarithmic distribution from the uniform distribution.
Various asymptotic results for $ \Delta $ are
included.",
acknowledgement = ack-nhfb,
classification = "723",
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
journalabr = "J Assoc Comput Mach",
keywords = "Benford's Law; computer arithmetic; computer
programming; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Garner:1976:SSR,
author = "H. L. Garner",
title = "A Survey of Some Recent Contributions to Computer
Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "12",
pages = "1277--1282",
month = dec,
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.1674595",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:14:15 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Goldstein:1976:FCF,
author = "M. J. Goldstein",
title = "Further Comparison of Floating Point Summation
Methods",
journal = j-SIAM-REVIEW,
volume = "18",
number = "4",
pages = "805--805",
month = "????",
year = "1976",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
keywords = "accurate floating-point summation",
}
@Article{Goodman:1976:EGD,
author = "R. Goodman and A. Feldstein",
title = "Effect of Guard Digits and Normalization Options on
Floating Point Multiplication",
journal = j-SIAM-REVIEW,
volume = "18",
number = "4",
pages = "806--806",
month = "????",
year = "1976",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Goodman:1976:REF,
author = "Richard Goodman",
title = "On round-off error in fixed-point multiplication",
journal = j-BIT,
volume = "16",
number = "1",
pages = "41--51",
month = mar,
year = "1976",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01940776",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:14 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=16&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=16&issue=1&spage=41",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "fixed-point arithmetic; floating-point arithmetic;
rounding errors",
}
@Article{Goyal:1976:NAR,
author = "L. N. Goyal",
title = "A Note on {Atrubin}'s Real-Time Iterative Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "5",
pages = "546--548",
month = may,
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.1674646",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 06:24:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674646",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Hannington:1976:FPM,
author = "G. Hannington and D. G. Whitehead",
title = "A Floating-Point Multiplexed {DDA} System",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "11",
pages = "1074--1077",
month = nov,
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.1674557",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 06:24:54 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See comments \cite{McCrea:1978:CFP}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674557",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Higbie:1976:VFP,
author = "L. C. Higbie",
title = "Vector Floating-Point Data Format",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "1",
pages = "25--32",
month = jan,
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.5009201",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 06:24:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009201",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{IBM:1976:ISP,
author = "{IBM Corporation}",
title = "{IBM System}\slash 370: Principles of Operation:
Systems",
publisher = pub-IBM,
address = pub-IBM:adr,
pages = "326",
year = "1976",
LCCN = "QA76.8.I122 I57 1976",
bibdate = "Fri Sep 16 16:30:13 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Jayashree:1976:BMU,
author = "T. Jayashree and D. Basu",
title = "On Binary Multiplication Using the Quarter Square
Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "9",
pages = "957--960",
month = sep,
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.1674723",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 06:24:54 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674723",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kulisch:1976:FIF,
author = "U. Kulisch and G. Bohlender",
title = "Formalization and implementation of floating-point
matrix operations",
journal = j-COMPUTING,
volume = "16",
number = "3",
pages = "239--261",
year = "1976",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G05 (68A10)",
MRnumber = "53 7010",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
reviewer = "F. Szidarovszky",
}
@Book{Kulisch:1976:GNR,
author = "Ulrich W. Kulisch",
title = "{Grundlagen des numerischen Rechnens: mathematische
Begr{\"u}ndung der Rechnerarithmetik} \toenglish
{Fundamental Principles of Numerical Computation:
Mathematical Foundations of Computer Arithmetic}
\endtoenglish",
volume = "19",
publisher = pub-BIB-INST,
address = pub-BIB-INST:adr,
pages = "467",
year = "1976",
ISBN = "3-411-01517-9",
ISBN-13 = "978-3-411-01517-7",
LCCN = "QA162 .K85",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Reihe Informatik",
acknowledgement = ack-nhfb,
keywords = "Algebra, Abstract.; Floating-point arithmetic.;
Mathematics --- Data processing.",
}
@Article{Lacroix:1976:LCF,
author = "Arild Lacroix",
title = "Limit cycles in floating point digital filters",
journal = "AE{\"U}---Arch. Elektron. {\"U}bertragungstech.",
volume = "30",
number = "7/8",
pages = "277--284",
year = "1976",
MRclass = "94A05",
MRnumber = "56 15123",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Linnainmaa:1976:TEA,
author = "Seppo Linnainmaa",
title = "{Taylor} expansion of the accumulated rounding error",
journal = j-BIT,
volume = "16",
number = "2",
pages = "146--160",
month = jun,
year = "1976",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01931367",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:14 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=16&issue=2;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=16&issue=2&spage=146",
abstract = "The article describes analytic and algorithmic methods
for determining the coefficients of the Taylor
expansion of an accumulated rounding error with respect
to the local rounding errors, and hence determining the
influence of the local errors on the accumulated error.
Second and higher order coefficients are also
discussed, and some possible methods of reducing the
extensive storage requirements are analyzed.",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@MastersThesis{Lipschutz:1976:OPS,
author = "David Lipschutz",
title = "Optimization of a practical system for high fidelity
digital audio",
type = "Thesis ({M.S.})",
school = "Massachusetts Institute of Technology. Dept. of
Electrical Engineering and Computer Science",
address = "Cambridge, MA, USA",
pages = "53",
year = "1976",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supervised by Francis F. Lee.",
acknowledgement = ack-nhfb,
keywords = "Computer sound processing.; Digital electronics.;
Floating-point arithmetic.; High-fidelity sound
systems.; Noise --- Psychological aspects.",
}
@Article{Majithia:1976:SCC,
author = "J. C. Majithia",
title = "Some Comments Concerning Design of Pipeline Arithmetic
Arrays",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "11",
pages = "1132--1134",
month = nov,
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.1674565",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:06:10 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Maples:1976:FPI,
author = "Michael D. Maples",
title = "Floating-point package for {INTEL} 8008 and 8080
microprocessors",
institution = "Lawrence Livermore Laboratory, University of
California/Livermore; National Technical Information
Service [distributor]",
address = "Livermore, CA, USA",
pages = "8 + A-33",
year = "1976",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Intel 8080
(Microprocessor); Microprocessors.",
remark = "Prepared for U.S. Energy Research and Development
Administration, under Contract No. W-7405-Eng-43.
Microfiche reproduction: Springfield, Va.: National
Technical Information Service, 1976. --- 1 microfiche;
10 x 15 cm.",
}
@PhdThesis{Martinez:1976:SSS,
author = "Ralph Martinez",
title = "A semi-portable simulation system using both fixed and
floating point derivative blocks",
type = "Thesis ({Ph.D.} - Electrical Engineering)",
school = "University of Arizona",
address = "Tucson, AZ, USA",
pages = "xii + 169",
year = "1976",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Digital computer simulation.; Dynamics --- Data
processing.",
}
@TechReport{Metropolis:1976:MSA,
author = "N. Metropolis",
title = "Methods of significance arithmetic",
type = "Technical report",
number = "LA-UR-76-661;CONF-760428-1",
institution = inst-LASL,
address = inst-LASL:adr,
day = "1",
month = jan,
year = "1976",
bibdate = "Tue Mar 20 11:16:47 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Presented at the Conference on the state of the art in
numerical analysis, 12 April 1976, University of York,
England, UK",
URL = "http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=7189580&query_id=0",
abstract = "A preliminary report is given of two applications of
the methods of significance arithmetic. These are a
simple nonlinear partial differential equation and
matrix inversion.",
acknowledgement = ack-nhfb,
remark = "OSTI ID: 7189580",
}
@Article{Miller:1976:AGF,
author = "Webb Miller and David L. Spooner",
title = "Automatic Generation of Floating-Point Test Data",
journal = j-IEEE-TRANS-SOFTW-ENG,
volume = "SE-2",
number = "3",
pages = "223--226",
month = sep,
year = "1976",
CODEN = "IESEDJ",
DOI = "https://doi.org/10.1109/TSE.1976.233818",
ISSN = "0098-5589 (print), 1939-3520 (electronic)",
ISSN-L = "0098-5589",
MRclass = "68A05",
MRnumber = "55 1787",
bibdate = "Thu Feb 1 08:07:37 MST 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranssoftweng1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1702369",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Software Engineering",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=32",
keywords = "floating-point testing",
remark = "Special section on testing",
reviewer = "George Marsaglia",
}
@Article{Mohn:1976:IPA,
author = "K. Mohn and R. V. Roman",
title = "An interactive polynomial approximation algorithm",
journal = j-COMP-J,
volume = "19",
number = "1",
pages = "74--78",
month = feb,
year = "1976",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Thu Sep 15 18:39:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Ni:1976:EAT,
author = "Ming Duenn Ni and J. K. Aggarwal",
title = "Error analysis of two-dimensional recursive digital
filters employing floating-point arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "7",
pages = "755--759",
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.1674684",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "65D99 (93E10)",
MRnumber = "55 6802",
bibdate = "Sat Dec 16 16:45:24 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
reviewer = "Sven-{\AA}ke Gustafson",
}
@TechReport{Paoni:1976:PFI,
author = "C. Paoni and M. Maples",
title = "A {PLM} floating-point interface program",
institution = "Lawrence Livermore Laboratory; National Technical
Information Service",
address = "Livermore, CA, USA",
pages = "iii + 39",
year = "1976",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Parker:1976:STR,
author = "Douglass Stott Parker",
title = "The statistical theory of relative errors in
floating-point computation",
type = "Thesis ({M.S.})",
school = "Department of Computer Science, University of Illinois
at Urbana-Champaign",
address = "Urbana, IL, USA",
pages = "62",
year = "1976",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Report no. UIUCDCS-R-76-787",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Roundoff errors.",
}
@Article{Patel:1976:ASB,
author = "M. R. Patel and K. H. Bennett",
title = "Analysis of Speed of a Binary Multiplier Using a
Variable Number of Shifts Per Cycle",
journal = j-COMP-J,
volume = "19",
number = "3",
pages = "254--257",
month = aug,
year = "1976",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/19.3.254",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:58 MST 2012",
bibsource = "Compendex database;
http://comjnl.oxfordjournals.org/content/19/3.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/;
https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/19/3/254.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/tiff/254.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/tiff/255.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/tiff/256.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/tiff/257.tif",
acknowledgement = ack-nhfb,
classcodes = "C5210 (Logic design methods); C5230 (Digital
arithmetic methods)",
classification = "723",
corpsource = "Department of Computer Sci., University of Keele,
Keele, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "binary multiplication; binary multiplier; computers,
digital; digital arithmetic; logic design;
multiplication; multiplying circuits; shift per cycle;
speed",
}
@Article{Paul:1976:SEF,
author = "George Paul and M. Wayne Wilson",
title = "Should the Elementary Function Library Be Incorporated
Into Computer Instruction Sets?",
journal = j-TOMS,
volume = "2",
number = "2",
pages = "132--142",
month = jun,
year = "1976",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355681.355684",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Aug 27 00:30:21 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@PhdThesis{Pichat:1976:CEE,
author = "Mich{\`e}le Pichat",
title = "Contributions {\`a} l'{\`e}tude des erreurs d'arrondi
en arithm{\`e}tique {\`a} virgule flottante. ({French})
[Contributions to the error analysis of rounding errors
in floating-point arithmetic]",
type = "Th{\`e}se",
school = "Universit{\'e} de Grenoble 1",
address = "Grenoble, France",
year = "1976",
bibdate = "Thu May 27 07:44:27 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://tel.archives-ouvertes.fr/tel-00287209/",
acknowledgement = ack-nhfb,
language = "French",
}
@TechReport{Randell:1976:ODC,
author = "Brian Randell",
title = "The origins of digital computers: supplementary
bibliography to {``Origins of digital computers:
selected papers''}",
type = "Technical report",
number = "91",
institution = "Computing Laboratory, University of Newcastle upon
Tyne",
address = "Newcastle upon Tyne, UK",
pages = "3 + 37",
year = "1976",
LCCN = "Z5642.2 .R36 1979",
bibdate = "Wed Oct 13 09:24:25 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
subject = "electronic digital computers; history; calculators",
}
@Article{Rankin:1976:FPR,
author = "Roy Rankin and Steve Wozniak",
title = "Floating Point Routines for the 6502",
journal = j-DDJ,
volume = "1",
number = "??",
pages = "17--19",
month = aug,
year = "1976",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Sat Jan 15 06:04:06 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.6502.org/source/floats/wozfp1.txt",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "HP 2100; MOS Technology",
}
@Article{Riesel:1976:FPU,
author = "Zvi H. Riesel",
title = "The floating point unit of the {Golem B} computer",
journal = j-RADIO-ELECTRON-ENG,
volume = "46",
number = "7",
pages = "355--359",
month = jul,
year = "1976",
CODEN = "RDEEA4",
DOI = "https://doi.org/10.1049/ree.1976.0057",
ISSN = "0033-7722",
bibdate = "Fri Dec 03 15:11:57 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Golem B computer is a fast machine using
emitter-coupled logic and multi-layer circuits. The
autonomous floating point arithmetic unit obtains its
instructions and operands from buffers loaded ahead of
need. Its main part, for 56-bit fractions, uses two
4-operand adder complexes with stored carries. In
multiplication instructions, 4 bits of the multiplier
are used to form a new partial product in each pass
through an adder complex. Division instructions use a
base-4 non-restoring algorithm. Addition favours the
case of equal or nearly equal exponents, but 112 sum
bits are accumulated for all exponent differences. An
effort has been made to provide instructions and number
formats that will aid the writing of compilers and
operating systems.",
acknowledgement = ack-nhfb,
fjournal = "The Radio and Electronic Engineer",
keywords = "adder complex; autonomous floating point arithmetic
unit; buffers; division instructions; emitter coupled
logic; exponent differences; Golem B computer; multi
layer circuits; multiplication instructions; partial
product",
}
@Article{Ris:1976:UDF,
author = "Frederic N. Ris",
title = "A Unified Decimal Floating-Point Architecture For the
Support of High-Level Languages",
journal = j-SIGNUM,
volume = "11",
number = "3",
pages = "18--23",
month = oct,
year = "1976",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:03 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper summarizes a proposal for a decimal
floating-point arithmetic interface for the support of
high-level languages, consisting both of the arithmetic
operations observed by application programs and
facilities to produce subroutine libraries accessible
from these programs. What is not included here are the
detailed motivations, examinations of alternatives, and
implementation considerations which will appear in the
full work.",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods); C6120 (File
organisation)C6140D (High level languages)",
corpsource = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "arithmetic operations; decimal floating point
arithmetic; digital arithmetic; high level languages;
one level store",
remark = "Normalized decimal floating-point arithmetic with a
fractional coefficient, three directed rounding modes,
and a trap mechanism. Three precisions are provided,
with up to 31 decimal digits, and an exponent range of
$ \pm 9999 $. Cowlishaw \cite{Cowlishaw:2003:DFP} says
that this is the first implementation of the Chen-Ho
\cite{Chen:1975:SER} compressed format, allowing
storage of 31 digits and 4 exponent digits in a 128-bit
value. More modern encodings get 34 digits in the same
number of bits, at somewhat reduced exponent range ($ [
- 6143, 6144] $).",
treatment = "P Practical; T Theoretical or Mathematical",
}
@TechReport{Rosser:1976:CRE,
author = "J. Barkley Rosser and J. Michael Yohe",
title = "Cancellation and Rounding Errors",
type = "Technical Summary Report",
number = "1588",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
month = apr,
year = "1976",
bibdate = "Sun Dec 30 21:30:27 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The fact that a calculating machine can usually hold
only an approximation to the number that one is
concerned with leads to cancellation errors and
rounding errors. These concepts are defined precisely
and examples are given. Suggestions are given for
reducing (when possible) the size of errors arising
from these two effects.",
acknowledgement = ack-nhfb,
}
@Article{Rowland:1976:BRB,
author = "John H. Rowland",
title = "Book Review: {{\booktitle{Floating-Point Computation}}
(Pat H. Sterbenz)}",
journal = j-SIAM-REVIEW,
volume = "18",
number = "1",
pages = "138--139",
month = "????",
year = "1976",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1018026",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:52:30 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/18/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1976",
}
@Article{Rudeanu:1976:SRF,
author = "S. Rudeanu",
title = "Square Roots and Functional Decompositions of
{Boolean} Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "5",
pages = "528--532",
month = may,
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.1674641",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 06:24:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674641",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@PhdThesis{Sanderson:1976:PCT,
author = "James George Sanderson",
title = "A proof of convergence for the tridiagonal {QL}
algorithm in floating-point arithmetic",
type = "Thesis ({Ph.D.})",
school = "University of New Mexico",
address = "Albuquerque, NM, USA",
pages = "vi + 69",
year = "1976",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Algorithms.; Arithmetic --- Foundations.",
}
@Article{Shi:1976:SLC,
author = "S.-Y. Shi",
title = "Shortcut to Logarithms Combines Table Lookup and
Computation",
journal = j-COMP-DESIGN,
volume = "15",
number = "5",
pages = "184--186",
month = may,
year = "1976",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Thu Sep 08 08:07:38 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Design",
}
@PhdThesis{Slekys:1976:DCN,
author = "Arunas George Slekys",
title = "Design of complex number digital arithmetic units
based on a modified bi-imaginary number system",
type = "{Ph.D. thesis}",
school = "University of California, Los Angeles",
address = "Los Angeles, CA, USA",
pages = "223",
year = "1976",
bibdate = "Sat Aug 22 09:03:47 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "ProQuest order number AAI7707685.",
}
@Book{Spaniol:1976:AR,
author = "Otto Spaniol",
title = "{Arithmetik in Rechenanlagen: Logik und Entwurf}
\toenglish {Computer Arithmetic: Logic and Design}
\endtoenglish",
publisher = pub-TEUBNER,
address = pub-TEUBNER:adr,
pages = "208",
year = "1976",
ISBN = "3-519-02332-6",
ISBN-13 = "978-3-519-02332-6",
LCCN = "QA76.6 .S66",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "For an English translation, see
\cite{Spaniol:1981:CAL}.",
price = "DM24.80",
acknowledgement = ack-nj,
}
@TechReport{Warren:1976:MDT,
author = "H. S. {Warren, Jr.} and A. S. Fox and P. W.
Markstein",
title = "Modulus Division on a Two's Complement Machine",
type = "Research Report",
number = "RC7712",
institution = "IBM",
address = "Yorktown Heights, NY, USA",
month = jun,
year = "1976",
bibdate = "Fri Nov 09 19:32:44 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
xxnote = "Check: Waser/Flynn book dates this as 1979.",
}
@Article{Wyatt:1976:PEP,
author = "W. T. {Wyatt Jr.} and D. W. Lozier and D. J. Orser",
title = "A Portable Extended Precision Arithmetic Package and
Library With {Fortran} Precompiler",
journal = j-TOMS,
volume = "2",
number = "3",
pages = "209--231",
month = sep,
year = "1976",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Sep 12 08:07:55 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1976-2-3/p209-lozier/",
acknowledgement = ack-nj,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Yau:1976:DMA,
author = "S. S. Yau and J. Chung",
title = "On the Design of Modulo Arithmetic Units Based on
Cyclic Groups",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "11",
pages = "1057--1067",
month = nov,
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.1674555",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 06:24:54 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674555",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Zohar:1976:RTR,
author = "S. Zohar",
title = "Rounding and Truncation in Radix (-2) Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "5",
pages = "464--469",
month = may,
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.1674634",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 06:24:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674634",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Agrawal:1977:CNB,
author = "D. P. Agrawal",
title = "Comments on {``A Note on Base-$2$ Arithmetic
Logic''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "5",
pages = "511--511",
month = may,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674869",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:54 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Yuen:1975:NBA}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674869",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Albrecht:1977:GC,
author = "Rudolf Albrecht and Ulrich Kulisch",
title = "{Grundlagen der Computer-Arithmetik}",
publisher = "Springer-Verlag",
address = "Wien, Austria",
pages = "viii + 150",
year = "1977",
ISBN = "0-387-81410-8",
ISBN-13 = "978-0-387-81410-0",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Computing: Supplementum; 1 Computing
(Springer-Verlag). Supplementum; 1.",
acknowledgement = ack-nhfb,
keywords = "Algebra, Abstract.; Floating-point arithmetic.;
Mathematics --- Data processing.",
remark = "``Diese Artikel stellen eine Auswahl von Vortragen
dar, die auf einer vom 4. bis 8. August 1975 im
`Mathematischen Forschungsinstitut Oberwolfach'
stattgefundenen Tagung gehalten wurden.''",
}
@Book{Albrecht:1977:GCA,
editor = "R. Albrecht and U. Kulisch",
title = "{Grundlagen der Computer-Arithmetik} \toenglish
{Foundations of Computer Arithmetic} \endtoenglish",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 150",
year = "1977",
ISBN = "0-387-81410-8",
ISBN-13 = "978-0-387-81410-0",
LCCN = "QA162 .G78",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Diese Artikel stellen eine Auswahl von Vortragen dar,
die auf einer vom 4. bis 8. August 1975 im
`Mathematischen Forschungsinstitut Oberwolfach'
stattgefundenen Tagung gehalten wurden.",
acknowledgement = ack-nhfb,
}
@Article{Alexander:1977:SRR,
author = "V. L. Alexander",
title = "Square Root Routine",
journal = j-IBM-TDB,
volume = "20",
number = "3",
pages = "1222",
month = aug,
year = "1977",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Article{Anonymous:1977:CAF,
author = "Anonymous",
title = "Computer Arithmetic: Foreword and Survey",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "609--609",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674892",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:55 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674892",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Manual{AppleComputer:1977:ARM,
author = "{Apple Computer, Inc}",
title = "{APPLESOFT} reference manual: extended precision
floating point {BASIC} language",
organization = "Apple Computer, Inc.",
address = "Cupertino, CA, USA",
pages = "75",
year = "1977",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Apple computer --- Programming.; BASIC (Computer
program language) --- Programming.; Microcomputers ---
Programming.",
}
@Article{Barak:1977:MAT,
author = "A. B. Barak",
title = "Multiplicative Algorithms for Ternary Arithmetic Using
Binary Logic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "8",
pages = "823--826",
month = aug,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674922",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674922",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Bauer:1977:CFP,
author = "Henry R. Bauer",
title = "Comments on {``On the Floating Point Representation of
Complex Numbers''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "2",
pages = "191--191",
month = feb,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.5009301",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:52 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Yuen:1975:FPR}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009301",
abstract = "A recent paper [Burroughs B7700 Information Processing
Systems Reference Manual, p. 2-9, 1973, Burroughs
Corporation] discussed an integrated notation for
complex numbers. A second choice of the radix point
position will increase the number of values near the
origin. An argument is also made for unnormalized
notation of both parts of a complex number.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Bivins:1977:SAA,
author = "Robert L. Bivins and Nicholas C. Metropolis",
title = "Significance Arithmetic: Application to a Partial
Differential Equation",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "639--642",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674896",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "http://dblp.uni-trier.de/db/journals/tc/tc26.html#BivinsM77;
https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/iel5/12/35159/01674896.pdf?tp=&isnumber=35159&arnumber=1674896&punumber=12",
ZMnumber = "0405.65056",
abstract = "The methods of significance arithmetic are applied to
the numerical solution of a nonlinear
partial-differential equation. Our approach permits the
use of initial values having imprecision considerably
greater than that of rounding error; moreover, the
intermediate and final quantities are monitored so that
at any stage the precision of such quantities is
available. An algorithm is found that represents
faithfully the solution to a difference-equation
approximation to Burgers' equation.",
acknowledgement = ack-jr,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Bohlender:1977:FPC,
author = "Gerd Bohlender",
title = "Floating-Point Computation of Functions with Maximum
Accuracy",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "621--632",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674894",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "65D15 (68A99)",
MRnumber = "56 9908",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "accurate floating-point summation",
reviewer = "Bernard H. Rosman",
}
@MastersThesis{Brinkmann:1977:FPT,
author = "Hubert Eldie Brinkmann",
title = "A floating-point processor for the {Texas Instruments}
model {980A} computer",
type = "Electrical Engineering Thesis ({M.S.})",
publisher = "Brinkmann",
school = "Texas A\&M University",
address = "College Station, TX, USA",
pages = "x + 68",
year = "1977",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Microprocessors.; Microprogramming.; Miniature
computers --- Programming.",
}
@InProceedings{Brown:1977:MSI,
author = "W. S. Brown",
title = "A realistic model of floating-point computation",
crossref = "Rice:1977:MSI",
number = "39",
pages = "343--360",
year = "1977",
DOI = "https://doi.org/10.1016/B978-0-12-587260-7.50017-0",
MRclass = "68A05",
MRnumber = "58 3605",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/unix.bib",
URL = "https://www.sciencedirect.com/science/article/abs/pii/B9780125872607500170",
acknowledgement = ack-nhfb,
reviewer = "Costica Cazacu",
}
@Article{Collins:1977:APS,
author = "George E. Collins and David R. Musser",
title = "Analysis of the {Pope--Stein} Division Algorithm",
journal = j-INFO-PROC-LETT,
volume = "6",
number = "5",
pages = "151--155",
day = "??",
month = oct,
year = "1977",
CODEN = "IFPLAT",
DOI = "https://doi.org/10.1016/0020-0190(77)90012-6",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Tue Nov 17 10:49:43 MST 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/infoproc1970.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
classification = "C4240 (Programming and algorithm theory)",
corpsource = "Computer Sci. Dept., University of Wisconsin, Madison,
WI, USA",
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190/",
keywords = "algorithm; algorithm theory; digital arithmetic;
integer division; multiple precision integer division;
trial quotient digits",
treatment = "T Theoretical or Mathematical",
}
@Article{Colquhoun:1977:FAS,
author = "D. G. Colquhoun",
title = "A Fast Approximation to the Sine Function",
journal = j-SPE,
volume = "7",
number = "2",
pages = "227--229",
month = mar # "--" # apr,
year = "1977",
CODEN = "SPEXBL",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Fri Dec 08 13:06:08 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}
@Book{DEC:1977:VAH,
author = "{Digital Equipment Corporation}",
title = "{VAX-11}\slash 780 Architecture Handbook",
publisher = pub-DP,
address = pub-DP:adr,
pages = "328",
year = "1977",
LCCN = "QA76.8 .V12D5 B 2 829 348",
bibdate = "Thu Sep 15 18:50:55 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
xxISBN = "(none)",
}
@InProceedings{Dekker:1977:MRR,
author = "T. J. Dekker",
title = "Machine Requirements for Reliable Portable Software",
crossref = "Cowell:1977:PMS",
pages = "22--36",
year = "1977",
bibdate = "Wed Nov 07 08:38:01 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Derenzo:1977:AHC,
author = "Stephen E. Derenzo",
title = "Approximations for Hand Calculators Using Small
Integer Coefficients",
journal = j-MATH-COMPUT,
volume = "31",
number = "137",
pages = "214--222",
month = jan,
year = "1977",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb # " and " # ack-nj,
ajournal = "Math. Comput.",
classcodes = "B0290D (Functional analysis); B0290F (Interpolation
and function approximation); C4120 (Functional
analysis); C4130 (Interpolation and function
approximation); C7310 (Mathematics computing)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "approximations; function approximation; function
evaluation; hand calculators; programmable calculators;
small integer coefficients",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Egbert:1977:PCAa,
author = "W. E. Egbert",
title = "Personal Calculator Algorithms {I}: Square Roots",
journal = j-HEWLETT-PACKARD-J,
volume = "28",
number = "9",
pages = "22--24",
month = may,
year = "1977",
CODEN = "HPJOAX",
ISSN = "0018-1153",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5420 (Mainframes and minicomputers); C7310
(Mathematics computing)",
fjournal = "Hewlett-Packard Journal: technical information from
the laboratories of Hewlett-Packard Company",
keywords = "electronic calculators; HP personal calculator; square
root algorithm",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Egbert:1977:PCAb,
author = "W. E. Egbert",
title = "Personal Calculator Algorithms {II}: Trigonometric
Functions",
journal = j-HEWLETT-PACKARD-J,
volume = "28",
number = "10",
pages = "17--20",
month = jun,
year = "1977",
CODEN = "HPJOAX",
ISSN = "0018-1153",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Hewlett-Packard Journal: technical information from
the laboratories of Hewlett-Packard Company",
}
@Article{Egbert:1977:PCAc,
author = "W. E. Egbert",
title = "Personal Calculator Algorithms {III}: Inverse
Trigonometric Functions",
journal = j-HEWLETT-PACKARD-J,
volume = "29",
number = "3",
pages = "22--23",
month = nov,
year = "1977",
CODEN = "HPJOAX",
ISSN = "0018-1153",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Hewlett-Packard Journal: technical information from
the laboratories of Hewlett-Packard Company",
}
@Article{Ercegovac:1977:GHO,
author = "Milo{\v{s}} D. Ercegovac",
title = "A General Hardware-Oriented Method for Evaluation of
Functions and Computations in a Digital Computer",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "667--680",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674900",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674900",
abstract = "A parallel computational method, amenable for
efficient hardware-level implementation, is described.
It provides a simple and fast algorithm for the
evaluation of polynomials, certain rational functions
and arithmetic expressions, solving a class of systems
of linear equations, or performing the basic arithmetic
operations in a fixed-point number representation
system. The time required to perform the computation is
of the order of $m$ carry-free addition operations, $m$
being the number of digits in the solution. In
particular, the method is suitable for fast evaluation
of mathematical functions in hardware.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Arithmetic expressions; digital computer arithmetic;
E-method; evaluation of real-valued functions;
fixed-point representation; hardware-level
implementation; integral powers; linear systems;
on-line algorithms; parallel computation; polynomials;
rational functions; redundant number systems",
}
@Article{Evans:1977:AAT,
author = "Gillian R. Evans",
title = "From abacus to algorism: Theory and practice in
medieval arithmetic",
journal = j-BRITISH-J-HIST-SCI,
volume = "10",
number = "2",
pages = "114--131",
month = jul,
year = "1977",
CODEN = "BJHSAT",
DOI = "https://doi.org/10.1017/S0007087400015375",
ISSN = "0007-0874 (print), 1474-001X (electronic)",
ISSN-L = "0007-0874",
MRclass = "01A35 (Mathematics in the medieval)",
MRnumber = "522510 (80e:01006)",
MRreviewer = "M. Folkerts",
bibdate = "Thu Sep 23 07:34:43 MDT 2010",
bibsource = "http://journals.cambridge.org/action/displayJournal?jid=BJH;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
URL = "http://www.jstor.org/stable/4025865",
ZMnumber = "0358.01003",
abstract = "This paper deals primarily with the change in
practical procedures of calculation which took place
during the course of the twelfth century in Western
Europe. At the beginning of the period, the abacus was
in relatively common use; towards the end, it was being
superseded by the method of calculation which was known
as the algorism. Certain differences of theory are
apparent. Among the textbooks which were most
influential in bringing about the change was
Sacrobosco's Algorithmus Vulgaris. Authors of both
abacus and algorism treatises give an account of
number-symbols and discuss elementary number theory
briefly, but the algorism treatise show how much more
confident the authors were in using Arabic numerals.
The algorisms employ a symbol for zero; although it has
antecedents in some abacus treatises, its usefulness
was clearly not fully perceived by the authors, because
the columns of the abacus made it unnecessary to use a
counter to indicate that the number under consideration
was, for example, 306, not 36. The algorisms deal with
a far wider range of operations; while the abacus
treatises confine themselves to multiplication and
division of whole numbers and fractions, the algorisms
have addition, subtraction, doubling, halving,
multiplication, division, the extraction of roots and
progression, as well as numeration. Changes in
technical terminology are discussed. There are two
appendices, one dealing with the compilation of
arithmetical texts in Bodleian Library Oxford,
MS.~Laud.~Misc.~644, and the other on the arithmetical
sense of the term equipollentia, which was a technical
term of dialectic.",
acknowledgement = ack-nhfb,
fjournal = "British Journal for the History of Science",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BJH",
ZMreviewer = "Gillian R. Evans",
}
@Article{Feldman:1977:EEA,
author = "Michael B. Feldman",
title = "Embedding extended arithmetic in {SNOBOL4}",
journal = j-SIGPLAN,
volume = "12",
number = "1",
pages = "67--72",
month = jan,
year = "1977",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:13:59 MST 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods); C6140D (High
level languages)",
corpsource = "George Washington University, Washington, DC, USA",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "complex numbers; data structure; data structures;
digital arithmetic; embedded; extended arithmetic;
procedure oriented languages; rotational numbers;
SNOBOL4",
treatment = "P Practical",
}
@Book{Forsythe:1977:CMM,
author = "George E. (George Elmer) Forsythe and Michael A.
Malcolm and Cleve B. Moler",
title = "Computer Methods for Mathematical Computations",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xi + 259",
year = "1977",
ISBN = "0-13-165332-6",
ISBN-13 = "978-0-13-165332-0",
LCCN = "QA297 .F5681",
MRclass = "65-01",
MRnumber = "MR0458783 (56 \#16983)",
MRreviewer = "Sven-{\AA}ke Gustafson",
bibdate = "Tue May 25 09:01:08 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available by anonymous ftp from
\path=math.liu.se= in \path=pub/references=",
price = "US\$16.95",
series = "Prentice-Hall series in automatic computation",
ZMnumber = "0361.65002",
acknowledgement = ack-nhfb,
classmath = "*65-01 Textbooks (numerical analysis) 68-01 Textbooks
(computer science)",
keywords = "Fortran (computer program language); numerical
analysis -- data processing",
remark = "Subroutines and exercises for the computer solution of
problems involving matrices, integrals, differential
equations, spline functions, zeros and extrema of
functions, least squares, and Monte Carlo techniques.",
subject = "Numerical analysis; Data processing; Computer
programs; Problems, exercises, etc; FORTRAN (Computer
program language)",
tableofcontents = "Introduction \\
Floating-point computation \\
Linear systems of equations \\
Interpolation \\
Numerical integration \\
Initial value problems in ordinary differential
equations \\
Solution of nonlinear equations \\
Optimization \\
Least squares and the singular value decomposition \\
Random number generation and Monte Carlo methods",
}
@TechReport{Frenckner:1977:MFP,
author = "K. Frenckner and M. Persson and S. Romberger and Y.
Sundblad",
title = "Microprogrammed floating-point arithmetic for the
{Varian-73} computer",
type = "Technical report",
number = "TRITA-NA-7702",
institution = "Kungl. Tekniska H{\"o}gskolan",
address = "Stockholm, Sweden",
pages = "37",
month = jun,
year = "1977",
bibdate = "Fri May 25 05:52:09 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0028467",
acknowledgement = ack-nhfb,
}
@TechReport{Ginsberg:1977:NID,
author = "Myron Ginsberg",
title = "Numerical influences on the design of floating-point
arithmetic for microcomputers",
type = "Technical report",
number = "CS 7708",
institution = "Department of Computer Science, Southern Methodist
University",
address = "Dallas, TX, USA",
pages = "72",
year = "1977",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic --- Data processing.",
}
@TechReport{Goldsmith:1977:ICF,
author = "Theodore C. Goldsmith",
title = "An integrated circuit floating point accumulator",
type = "{NASA} technical note",
number = "NASA TN D-8509 NASA",
institution = "National Aeronautics and Space Administration; for
sale by the National Technical Information Service",
address = "Washington, DC, USA",
pages = "26",
year = "1977",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
govtdocnumber = "NAS 1.14:D-8509",
remark = "Issued June 1977.",
}
@Article{Goodman:1977:EGD,
author = "R. Goodman and A. Feldstein",
title = "Effect of Guard Digits and Normalization Options on
Floating Point Multiplication",
journal = j-COMPUTING,
volume = "18",
number = "2",
pages = "93--106",
month = "????",
year = "1977",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G05",
MRnumber = "55 11596",
bibdate = "Fri Dec 08 12:02:42 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
reviewer = "N. N. Abdelmalek",
}
@Article{Goodwin:1977:CUO,
author = "D. T. Goodwin",
title = "Conditions for Underflow and Overflow of an Arithmetic
Stack",
journal = j-COMP-J,
volume = "20",
number = "1",
pages = "56--62",
month = feb,
year = "1977",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/20.1.56",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:59 MST 2012",
bibsource = "Compendex database;
http://comjnl.oxfordjournals.org/content/20/1.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/;
https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/20/1/56.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/56.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/57.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/58.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/59.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/60.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/61.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/62.tif",
acknowledgement = ack-nhfb,
classcodes = "C4210 (Formal logic)",
classification = "721; 723",
corpsource = "Department of Computer Sci., University of Keele,
Keele, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "arbitrary string; arithmetic stack; automata theory
--- Context Free Languages; behaviour; computer
metatheory; computer operating systems --- Program
Compilers; context free language; context-free
languages; loading; overflow; underflow",
treatment = "T Theoretical or Mathematical",
}
@Article{Gregory:1977:BCR,
author = "Robert Todd Gregory and David W. Matula",
title = "Base conversion in residue number systems",
journal = j-BIT,
volume = "17",
number = "3",
pages = "286--302",
month = sep,
year = "1977",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01932149",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "10A30 (68A10)",
MRnumber = "MR0476627 (57 \#16186)",
MRreviewer = "L. Carlitz",
bibdate = "Wed Jan 4 18:52:15 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=17&issue=3;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=17&issue=3&spage=286",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "Interval arithmetic; residue arithmetic",
}
@Article{Hashizume:1977:FPA,
author = "B. Hashizume",
title = "Floating Point Arithmetic",
journal = j-BYTE,
volume = "2",
number = "11",
pages = "76--78, 180--188",
month = nov,
year = "1977",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 1 10:14:44 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "BYTE Magazine",
}
@Article{Hastings:1977:FPH,
author = "Jordan Towner Hastings",
title = "Floating point half-word packing for {Control Data
Corporation 6000/7000 series} hardware",
journal = j-SPE,
volume = "7",
number = "1",
pages = "146--147",
month = jan,
year = "1977",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.4380070111",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Wed Sep 10 12:36:39 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/spe.bib",
acknowledgement = ack-nhfb,
fjournal = "Software --- Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
onlinedate = "27 Oct 2006",
}
@PhdThesis{Hough:1977:EAI,
author = "David Granville Hough",
title = "Explaining and ameliorating the ill-condition of zeros
of polynomials",
type = "{Ph.D.} Thesis",
school = "Electronics Research Lab., University of California,
Berkeley",
address = "Berkeley, CA, USA",
pages = "303",
month = feb,
year = "1977",
bibdate = "Thu Jan 12 09:05:57 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://wwwlib.umi.com/dissertations/fullcit/7731401",
acknowledgement = ack-nhfb,
}
@Article{Jenkins:1977:URN,
author = "W. Jenkins and B. Leon",
title = "The use of residue number systems in the design of
finite impulse response digital filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "24",
number = "4",
pages = "191--201",
month = apr,
year = "1977",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1109/PGEC.1967.264810",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23467",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "A technique is presented for implementing a finite
impulse response (FIR) digital filter in a residue
number system (RNS). For many years residue number
coding has been recognized as a system which provides a
capability for the implementation of \ldots{}",
}
@InProceedings{Jullien:1977:HRD,
author = "G. Jullien and W. Miller and J. Soltis and A.
Baraniecka and B. Tseng",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '77}",
title = "Hardware realization of digital signal processing
elements using the residue number system",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "506--510",
year = "1977",
CODEN = "????",
DOI = "https://doi.org/10.1049/el:19770117",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "In the past, hardware realization of digital signal
processing elements have been based upon binary
arithmetic concepts. Because of the dependence between
digits in binary arithmetic operations, the hardware
required to construct arithmetic elements \ldots{}",
}
@TechReport{Kahan:1977:CYC,
author = "W. M. Kahan and B. N. Parlett",
title = "Can You Count on Your Calculator?",
type = "Memorandum",
number = "UCB/ERL M77/21",
institution = "Electronics Research Laboratory, College of
Engineering, University of California, Berkeley",
address = "Berkeley, CA, USA",
pages = "ii + 28",
day = "6",
month = apr,
year = "1977",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "German Transl. Published In: Jahrbuch {\"U}berblicke
Mathematik 1978, Ed. by B. Fuchssteiner and others,
Bibliographisches Institut, Mannheim-Wien-Z{\"u}rich,
199--216, 1978",
URL = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
acknowledgement = ack-jr,
}
@Article{Kent:1977:HSF,
author = "J. G. Kent",
title = "Highlights of a Study of Floating-Point Instructions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "660--666",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674899",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:14:15 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The research work that this paper is based on resulted
in the development of tools for the theoretical
definition, analysis and comparison of floating-point
instructions as mathematical mappings. These tools can
be used to study the properties of most floating-point
instructions and their operands.",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kent:1977:HST,
author = "S. A. Kent",
title = "A High-Speed Threshold Gate Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "12",
pages = "1279--1283",
month = dec,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674790",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:59 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674790",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kornerup:1977:UNR,
author = "P. Kornerup and B. D. Shriver",
title = "A Unified Numeric Representation Arithmetic Unit and
Its Language Support",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "651--659",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674898",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:55 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674898",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Krishnamurthy:1977:MPU,
author = "E. V. Krishnamurthy",
title = "Matrix Processors Using $p$-adic Arithmetic for Exact
Linear Computations",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "633--639",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674895",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:55 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674895",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kuck:1977:ARM,
author = "David J. Kuck and Douglass S. {Parker Jr.} and Ahmed
H. Sameh",
title = "Analysis of Rounding Methods in Floating-Point
Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "643--650",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674897",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "65G05",
MRnumber = "57 7979",
bibdate = "Fri Dec 08 12:00:49 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
reviewer = "V. V. Ivanov",
}
@Article{Kulisch:1977:MFC,
author = "Ulrich Kulisch",
title = "Mathematical foundations of computer arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "610--620",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674893",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat May 18 14:33:16 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Lee:1977:FNS,
author = "S. C. Lee and A. D. Edgar",
title = "The {Focus} Number System",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "11",
pages = "1167--1170",
month = nov,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674770",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See comments
\cite{Lee:1979:AFN,Swartzlander:1979:CFN}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674770",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Ligomenides:1977:SSF,
author = "P. A. Ligomenides",
title = "The Skip-and-Set Fast-Division Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "10",
pages = "1030--1032",
month = oct,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674740",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 10:17:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674740",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Luke:1977:ACM,
author = "Yudell L. Luke",
title = "Algorithms for the Computation of Mathematical
Functions",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xiii + 284",
year = "1977",
ISBN = "0-12-459940-0",
ISBN-13 = "978-0-12-459940-6",
LCCN = "QA351 .L7961",
bibdate = "Wed Dec 15 10:38:19 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Preface / xi \\
1: Basic Formulas / 1 \\
1.1 Introduction / 1 \\
1.2 The Generalized Hypergeometric Function and the
$G$-Function / 1 \\
1.3 Expansion of $_pF_q(z)$ and $G^{q - r, 1}_{p + 1,
q}(z)$, $r = 0$ or $r = 1$, in Series of Chebyshev
Polynomials of the First Kind / 4 \\
1.4 Efficient Evaluation of Series of Chebyshev
Polynomials / 17 \\
1.5 Rational Approximations for Generalized
Hypergeometric Functions / 20 \\
1.6 The Pad{\'e} Table / 27 \\
1.7 Computations of and Checks on Coefficients and
Tables / 29 \\
1.8 Tables of the Functions $e^{-\zeta}$, and
$e^{-\xi}$ / 35 \\
2: Identification of Functions / 41 \\
2.1 Introduction / 41 \\
2.2 The Generalized Hypergeometric Function $_pF_q(z)$
/ 41 \\
2.3 The G-Function / 47 \\
2.4 Miscellaneous Functions / 48 \\
3: General Remarks on the Algorithms and Programs / 49
\\
3.1 Introduction / 49 \\
3.2 Precision and Complex Arithmetic / 49 \\
4: Chebyshev Coefficients for $_2F_1(a.b;c;z)$ / 52 \\
5: Coefficients for the Expansion of the Confluent
Hypergeometric Function $_1F_1(a;c;z)$ in Ascending
Series of Chebyshev Polynomials / 70 \\
6: Chebyshev Coefficients for $_0F_1(c;z)$ / 77 \\
7: Coefficients for the Expansion of $_1F_2(a;b,c;z)$
in Ascending Series of Chebyshev Polynomials / 82 \\
8: Coefficients for the Expansion of the Confluent
Hypergeometric Functions $U(a;c;z)$ and $_1F_1(a;c;-z)$
in Descending Series of Chebyshev Polynomials / 88 \\
9: Coefficients for the Expansion of the Functions
$G^{m,1}_{1,3}(z^2/4|^1_{a,b,c})$, $m = 3$ or $m = 2$,
in Descending Series of Chebyshev Polynomials / 101 \\
10: Differential and Integral Properties of Expansions
in Series of Chebyshev Polynomials of the First Kind /
116 \\
11: Expansion of Exponential Type Integrals in Series
of Chebyshev Polynomials of the First Kind / 126 \\
11.1 Introduction / 126 \\
11.2 The Representation for $g(x)$ / 127 \\
11.3 The Representation for $G(x)$ / 129 \\
11.4 Exponential Type Integrals Involving Logarithms /
133 \\
11.5 Numerical Examples / 135 \\
11.6 Errata / 139 \\
12: Conversion of a Power Series into a Series of
Chebyshev Polynomials of the First Kind / 154 \\
13: Rational Approximations for $_2F_1(a,b;c;-z)$ / 159
\\
14: Pad{\'e} Approximations for $_2F_1(1,b;c;-z)$ / 174
\\
15: Rational Approximations for $_1F_1(a;c;-z)$ / 182
\\
16: Pad{\'e} Approximations for $_1F_1(1;c;-z)$ / 192
\\
17: Rational Approximations for Bessel Functions of the
First Kind / 203 \\
18: Pad{\'e} Approximations for $I_{\nu +
1}(z)/I_\nu(z)$ / 220 \\
19: Evaluation of Bessel Functions of the First Kind by
Use of the Backward Recurrence Formula \\
19.1 Introduction / 230 \\
19.2 Backward Recurrence Schemata for $I_\nu(z)$ and
$J_\nu(z)$ / 230 \\
19.3 Numerical Examples / 240 \\
19.4 Mathematical Description of Programs / 243 \\
19.4.1 Evaluation of Functions Related to $I_{m +
\nu}(z)$ and $J_{m + \nu}(z)$ / 243 \\
19.4.2 Evaluation of Functions Related to $e^{-l}I_{m +
\nu}(z)$ / 245 \\
20: Rational Approximations for $z^aU(a;1 + a - b;z)$ /
252 \\
21: Pad{\'e} Approximations for $z U(1;2-b;z)$ / 265
\\
Appendices \\
Bibliography / 280 \\
Notation Index / 281 \\
Subject Index / 283",
wrongisbn = "0-12-459940-6",
}
@TechReport{Maag:1977:SRE,
author = "Werner Maag and Rudolf Wehrli",
title = "Survey on rounding effects in floating-point
arithmetic",
type = "Report",
institution = "CM Sch{\"a}nis AG",
address = "Sch{\"a}nis, Switzerland",
pages = "73",
year = "1977",
bibdate = "Thu May 09 09:10:32 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Merzbach:1977:GSF,
author = "Uta C. Merzbach",
title = "{Georg Scheutz} and the first printing calculator",
volume = "36",
publisher = "Smithsonian Institution Press",
address = "Washington, DC, USA",
pages = "iii + 74",
year = "1977",
LCCN = "QA75 .M46",
bibdate = "Mon Jan 21 21:21:54 MST 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "Smithsonian studies in history and technology",
acknowledgement = ack-nhfb,
subject = "Calculators; History; Scheutz, George",
subject-dates = "1785--1873",
}
@InCollection{Metropolis:1977:MSA,
author = "N. Metropolis",
title = "Methods of significance arithmetic",
crossref = "Jacobs:1977:SAN",
pages = "179--192",
year = "1977",
MRclass = "65G05 (68A99)",
MRnumber = "MR0451673 (56 \#9955)",
MRreviewer = "N. N. Abdelmalek",
bibdate = "Thu Nov 8 14:50:25 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Metropolis:1977:SAP,
author = "N. Metropolis and Stephen M. Tanny",
title = "Significance arithmetic: the probability of carrying",
journal = j-COMPUT-MATH-APPL,
volume = "3",
number = "1",
pages = "77--81",
year = "1977",
CODEN = "CMAPDK",
ISSN = "0886-9561",
ISSN-L = "0898-1221",
MRclass = "65G05 (10A30 65C10)",
MRnumber = "MR0458846 (56 \#17046)",
MRreviewer = "Artenio De Matteis",
bibdate = "Thu Nov 8 14:50:26 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0371.60015",
abstract = "This article develops a number of probabilistic
results related to a combinatorial representation of
the real number system. This representation employs an
algorithmic definition of the arithmetic operations
analogous to that used by a computer. A carry function
for each place is defined and the distribution of these
functions is characterized in terms of classical
combinatorial polynomials",
acknowledgement = ack-nhfb,
fjournal = "Computers \& Mathematics with Applications. An
International Journal. Part B",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Mitra:1977:CDI,
author = "Debasis Mitra",
title = "Criteria for Determining if a High-Order Digital
Filter Using Saturation Arithmetic is Free of Overflow
Oscillations",
journal = j-BELL-SYST-TECH-J,
volume = "56",
number = "9",
pages = "1679--1699",
month = nov,
year = "1977",
CODEN = "BSTJAN",
ISSN = "0005-8580",
bibdate = "Tue Nov 9 11:15:56 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1977/BSTJ.1977.5609.html;
http://www.alcatel-lucent.com/bstj/vol56-1977/bstj-vol56-issue09.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol56/bstj56-9-1679.pdf;
http://www.alcatel-lucent.com/bstj/vol56-1977/articles/bstj56-9-1679.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Ninke:1977:SRB,
author = "W. H. Ninke and G. R. Ritchie",
title = "Shift Register Binary Rate Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "3",
pages = "276--278",
month = mar,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674819",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:53 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674819",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Oliver:1977:EAM,
author = "J. Oliver",
title = "An Error Analysis of the Modified {Clenshaw} Method
for Evaluating {Chebyshev} and {Fourier} Series",
journal = j-J-INST-MATH-APPL,
volume = "20",
number = "3",
pages = "379--391",
year = "1977",
CODEN = "JMTAA8",
ISSN = "0020-2932",
ISSN-L = "0020-2932",
MRclass = "65G05 (41A50)",
MRnumber = "57 #4508",
MRreviewer = "David L. Elliott",
bibdate = "Fri Apr 5 07:38:01 MST 2002",
bibsource = "https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jinstmathappl.bib",
ZMnumber = "0397.65013",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Institute of Mathematics and its
Applications",
journal-URL = "http://imamat.oxfordjournals.org/content/by/year",
xxtitle = "An error analysis of the modified {Clenshaw} methods
for evaluating {Chebyshev} and {Fourier} series",
}
@Article{Oliver:1977:SRE,
author = "J. Oliver",
title = "On the sensitivity to rounding errors of {Chebyshev}
series approximations",
journal = j-J-COMPUT-APPL-MATH,
volume = "3",
number = "2",
pages = "89--98",
month = jun,
year = "1977",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 11:59:16 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0771050X77900031",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Palmer:1977:ISF,
author = "J. Palmer",
title = "The {Intel} Standard for Floating Point Arithmetic",
crossref = "IEEE:1977:ICS",
pages = "107--112",
year = "1977",
bibdate = "Fri Nov 09 19:09:10 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Papantoni-Kazakos:1977:CRE,
author = "P. Papantoni-Kazakos",
title = "Consideration of round off errors in the design of
mean square estimators",
journal = j-IEEE-TRANS-AUTOMAT-CONTR,
volume = "22",
number = "2",
pages = "276--279",
month = apr,
year = "1977",
CODEN = "IETAA9",
ISSN = "0018-9286 (print), 1558-2523 (electronic)",
ISSN-L = "0018-9286",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Automatic Control",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
summary = "In this correspondence, a search for the optimal
polynomial mean-square (ms) estimator is undertaken;
when the input is a vector with fixed dimensionality
and at the calculation of the estimator characteristics
the round off errors are considered. \ldots{}",
}
@Article{Randell:1977:CGC,
author = "B. Randell",
title = "{Colossus}: Godfather of the Computer",
journal = j-NEW-SCIENTIST,
volume = "73",
number = "1038",
pages = "346--348",
day = "10",
month = feb,
year = "1977",
CODEN = "NWSCAL",
ISSN = "0262-4079, 0028-6664",
ISSN-L = "0262-4079",
bibdate = "Wed Oct 13 11:51:16 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.5]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "New Scientist",
journal-URL = "http://www.sciencedirect.com/science/journal/02624079",
}
@Article{Reimer:1977:AFO,
author = "M. Reimer",
title = "{Auswertungsalgorithmen fast-optimaler numerischer
Stabilit{\"a}t f{\"u}r Polynome} \toenglish {Algorithms
of Near-optimal Numerical Stability for the Evaluation
of Polynomials} \endtoenglish",
journal = j-COMPUTING,
volume = "17",
number = "4",
pages = "289--296",
month = "????",
year = "1977",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Ris:1977:UDF,
author = "Frederic N. Ris",
title = "A unified decimal floating-point architecture for the
support of high-level languages",
journal = j-SIGPLAN,
volume = "12",
number = "9",
pages = "60--70",
month = sep,
year = "1977",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:14:09 MST 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods); C6140D (High
level languages)",
corpsource = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "architecture; decimal floating-point arithmetic;
digital arithmetic; high level languages; procedure
oriented languages; unified",
treatment = "P Practical",
}
@Article{Rjabko:1977:AHM,
author = "B. Ja. Rjabko",
title = "An analogue of {Haffmen}'s method for the optimal
summation of floating point numbers. ({Russian})",
journal = "Diskret. Analiz",
volume = "30",
pages = "38--45, 77",
year = "1977",
MRclass = "68C05 (68E99)",
MRnumber = "80c:68023",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Russian",
reviewer = "Vladimir Sleinikov",
xxjournal = "Metody Diskret. Anal. v Reshenii Kombinatornykh
Zadach",
}
@Article{Sanyal:1977:AND,
author = "S. Sanyal",
title = "An algorithm for nonrestoring division",
journal = j-COMP-DESIGN,
volume = "16",
number = "5",
pages = "124--127",
month = may,
year = "1977",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Design",
}
@MastersThesis{Simmons:1977:SRA,
author = "David Michael Simmons",
title = "Signal-to-noise ration analysis of block floating
point {FFTS}",
type = "Electrical Engineering Thesis ({M.S.})",
school = "University of Missouri--Rolla",
address = "Rolla, MO, USA",
pages = "114",
year = "1977",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Soderstrand:1977:HSL,
author = "M. A. Soderstrand",
title = "A high-speed low-cost recursive digital filter using
residue number arithmetic",
journal = j-PROC-IEEE,
volume = "65",
number = "7",
pages = "1065--1067",
month = jul,
year = "1977",
CODEN = "IEEPAD",
DOI = "https://doi.org/10.1109/PGEC.1967.264810",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=31255",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
keywords = "residue arithmetic; residue number system",
summary = "Use of table look-up multiplication by fractional
coefficients allows implementation of high-speed,
low-cost recursive digital filters using residue number
arithmetic. An 8-bit equivalent filter based on the
lossless discrete integrator (LDI) \ldots{}",
}
@Article{Soderstrand:1977:MRN,
author = "M. A. Soderstrand and E. L. Fields",
title = "Multipliers for residue-number-arithmetic digital
filters",
journal = j-ELECT-LETTERS,
volume = "13",
number = "6",
pages = "164--166",
day = "17",
month = mar,
year = "1977",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:19770117",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4249252",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "residue arithmetic; residue number system",
summary = "A recently proposed residue-number-arithmetic digital
filter offers major cost and speed advantages over
binary-arithmetic digital filters, but suffers one
major drawback. The filter coefficients must be
constant, since the lack of a fast method of \ldots{}",
}
@Article{Steer:1977:DHS,
author = "D. G. Steer and S. R. Penstone",
title = "Digital Hardware for Sine-Cosine Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "12",
pages = "1283--1286",
month = dec,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674791",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Stenzel:1977:CHS,
author = "W. J. Stenzel",
title = "A Compact High-Spped Multiplication Scheme",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "10",
pages = "948--957",
month = oct,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674730",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:20:56 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Stoutemyer:1977:AEA,
author = "David R. Stoutemyer",
title = "Automatic Error Analysis Using Computer Algebraic
Manipulation",
journal = j-TOMS,
volume = "3",
number = "1",
pages = "26--43",
month = mar,
year = "1977",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355719.355721",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Sep 02 22:30:11 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper shows how the inherent error and the
fixed-point or floating-point roundoff of chopoff error
of an expression can be determined automatically using
a computer algebra language such as {REDUCE}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Thong:1977:ARE,
author = "Tran Thong and Bede Liu",
title = "Accumulation of roundoff errors in floating point
{FFT}",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "24",
number = "3",
pages = "132--143",
month = mar,
year = "1977",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
MRclass = "65G05",
MRnumber = "55 1722",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
reviewer = "Sven-{\AA}ke Gustafson",
summary = "A statistical model for roundoff error is used to
predict the output noise to signal ratio of the two
common FFT algorithms, the decimation in time and the
decimation in frequency algorithms. A unified approach
is used to obtain the error in both algorithms
\ldots{}",
}
@Article{Tran-Thong:1977:FPF,
author = "Tr{\^a}{\`n}-Th{\^o}{\'n}g and Bede Liu",
title = "Floating Point Fast {Fourier} Transform Computation
Using Double Precision Floating Point Accumulators",
journal = j-TOMS,
volume = "3",
number = "1",
pages = "54--59",
month = mar,
year = "1977",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355719.355723",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65T05",
MRnumber = "55 \#11658",
bibdate = "Sat Aug 27 22:12:55 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "Most commonly available fast Fourier transform (FFT)
subroutines use single precision chopping arithmetic,
and the resulting normalized roundoff error, in
computing an $N$-point transform with $ N = \prod_{i =
1}^M a_i $ is $ O(M^2) $. This paper proposes a
modification of these subroutines for use on computers
with a hardwired double precision arithmetic unit. The
resulting normalized roundoff error is $ O(M) $ and is
independent of the $ a_i $. The modification leads to a
negligible increase in storage. For most computers, the
increase in the execution time is small. For certain
computers, such as IBM System/360 models 91 and 195,
the modification can result in a decrease in the
execution time.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "computer arithmetic; double-length summation; fast
Fourier transform; roundoff error",
}
@Article{Trivedi:1977:LAD,
author = "Kishor S. Trivedi and Milo{\v{s}} D. Ercegovac",
title = "On-line algorithms for division and multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "681--687",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674901",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 30 07:29:16 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Trivedi:1977:UCF,
author = "K. S. Trivedi",
title = "On the Use of Continued Fractions for Digital Computer
Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "700--704",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674903",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See corrections \cite{Trivedi:1978:CUC}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674903",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Ushijima:1977:SEP,
author = "Kazuo Ushijima",
title = "Step to an Efficient Program for Floating-point
Summation",
journal = j-SPE,
volume = "7",
number = "6",
pages = "759--769",
month = nov # "\slash " # dec,
year = "1977",
CODEN = "SPEXBL",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Sat May 31 13:36:16 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}
@Article{Williams:1977:SIA,
author = "R. P. Williams",
title = "Serial Integer Arithmetic with Magnetic Bubbles",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "3",
pages = "260--264",
month = mar,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674814",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:52 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674814",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Wozniakowski:1977:NSC,
author = "H. Wo{\'z}niakowski",
title = "Numerical Stability of the {Chebyshev} Method for the
Solution of Large Linear Systems",
journal = j-NUM-MATH,
volume = "28",
number = "2",
pages = "191--209",
year = "1977",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C4110 (Error analysis in numerical methods); C4140
(Linear algebra)",
corpsource = "Department of Computer Sci., Carnegie-Mellon
University, Pittsburgh, PA, USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "Chebyshev approximation; Chebyshev method; computed
residuals; error analysis; floating point arithmetic;
iterative methods; large linear systems; linear
systems; numerical stability; rounding error analysis",
treatment = "T Theoretical or Mathematical",
}
@Article{Yuen:1977:NRD,
author = "C. K. Yuen",
title = "A New Representation for Decimal Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "12",
pages = "1286--1288",
month = dec,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674792",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Aug 07 18:00:38 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A new representation for decimal numbers is proposed.
It uses a mixture of positive and negative radixes to
ensure that the maximum value of a four bit decimal
digit is 9. This eliminates the more complex carry
generation process required in BCD addition.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "decimal arithmetic",
}
@InProceedings{Abu-El-Haija:1978:AER,
author = "A. Abu-El-Haija and A. Peterson",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP '78}",
title = "An approach to eliminate roundoff errors in digital
filters",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "75--78",
year = "1978",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Roundoff noise and limit cycle oscillations due to
postmultiplication rounding can seriously limit the
application of recursive digital filters in practice,
particularly for poles near the unit circle or near z =
+1. Rounding is usually performed by \ldots{}",
}
@InProceedings{Agrawal:1978:AIR,
author = "Dharma P. Agrawal",
title = "On Arithmetic Inter-relationships and Hardware
Interchangeability of Negabinary and Binary Systems",
crossref = "IEEE:1978:PSC",
pages = "88--96",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Agrawal.pdf",
abstract = "Recent use of the negabinary system in the application
oriented digital hardware, has encouraged the search
for suitable arithmetic algorithms in $ - 2 $ base.
These algorithms have been directly utilized in
designing logic circuits and several logic
implementations have been reported in the literature.
The main objective of this paper is to show the close
relationship between $ + 2 $ base addition and $ - 2 $
base negative addition. Two possible ways of utilizing
binary adders for performing negabinary addition and
their underlying theories are presented. Two similar
techniques of using negabinary adders for binary
addition are also considered in detail. An interesting
aspect of this investigation about negabinary base is
that negative addition (rather than just addition)
seems to be the primitive operation from logic
complexity and interchangeability of $ + 2 $ and $ - 2
$ adders point of view.\par
The technique of adding two numbers in one system by
the adders of the other system is extended here for
multiple operand addition. This requires inclusion of
an additional correction factor. Further, the additive
algorithms of this work lead to four simple conversion
processes of number from one system to another. This
paper seems to be a realistic step towards the use of
similar hardware for $ + 2 $ and $ - 2 $ bases and
hence this allows an instantaneous flexibility on the
selection of number system. It is believed that this
paper will attract more attention on the use of $ - 2 $
base system for the design of special purpose digital
machines and process controllers.",
acknowledgement = ack-nhfb,
keywords = "Addition; ARITH-4; base conversion; binary numbers;
even positioned bits; multiple addition; negabinary
system; negative addition; negative radix; odd
positioned bits.",
}
@InProceedings{Agrawal:1978:MAL,
author = "Dharma P. Agrawal and T. R. N. Rao",
title = "On Modular $ (2^n + 1) $ Arithmetic Logic",
crossref = "IEEE:1978:PSC",
pages = "104--108",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Agrawal_Rao.pdf",
abstract = "A novel format for representing modulo $ (2^n + 1) $
numbers, is shown to be helpful in achieving modular
addition and complementation. Logic for fast addition
using carry-look-ahead and modular complementation is
also presented.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@Article{Andrews:1978:EFM,
author = "M. Andrews and S. F. McCormick and G. D. Taylor",
title = "Evaluation of Functions on Microcomputers: Square
Root",
journal = j-COMPUT-MATH-APPL,
volume = "4",
number = "4",
pages = "359--367",
year = "1978",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Thu Sep 15 18:40:29 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
xxmonth = "(none)",
}
@Article{Andrews:1978:IAN,
author = "M. Andrews",
title = "Influence of architecture on numerical algorithms",
journal = j-MICROPROC-MICROSYS,
volume = "2",
number = "3",
pages = "130--137",
month = jun,
year = "1978",
CODEN = "MIMID5",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Thu Sep 1 10:14:44 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Microprocessors and Microsystems",
}
@Article{Andrews:1978:UEF,
author = "M. Andrews and T. Mraz",
title = "Unified elementary function generator",
journal = j-MICROPROC-MICROSYS,
volume = "2",
number = "5",
pages = "270--273",
month = oct,
year = "1978",
CODEN = "MIMID5",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Thu Sep 1 10:15:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Microprocessors and Microsystems",
}
@Manual{Apple:1978:AIR,
key = "Apple",
title = "{Applesoft II} reference manual: extended
floating-point {BASIC}",
organization = "Apple Computer, Inc.",
address = "Cupertino, CA, USA",
pages = "63",
year = "1978",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Apple II (Computer) --- Programming; BASIC (Computer
program language)",
}
@InProceedings{Atkins:1978:CTA,
author = "D. E. Atkins and S. C. Ong",
title = "A Comparison of Two Approaches to Multi-Operand Binary
Addition",
crossref = "IEEE:1978:PSC",
pages = "125--139",
year = "1978",
bibdate = "Wed Nov 14 17:47:38 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Atkins.pdf",
abstract = "This paper presents the results of one phase of a
study concerning methods for addition of $ P > 2 $
numbers, each encoded as a vector of digits (digit
vector) of length $N$. Such multi-operand addition has
been studied most often in the context of reducing a
set of partial products to a single result in the
implementation of multiplication. More generalized
multi-operand addition, most notably in the form of
inner product calculations is, however, central to
numerous scientific applications of digital computers.
Although multioperand addition is trivially
accomplished by accumulation (iteration in time) in any
general purpose machine, demands for very high-speed
computation, typified by 2- and 3-D signal processing
prompt implementation of dedicated, hardware-intensive
structures for multi-operand addition. This study, for
example, is motivated in part by requirements for rapid
simultaneous addition of up to 100, 16-bit operands in
the design of a dedicated processor for real-time
reconstruction of 3-D images of the beating heart and
breathing lungs.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@TechReport{Banerji:1978:HSD,
author = "Dilip K. Banerji and To-Yat Cheung and V. Ganesan",
title = "A high speed division method in residue arithmetic",
institution = "Department of Computer Science, University of Ottawa",
address = "Ottawa, ON, Canada K1N 6N5",
pages = "7",
year = "1978",
bibdate = "Thu Nov 18 09:44:27 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://books.google.com/books?id=q8fBIwAACAAJ",
acknowledgement = ack-nhfb,
remark = "Credited to CH1630-3/81/0000/0158 IEEE 1981; where did
this appear?",
}
@Article{Baraniecka:1978:DTR,
author = "A. Baraniecka and G. Jullien",
title = "On decoding techniques for residue number system
realizations of digital signal processing hardware",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "25",
number = "11",
pages = "935--936",
month = nov,
year = "1978",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1049/el:19770117",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23475",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "In a recent issue of this journal, a hardware
implementation of the Chinese Remainder Theorem was
proposed for the translation of residue coded outputs
into natural integer for an FIR filter realization. The
method requires a modulo M adder- \ldots{}",
}
@Book{Bareiss:1978:PEA,
author = "Erwin H. Bareiss and Jesse L. Barlow",
title = "Probabilistic error analysis of computer arithmetics",
publisher = "Department of Electrical Engineering and Computer
Science, Northwestern University",
address = "Evanston, IL, USA",
pages = "97",
year = "1978",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Nov 29 12:09:29 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Barsi:1978:ACR,
author = "F. Barsi and P. Maestrini",
title = "Arithmetic Codes in Residue Number Systems with
Magnitude Index",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-27",
number = "12",
pages = "1185--1188",
month = dec,
year = "1978",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1978.1675023",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 08:13:33 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675023;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35165",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "The idea of adding a magnitude index to the residue
representation of numbers is reconsidered. The range of
a given residue number system is supposed to be divided
into intervals of equal width, and the magnitude index
of a number X is defined as an \ldots{}",
}
@Manual{BellHowellCo:1978:BHF,
author = "{Bell and Howell Co} and {Apple Computer, Inc}",
title = "[{Bell and Howell} floating point {Basic} programming
reference manual]",
organization = "Bell and Howell, Audio-Visual Products Division",
address = "Chicago, IL, USA",
pages = "xiii + 168",
year = "1978",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Apple II (Computer) --- Programming.; BASIC (Computer
program language)",
remark = "Cover title. ``Reprinted with permission of Apple
Computer, Inc.'' Companion volume: Floating point Basic
tutorial manual. Quick reference guide on folded,
inserted leaf.",
}
@Article{Blue:1978:PFP,
author = "James L. Blue",
title = "A Portable {Fortran} Program to Find the {Euclidean}
Norm of a Vector",
journal = j-TOMS,
volume = "4",
number = "1",
pages = "15--23",
month = mar,
year = "1978",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355769.355771",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "68A10",
MRnumber = "57 \#18205",
bibdate = "Sat Aug 27 23:14:36 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib;
https://www.math.utah.edu/pub/tex/bib/unix.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "BLAS; floating-point arithmetic; floating-point
overflow; floating-point underflow; nla; norm;
software",
reviewer = "A. D. Booth",
}
@TechReport{Boehmer:1978:TAF,
author = "K. Boehmer and J. M. Yohe",
title = "{Triplex} Arithmetic for {Fortran}",
type = "MRC Technical Summary",
number = "1901",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
pages = "38",
month = dec,
year = "1978",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/intarith.bib",
abstract = "Triplex arithmetic is a variant of interval arithmetic
in which a 'main' value is computed in addition to the
endpoints of the containing interval. The 'main' value
is, in general, the value that would have been computed
had properly-rounded real arithmetic been used to
compute the results of the calculation; it may in some
sense, be regarded as the 'most probable' value of the
result of the calculation. The endpoints of the
interval define the worst-case range of the possible
values of the computation. This report describes a
FORTRAN implementation of triplex arithmetic in both
single and multiple precision. The package described in
this report is designed to be used with the AUGMENT
precompiler: this makes triplex arithmetic particularly
easy to use.",
acknowledgement = ack-jr,
keywords = "Approximation theory.; Equations, Abelian.; Spline
theory.",
}
@PhdThesis{Bohlender:1978:GBM,
author = "G. Bohlender",
title = "{Genaue Berechnung mehrfacher Summen, Produkte und
Wurzeln von Gleitkommazahlen und allgemeine Arithmetik
in h{\"o}heren Programmiersprachen} \toenglish
{Accurate Computation of Multiple Sums, Products and
Roots of Floating-Point Numbers and General Arithmetic
in High-Level Programming Languages} \endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "??",
year = "1978",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
keywords = "accurate floating-point summation",
}
@Article{Boney:1978:MRW,
author = "J. Boney",
title = "Math in the Real World",
journal = j-BYTE,
volume = "3",
number = "9",
pages = "114--119",
month = sep,
year = "1978",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 1 10:14:44 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "BYTE Magazine",
}
@Article{Brady:1978:MBL,
author = "W. G. Brady",
title = "More on {Benford}'s Law",
journal = j-FIB-QUART,
volume = "16",
number = "1",
pages = "51--52",
month = feb,
year = "1978",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:59:24 MDT 2011",
bibsource = "http://www.fq.math.ca/16-1.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/16-1/brady.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@TechReport{Brent:1978:AIB,
author = "R. P. Brent and J. A. Hooper and J. M. Yohe",
title = "An {Augment} Interface for {Brent}'s {Multiple
Precision Arithmetic Package}",
type = "MRC Technical Summary",
number = "1868",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
year = "1978",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Published In: ACM Trans. Math. Software 6, 146--149,
1980",
acknowledgement = ack-jr,
}
@Article{Brent:1978:AMF,
author = "Richard P. Brent",
title = "Algorithm 524: {MP}, {A Fortran} Multiple-Precision
Arithmetic Package [{A1}]",
journal = j-TOMS,
volume = "4",
number = "1",
pages = "71--81",
month = mar,
year = "1978",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355769.355776",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Sep 05 22:49:15 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Brent:1979:RMF,Brent:1980:AIB}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Brent:1978:FMP,
author = "Richard P. Brent",
title = "{A Fortran} Multiple-Precision Arithmetic Package",
journal = j-TOMS,
volume = "4",
number = "1",
pages = "57--70",
month = mar,
year = "1978",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355769.355775",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Aug 27 23:13:25 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Case:1978:AIS,
author = "Richard P. Case and Andris Padegs",
title = "Architecture of the {IBM System}\slash 370",
journal = j-CACM,
volume = "21",
number = "1",
pages = "73--96",
month = jan,
year = "1978",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Jan 29 18:00:28 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@TechReport{Cherry:1978:BAP,
author = "Lorinda L. Cherry and Robert Morris",
title = "{BC} --- An Arbitrary Precision Desk Calculator
Language",
type = "Technical Memorandum",
number = "1053",
institution = inst-ATT-BELL,
address = inst-ATT-BELL:adr,
pages = "2 + 14",
day = "12",
month = nov,
year = "1978",
bibdate = "Tue Jun 06 08:07:45 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/unix.bib",
abstract = "BC is a language and a compiler for doing arbitrary
precision arithmetic on the PDP-11 under the UNIX
time-sharing system. The output of the compiler is
interpreted and executed by a collection of routines
which can input, output. and do arithmetic on
indefinitely large integers and on scaled fixed-point
numbers.\par
These routines are themselves based on a dynamic
storage allocator. Overflow does not occur until all
available core storage is exhausted.\par
The language has a complete control structure as well
as immediate-mode operation. Functions can be defined
and saved for later execution.\par
Two five hundred-digit numbers can be multiplied to
give a thousand digit result in about ten
seconds.\par
A small collection of library functions is also
available, including sin. cos, arctan, log,
exponential, and Bessel functions of integer
order.\par
Some of the uses of this compiler are\par
* to do computation with large integers.\par
* to do computation accurate to many decimal
places,\par
* conversion of numbers from one base to another
base.",
abstract-2 = "BC is a language and a compiler for doing arbitrary
precision arithmetic on the PDP-11 und UNIX
Time-Sharing System.",
acknowledgement = ack-nhfb,
author-dates = "Lorinda L. Cherry (18 November 1944--February 2022);
Robert Morris (25 July 1932--26 June 2011)",
remark = "Available in PDF file of \cite[pp.
383--398]{Dolotta:1977:DPU}.",
}
@InProceedings{Chow:1978:LDR,
author = "Catherine Y. Chow and James E. Robertson",
title = "Logical Design of a Redundant Binary Adder",
crossref = "IEEE:1978:PSC",
pages = "109--115",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Chow.pdf",
abstract = "This paper investigates the logical design of a
redundant binary adder with two input digits and one
output digit, all in the digit set $ \{ \bar {1}, 0, 1
\} $. Redundant binary arithmetic structures in which
all digit sets are $ \{ \bar {1}, 0, 1 \} $ were first
discussed by Avizienis in 1961. Borovec studied the
logical design of a class of such binary adders and
subtracters in 1968. At that time, a variation of the
adder\slash subtracter was overlooked. This paper
studies the logical design of this variation. The sum
digit is still a function only of the digits in three
adjacent digital positions of the operands. ``Coupled
don't cares'' are encountered, but have not introduced
too much difficulty. The nine distinct formats (under
permutation and negation) of representing three values
with two bits given by Robertson are used. The simplest
adder\slash subtracter designs from this variation are
less complex than the simplest designs previously
known.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@InProceedings{Cohen:1978:MAI,
author = "Danny Cohen",
title = "Mathematical Approach to Iterative Computation
Networks",
crossref = "IEEE:1978:PSC",
pages = "226--237",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Cohen.pdf",
abstract = "This paper deals with design principles for iterative
computation networks. Such computation networks are
used for performing repetitive computations which
typically are not data dependent. Most of the signal
processing algorithms. like FFT and filtering, belong
to this class.\par
The main idea in this paper is the development of
mathematical notation for expressing such designs. This
notation captures the important features and properties
of these computation networks, and can be used both for
analyzing and for designing computational networks.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@TechReport{Coonen:1978:SPS,
author = "Jerome T. Coonen",
title = "Specification for a proposed standard for floating
point arithmetic",
type = "Memorandum",
number = "ERL M78/72",
institution = "University of California, Berkeley",
address = "Berkeley, CA, USA",
year = "1978",
bibdate = "Wed Nov 24 09:10:35 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Corsini:1978:USM,
author = "P. Corsini and G. Frosini",
title = "Uniform Shift Multiplication Algorithms Without
Overflow",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-27",
number = "3",
pages = "256--258",
month = mar,
year = "1978",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1978.1675081",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 08:13:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675081",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Crary:1978:APT,
author = "F. D. Crary and J. M. Yohe",
title = "The {Augment} Precompiler as a Tool for the
Development of Special Purpose Arithmetic Packages",
type = "MRC Technical Summary",
number = "1892",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
year = "1978",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-jr,
}
@InProceedings{Dadda:1978:MAB,
author = "Luigi Dadda",
title = "Multiple Addition of Binary Serial Numbers",
crossref = "IEEE:1978:PSC",
pages = "140--148",
year = "1978",
bibdate = "Wed Nov 14 17:48:30 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Dadda.pdf",
abstract = "It is shown how circuits for the addition of several
serial binary numbers can be obtained as a combination
of parallel counters and memory cells.\par
The various schemes belong to one of three different
classes, characterized by the way in which carries,
produced by parallel counters, are treated.\par
A comparison is made between the various schemes, in
terms of speed and complexity.",
acknowledgement = ack-nhfb,
author-dates = "29 April 1923--26 October 2012",
keywords = "ARITH-4",
}
@Article{Debnath:1978:EMO,
author = "R. C. Debnath and D. A. Pucknell",
title = "Erratum: On multiplicative overflow detection in
residue number system",
journal = j-ELECT-LETTERS,
volume = "14",
number = "12",
pages = "385",
day = "8",
month = jun,
year = "1978",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:19780260",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Debnath:1978:MOD}",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4241130",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "residue arithmetic; residue number system",
}
@Article{Debnath:1978:MOD,
author = "R. C. Debnath and D. A. Pucknell",
title = "On multiplicative overflow detection in residue number
system",
journal = j-ELECT-LETTERS,
volume = "14",
number = "5",
pages = "129--130",
month = "????",
year = "1978",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:19780088",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See erratum \cite{Debnath:1978:EMO}.",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4240881",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "residue arithmetic; residue number system",
summary = "A general method for the detection of multiplicative
overflow has been developed. The method has been found
suitable in 16--15-mod residue system from the
consideration of cost and speed. A circuit for
16--15-mod-multiplicative overflow detection \ldots{}",
}
@Misc{DEC-ES:1978:VIS,
author = "{Digital Equipment Corporation.Educational Services}",
title = "{VAX-11} instruction set",
publisher = "Digital Equipment Corporation",
address = "Maynard, MA, USA",
year = "1978",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "13 videocassettes (ca. 585 min.)",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic; VAX-11 (Computer)
--- Programming.",
remark = "Accompanied by 11 volumes of print materials, 1981.
[1] Instruction formats and addressing modes, lesson 1
--- [2] Instruction formats and addressing modes,
lessons 2 and 3 --- [3] Integer, logical, and branch
instructions, lessons 1 and 2 --- [4] Integer, logical,
and branch instructions, lessons 3 and 4 --- [5]
Character string instructions, lessons 1 and 2 --- [6]
Character string instructions, lessons 3 and 4 --- [7]
Decimal string instructions, lessons 1 and 2 --- [8]
Decimal string instructions, lessons 3, 4, and 5 ---
[9] Special instructions --- [10] Procedures and
subroutine instructions --- [11] Stack and address
instructions --- [12] Variable bit field instructions
--- [13] Floating point instructions. Provides an
introduction to the VAX-11 computer system.",
}
@Article{Diamond:1978:SRI,
author = "Harold G. Diamond",
title = "Stability of Rounded Off Inverses Under Iteration",
journal = j-MATH-COMPUT,
volume = "32",
number = "141",
pages = "227--232",
month = jan,
year = "1978",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
JSTOR database; Parallel/par.lin.alg.bib",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Department of Math., University of Illinois, Urbana,
IL, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "function approximation; iterative methods; positive
integer; rounded off inverse stability",
treatment = "T Theoretical or Mathematical",
}
@Article{Egbert:1978:PCA,
author = "W. E. Egbert",
title = "Personal Calculator Algorithms {IV}: Logarithmic
Functions",
journal = j-HEWLETT-PACKARD-J,
volume = "29",
number = "8",
pages = "29--32",
month = apr,
year = "1978",
CODEN = "HPJOAX",
ISSN = "0018-1153",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Hewlett-Packard Journal: technical information from
the laboratories of Hewlett-Packard Company",
}
@InProceedings{Ercegovac:1978:AME,
author = "M. D. Ercegovac and M. M. Takata",
title = "An Arithmetic Module for Efficient Evaluation of
Functions",
crossref = "IEEE:1978:PSC",
pages = "190--199",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Ercegovac_Takata.pdf",
abstract = "The organization and design of an arithmetic module
(Basic Byte-Slice Module --- BBM) is presented. A
network of BBWs implements an efficient digit-by-digit
method for fast evaluation of polynomial and rational
functions. Verification of the BBW design, its
feasibility in present LSI technologies and its
performance are discussed. The proposed BBW is
characterized by a small number of input\slash output
terminals, a uniform internal structure, and simple
control and inter-module communication requirements.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@InProceedings{Ercegovac:1978:FIS,
author = "Milo{\v{s}} D. Ercegovac and Algirdas Avizienis",
title = "The {Fourth IEEE Symposium on Computer Arithmetic}:
Foreword",
crossref = "IEEE:1978:PSC",
pages = "v--v",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_contents.pdf;
http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_foreword.pdf;
http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_preface.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@InProceedings{Ercegovac:1978:LSR,
author = "Milo{\v{s}} D. Ercegovac",
title = "An On-Line Square Rooting Algorithm",
crossref = "IEEE:1978:PSC",
pages = "183--189",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Ercegovac.pdf",
abstract = "An on-line algorithm for computing square roots in a
radix 2, normalized floating-point number system with
the redundant digit set $ \{ - 1, 0, 1 \} $ is
described. The algorithm has on-line delay of one and
it is amenable for modular implementation. A systematic
approach, used in deriving this algorithm, is presented
in detail.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@TechReport{Espelid:1978:FPS,
author = "Terje O. Espelid",
title = "On floating-point summation",
type = "Report",
number = "67",
institution = "Department of Applied Mathematics, University of
Bergen",
address = "Bergen, Norway",
pages = "24",
year = "1978",
bibdate = "Thu May 09 08:03:27 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}
@Periodical{FloatingPointSystems:1978:P,
author = "{Floating Point Systems, Inc}",
title = "To the point",
publisher = "Floating Point Systems",
address = "Portland, OR, USA",
year = "1978",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
alttitle = "To the point (Portland, Or.)",
keywords = "Floating Point Systems, Inc. --- Periodicals.",
remark = "``Employee newsletter.'' Title from caption.",
}
@Article{Fox:1978:AFP,
author = "P. A. Fox and A. D. Hall and N. L. Schryer",
title = "{Algorithm 528}: Framework for a Portable Library
[{Z}]",
journal = j-TOMS,
volume = "4",
number = "2",
pages = "177--188",
month = jun,
year = "1978",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355780.355789",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Aug 27 23:30:46 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See remarks \cite{Fox:1979:RFP,Gay:1999:SAF}.",
acknowledgement = ack-nhfb,
annote = "The three program packages presented here provide a
framework for a portable FORTRAN subroutine library.
They were developed for the BELL Laboratories library
PORT(1). The packages are: machine-dependent constants,
automatic error handling, and dynamic storage
allocation using a stack.",
country = "USA",
date = "19/03/80",
descriptors = "Reliability; program construction; mathematical
method; FORTRAN; portability; error handling; memory
management; library",
enum = "988",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
language = "English",
location = "RWTH-AC-DFV: TELL",
references = "1",
revision = "20/03/92",
}
@Article{Fox:1978:PMS,
author = "P. A. Fox and A. D. Hall and N. L. Schryer",
title = "The {PORT} Mathematical Subroutine Library",
journal = j-TOMS,
volume = "4",
number = "2",
pages = "104--126",
month = jun,
year = "1978",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355780.355783",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Aug 27 23:13:25 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The development at Bell Laboratories of PORT, a
library of portable Fortran programs for numerical
computation, is discussed. Portability is achieved by
careful language specification, together with the key
technique of specifying computer classes by means of
predefined machine constants. The library is built
around an automatic error-handling facility and a
dynamic storage allocation scheme, both of which are
implemented portably. These, together with the modular
structure of the library, lead to simplified calling
sequences and ease of use.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "dynamic storage allocation; error handling; libraries;
numerical analysis; portability",
}
@Manual{FPS:1978:AAP,
key = "FPS",
title = "{AP-120B} Array Processor handbook",
organization = "Floating Point Systems, Inc.",
address = "Portland, OR, USA",
pages = "????",
year = "1978",
bibdate = "Fri Nov 09 10:52:30 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Fraley:1978:ZIR,
author = "B. Fraley",
title = "Zeros and Infinities Revisited and Gradual Underflow",
type = "Technical report",
institution = "HP Laboratories",
address = "3500 Deer Creek Road, Palo Alto, CA 94304, USA",
pages = "????",
day = "28",
month = dec,
year = "1978",
bibdate = "Fri Nov 09 10:53:38 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Frankowski:1978:RME,
author = "Krzysztof S. Frankowski",
title = "A Realistic Model for Error Estimates in the
Evaluation of Elementary Functions",
crossref = "IEEE:1978:PSC",
pages = "70--74",
year = "1978",
bibdate = "Thu Sep 01 11:22:03 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Frankowski.pdf",
abstract = "Floating point error analysis, as described by J. H.
Wilkinson (1963) has two known drawbacks: it is too
pessimistic and too cumbersome for everyday use. This
paper describes a realistic model for error analysis,
gives examples of simple formulae frequently used in
the calculation of elementary functions, and analyses
the error generated in single precision computations
with these formulae, using the proposed model for error
analysis. The paper also presents error bounds for
various polynomial evaluations, as predicted by the
model. Model verification is done using double
precision arithmetic.",
acknowledgement = ack-nj,
keywords = "ARITH-4",
}
@InProceedings{Gajski:1978:DAE,
author = "Daniel D. Gajski and L. P. Rubinfield",
title = "Design of Arithmetic Elements for {Burroughs
Scientific Processor}",
crossref = "IEEE:1978:PSC",
pages = "245--256",
year = "1978",
bibdate = "Fri Nov 09 10:54:59 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Gajski.pdf",
abstract = "The design criteria and implementation of the
Arithmetic Element (AE) of the Burroughs Scientific
Processor, a vector machine intended for scientific
computation requiring speed of up to 50 million
floating-point operations per second, is discussed. An
array of 16 AEs operate in lockstep mode, executing the
same instruction on 16 sets of data. The 16 AEs are one
stage in a pipeline which consists of 17 memory
modules, an input alignment network, and an output
alignment net-work. The AE itself is not pipelined. It
can perform over one hundred different operations
including a floating-point addition\slash subtraction
and multiplication, division, square root, among the
others. Eight registers are provided for the storage of
intermediate values and results. Modulo 3 residue
arithmetic is used for checking hardware failures.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@InProceedings{Garcia:1978:AES,
author = "Oscar N. Garcia and Harvey Glass and Stanley C.
Haines",
title = "An Approximate and Empirical Study of the Distribution
of Adder Inputs and Maximum Carry Length Propagation",
crossref = "IEEE:1978:PSC",
pages = "97--103",
year = "1978",
bibdate = "Wed Nov 14 17:49:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Garcia.pdf",
abstract = "This paper investigates, using sampled data, the
commonly used hypothesis that integer operands reaching
the adder of a computer are uniformly distributed.
Questions raised on the validity of that hypothesis are
reinforced and their impact on the calculation of the
average of the worst case length of carry propagation
is considered. An approximate formula is developed for
the worst case carry chain length when the arithmetic
operands are restricted in magnitude.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4; average worst case carry chain; binary
addition; carry propagation",
}
@Article{Garner:1978:TCA,
author = "H. L. Garner",
title = "Theory of Computer Addition and Overflows",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-27",
number = "4",
pages = "297--301",
month = apr,
year = "1978",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1978.1675101",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 08:13:28 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675101",
abstract = "Computer addition is a groupoid. If an additive
identity exists it is unique. If(and only if) addition
is defined with the compute through the overflow (CTO)
property, then a finite ring of integers is the
homomorphic image of the computer number system and
addition. Stated another way, the necessary and
sufficient condition for CTO is a congruence relation
on the integers. Also, if the number system has CTO
capabilities for addition, it also has extended CTO
properties for addition. A technique is presented for
determining the correct sum in the extended compute
through overflow (ECTO) mode of computation.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "additive identity; compute through overflow (CTO);
computer arithmetic; models of computer arithmetic;
number systems; overflow behavior",
}
@InCollection{Gautschi:1978:QNC,
author = "Walter Gautschi",
booktitle = "Recent advances in numerical analysis ({Proc. Sympos.,
Math. Res. Center, University of Wisconsin, Madison,
Wis., 1978})",
title = "Questions of numerical conditions related to
polynomials",
volume = "41",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "45--72",
year = "1978",
MRclass = "65D99",
MRnumber = "519056",
MRreviewer = "Gerhard Merz",
bibdate = "Fri Feb 9 15:26:45 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Publ. Math. Res. Center University of Wisconsin",
acknowledgement = ack-nhfb,
}
@Article{Good:1978:CMA,
author = "I. J. Good",
title = "{C 24}. {A} method for avoiding overflows and
underflows",
journal = j-J-STAT-COMPUT-SIMUL,
volume = "8",
number = "2",
pages = "162--163",
year = "1978",
CODEN = "JSCSAJ",
DOI = "https://doi.org/10.1080/00949657808810261",
ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
ISSN-L = "0094-9655",
bibdate = "Tue Apr 22 09:10:43 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Computation and Simulation",
journal-URL = "http://www.tandfonline.com/loi/gscs20",
}
@Article{Goodman:1978:ITD,
author = "R. Goodman and J. Bustoz and A. Feldstein",
title = "Improved Trailing Digits Estimates Applied to Optimal
Computer Arithmetic",
journal = j-SIAM-REVIEW,
volume = "20",
number = "3",
pages = "625--625",
month = "????",
year = "1978",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Book{Hamacher:1978:CO,
author = "V. Carl Hamacher and Zvonko G. Vranesic and Safwat G.
Zaky",
title = "Computer Organization",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xiv + 465",
year = "1978",
ISBN = "0-07-025681-0",
ISBN-13 = "978-0-07-025681-1",
LCCN = "QA76.9.A73 H35",
bibdate = "Sat May 18 14:24:11 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "McGraw-Hill series in computer organization and
architecture",
acknowledgement = ack-nhfb,
tableofcontents = "Preface \\
Basic Structure of Computer Hardware and Software / 1
\\
Addressing Methods and Machine Program Sequencing / 21
\\
The Processing Unit / 111 \\
Input-Output Organization / 152 \\
The Memory / 207 \\
Arithmetic / 257 \\
Pipelining / 302 \\
Examples of CISC, RISC, and Stack Processors / 339 \\
Computer Peripherals / 370 \\
Large Computer Systems / 398 \\
Appendix A: Logic Circuits / 441 \\
Appendix B: PowerPC Instruction Set / 509 \\
Appendix C: Character Set for Motorola 68000
Microprocessor / 523 \\
Appendix D: Character Codes and Number Conversion / 541
\\
Index / 547",
}
@InProceedings{Horspool:1978:EAU,
author = "R. Nigel Horspool and Eric C. R. Hehner",
title = "Exact Arithmetic Using a Variable-Length $p$-adic
Representation",
crossref = "IEEE:1978:PSC",
pages = "10--14",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Horspool.pdf",
abstract = "The $p$-adic number system is introduced and developed
into a form suitable for performing exact arithmetic in
computers. The proposed representation has several
desirable attributes: the four standard arithmetic
operations have a simple consistent form, the
programmer has the ability to choose the precise degree
of accuracy in his calculations and the variable-length
nature of the representation achieves compact
encodings",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@InProceedings{Hull:1978:DFP,
author = "T. E. Hull",
title = "Desirable Floating-Point Arithmetic and Elementary
Functions for Numerical Computation",
crossref = "IEEE:1978:PSC",
pages = "63--69",
year = "1978",
DOI = "https://doi.org/10.1109/arith.1978.6155780",
bibdate = "Thu Sep 01 12:14:34 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Hull.pdf",
abstract = "The purpose of this paper is to summarize proposed
specifications for floating-point arithmetic and
elementary functions. The topics considered are: the
base of the number system, precision control, number
representation, arithmetic operations, other basic
operations, elementary functions, and exception
handling. The possibility of doing without fixed-point
arithmetic is also discussed.\par
The specifications are intended to be entirely at the
level of a programming language such as Fortran. The
emphasis is on convenience and simplicity from the
user's point of view. The specifications are not
complete in every detail, but it is intended that they
be complete ``in spirit'' --- some further details,
especially syntactic details, would have to be
provided, but the proposals are otherwise relatively
complete.",
acknowledgement = ack-nj,
keywords = "ARITH-4; decimal floating-point arithmetic",
remark = "Refined and implemented later by
\cite{Cohen:1983:CCP}. The paper begins with the
quote
``\ldots{} the expression $ 25 + 1 / 3 $ yields the
value $ 5.333333 $ in PL/I, and $ .333334 $ in PL/C
\ldots{}'', Conway and Gries, An Introduction to
Programming, 1975, p. 24.",
}
@InProceedings{Hwang:1978:IRR,
author = "Kai Hwang and T. P. Chang",
title = "An Interleaved Rational\slash Radix Arithmetic System
for High-Precision Computations",
crossref = "IEEE:1978:PSC",
pages = "15--24",
year = "1978",
bibdate = "Wed Nov 14 17:49:59 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Hwang.pdf",
abstract = "A new interleaved rational\slash radix number system
is proposed for upgrading the precision of normalized
Floating-Point (FLP) arithmetic operations without
increasing the basic word length. A complete set of
rational rounding and arithmetic algorithms are
developed. The Average Relative Representation Error
(ARRE) of the proposed flexible FLP system is computed
through a series of simulation studies on CDC 6500. Our
results show a 10\% improvement of representation
accuracy when compared with the ARRE of conventional
FLP system. The architecture of a rational FLP
arithmetic processor is also presented. Tradeoffs
between operating speed and computing accuracy are
discussed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4; Farey rational numbers",
}
@Manual{Intel:1978:FAL,
author = "{Intel Corporation}",
title = "8080\slash 8085 floating-point arithmetic library:
user's manual",
organization = "Intel Corporation",
address = "Santa Clara, CA, USA",
pages = "various",
year = "1978",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Intel 8080 (Microprocessor) --- Programming.; Intel
8085 (Microprocessor) --- Programming.",
remark = "``Manual order number: 9800452B.''",
}
@InProceedings{Jullien:1978:ARN,
author = "G. A. Jullien and W. C. Miller",
title = "Application of the Residue Number System to Computer
Processing of Digital Signals",
crossref = "IEEE:1978:PSC",
pages = "220--225",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Jullien.pdf",
abstract = "The residue number system offers parallel processing,
digital hardware implementations for the binary
operations of addition, subtraction and multiplication.
This paper discusses the use of the residue number
system in implementing digital signal processing
functions, in which these binary operations abound. The
paper covers implementations using arrays of read only
memories, and briefly discusses the use of parallel
microprocessor structures. ROM array implementations of
scaling operations are also presented.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4; residue number system",
}
@Article{Jullien:1978:RNS,
author = "G. A. Jullien",
title = "Residue Number Scaling and Other Operations Using
{ROM} Arrays",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-27",
number = "4",
pages = "325--336",
month = apr,
year = "1978",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1978.1675105",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 08:13:28 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675105;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35168",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "Over the last two decades there has been considerable
interest in the implementation of digital computer
elements using hardware based on the residue number
system. This paper considers implementing such systems
with arrays of look-up tables placed \ldots{}",
}
@Article{Kahan:1978:KSI,
author = "W. Kahan and B. N. Parlett",
title = "{K{\"o}nnen Sie sich auf Ihren Rechner verlassen?}
({German}) [Can you count on your calculator?]",
journal = "{Jahrbuch {\"U}berblicke Mathematik}",
volume = "??",
pages = "199--216",
year = "1978",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0397.65081",
acknowledgement = ack-nhfb,
classmath = "*65Y99 Computer aspects of numerical algorithms 65D20
Computation of special functions 00A99 Miscellaneous
topics in general mathematics",
keywords = "Automated Algorithms; Error of Computation; Pocket
Calculator",
language = "German",
}
@InProceedings{Koren:1978:UAC,
author = "Israel Koren and Yoram Maliniak",
title = "A Unified Approach to a Class of Number Systems",
crossref = "IEEE:1978:PSC",
pages = "25--28",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Koren.pdf",
abstract = "A unified approach to a broad class of number systems
is proposed in this paper. This class contains all
positive and negative radix systems and other
well-known number systems. The proposed approach
enables us to develop a single set of algorithms for
arithmetic operations and conversion methods between
number systems.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@InProceedings{Kornerup:1978:FAF,
author = "Peter Kornerup and David W. Matula",
title = "A Feasibility Analysis of Fixed-Slash and
Floating-Slash Arithmetic",
crossref = "IEEE:1978:PSC",
pages = "{39--47}",
year = "1978",
bibdate = "Wed Nov 14 17:50:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Kornerup.pdf",
abstract = "An investigation of the feasibility of a finite
precision approximate rational arithmetic based on
fixed-slash representation of rational numbers is
presented. Worst-case and average-case complexity
analyses of the involved rounding algorithm (an
extended shift-subtract gcd algorithm) are presented.
The results are applied to a proposed hardware
realization of a fixed-slash arithmetic unit.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@InProceedings{Krishnamurthy:1978:MPP,
author = "E. V. Krishnamurthy and H. Venkateswaran",
title = "Multivariable Polynomial Processing --- Applications
to Interpolation",
crossref = "IEEE:1978:PSC",
pages = "81--87",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Krishnamurthy.pdf",
abstract = "A data-structure suitable for multivariable polynomial
processing in introduced. Using this data structure,
arithmetic algorithms are described for addition,
subtraction and multiplication of multivariable
polynomials; also algorithms are described for forming
the inner product and tensor product of vectors, Those
components are multivariable polynomials. Application
of these algorithms for multivariable cardinal spline
approximation is described in detail.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@Book{Kuck:1978:SCC,
author = "David J. Kuck",
title = "The structure of computers and computations",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xxii + 611",
year = "1978",
ISBN = "0-471-02716-2 (vol. 1), 0-471-08138-8",
ISBN-13 = "978-0-471-02716-4 (vol. 1), 978-0-471-08138-8",
LCCN = "QA76.9.A73 K83",
bibdate = "Mon May 20 05:05:46 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See Chapter 3 for floating-point arithmetic
discussion.",
acknowledgement = ack-nhfb,
}
@InProceedings{Liddiard:1978:RSF,
author = "L. A. Liddiard",
title = "Required Scientific Floating Point Arithmetic",
crossref = "IEEE:1978:PSC",
pages = "56--62",
year = "1978",
bibdate = "Thu Sep 01 11:06:57 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Liddiard.pdf",
abstract = "Previous papers in computer arithmetic have shown that
correct rounded floating point with good arithmetic
properties can be attained using guard digits and
careful algorithms on the floating point fractions.
This paper combines that body of knowledge with
proposed exponent forms that are closed with respect to
inversion and detection and recovery of exponent under-
and overflow. In addition radix 2 is shown to be the
only base radix meeting minimal variation of precision,
a condition necessary for the safe use of floating
point. An effort is made to establish objective
criteria in answer to the question ``What is the best
division of the computer word into exponent and
fraction parts?''. Combining the previous results
allows a required scientific floating point arithmetic
to be portrayed and compared with available arithmetic
on current computers.",
acknowledgement = ack-nj,
keywords = "ARITH-4; arithmetic properties; correct rounding;
exponent over; Floating point exponents; floating-point
arithmetic; optimal base radix",
}
@InProceedings{Lillevik:1978:CDA,
author = "Sigurd L. Lillevik and P. David Fisher",
title = "Computational Design Alternatives with
Microprocessor-Based Systems",
crossref = "IEEE:1978:PSC",
pages = "267--272",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Lillevik.pdf",
abstract = "This paper examines and characterizes four elemental
hardware computational design alternatives (CDA's) and
presents a structured approach to computational section
design which incorporates a rigorous, theoretic
foundation. The DIRECT CDA incorporates a single
microprocessor ($ \mu $P) and memory. The AU CDA
contains a $ \mu $P, memory, and arithmetic unit. $ \mu
$P, memory, and calculator chip comprise the CALC CDA.
Finally, several $ \mu $P's and memories in a
Master\slash Slave arrangement implement the multiple-$
\mu $P m$ \mu $P CDA. A common set of attributes ---
precision, speed and cost --- facilitates comparison.
Using these attributes, Multiattribute Utility Theory
assesses a numeric quantity, the utility, to represent
each CDA's relative usefulness. Thus, design involves
selecting the CDA with the greatest utility.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@InProceedings{Lim:1978:HSM,
author = "Raymond S. Lim",
title = "High-Speed Multiplication and Multiple Summand
Addition",
crossref = "IEEE:1978:PSC",
pages = "149--153",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Lim.pdf",
abstract = "The problem of high-speed multiplication is considered
from the viewpoint of summand generation and summand
summation. The goal is to obtain at least a
2's-complement, 32-bit floating-point (sign plus 24-bit
fraction) multiplication in 10 to 20 ns using ECL LSI
packages. Summand generation is implemented by $ m
\times m $-bit multipliers. The optimum values for $m$
are 9, 13, 17, or 21. Summand summation is implemented
by a row of $ (p, 2) $ column-summing counters. The $
(0, 2) $, $ (5, 2) $, and $ (7, 2) $ counters are
optimum choices. These counters compress $p$ inputs
into two outputs plus nonpropagating carry bits, where
these bits are added to the next higher-order stage
with at most two full adder delays.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@Article{Liu:1978:ECC,
author = "Chao-Kai Liu and Tse Lin Wang",
title = "Error-Correcting Codes in Binary-Coded-Decimal
Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-27",
number = "11",
pages = "977--984",
month = nov,
year = "1978",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1978.1674987",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Aug 07 17:26:15 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Error-correcting coding schemes devised for binary
arithmetic are not in general applicable to BCD
arithmetic. In this paper, we investigate the new
problem of using such coding schemes in BCD systems. We
first discuss the general characteristics of arithmetic
errors and define the arithmetic weight and distance in
BCD systems. We show that the distance is a metric
function. Number theory is used to construct a class of
single-error-correcting codes for BCD arithmetic. It is
shown that the generator of these codes possesses a
very simple form and the structure of these codes can
be analytically determined.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "BCD arithmetic; decimal arithmetic",
}
@Article{Logan:1978:FDP,
author = "Jonothan L. Logan and Samuel A. Goudsmit",
title = "The First Digit Phenomenon",
journal = j-PROC-AMER-PHIL-SOC,
volume = "122",
number = "4",
pages = "193--197",
day = "18",
month = aug,
year = "1978",
CODEN = "PAPCAA",
ISSN = "0003-049X (print), 2326-9243 (electronic)",
ISSN-L = "0003-049X",
bibdate = "Fri Mar 30 11:20:35 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "This paper contains derivations of both Stigler's Law
and Benford's Law, and receives strong criticism in
\cite{Raimi:1985:FDP}. This paper contains an important
historical note that is recorded in entry
\cite{Benford:1938:LAN}.",
URL = "http://links.jstor.org/sici?sici=0003-049X(19780818)122%3A4%3C193%3ATFDP%3E2.0.CO%3B2-C;
http://www.jstor.org/stable/986530",
abstract = "Forty years ago an article appeared in these
Proceedings, which has since then attracted much
attention of mathematicians and some physicists. It was
written by Frank Benford, a physicist from the General
Electric Company at Schenectady. He had examined a
large number of numerical tables, the kind that are
printed in almanacs, and in scientific and technical
handbooks. He noticed a most unusual and unexpected
property of many of these tables. Consider, for
example, the numbers representing the populations of
states or all the countries in the world, or their
areas, their budgets, their numbers of hospital beds,
etc. One would expect that on the average just as many
of these entries would begin with the digit $1$ as with
$2$ or $3$ or $4$, and so on. But Benford noticed that
small values of the first digits occur far more
often.",
acknowledgement = ack-nhfb,
author-dates = "Samuel A. Goudsmit (July 11, 1902--December 4, 1978)",
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
journal-URL = "http://www.jstor.org/journal/procamerphilsoci",
remark = "In 1925, Samuel Goudsmit and George Uhlenbeck proposed
the concept of electron spin, a critical step forward
in the quantum mechanics of many-electron systems.
Surprisingly, that work did not get them the Nobel
Prize, but it did spur Wolfgang Pauli to present his
Exclusion Principle in 1925, for which he received the
1945 Nobel Prize in Physics. After World War II,
Goudsmit was the scientific head of the Alsos mission
to capture German nuclear scientists. In the 1950s, he
founded the journal Physical Review Letters. During the
1960s and 1970s, he was Editor-in-Chief of the main
American physics journal, the Physical Review.",
}
@InProceedings{Matula:1978:BDS,
author = "David W. Matula",
title = "Basic Digit Sets for Radix Representation of the
Integers",
crossref = "IEEE:1978:PSC",
pages = "1--9",
year = "1978",
bibdate = "Wed Nov 14 17:51:32 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Matula.pdf",
abstract = "Let $Z$ denote the set of integers. A digit set $ D
\in Z $ is basic for base $ \beta \in Z $ if the set of
polynomials $ \{ d_m \beta^m + d_{m - 1} \beta^{m - 1}
+ \ldots {} + d_1 \beta + d_0 | d_i \in D \} $ contains
a unique representation for every $ n \in Z $. We give
necessary and sufficient conditions for D to be basic
for $ \beta $. We exhibit efficient procedures for
verifying that $D$ is basic for $S$, and for computing
the representation of any $ n \in Z $ when a
representation exists. There exist $D$, $S$ with $D$
basic for $S$ where $ \max \{ |d| \vert d \in D \} > |
\beta | $, and more generally, an infinite class of
basic digit sets is shown to exist for every base $S$
with $ \beta \geq 3 $. The natural extension to
infinite precision radix representation using basic
digit sets is considered and a summary of results is
presented.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4; base; digit representation; finite and
infinite precision; non-standard number",
}
@InProceedings{Matula:1978:FAF,
author = "David W. Matula and Peter Kornerup",
title = "A Feasibility Analysis of Fixed-Slash and
Floating-Slash Number Systems",
crossref = "IEEE:1978:PSC",
pages = "{29--38}",
year = "1978",
bibdate = "Wed Nov 14 17:52:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Matula_Kornerup.pdf",
abstract = "Design and analysis of finite precision rational
number systems based on fixed-slash and floating-slash
representation is pursued. Natural formats for binary
fixed-slash and binary floating-slash number
representation in computer words are described.
Compatibility with standard integer representation is
obtained. Redundancy in the representation is shown to
be minimal. Arithmetic register requirements are
considered. Worst case and average case rounding errors
are determined, and the concept of adaptive variable
precision in the rounding is developed.",
acknowledgement = ack-nhfb,
keywords = "adaptive variable precision; adjacent fractions;
ARITH-4; binary numeric word format; Farey fractions;
finite precision; fixed-slash numbers; floating-slash
numbers; integer compatibility; mediant roundings;
range of number system; rational arithmetic;
redundancy; worst case and average case rounding
error",
}
@Article{McCrea:1978:CFP,
author = "P. G. McCrea and P. C. Maxwell and P. W. Baker",
title = "Comments on {``A Floating-Point Multiplexed DDA
System''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-27",
number = "12",
pages = "1226--1226",
month = dec,
year = "1978",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1978.1675033",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 08:13:33 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Hannington:1976:FPM}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675033",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Mitra:1978:ITD,
author = "S. K. Mitra and G. K. Sorknes",
title = "On the Implementation of a Two-Dimensional {FIR}
Filter Using a Single Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-27",
number = "8",
pages = "762--764",
month = aug,
year = "1978",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1978.1675186",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 08:13:30 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675186",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Morris:1978:DID,
author = "Robert Morris and Lorinda Cherry",
title = "{DC} --- An Interactive Desk Calculator",
type = "Technical Memorandum",
number = "1056",
institution = inst-ATT-BELL,
address = inst-ATT-BELL:adr,
pages = "8",
day = "15",
month = nov,
year = "1978",
bibdate = "Tue Jun 06 08:07:45 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/unix.bib",
abstract = "DC is an arbitrary precision arithmetic package
implemented on the UNIX time-sharing system in the form
of an interactive desk calculator. It works like a
stacking calculator using reverse Polish notation.
Ordinarily DC operates on decimal integers, but one may
specify an input base, output base, and a number of
fractional digits to be maintained.",
abstract-2 = "DC is an interactive desk calculator program
implemented on the UNIX Time-Sharing System \ldots{}
arbitrary-precision integer arithmetic.",
acknowledgement = ack-nhfb,
author-dates = "Lorinda L. Cherry (18 November 1944--February 2022);
Robert Morris (25 July 1932--26 June 2011)",
remark = "Available in PDF file of \cite[pp.
399--406]{Dolotta:1977:DPU}.",
}
@Article{Murphy:1978:SRP,
author = "T. R. Murphy and P. L. Rickard",
title = "Square-Root Procedure for Floating-Point Numbers",
journal = j-IBM-TDB,
volume = "21",
number = "2",
pages = "785",
month = jul,
year = "1978",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Article{Nussabaumer:1978:FMN,
author = "H. J. Nussabaumer",
title = "Fast Multipliers for Number Theoretic Transforms",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-27",
number = "8",
pages = "764--765",
month = aug,
year = "1978",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1978.1675187",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 08:13:30 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675187",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{OLeary:1978:DHS,
author = "G. P. O'Leary",
title = "The design of a high-speed arithmetic processor",
crossref = "COMPSAC:1978:CPC",
pages = "175--176",
year = "1978",
bibdate = "Wed Sep 07 22:19:45 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Olver:1978:NAE,
author = "F. W. J. Olver",
title = "New Approach to Error Arithmetic",
journal = j-SIAM-REVIEW,
volume = "20",
number = "3",
pages = "632--632",
month = "????",
year = "1978",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Patel:1978:ASB,
author = "M. R. Patel and K. H. Bennett",
title = "Analysis of Speed of a Binary Divider Using a Variable
Number of Shifts Per Cycle",
journal = j-COMP-J,
volume = "21",
number = "3",
pages = "246--252",
month = aug,
year = "1978",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/21.3.246",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:48:03 MST 2012",
bibsource = "Compendex database;
http://comjnl.oxfordjournals.org/content/21/3.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/;
https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/21/3/246.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/246.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/247.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/248.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/249.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/250.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/251.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/252.tif",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
classification = "721",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "analysis; computers, digital; cycle; digital
arithmetic; discrete time; discrete time systems;
finite state system model; ICL 2980; optimisation;
optimum hardware configuration; Patel and Bennett
(1976); speed of a binary divider; variable number of
shifts per",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Payne:1978:DPF,
author = "M. Payne and W. Strecker",
title = "Draft Proposal for Floating Point Standard",
type = "Technical report",
institution = "Digital Equipment Corporation",
address = "Maynard, MA, USA",
day = "11",
month = dec,
year = "1978",
bibdate = "Fri Nov 09 19:11:42 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Preston:1978:NAT,
author = "F. S. Preston",
title = "A New Algorithm for the Tangent",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-27",
number = "2",
pages = "167",
month = feb,
year = "1978",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1978.1675052",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Ralston:1978:FCN,
author = "Anthony Ralston and Philip Rabinowitz",
title = "A first course in numerical analysis",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
edition = "Second",
pages = "xix + 556",
year = "1978",
ISBN = "0-07-051158-6",
ISBN-13 = "978-0-07-051158-3",
LCCN = "QA297 .R3 1978",
bibdate = "Fri Aug 20 10:13:32 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$19.50",
series = "International series in pure and applied mathematics",
acknowledgement = ack-nhfb,
remark = "See also first edition \cite{Ralston:1965:FCN}.
Reprinted in \cite{Ralston:2001:FCN}.",
subject = "Numerical analysis",
}
@Article{Rashed:1978:LRI,
author = "Roshd{\=\i} R{\=a}shed",
title = "{L}'Extraction de la Racine $ n^{\rm \scriptstyle
i{\grave e}me} $ et {l'Invention} des Fractions
D{\'e}cimales ({XI}$^e$--{XII}$^e$ Si{\`e}cles).
({French}) [{The} extraction of the n$^{{\rm th}}$ root
and the invention of decimal fractions (11$^{{\rm
th}}$--12$^{{\rm th}}$ centuries)]",
journal = j-ARCH-HIST-EXACT-SCI,
volume = "18",
number = "3",
pages = "191--243",
month = sep,
year = "1978",
CODEN = "AHESAN",
ISSN = "0003-9519 (print), 1432-0657 (electronic)",
ISSN-L = "0003-9519",
MRclass = "01A35",
MRnumber = "0484970 (58 \#4829)",
MRreviewer = "H. L. L. Busard",
bibdate = "Fri Feb 4 21:50:14 MST 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=18&issue=3;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=18&issue=3&spage=191",
acknowledgement = ack-nhfb,
fjournal = "Archive for History of Exact Sciences",
journal-URL = "http://link.springer.com/journal/407",
language = "French",
MRtitle = "{L}'extraction de la racine {$n$}i{\`e}me et
l'invention des fractions d{\'e}cimales ({XIe--XIIe}
si{\`e}cles)",
MRyear = "1977/78",
}
@InProceedings{Reuter:1978:SEU,
author = "Eric K. Reuter and John P. Jeter and J. Wayne Anderson
and Bruce D. Shriver",
title = "Some Experiments Using Interval Arithmetic",
crossref = "IEEE:1978:PSC",
pages = "75--80",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Reuter.pdf",
abstract = "This paper reviews past experiences and discusses
future work in the area of interval arithmetic at the
University of Southwestern Louisiana (USL). Two
versions of interval arithmetic were developed and
implemented at USL. An interval data type declaration
and the necessary mathematical functions for this data
type were added to Fortran via the preprocessor Augment
(4,5). In the first version the endpoints of the
intervals were represented as single precision floating
point numbers. In the other version, the endpoints were
represented to 56 decimal digits. Production
engineering programs were run as benchmarks (8). The
accumulation of computational and algorithmic error
could be observed as a widening of the intervals. The
benchmarks were also run in normal single and double
precision arithmetic. In some instances, the result
obtained from a single or double precision calculation
was not bounded by the corresponding interval result
indicating some problem with the algorithm. The
widening of an interval does not necessarily indicate a
data sensitivity nor error in an algorithm. However,
these large intervals can be used as indicator of no
problems. As could be expected, the 56-decimal digit
precision interval gave better results in terms of
smaller intervals due to the increased amount of
precision. The obvious problem with this version is
that the amount of overhead required for its execution
is high.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@Manual{Richardson:1978:ATB,
author = "Caryl Richardson and Jef Raskin",
title = "The {Apple} tutorial: based on the {Apple} {II} Basic
programming manual",
organization = "Bell and Howell, Audio-Visual Products Division",
address = "Chicago, IL, USA",
pages = "vii + 157",
year = "1978",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Apple II (Computer) --- Programming.; BASIC (Computer
program language)",
remark = "Cover title: Floating point Basic tutorial manual.
``Reprinted with the permission of Apple Computer
Inc.'' Companion volume: Bell and Howell floating point
Basic programming reference manual.",
}
@Article{Ruckdeschel:1978:FA,
author = "F. Ruckdeschel",
title = "Functional Approximations",
journal = j-BYTE,
volume = "3",
number = "11",
pages = "34--46",
month = nov,
year = "1978",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "BYTE Magazine",
}
@Article{Russell:1978:CCS,
author = "Richard M. Russell",
title = "The {Cray-1} Computer System",
journal = j-CACM,
volume = "21",
number = "1",
pages = "63--72",
month = jan,
year = "1978",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Dec 08 13:08:43 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "grecommended91, existing classic architecture, maeder
biblio: parallel hardware and devices, implementation,
ginsberg biblio: bhibbard enm, j\-lb",
remark = "The original paper describing the Cray-1. This paper
is reproduced in Kuhn and Padua's (1981, IEEE) survey
``Tutorial on Parallel Processing.'' Also reproduced in
``Computer Structures: Principles and Examples'' by
Daniel P. Siewiorek, C. Gordon Bell, and Allen Newell,
McGraw-Hill, 1982, pp. 743-752. Reproduced in Dharma P.
Agrawal's (ed.) ``Advanced Computer Architecture,''
IEEE, 1986, pp. 15--24. Literature search yields:
00712248 E. I. Monthly No: EI7804023850 E. I. Yearly
No: EI78014612 Title: Cray-1 Computer System. Author:
Russell, Richard M. Corporate Source: Cray Res Inc,
Minneapolis, Minn Source: Communications of the ACM v
21 n 1 Jan 1978 p 63--72 Publication Year: 1978 CODEN:
CACMA2 ISSN: 0001-0782 Language: ENGLISH Journal
Announcement: 7804 Abstract: The CRAY-1 is described,
the evolution of its architecture is discussed, and an
account is given of some of the problems that were
overcome during its manufacture. The CRAY-1 is the only
computer to have been built to date that satisfies
ERDA's Class VI requirement (a computer capable of
processing from 20 to 60 million floating point
operations per second). The CRAY-1's Fortran compiler
(CFT) is designed to give the scientific user immediate
access to the benefits of the CRAY-1's vector
processing architecture. An optimizing compiler, CFT,
``vectorizes'' innermost DO loops. Compatible with the
ANSI 1966 Fortran Standard and with many commonly
supported Fortran extensions, CFT does not require any
source program modifications or the use of additional
nonstandard Fortran statements to achieve
vectorization. 6 refs. Descriptors: *COMPUTER
ARCHITECTURE; COMPUTER SYSTEMS, DIGITAL Classification
Codes: 722 (Computer Hardware); 723 (Computer Software)
72 (COMPUTERS \& DATA PROCESSING)",
}
@Book{Schmid:1978:EDS,
author = "Hermann Schmid",
title = "{Elektronische Dezimalrechner, Schaltungen und
Verfahren} \toenglish {Electronic Decimal Computers,
Wiring and Methods} \endtoenglish",
publisher = pub-OLDENBOURG,
address = pub-OLDENBOURG:adr,
pages = "275",
year = "1978",
ISBN = "3-486-20211-1",
ISBN-13 = "978-3-486-20211-3",
LCCN = "????",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
keywords = "decimal floating-point arithmetic",
}
@InProceedings{Schreiber:1978:TMF,
author = "F. A. Schreiber and R. Stefanelli",
title = "Two Methods for Fast Binary-{BCD} Conversion",
crossref = "IEEE:1978:PSC",
pages = "200--207",
year = "1978",
bibdate = "Sat Nov 12 21:58:26 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Schreiber.pdf",
abstract = "Two methods for performing binary--BCD conversion of
positive integers are discussed. The principle which
underlies both methods in the repeated division by five
and then by two, obtained the first by means of
subtractions performed from left to right, the second
by shifting bits before next subtraction.\par
It is shown that these methods work in a time which is
linear with the length in bit of the number to be
converted.\par
A ROM solution is proposed and its complexity is
compared with that of other methods.",
acknowledgement = ack-nj,
keywords = "ARITH-4",
}
@Book{Seck:1978:WSA,
editor = "Friedrich Seck",
title = "{Wilhelm Schickard, 1592--1635: Astronom, Geograph,
Orientalist, Erfinder der Rechenmaschine}. ({German})
[{Wilhelm Schickard}, 1592--1635: Astronomer,
Geographer, Orientalist, Inventor of the calculator]",
volume = "25",
publisher = "Mohr",
address = "T{\"u}bingen, West Germany",
pages = "422",
year = "1978",
ISBN = "3-16-939772-9",
ISBN-13 = "978-3-16-939772-3",
LCCN = "QB36.S312 W54",
bibdate = "Sat Jul 27 11:00:08 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/scicontext.bib;
z3950.loc.gov:7090/Voyager",
series = "Contubernium",
acknowledgement = ack-nhfb,
language = "German",
remark = "Includes texts in Latin.",
subject = "Schickard, Wilhelm; Astronomers; Germany; Biography;
Middle East specialists",
subject-dates = "1592--1635",
}
@Article{Shen:1978:CSA,
author = "D. T. Shen and A. Weinberger",
title = "4-2 carry-save adder implementation using send
circuits",
journal = j-IBM-TDB,
volume = "20",
number = "9",
pages = "??--??",
month = feb,
year = "1978",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Mon Dec 24 10:18:16 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
}
@InProceedings{Slekys:1978:MBI,
author = "Arunas G. Slekys and Algirdas Avi{\v{z}}ienis",
title = "A Modified Bi-Imaginary Number Systems",
crossref = "IEEE:1978:PSC",
pages = "48--55",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Slekys.pdf",
abstract = "In this paper the properties of $p$-imaginary number
systems are reviewed and a modified bi-imaginary number
system is introduced as a special case with $ p = 2 $.
Major properties, including conversion of integer and
floating point operands represented in a radix $ + p $
system, range, sign and zero tests, and shifting are
discussed. The ability to represent the operands as
vectors of radix-2 digits suggests advantages in
implementing machine-usable arithmetic algorithms.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@Article{Sripad:1978:QEF,
author = "A. Sripad and D. Snyder",
title = "Quantization errors in floating-point arithmetic",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "26",
number = "5",
pages = "456--463",
month = oct,
year = "1978",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "In this paper, the quantization of the mantissa in a
normalized floating-point number is investigated. A
necessary and sufficient condition is given for the
mantissa to have a reciprocal probability density. A
model to represent a floating-point quantity \ldots{}",
}
@InProceedings{Svoboda:1978:ACF,
author = "Antonin Svoboda",
title = "Arithmetic Circuit Fault Detection by Modular
Encoding",
crossref = "IEEE:1978:PSC",
pages = "208--219",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Svoboda.pdf",
abstract = "Design principles of self checking digital circuits
are in the focus of the general interest and many
papers exist treating that subject. The use of special
data encoding techniques, suitable algorithms of
arithmetic, special hardware elements have been
proposed long ago. The purpose of this paper is to show
that the design can produce rather simple self checking
circuit when the design principles are chosen which
collaborate harmoniously:\par
(1) decimal numerical system is used\par
(2) decimal digit $ d \in \{ 0, 1, \ldots {}, 9 \} $ is
represented in the Diamond Code by the 5-bit binary
number $ f = 3 d + 2 $ \par
(3) decimal digit' addition algorithm introduced here
is simple and effective so that 10 decimal digits can
be added in parallel\par
(4) implementation of the addition algorithm by
conventional Full Adders results in a single fault
detecting circuit.\par
The design of a decimal adder for 10 decimal numbers,
each with 10 digits. is described here as an
illustration. It shows the way how to design other
decimal arithmetic circuits which are single fault
detecting, for instance a multiplier (derived from the
adder for 10 decimal numbers).",
acknowledgement = ack-nhfb,
keywords = "ARITH-4; decimal arithmetic",
}
@InProceedings{Swartzlander:1978:MAS,
author = "E. E. {Swartzlander, Jr.}",
title = "Merged Arithmetic for Signal Processing",
crossref = "IEEE:1978:PSC",
pages = "239--244",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Swartzlander.pdf",
abstract = "The concept of merged arithmetic is introduced and
applied to signal processing. The basic idea involves
synthesizing a composite arithmetic function (e.g., a
complex multiply) directly instead of decomposing it
into multiply and add operations as is conventional
practice. This approach results in a simpler design
which is also faster.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@InProceedings{Tan:1978:TIH,
author = "Kwang G. Tan",
title = "The theory and implementation of high-radix division",
crossref = "IEEE:1978:PSC",
pages = "154--163",
year = "1978",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Tan.pdf",
abstract = "This report derives the theory of high-radix division
in terms of the properties of the overlapped regions of
the P-D plot. The minimum precision requirements in
quotient selection are discussed. The methods of
implementations in hardware and in read-only memory are
explored.",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "ARITH-4",
}
@Article{Trivedi:1978:CUC,
author = "K. S. Trivedi",
title = "Corrections to {``On the Use of Continued Fractions
for Digital Computer Arithmetic''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-27",
number = "3",
pages = "288--288",
month = mar,
year = "1978",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1978.1675093",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 08:13:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Trivedi:1977:UCF}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675093",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Trivedi:1978:HRL,
author = "Kishor S. Trivedi and Joseph G. Rusnak",
title = "Higher Radix On-Line Division",
crossref = "IEEE:1978:PSC",
pages = "164--174",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Trivedi.pdf",
abstract = "We present a formal proof of correctness of the
on-line division algorithm specified in an earlier
paper [1]. We also derive two radix 4 on-line division
algorithms, with non-redundant and redundant operands
respectively.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@InProceedings{Tseng:1978:EAF,
author = "B. Tseng and W. Miller and G. Jullien and J. Soltis
and A. Baraniecka",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '78}",
title = "An error analysis of a {FFT} implementation using the
residue number system",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "800--803",
year = "1978",
CODEN = "????",
DOI = "https://doi.org/10.1049/el:19780088",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper considers an implementation of the FFT
based upon the residue number system. This system
offers the advantages of using integer based arithmetic
operations and a simple hardware realization involving
table look-up arrays. The proposed \ldots{}",
}
@Article{Wang:1978:EPF,
author = "J. Y. Wang",
title = "The Evaluation of Periodic Functions with Large Input
Arguments",
journal = j-SIGNUM,
volume = "13",
number = "4",
pages = "7--9",
month = dec,
year = "1978",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@Article{Waser:1978:HMM,
author = "Shlomo Waser",
title = "High-speed monolithic multipliers for real-time
digital signal processing",
journal = j-COMPUTER,
volume = "11",
number = "10",
pages = "19--29",
month = oct,
year = "1978",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Thu Dec 12 07:20:54 MST 1996",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An analysis is made of arithmetic requirements for
signal processing and monolithic multipliers are
characterized. It is shown that real-time digital
signal processing requires very fast multiplication,
which is now becoming possible using mathematical
techniques to take advantage of single-chip
multipliers.",
acknowledgement = ack-nhfb,
classification = "713; 721; 723",
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
journalabr = "Computer",
keywords = "signal processing",
}
@Article{Waser:1978:SAH,
author = "S. Waser",
title = "State of the Art in High-Spped Arithmetic {ICs}",
journal = j-COMP-DESIGN,
volume = "??",
number = "??",
pages = "??--??",
month = jul,
year = "1978",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Fri Nov 09 19:34:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Design",
}
@InProceedings{Waser:1978:SAI,
author = "Shlomo Waser",
title = "Survey of Arithmetic Integrated Circuits",
crossref = "IEEE:1978:PSC",
pages = "257--266",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Waser.pdf",
abstract = "The purpose of this report is to provide the
state-of-the-art of high performance arithmetic
integrated circuits (ICs). The survey concentrates on
arithmetic ICs that are designed to improve execution
speed over software techniques, therefore, no
calculator chips are surveyed.\par
In order to understand the difficulties encountered in
fabricating high speed arithmetic ICs, we start the
article with a discussion on semiconductor technology.
Next, we survey the various arithmetic elements that
are available in monolithic form: ALUs, Data Slices,
Multipliers, Floating Point Processors, and ROMs.
Finally, we conclude with a comment on digital signal
processing and a discussion of the future trends in
arithmetic ICs.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@InProceedings{Weinberger:1978:PAU,
author = "Arnold Weinberger",
title = "Parallel Adders Using Standard {PLAs}",
crossref = "IEEE:1978:PSC",
pages = "116--124",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Weinberger.pdf",
abstract = "PLA adders are described that add in one cycle and
require a reasonable number of product terms for an 8,
16, or even a 32-bit adder. A procedure is also
described for minimizing the number of product terms
for any size adder.",
acknowledgement = ack-nhfb,
keywords = "adder; ARITH-4; carry-look-ahead; input decoders;
output exclusive-ors; product term minimization;
Programmable Logic Array (PLA)",
}
@Article{Wittmayer:1978:APP,
author = "W. R. Wittmayer",
title = "Array Processor Provides High Throughput Rate",
journal = j-COMP-DESIGN,
volume = "??",
number = "??",
pages = "93--100",
month = mar,
year = "1978",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Fri Nov 09 19:45:09 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Design",
}
@Article{Wozniakowski:1978:REA,
author = "H. Wo{\'z}niakowski",
title = "Round-off error analysis of iterations for large
linear systems",
journal = j-NUM-MATH,
volume = "30",
number = "3",
pages = "301--314",
year = "1978",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "B0290B (Error analysis in numerical methods); C4110
(Error analysis in numerical methods)",
corpsource = "Department of Computer Sci., Carnegie-Mellon
University, Pittsburgh, PA, USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "equations; error analysis; floating point arithmetic;
Gauss Seidel iteration; iteration round off error
analysis; iterative methods; residual vector; sparse
linear systems",
treatment = "A Application; T Theoretical or Mathematical",
}
@InProceedings{Wrathall:1978:CGI,
author = "Celia Wrathall and Tien Chi Chen",
title = "Convergence Guarantee and Improvements for a fast
Hardware Exponential and Logarithm Evaluation Scheme",
crossref = "IEEE:1978:PSC",
pages = "175--182",
year = "1978",
bibdate = "Thu Sep 01 11:46:12 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Wrathall.pdf",
abstract = "In one iteration, Chen's algorithm for evaluating
exponentials and logarithms advances by 2 bits on the
average, yet may not advance at all. Analysis reveals
that the no-advance situation actually paves the way
for sizable advance in the next iteration, and the
guaranteed advance, after a one iteration overhead, is
one bit per iteration.\par
Two new schemes raise the guaranteed advance to 1.5
bits per iteration, after a two-iteration overhead,
while maintaining the original requirement of one
stored constant per operand bit.\par
Adopting as a figure of merit the following
quantity\par
$$ Q = \textrm {advance per iteration} \over \textrm
{memory words per operand hit} $$ \par
for the steady-state iterations, the new schemes
appears to be better than other methods heretofore
proposed.",
acknowledgement = ack-nj,
keywords = "ARITH-4",
}
@Article{Abu-El-Haija:1979:AER,
author = "A. Abu-El-Haija and A. Peterson",
title = "An approach to eliminate roundoff errors in digital
filters",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "27",
number = "2",
pages = "195--198",
month = apr,
year = "1979",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "``Second-order quantizers'' are introduced which can
be used for implementing recursive digital filters with
practically no roundoff errors or limit-cycle
oscillations. Based on the idea of changing the
transfer function used to compute roundoff \ldots{}",
}
@Article{Aggarwal:1979:REM,
author = "Vijay B. Aggarwal and James W. Burgmeier",
title = "A round-off error model with applications to
arithmetic expressions",
journal = j-SIAM-J-COMPUT,
volume = "8",
number = "1",
pages = "60--72",
month = "????",
year = "1979",
CODEN = "SMJCAT",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
MRclass = "68C01 (65G05)",
MRnumber = "81b:68031",
bibdate = "Mon Nov 29 10:58:59 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/8/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
}
@Article{Agrawal:1979:HSA,
author = "D. P. Agrawal",
title = "High-Speed Arithmetic Arrays",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-28",
number = "3",
pages = "215--224",
month = mar,
year = "1979",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1979.1675322",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 06:49:36 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675322",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Alt:1979:SRD,
author = "H. Alt",
title = "Square Rooting Is as Difficult as Multiplication",
journal = j-COMPUTING,
volume = "21",
number = "3",
pages = "221--232",
year = "1979",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "68C25",
MRnumber = "82m:68081",
bibdate = "Tue Jan 2 17:40:54 MST 2001",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date); MathSciNet
database",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "Math. \& Information, University of Saarlandes,
Saarbrucken, West Germany",
classification = "723; C5230",
description = "digital arithmetic",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Computing (Vienna/New York)",
keywords = "algorithm; computer programming; square rooting",
}
@Article{Atkins:1979:FSC,
author = "D. E. Atkins",
title = "{Fourth Symposium on Computer Arithmetic}: crunching
with quality and {LSI}",
journal = j-COMPUTER,
volume = "12",
number = "4",
pages = "94--97",
month = apr,
year = "1979",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Thu Dec 12 07:20:54 MST 1996",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Computer arithmetic problems --- faster computation
rates and more efficient representations of real
numbers --- are considered in the paper. Floating-point
arithmetic standardization, novel implementation of
basic arithmetic operators, evaluation of elementary
functions --- these are the main considerations of the
conference review.",
acknowledgement = ack-nhfb,
classification = "722; 723",
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
journalabr = "Computer",
keywords = "computer arithmetic; computer systems, digital; data
processing --- data description; mathematical
techniques --- digital arithmetic",
}
@MastersThesis{Barlow:1979:PEA,
author = "Jesse Louis Barlow",
title = "Probabilistic error analysis of computer arithmetics",
type = "{M.S. (Computer Science)}",
school = "Northwestern University",
address = "Evanston, IL, USA",
pages = "????",
year = "1979",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.; Numbers, Real.; Numerical
calculations --- Computer programs.",
}
@MastersThesis{Biddulph:1979:MFC,
author = "Thomas P. Biddulph",
title = "A modified {FORTRAN\slash 77} compiler that will
implement the proposed {IEEE\slash KCS} floating point
standard via calls to emulation routines",
type = "{Master of Science, Plan II}",
school = "Department of Electrical Engineering and Computer
Sciences",
address = "Berkeley, CA, USA",
pages = "????",
year = "1979",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Brent:1979:RLP,
author = "R. P. Brent and H. T. Kung",
title = "A regular layout for parallel adders",
institution = "Computer Science Department, Carnegie-Mellon
University",
address = "Pittsburgh, PA, USA",
pages = "20",
year = "1979",
bibdate = "Thu Nov 18 09:31:44 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://books.google.com/books?id=mutgGwAACAAJ",
abstract = "With VLSI architecture the chip area is a better
measure of cost than the conventional gate count. We
show that addition of n-bit binary numbers can be
performed on a chip in time proportional to $ \log n $
and with area proportional to $ n \log n $.",
acknowledgement = ack-nhfb,
}
@Article{Brent:1979:RMF,
author = "R. P. Brent",
title = "Remark on ``{Algorithm} 524: {MP}, {A Fortran}
Multiple-Precision Arithmetic Package [{A1}]''",
journal = j-TOMS,
volume = "5",
number = "4",
pages = "518--519",
month = dec,
year = "1979",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355853.355868",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Sep 05 22:49:18 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Brent:1978:AMF,Brent:1980:AIB}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@InProceedings{Brown:1979:EPB,
author = "W. S. Brown and S. I. Feldman",
title = "Environment parameters and basic functions for
floating-point computation",
crossref = "ACM:1979:PSC",
pages = "42--45",
year = "1979",
bibdate = "Fri Nov 28 17:31:00 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Bustoz:1979:ITD,
author = "Joaqu{\'i}n Bustoz and Alan Feldstein and Richard
Goodman and Seppo Linnainmaa",
title = "Improved Trailing Digits Estimates Applied to Optimal
Computer Arithmetic",
journal = j-J-ACM,
volume = "26",
number = "4",
pages = "716--730",
month = oct,
year = "1979",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Wed Oct 26 23:35:40 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "New results are given on the distribution of trailing
digits for logarithmically distributed numbers and on
error in floating-point multiplication. Some of the
results have application to computer design. In
particular, there are certain values of the base
(indeed, $ \beta = 2, 4, 6 $, and sometimes, $8$, but
{\em not} $ 16 $) which, when carefully balanced with
other design parameters, minimize the mean
multiplicative error. For these special minimizing
situations, it suffices to have only one guard $ \beta
$ it provided that postnormalization occurs after
symmetric rounding.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "computer arithmetic; floating-point multiplication;
floating-point numbers; floating-point precision and
significance; fraction error; guard digits;
logarithmically distributed numbers; mean and standard
deviation of error; nonleading digits; normalization
options; roundoff error; trailing digits; uniformly
distributed numbers",
}
@Article{Chen:1979:PMB,
author = "I-Ngo Chen and R. Willoner",
title = "An {$ O(n) $} Parallel Multiplier with Bit-Sequential
Input and Output",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-28",
number = "10",
pages = "721--727",
month = oct,
year = "1979",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1979.1675239",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 06:49:41 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675239",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Cody:1979:IPI,
author = "W. J. Cody",
title = "Impact of The Proposed {IEEE} Floating Point Standard
on Numerical Software",
journal = j-SIGNUM,
volume = "14",
number = "3S (Special issue)",
pages = "29--30",
month = oct,
year = "1979",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:07 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C4100 (Numerical analysis); C5230 (Digital arithmetic
methods); C7310 (Mathematics computing)",
corpsource = "Appl. Math. Div., Argonne Nat. Lab., Argonne, IL,
USA",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "digital arithmetic; floating point; IEEE; numerical
analysis; numerical software; standard; standards",
treatment = "P Practical",
xxnumber = "si-2",
}
@Article{Coonen:1979:PSB,
author = "Jerome Coonen and William Kahan and John Palmer and
Tom Pittman and David Stevenson",
title = "A Proposed Standard for Binary Floating Point
Arithmetic: Draft 5.11",
journal = j-SIGNUM,
volume = "14",
number = "3S (Special issue)",
pages = "4--12",
month = oct,
year = "1979",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/1057520.1057521",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:07 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/signum.bib",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "arithmetic; binary; digital arithmetic; floating
point; IEEE Computer Society; Microprocessor; standard;
standards; Standards Subcommittee",
treatment = "P Practical",
xxnumber = "si-2",
}
@TechReport{Coonen:1979:SPS,
author = "Jerome T. Coonen",
title = "Specifications for a Proposed Standard for
Floating-Point Arithmetic",
type = "Memorandum",
number = "{UCB\slash ERL M78\slash 72}",
institution = "University of California, Berkeley",
address = "Berkeley, CA, USA",
day = "25",
month = jan,
year = "1979",
bibdate = "Mon Dec 24 08:33:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Cybenko:1979:REP,
author = "G. Cybenko",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP '79}",
title = "Round-off error propagation in {Durbin}'s,
{Levinson}'s, and {Trench}'s algorithms",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "498--501",
year = "1979",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The subject matter of this paper concerns the
round-off error propagation in order $n^2$ algorithms
for solving problems involving Toeplitz matrices. Since
linear predictive techniques owe much of their appeal
to the computational efficiency \ldots{}",
}
@Article{Diaconis:1979:RP,
author = "Persi Diaconis and David Freedman",
title = "On Rounding Percentages",
journal = j-J-AM-STAT-ASSOC,
volume = "74",
number = "366",
pages = "359--364",
month = jun,
year = "1979",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Nov 23 11:24:59 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
note = "The authors extend prior work on correctness of sums
of rounded percentages \cite{Mosteller:1967:DSR}, and
criticize biased rounding practices in
\cite{Benford:1938:LAN}.",
URL = "http://www.jstor.org/stable/2284288",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
keywords = "Benford's Law; correct rounding; floating-point
arithmetic",
remark = "When percentage-column entries are rounded, their sum
may differ from 100\%. The authors use a prior proof
\cite{Mosteller:1967:DSR} that for $ n \gg 2 $ rounded
values, the probability of a correct sum is $ \sqrt {6
/ (\pi n)} \approx 1.382 / \sqrt {n} $. They show that
rounding may produce large changes in computed
chi-squared values, and they conclude their article
with this recommendation: ``it is important to
calculate with many-digit accuracy when computing $
\chi^2 $ for large sample sizes.''",
}
@Article{Edgar:1979:FMN,
author = "Albert D. Edgar and Samuel C. Lee",
title = "{FOCUS} Microcomputer Number System",
journal = j-CACM,
volume = "22",
number = "3",
pages = "166--177",
month = mar,
year = "1979",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:37:26 MST 2001",
bibsource = "Compendex database;
http://dblp.uni-trier.de/db/journals/cacm/cacm22.html#EdgarL79;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "FOCUS is a number system and supporting computational
algorithms especially useful for microcomputer control
and other signal processing applications. FOCUS has the
wide-ranging character of floating-point numbers with a
uniformity of state distributions that give FOCUS
better than a twofold accuracy advantage over an equal
word length floating-point system. FOCUS computations
are typically five times faster than single precision
fixed-point or integer arithmetic for a mixture of
operations, comparable in speed with hardware
arithmetic for many applications. Algorithms for 8-bit
and 16-bit implementations of FOCUS are included.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods); C5250
(Microcomputer techniques)",
classification = "723",
corpsource = "University of Oklahoma, Norman, OK, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "algorithms; arithmetic; computational; computers,
microprocessor; digital arithmetic; floating point
numbers; FOCUS; microcomputer; microcomputer control;
microcomputers; number system; signal processing",
oldlabel = "EdgarL79",
treatment = "P Practical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/EdgarL79",
}
@InProceedings{Eggers:1979:HFP,
author = "Thomas W. Eggers and Judson S. Leonard and Mary H.
Payne",
title = "Handling of floating point exceptions",
crossref = "ACM:1979:PSC",
pages = "100--108",
year = "1979",
bibdate = "Fri Nov 28 17:31:00 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Feldman:1979:IPS,
author = "Stuart I. Feldman",
title = "The Impact of the Proposed Standard for Floating Point
Arithmetic on Languages and Systems",
journal = j-SIGNUM,
volume = "14",
number = "3S (Special issue)",
pages = "31--32",
month = oct,
year = "1979",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:07 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods); C6140D (High level
languages)",
corpsource = "Bell Labs., Murray Hill, NJ, USA",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "arithmetic; digital arithmetic; floating point;
languages; programming languages; proposed; standard;
standards; systems",
xxnumber = "si-2",
}
@MastersThesis{Fogler:1979:BFP,
author = "Robert Joseph Fogler",
title = "On a block floating point implementation of an
intrusion-detection algorithm",
type = "Thesis ({M.S.})",
school = "Kansas State University",
address = "Manhattan, KS, USA",
pages = "71",
year = "1979",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic alarm systems.; Signal processing.",
}
@Article{Fox:1979:RFP,
author = "Phyllis Fox",
title = "Remark on ``{Algorithm} 528: Framework for a Portable
Library [{Z}]''",
journal = j-TOMS,
volume = "5",
number = "4",
pages = "524--524",
month = dec,
year = "1979",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355853.355871",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Aug 30 00:28:06 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Fox:1978:AFP}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Fraley:1979:PED,
author = "Bob Fraley and Steve Walther",
title = "Proposal to Eliminate Denormalized Numbers",
journal = j-SIGNUM,
volume = "14",
number = "3S (Special issue)",
pages = "22--23",
month = oct,
year = "1979",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:07 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Hewlett--Packard Labs., Palo Alto, CA, USA",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "denormalized numbers; digital arithmetic; expense;
floating point",
treatment = "P Practical",
xxnumber = "si-2",
}
@Article{Gargantini:1979:NSS,
author = "Irene Gargantini",
title = "The Numerical Stability of Simultaneous Iterations Via
Square-Rooting",
journal = j-COMPUT-MATH-APPL,
volume = "5",
number = "1",
pages = "25--31",
month = "????",
year = "1979",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(81)90136-X",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 18:51:16 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/089812218190136X",
acknowledgement = ack-jr # " and " # ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@TechReport{Ginsberg:1979:MFE,
author = "Myron Ginsberg",
title = "Monitoring floating-point error propagation in
scientific computation",
type = "Technical report",
number = "CSE 7910",
institution = "Department of Computer Science and Engineering,
Southern Methodist University",
address = "Dallas, TX, USA",
pages = "32",
year = "1979",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.",
}
@Article{Gregory:1979:EFC,
author = "Robert Todd Gregory",
title = "Error-free computation with finite number systems",
journal = j-SIGNUM,
volume = "14",
number = "3",
pages = "9--16",
month = sep,
year = "1979",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:07 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "University of Tennessee, Knoxville, TN, USA",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "automatic digital computer; computer-representable
numbers; error free computation; finite; finite number
systems; floating point numbers; machine; numerical
methods; real numbers",
treatment = "T Theoretical or Mathematical",
}
@PhdThesis{Gruener:1979:ARD,
author = "K. Gr{\"u}ner",
title = "{Allgemeine Rechnerarithmetik und deren
Implementierung mit optimaler Genauigkeit} \toenglish
{General Computer Arithmetic and its Implementation
with Optimal Accuracy} \endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "??",
year = "1979",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Book{Hardy:1979:ITN,
author = "G. H. (Godfrey Harold) Hardy and E. M. (Edward
Maitland) Wright",
title = "An Introduction to the Theory of Numbers",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
edition = "Fifth",
pages = "xvi + 426",
year = "1979",
ISBN = "0-19-853170-2, 0-19-853171-0 (paperback)",
ISBN-13 = "978-0-19-853170-8, 978-0-19-853171-5 (paperback)",
LCCN = "A241 .H28 1979",
bibdate = "Fri Nov 30 06:49:15 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Reprinted in 1988 and 1998 with corrections.",
}
@InProceedings{Hastings:1979:SMM,
author = "C. Hastings",
title = "Shift Matrices: The Missing Teeth in the Number
Cruncher",
crossref = "Anonymous:1979:WCR",
pages = "??--??",
year = "1979",
bibdate = "Fri Nov 09 18:59:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Paper number 18/3.",
acknowledgement = ack-nhfb,
}
@Article{Heath:1979:RDF,
author = "J. Heath and H. {Nagle, Jr.} and S. Shiva",
title = "Realization of digital filters using input-scaled
floating-point arithmetic",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "27",
number = "5",
pages = "469--477",
month = oct,
year = "1979",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See note \cite{Heath:1986:NRD}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "Fixed-point and floating-point realizations of digital
filters are abundant in the literature of digital
signal processing. A block-floating-point realization
which has some advantages of both fixed-point and
floating-point has been reported and \ldots{}",
}
@Article{Hehner:1979:NRR,
author = "E. C. R. Hehner and R. N. S. Horspool",
title = "A new representation of the rational numbers for fast
easy arithmetic",
journal = j-SIAM-J-COMPUT,
volume = "8",
number = "2",
pages = "124--134",
month = "????",
year = "1979",
CODEN = "SMJCAT",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
MRclass = "68C05 (10A30 68A05)",
MRnumber = "80h:68027",
MRreviewer = "P. J. Weinberger",
bibdate = "Mon Nov 29 10:59:01 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/8/2;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See corrigendum \cite{Hehner:1980:CNR}.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
}
@InProceedings{Hull:1979:DFP,
author = "T. E. Hull",
title = "Desirable floating-point arithmetic and elementary
functions for numerical computation",
crossref = "ACM:1979:PSC",
pages = "96--99",
year = "1979",
bibdate = "Mon Jan 08 11:06:31 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The purpose of this talk is to summarize proposed
specifications for floating-polar arithmetic and
elementary functions. The topics considered are: the
base of the number system, precision control, number
representation, arithmetic operations, ocher basic
operations, elementary functions, and exception
handling. The possibility of doing without fixed-point
arithmetic is also mentioned. The specifications are
intended to be entirely at the level of a programming
language such as Fortran. The emphasis is on
convenience and simplicity from the user's point of
view. Conforming to such specifications would have
obvious beneficial implications for the portability of
numerical software, and for proving programs correct,
as well as attempting to provide facilities which are
most suitable for the user. The specifications are not
complete in every detail, but it is intended that they
be complete ``in spirit'' --- some further details,
especially syntactic details, would have to be
provided, but the proposals are otherwise relatively
complete.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Book{Hwang:1979:CAP,
author = "Kai Hwang",
title = "Computer Arithmetic: Principles, Architecture, and
Design",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xiii + 423",
year = "1979",
ISBN = "0-471-03496-7",
ISBN-13 = "978-0-471-03496-4",
LCCN = "TK7888.3 .H9",
bibdate = "Sat May 18 14:15:19 2002",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Hwang:1979:GMT,
author = "Kai Hwang",
title = "Global and Modular Two's Complement Cellular Array
Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-28",
number = "4",
pages = "300--306",
month = apr,
year = "1979",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1979.1675350",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 06:49:37 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675350",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{IEEE:1979:PIF,
author = "Anonymous",
title = "The Proposed {IEEE} floating-point standard",
journal = j-SIGNUM,
pages = "32",
month = oct,
year = "1979",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "Floating-point arithmetic --- Standards.",
}
@Manual{IntelCorporation:1979:FAL,
author = "Intel Corporation",
title = "8080\slash 8085 floating-point arithmetic library
user's manual",
organization = "The Corporation",
address = "Santa Clara, CA, USA",
pages = "v + 20",
year = "1979",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Assembly language (Computer program language).; Intel
8080 (Microprocessor) --- Programming.; INTEL 8085
(Computer) --- Programming.; PL/M-80 (Computer program
language).",
remark = "``Manual Order Number: 9800452-03''.",
}
@Article{Jenkins:1979:RAR,
author = "W. Jenkins",
title = "Recent advances in residue number techniques for
recursive digital filtering",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "27",
number = "1",
pages = "19--30",
month = feb,
year = "1979",
CODEN = "IETABA",
DOI = "https://doi.org/10.1049/el:19780088",
ISSN = "0096-3518",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26137",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
keywords = "residue arithmetic; residue number system",
summary = "A new algorithm for scaling in residue number systems
(RNS's) is presented for applying residue number theory
to recursive digital filtering. The algorithm provides
an efficient method for scaling the output of each
recursive filter section for use \ldots{}",
}
@Article{Johnson:1979:RAF,
author = "Donald B. Johnson and Webb Miller and Brian Minnihan
and Celia Wrathall",
title = "Reducibility Among Floating-Point Graphs",
journal = j-J-ACM,
volume = "26",
number = "4",
pages = "739--760",
month = oct,
year = "1979",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "65G05",
MRnumber = "80i:65045",
bibdate = "Fri Dec 08 11:55:10 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The graph-theoretic models of this paper can be used
to compare the rounding-error behavior of numerical
programs. The models follow the approach, popularized
by Wilkinson, of assuming independent rounding errors
in each arithmetic operation. Models constructed on
this assumption are more tractable than would be the
case under more realistic assumptions. There are
identified two easily tested conditions on programs
which guarantee that error analyses are relatively
insensitive to the particular graph model employed. The
development has the additional benefit of sometimes
providing an elementary proof that one program is
comparable in stability to another. Examples of such
results are given.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Kahan:1979:PCK,
author = "William M. Kahan",
title = "Personal Calculator Has Key to Solve Any Equation $
f(x) = 0 $",
journal = j-HEWLETT-PACKARD-J,
volume = "30",
number = "12",
pages = "20--26",
month = dec,
year = "1979",
CODEN = "HPJOAX",
ISSN = "0018-1153",
MRclass = "65-01 (65G05 65H05)",
MRnumber = "MR574853 (81k:65002)",
MRreviewer = "R. P. Brent",
bibdate = "Tue Mar 25 14:12:15 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/hpj.bib",
note = "Lecture notes for Math 128.",
URL = "http://www.cs.berkeley.edu/~wkahan/Math128/SOLVEkey.pdf",
acknowledgement = ack-nhfb,
classcodes = "C5420 (Mainframes and minicomputers); C7310
(Mathematics computing)",
corpsource = "Univ. of California, Berkeley, CA, USA",
fjournal = "Hewlett--Packard Journal",
keywords = "electronic calculators; equation solving; finding;
handheld calculator; HP 34C; linear algebra; personal
calculator; root; SOLVE",
reviewer = "R. P. Brent",
treatment = "P Practical",
}
@Article{Kahan:1979:PFP,
author = "W. Kahan and J. Palmer",
title = "On a Proposed Floating-Point Standard",
journal = j-SIGNUM,
volume = "14",
number = "3S (Special issue)",
pages = "13--21",
month = oct,
year = "1979",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/1057520.1057522",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Wed Mar 19 23:00:11 MST 1997",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/signum.bib",
abstract = "A standard for binary floating-point arithmetic is
being proposed and there is a very real possibility
that it will be adopted by many manufacturers and
implemented on a wide range of computers. This
development matters to all of us concerned with
numerical software. One of the principal motivations
for the standard is to distribute more evenly the
burden of portability between hardware and software. At
present, any program intended to be portable must be
designed for a mythical computer that enjoys no
capability not supported by every computer on which the
program will be run. That mythical computer is so much
grubbier than almost any real computer that a portable
program will frequently be denigrated as ``suboptimal''
and then supplanted by another program supposedly
``optimal'' for the real computer in question but often
inferior in critical respects like reliability. A
standard --- almost any reasonable standard --- will
surely improve the situation. A standard environment
for numerical programs will promote fair comparisons
and sharing of numerical codes, thereby lowering costs
and prices. Furthermore, we have chosen repeatedly to
enrich that environment in order that applications
programs be simpler and more reliable. Thus will the
onus of portability be shared among hardware
manufacturers and software producers.",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "University of California, Berkeley, CA, USA",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "arithmetic; digital arithmetic; floating point;
proposal; standard; standards",
treatment = "P Practical",
xxnumber = "si-2",
}
@PhdThesis{Kent:1979:TPS,
author = "Jan Kent",
title = "The theoretical and practical study of floating point
instructions: Consisting of Theoretical definition,
analysis and comparison of floating point instruction,
and procedures for the description and simulation of
floating point instructions",
type = "{Dr. Avhandling}",
school = "Universitetet i Oslo",
address = "Oslo, Norway",
year = "1979",
bibdate = "Thu May 09 08:05:31 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
xxnote = "Bibsys library catalog gave both 1977 and 1979 as
year??",
}
@TechReport{Kolze:1979:BFP,
author = "Thomas Joseph Kolze",
title = "Block floating point {FFT} statistical noise analysis
program",
type = "Technical report",
number = "CSR-79-2",
institution = "Department of Electrical Engineering, University of
Missouri--Rolla",
address = "Rolla, MO, USA",
pages = "vii + 180",
year = "1979",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Communications and signal processing research.",
acknowledgement = ack-nhfb,
keywords = "Radio noise --- Computer programs.; Signals and
signaling --- Computer programs.",
}
@MastersThesis{Kolze:1979:SNA,
author = "Thomas Joseph Kolze",
title = "Statistical noise analysis of a block floating point
{FFT} and an example application",
type = "Electrical Engineering Thesis ({M.S.})",
school = "University of Missouri--Rolla",
address = "Rolla, MO, USA",
pages = "viii + 88",
year = "1979",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Kornerup:1979:NRA,
author = "Peter Kornerup",
title = "A note on rational arithmetic",
journal = j-SIGMICRO,
volume = "10",
number = "2",
pages = "28--28",
month = jun,
year = "1979",
CODEN = "SIGMDJ",
DOI = "https://doi.org/10.1145/1218003.1218004",
ISSN = "0163-5751, 1050-916X",
ISSN-L = "0163-5751",
bibdate = "Fri Apr 16 10:27:24 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
note = "See \cite{Thacker:1979:MPR,Thacker:1979:R}.",
URL = "https://dl.acm.org/doi/10.1145/1218003.1218004",
abstract = "A recent paper in SIGMICRO [1] contained a comparison
of the accuracy of floating point vs. rational
representations, which is very unfair to the latter.
The format chosen for rational numbers utilizes 16 bits
for numerators and 16 bits for denominators. This
implies that the spacing between consecutive numbers in
the system is in most cases of the order $ 2 {-32} $.
Only around simple rational numbers (e.g. 1/1, 2/3) is
the spacing of the order $ 2 {-16}. $ However the
rounding algorithm presented in [1] will almost
certainly introduce a rounding error of the order $ 2
{-16} $, i.e. introduce an error which in most cases is
of the order $ 2^{16} $ larger than necessary.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMICRO Newsletter",
journal-URL = "https://dl.acm.org/loi/sigmicro",
}
@Article{Kusterer:1979:SEP,
author = "Roland Kusterer and Manfred Reimer",
title = "Stable Evaluation of Polynomials in Time $ \log n $",
journal = j-MATH-COMPUT,
volume = "33",
number = "147",
pages = "1019--1031",
month = jul,
year = "1979",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1979-0528054-X;
https://doi.org/10.2307/2006075",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65G05 (68C25)",
MRnumber = "80d:65050 (528054)",
MRreviewer = "C. W. Clenshaw",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Math. Inst., University of Dortmund, Dortmund, West
Germany",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "algorithm; approximation theory; number of
multiplications to evaluate a polynomial; polynomials",
reviewer-dates = "Charles William Clenshaw (15 March 1926--23
September 2004)",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Lautz:1979:JLD,
author = "G{\"u}nter Lautz",
title = "{300 Jahre leibnizsches dualzahlensystem}. ({German})
[300 years of the {Leibniz} binary number system]",
journal = j-BIOL-CYBERN,
volume = "35",
number = "3",
pages = "175--181",
month = dec,
year = "1979",
CODEN = "BICYAF",
DOI = "https://doi.org/10.1007/bf00337062",
ISSN = "0340-1200 (print), 1432-0770 (electronic)",
ISSN-L = "0340-1200",
bibdate = "Fri Mar 17 08:46:29 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "300 years ago G. W. Leibniz has invented his binary
number system, now widely used in computer sciences.
The paper recapitulates some informations about the
contents of the first private notes from 1679, partly
reproduced in facsimiles, and the scientific background
of that time. The circumstances and the genesis of the
first treatise on this matter, published in 1703/5 by
Leibniz at the Academy of Sciences, Paris, are
discussed in detail.",
acknowledgement = ack-nhfb,
fjournal = "Biological cybernetics",
journal-URL = "http://link.springer.com/journal/422",
language = "German",
}
@Article{Lee:1979:AFN,
author = "S. C. Lee and A. D. Edgar",
title = "Addendum to {``The Focus Number System''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-28",
number = "9",
pages = "693--693",
month = sep,
year = "1979",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1979.1675442",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 06:49:40 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Lee:1977:FNS,Swartzlander:1979:CFN}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675442",
abstract = "In 1971 Kingsbury and Rayner, publishing under the
title ``Digital Filtering Using Logarithmic
Arithmetic'' disclosed a sign-plus-logarithm number
system, and a means of performing addition through
single dimensional lookup using the formula $ c = b +
F(a b) $. The system was demonstrated on a computer. In
1975 Swartzlander and Alexopoulos disclosed Kingsbury's
logarithmic arithmetic as ``The Sign\slash Logarithm
Number System''. In 1977, without knowledge of prior
art, we reinvented the wheel a third time, dubbing it
``Focus,'' after the focus of resolution around the
zero origin [3]. We wish now to acknowledge Kingsbury
and Rayner as the pioneer authors, and also
Swartzlander and Alexopoulos as prior to our
publication.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{McDonnell:1979:FR,
author = "Eugene McDonnell",
title = "Fuzzy residue",
journal = j-APL-QUOTE-QUAD,
volume = "9",
number = "4",
pages = "42--46",
year = "1979",
CODEN = "APLQD9",
DOI = "https://doi.org/10.1145/390009.804437",
ISSN = "0163-6006 (print), 1558-3392 (electronic)",
ISSN-L = "0163-6006",
bibdate = "Thu Aug 07 19:13:11 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Certain pairs of arguments to the residue function, as
implemented on many APL systems, give results which
make it seem as if the ordinary decimal relationships
we remember from grade school no longer hold. As far as
we can tell, it looks as if a given modulus should
divide the right argument, but the implementation tells
us it doesn't. A definition for a fuzzed residue
function is proposed which resolves the difficulties
users have complained of. However, certain points of
continuing difficulty remain, where the limitations of
machine arithmetic continue to defeat the attempt to
model the real number system. The representation
function is defined in terms of the residue function,
and so is affected by the change in residue. The nature
of this effect is also discussed in this paper.",
acknowledgement = ack-nhfb,
fjournal = "APL Quote Quad",
}
@Book{Oberman:1979:DCB,
author = "R. M. M. (Roelof Maarten Marie) Oberman",
title = "Digital circuits for binary arithmetic",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xii + 340",
year = "1979",
ISBN = "0-470-26373-3",
ISBN-13 = "978-0-470-26373-0",
LCCN = "TK7868.L6 O23 1979",
bibdate = "Wed Nov 14 17:33:15 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "A Halsted Press book.",
subject = "logic circuits; digital integrated circuits; switching
theory",
}
@Article{Oliver:1979:REP,
author = "J. Oliver",
title = "Rounding error propagation in polynomial evaluation
schemes",
journal = j-J-COMPUT-APPL-MATH,
volume = "5",
number = "2",
pages = "85--97",
month = jun,
year = "1979",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 11:59:18 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0771050X79900020",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Payne:1979:DPB,
author = "Mary Payne and William Strecker",
title = "Draft Proposal for a Binary Normalized Floating Point
Standard",
journal = j-SIGNUM,
volume = "14",
number = "3S (Special issue)",
pages = "24--28",
month = oct,
year = "1979",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:07 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Digital Equipment Corp., Maynard, MA, USA",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "binary; digital arithmetic; floating point;
normalized; proposal; standard; standards",
treatment = "P Practical",
xxnumber = "si-2",
}
@TechReport{Randell:1979:ABO,
author = "Brian Randell",
title = "An annotated bibliography on the origins of digital
computers",
type = "Technical report",
number = "140",
institution = "Computing Laboratory, University of Newcastle upon
Tyne",
address = "Newcastle upon Tyne, UK",
pages = "146",
year = "1979",
LCCN = "Z5642.2 .R36 1979",
bibdate = "Wed Oct 13 09:24:25 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
subject = "Electronic digital computers; History; Bibliography;
Calculators",
}
@InCollection{Rauch:1979:EAA,
author = "E. Rauch",
title = "{Einige Aspekte der Auswahl und Realisierung
numerischer Verfahren in anwendungsorientierten
Systemen} \toenglish {Several Aspects of the Choice and
Realisation of Numerical Procedures in
Application-Oriented Systems} \endtoenglish",
crossref = "Meinardus:1979:ATP",
pages = "??--??",
year = "1979",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Redinbo:1979:FFA,
author = "G. R. Redinbo",
title = "Finite Field Arithmetic on an Array Processor",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-28",
number = "7",
pages = "461--471",
month = jul,
year = "1979",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1979.1675390",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 06:49:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675390",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Reid:1979:FMF,
author = "John Reid",
title = "Functions for Manipulating Floating-Point Numbers",
journal = j-SIGNUM,
volume = "14",
number = "4",
pages = "11--13",
month = dec,
year = "1979",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:08 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Computer Sci. and Systems Div., AERE, Harwell, UK",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "complex numbers; digital arithmetic; floating;
FORTRAN; point arithmetic; portability; precision",
treatment = "P Practical",
}
@Article{Reinsch:1979:PPC,
author = "Christian H. Reinsch",
title = "Principles and Preferences for Computer Arithmetic",
journal = j-SIGNUM,
volume = "14",
number = "1",
pages = "12--27",
month = mar,
year = "1979",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:06 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022)",
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Leibniz-Rechenzentrum, Munich, West Germany",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "computer arithmetic; digital arithmetic",
treatment = "T Theoretical or Mathematical",
}
@Article{Rink:1979:CEF,
author = "R. Rink and H. Chong",
title = "Covariance equation for a floating-point regulator
system",
journal = j-IEEE-TRANS-AUTOMAT-CONTR,
volume = "24",
number = "6",
pages = "980--982",
month = dec,
year = "1979",
CODEN = "IETAA9",
ISSN = "0018-9286 (print), 1558-2523 (electronic)",
ISSN-L = "0018-9286",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Automatic Control",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
summary = "Derived are linear equations that can be solved for
the steady-state covariance matrix of the plant and
observer states of a closed-loop regulator system which
employs finite wordlength A/D conversion and
floating-point computation in the observer/ \ldots{}",
}
@Article{Rink:1979:PSR,
author = "R. Rink and Hoi Chong",
title = "Performance of state regulator systems with
floating-point computation",
journal = j-IEEE-TRANS-AUTOMAT-CONTR,
volume = "24",
number = "3",
pages = "411--421",
month = jun,
year = "1979",
CODEN = "IETAA9",
ISSN = "0018-9286 (print), 1558-2523 (electronic)",
ISSN-L = "0018-9286",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See correction \cite{Rink:1980:CPS}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Automatic Control",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
summary = "The performance of a digital state regulator system
having an A/D converter of finite wordlength and a
floating-point estimator/ controller computer of finite
mantissa-length is analyzed. An upper bound on the
mean-square state error, as a function \ldots{}",
}
@Article{Robertson:1979:VPA,
author = "D. A. Robertson",
title = "Variable precision arithmetic on {CDC 6000\slash 7000}
machines",
journal = j-SPE,
volume = "9",
number = "3",
pages = "247--248",
month = mar,
year = "1979",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.4380090310",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Wed Sep 10 12:36:39 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/spe.bib",
acknowledgement = ack-nhfb,
fjournal = "Software --- Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
onlinedate = "27 Oct 2006",
}
@MastersThesis{Scharf:1979:HRW,
author = "Stuart Lee Scharf",
title = "A hardware realization of the {Winograd Fourier}
Transform Algorithm",
type = "Thesis ({M.S.})",
school = "Massachusetts Institute of Technology. Dept. of
Electrical and Engineering and Computer Science",
address = "Cambridge, MA, USA",
pages = "109",
year = "1979",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supervised by James H. McClellan.",
acknowledgement = ack-nhfb,
keywords = "Algorithms.; Computer engineering.; Floating-point
arithmetic.; Fourier transformations --- Computer
programs.",
}
@InProceedings{Shapiro:1979:ELM,
author = "G. Shapiro",
title = "Exploit {LSI} Memory Components Today, Instead of
Waiting for Arithmetic Devices",
crossref = "Anonymous:1979:WCR",
pages = "??--??",
year = "1979",
bibdate = "Fri Nov 09 19:15:35 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Paper 18/5.",
acknowledgement = ack-nhfb,
}
@Book{Shauman:1979:OMA,
author = "Aleksandr Mikhailovich Shauman",
title = "Osnovy mashinnoi arifmetiki \toenglish {Principles of
Machine Arithmetic} \endtoenglish",
publisher = "Izd-vo LGU (Leningrad State University Publishers)",
address = "Leningrad, USSR",
pages = "311",
year = "1979",
LCCN = "QA76.6 .S516",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units.; Electronic
digital computers --- Programming.; Floating-point
arithmetic.",
remark = "At head of title: Leningradskii Gosudarstvennyi
universitet imeni A. A. Zhdanova. Bibliography: p.
306-[309]",
}
@Article{Sheue:1979:TCM,
author = "A. E. Sheue",
title = "Two's-Complement Multiplication",
journal = j-SIGMICRO,
volume = "10",
number = "1",
pages = "21--23",
month = mar,
year = "1979",
CODEN = "SIGMDJ",
ISSN = "0163-5751, 1050-916X",
ISSN-L = "0163-5751",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIG Micro Newsletter",
}
@Article{Swartzlander:1979:CFN,
author = "E. E. {Swartzlander, Jr.}",
title = "Comment on {``The Focus Number System''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-28",
number = "9",
pages = "693--693",
month = sep,
year = "1979",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1979.1675441",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 06:49:40 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Lee:1977:FNS,Lee:1979:AFN}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675441",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Thacker:1979:MPR,
author = "William I. Thacker and G. W. Gorsline",
title = "Micro programming rational arithmetic operations",
journal = j-SIGMICRO,
volume = "10",
number = "1",
pages = "10--13",
month = mar,
year = "1979",
CODEN = "SIGMDJ",
DOI = "https://doi.org/10.1145/1217236.1217238",
ISSN = "0163-5751, 1050-916X",
ISSN-L = "0163-5751",
bibdate = "Fri Apr 16 10:27:24 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
note = "See critical comments \cite{Kornerup:1979:NRA} and
response \cite{Thacker:1979:R}.",
URL = "https://dl.acm.org/doi/10.1145/1217236.1217238",
abstract = "For many years, real number arithmetic, whether
accomplished in hardware, software, or firmware, has
utilized a floating point scheme. This paper summarizes
the results of a study assessing rational
representation as a possible replacement for floating
point representation. The Hewlett-Packard 2100A
microprogrammable computer was used as the test
vehicle. Both accuracy and speed comparisons were used
to judge the usefulness of the substitution.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMICRO Newsletter",
journal-URL = "https://dl.acm.org/loi/sigmicro",
}
@Article{Thacker:1979:R,
author = "W. I. Thacker and G. W. Gorsline",
title = "Response",
journal = j-SIGMICRO,
volume = "10",
number = "2",
pages = "29--29",
month = jun,
year = "1979",
CODEN = "SIGMDJ",
DOI = "https://doi.org/10.1145/1218003.1218005",
ISSN = "0163-5751, 1050-916X",
ISSN-L = "0163-5751",
bibdate = "Fri Apr 16 10:27:24 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
note = "See \cite{Thacker:1979:MPR,Kornerup:1979:NRA}.",
URL = "https://dl.acm.org/doi/10.1145/1218003.1218005",
abstract = "Within the context of our study; that is, the direct
substitution of a pure rational scheme for a floating
point scheme of arithmetic and storage within an extant
FORTRAN system with no changes to the compiler (and
thus to the storage space available for a single
numerical quantity), we continue to claim that our
results are valid. We again wish to note that our
investigation was limited to the pure rational scheme
using the same storage space available to a floating
point scheme.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMICRO Newsletter",
journal-URL = "https://dl.acm.org/loi/sigmicro",
}
@Article{Tseng:1979:IFS,
author = "Ben-Dau Tseng and G. A. Jullien and W. C. Miller",
title = "Implementation of {FFT} Structures Using the Residue
Number System",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-28",
number = "11",
pages = "831--845",
month = nov,
year = "1979",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1979.1675263",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 06:49:41 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675263;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35176",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "This paper considers the implementation of a fast
Fourier transform (FFT) structure using arrays of
read-only memories. The arithmetic operations are based
entirely on the residue number system. The most
important aspect of the structure relates to \ldots{}",
}
@Article{Ukkonen:1979:AER,
author = "Esko Ukkonen",
title = "An analysis of the effect of rounding errors on the
flow of control in numerical processes",
journal = j-BIT,
volume = "19",
number = "1",
pages = "116--133",
month = mar,
year = "1979",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01931229",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65G05",
MRnumber = "81a:65048",
bibdate = "Wed Jan 4 18:52:16 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=19&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=19&issue=1&spage=116",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@InProceedings{vanHulzen:1979:NMS,
author = "J. A. {van Hulzen}",
title = "A note on methods for solving systems of polynomial
equations with floating point coefficients",
crossref = "Ng:1979:SAC",
pages = "346--357",
year = "1979",
MRclass = "65H10",
MRnumber = "81h:65049",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "Frederick N. Fritsch",
}
@Article{Wichmann:1979:ID,
author = "B. A. Wichmann",
title = "Integer division",
journal = j-SPE,
volume = "9",
number = "6",
pages = "507--508",
month = jun,
year = "1979",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.4380090610",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Wed Sep 10 12:36:39 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/spe.bib",
acknowledgement = ack-nhfb,
fjournal = "Software --- Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
onlinedate = "27 Oct 2006",
}
@Article{Wichmann:1979:PCG,
author = "B. A. Wichmann and J. {Du Croz}",
title = "A program to calculate the {GAMM} measure",
journal = j-COMP-J,
volume = "22",
number = "4",
pages = "317--322",
month = nov,
year = "1979",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C4240 (Programming and algorithm theory); C7430
(Computer engineering)",
classification = "723",
corpsource = "Computing Services Unit, Nat. Phys. Lab., Teddington,
UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "analysis; complete computer programs; computer
performance; computer programs; computer selection and;
confidence check; error; evaluation; floating point
calculation; FORTRAN program; GAMM measure; performance
evaluation",
treatment = "P Practical",
}
@MastersThesis{Wilbanks:1979:MFI,
author = "Thomas D. Wilbanks",
title = "Microcoding floating-point instructions for a
bit-slice processor",
type = "Thesis ({M.S.})",
school = "University of South Carolina",
address = "Columbia, SC, USA",
pages = "vi + 131",
year = "1979",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Bit slice microprocessors.; Microprocessors ---
Programming.",
}
@InProceedings{Winnigstad:1979:ULC,
author = "C. N. Winnigstad",
title = "Using {LSI} to Crunch Numbers at High Speed: An
Overview",
crossref = "Anonymous:1979:WCR",
pages = "??--??",
year = "1979",
bibdate = "Fri Nov 09 19:43:13 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Yohe:1979:INA,
author = "J. M. Yohe",
title = "Implementing Nonstandard Arithmetics",
journal = j-SIAM-REVIEW,
volume = "21",
number = "1",
pages = "34--56",
month = "????",
year = "1979",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1021003",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb # " and " # ack-jr,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Agrawal:1980:NBA,
author = "D. P. Agrawal",
title = "On Negabinary-Binary Arithmetic Relationships and
Their Hardware Reciprocity",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-29",
number = "11",
pages = "1032--1035",
month = nov,
year = "1980",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1980.1675502",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 19:15:30 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675502",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Albrecht:1980:RAO,
author = "R. Albrecht",
title = "Roundings and Approximations in Ordered Sets",
crossref = "Alefeld:1980:FNC",
pages = "17--31",
year = "1980",
bibdate = "Tue Oct 23 08:17:48 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "interval arithmetic; rounding error",
}
@Article{Ambikairajah:1980:TPM,
author = "E. Ambikairajah and M. J. Carey",
title = "Technique for Performing Multiplication on a 16-bit
Microprocessor Using an Extension of {Booth}'s
Algorithm",
journal = j-ELECT-LETTERS,
volume = "16",
number = "2",
pages = "53--54",
month = jan,
year = "1980",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}
@Article{Baraniecka:1980:RNS,
author = "A. Baraniecka and G. Jullien",
title = "Residue number system implementations of number
theoretic transforms in complex residue rings",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "28",
number = "3",
pages = "285--291",
month = jun,
year = "1980",
CODEN = "IETABA",
DOI = "https://doi.org/10.1109/TC.1979.1675263",
ISSN = "0096-3518",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26146",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
keywords = "residue arithmetic; residue number system",
summary = "This paper discusses the implementation of number
theoretic transforms defined in complex residue rings.
A selection of transform parameters for lookup table
and microprocessor realizations are discussed. When the
length of the convolution is \ldots{}",
}
@Article{Bareiss:1980:RED,
author = "E. H. Bareiss and J. L. Barlow",
title = "Roundoff error distribution in fixed point
multiplication",
journal = j-BIT,
volume = "20",
number = "2",
pages = "247--250",
month = jun,
year = "1980",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01933198",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65G05",
MRnumber = "81j:65066",
MRreviewer = "Seppo Linnainmaa",
bibdate = "Wed Jan 4 18:52:16 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=20&issue=2;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=20&issue=2&spage=247",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Barsi:1980:ECC,
author = "Ferruccio Barsi and Piero Maestrini",
title = "Error codes constructed in residue number systems with
non-pairwise-prime moduli",
journal = j-INF-CONTROL,
volume = "46",
number = "1",
pages = "16--25",
month = jul,
year = "1980",
CODEN = "IFCNA4",
DOI = "https://doi.org/10.1016/S0019-9958(80)90471-4",
ISSN = "0019-9958 (print), 1878-2981 (electronic)",
ISSN-L = "0019-9958",
bibdate = "Thu Nov 18 09:54:38 2010",
bibsource = "http://www.sciencedirect.com/science/journal/00199958;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Codes constructed in a Residue Number System (RNS) of
moduli $ m_1, m_2, \ldots {}, m_n $ are non-binary,
arithmetic codes whose codewords are vectors where the
$i$ th component is $ m_i $-valued $ (1 \leq i \leq n)
$. A new class of codes in RNS is described, where
redundancy is introduced by removing the constraint
that the moduli of the RNS be pairwise prime. The
error-detecting and correcting capabilities of such
codes are discussed and a simple approach to error
detection, localization and correction is presented.
Although the codes under consideration are quite
inefficient in some respects, it is shown that codes is
examined in more detail. Codes in this subclass,
besides correcting all single errors, also correct
almost all of double errors and localize some errors of
higher multiplicity, with less redundancy than required
to construct optimal 2-correcting codes in RNS.",
acknowledgement = ack-nhfb,
fjournal = "Information and Control",
journal-URL = "http://www.sciencedirect.com/science/journal/00199958",
}
@Article{Brent:1980:AIB,
author = "Richard P. Brent and Judith A. Hooper and J. Michael
Yohe",
title = "An {AUGMENT} Interface for {Brent}'s Multiple
Precision Arithmetic Package",
journal = j-TOMS,
volume = "6",
number = "2",
pages = "146--149",
month = jun,
year = "1980",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355887.355889",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Sep 05 22:49:19 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Brent:1978:AMF,Brent:1979:RMF}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "arithmetic, multiple precision, extended precision,
floating point, portable software, software package,
precompiler interface, AUGMENT interface",
}
@InProceedings{Brent:1980:UAE,
author = "R. P. Brent",
title = "Unrestricted Algorithms for Elementary and Special
Functions",
crossref = "Lavington:1980:IPP",
pages = "613--619",
year = "1980",
bibdate = "Thu Sep 01 11:55:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Brown:1980:EPB,
author = "W. S. Brown and S. I. Feldman",
title = "Environment Parameters and Basic Functions for
Floating-Point Computation",
journal = j-TOMS,
volume = "6",
number = "4",
pages = "510--523",
month = dec,
year = "1980",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355921.355924",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Sep 1 10:15:05 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "environment parameters, floating-point arithmetic,
software portability",
}
@TechReport{Brown:1980:SRM,
author = "W. S. Brown",
title = "A Simple But Realistic Model of Floating-Point
Computation",
type = "Computer Science Technical Report",
number = "83",
institution = "Bell Laboratories",
address = "Murray Hill, NJ, 07974, USA",
month = may,
year = "1980",
bibdate = "Wed Oct 13 06:30:12 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Revised November 1980.",
acknowledgement = ack-nhfb,
remark = "See \cite[pp. 1.9--1.10]{Coonen:1984:CPS} for negative
comments about the model in this report.",
}
@Article{Burmeister:1980:OIE,
author = "W. Burmeister",
title = "Optimal interval enclosing of certain sets of
matrices, with application to monotone enclosing of
square roots",
journal = j-COMPUTING,
volume = "25",
number = "3",
pages = "283--295",
year = "1980",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65F30 (15A57)",
MRnumber = "82e:65044",
bibdate = "Tue Jan 2 17:40:54 MST 2001",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date); MathSciNet
database",
acknowledgement = ack-nhfb,
affiliation = "Sektion Math., Tech. University of Dresden, Dresden,
East Germany",
classification = "C4140",
description = "matrix algebra",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
keywords = "cone; elementwise inclusion; interval enclosing;
matrix interval; optimal bounds; partial ordering",
}
@Article{Chang:1980:CAE,
author = "T. Chang",
title = "Comments on {``An} approach to eliminate roundoff
errors in digital filters''",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "28",
number = "2",
pages = "244--244",
month = apr,
year = "1980",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
}
@InProceedings{Cheng:1980:ASC,
author = "S. Cheng and K. Rallapalli",
title = "Am9512: Single Chip Floating-Point Processor",
crossref = "Electro:1980:ECR",
pages = "14/4/1--6",
year = "1980",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
remark = "The Am 9512 floating-point processor is claimed on at
least one Web page to be compatible with the Intel
8232, and that page claims the 8232 has IEEE
floating-point, while the earlier 8231 and 8231A were
some other format (see \cite{Intel:19xx:IAP} for a
brief description of the 8231A 32-bit floating-point
encoding).",
}
@PhdThesis{Chow:1980:VPP,
author = "Catherine Yuk-Fun Chow",
title = "A variable precision processor module",
type = "Thesis ({Ph.D.})",
school = "Department of Computer Science, University of Illinois
at Urbana-Champaign",
address = "Urbana, IL, USA",
pages = "vi + 183",
month = jul,
year = "1980",
LCCN = "QA76 .I4 no. 1032",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "UIUCDCS-R 80-1032",
acknowledgement = ack-nj # " and " # ack-nhfb,
keywords = "Floating-point arithmetic.; Parallel processing
(Electronic computers)",
}
@Article{Cluley:1980:DCB,
author = "J. C. Cluley",
title = "Digital Circuits for Binary Arithmetic",
journal = j-COMP-J,
volume = "23",
number = "3",
pages = "269--269",
month = aug,
year = "1980",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/23.3.269",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:48:08 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/23/3.toc;
https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/23/3/269.full.pdf+html",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Book{Cody:1980:SME,
author = "William J. {Cody, Jr.} and William Waite",
title = "Software Manual for the Elementary Functions",
publisher = pub-PH,
address = pub-PH:adr,
pages = "x + 269",
year = "1980",
ISBN = "0-13-822064-6",
ISBN-13 = "978-0-13-822064-8",
LCCN = "QA331 .C635 1980",
bibdate = "Tue Dec 14 23:28:38 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
acknowledgement = ack-nhfb,
shorttableofcontents = "Preface / ix \\
1. Introduction / 1 \\
2. Preliminaries / 3 \\
3. Performance Testing / 11 \\
4. SQRT / 17 \\
5. ALOG/ALOG10 / 35 \\
6. EXP / 60 \\
7. POWER (**) / 84 \\
8. SIN/COS / 125 \\
9. TAN/COT / 150 \\
10. ASIN/ACOS / 174 \\
11. ATAN/ATAN2 / 194 \\
12. SINH/COSH / 217",
tableofcontents = "Preface / ix \\
1. Introduction / 1 \\
2. Preliminaries / 3 \\
3. Performance Testing / 11 \\
4. SQRT / 17 \\
a. General Discussion / 17 \\
b. Flow Chart for SQRT(X) / 18 \\
c. Implementation Notes, Non-Decimal Fixed-Point
Machines / 19 \\
d. Implementation Notes, Binary Floating-Point Machines
/ 23 \\
e. Implementation Notes, Non-Binary Floating-Point
Machines / 25 \\
f. Testing / 28 \\
5. ALOG/ALOG10 / 35 \\
a. General Discussion / 35 \\
b. Flow Chart for ALOG(X)/ALOG10(X) / 37 \\
c. Implementation Notes, Non-Decimal Fixed-Point
Machines / 38 \\
d. Implementation Notes, Non-Decimal Floating-Point
Machines / 42 \\
e. Implementation Notes, Decimal Floating-Point
Machines / 46 \\
f. Testing / 49 \\
6. EXP / 60 \\
a. General Discussion / 60 \\
b. Flow Chart for EXP(X) / 62 \\
c. Implementation Notes, Non-Decimal Fixed-Point
Machines / 63 \\
d. Implementation Notes, Non-Decimal Floating-Point
Machines / 67 \\
e. Implementation Notes, Decimal Floating-Point
Machines / 71 \\
f. Testing / 75 \\
7. POWER (**) / 84 \\
a. General Discussion / 84 \\
b. Flow Chart for POWER(X,Y) / 88 \\
c. Implementation Notes, Non-Decimal Fixed-Point
Machines / 90 \\
d. Implementation Notes, Non-Decimal Floating-Point
Machines / 97 \\
e. Implementation Notes, Decimal Floating-Point
Machines / 106 \\
f. Testing / 113 \\
8. SIN/COS / 125 \\
a. General Discussion / 125 \\
b. Flow Chart for SIN(X)/COS(X) / 127 \\
c. Implementation Notes, Non-Decimal Fixed-Point
Machines / 129 \\
d. Implementation Notes, All Floating-Point Machines /
134 \\
e. Testing / 139 \\
9. TAN/COT / 150 \\
a. General Discussion / 150 \\
b. Flow Chart for TAN(X)/COTAN(X) / 152 \\
c. Implementation Notes, Non-Decimal Fixed-Point
Machines / 154 \\
d. Implementation Notes, All Floating-Point Machines /
159 \\
e. Testing / 164 \\
10. ASIN/ACOS / 174 \\
a. General Discuss i on / 174 \\
b. Flow Chart for AS IN(X)/ACOS(X) / 176 \\
c. Implementation Not es, Non-Decimal Fixed-Point
Machines / 177 \\
d. Implementation Notes, All Floating-Point Machines /
181 \\
e. Testing / 185 \\
11. ATAN/ATAN2 / 194 \\
a. General Discussion / 194 \\
b. Flow Chart for ATAN(X)/ATAN2(V,U) / 196 \\
c. Implementation Notes, Non-Decimal Fixed-Point
Machines / 198 \\
d. Implementation Notes, All Floating-Point Machines /
203 \\
e. Testing / 207 \\
12. SINH/COSH / 217 \\
a. General Discussion / 217 \\
b. Flow Chart for SINH(X)/COSH(X) / 220 \\
c. Implementation Notes, Non-Decimal Fixed-Point
Machines / 221 \\
d. Implementation Notes, All Floating-Point Machines /
225 \\
e. Testing / 229",
}
@Article{Coonen:1980:IGP,
author = "Jerome T. Coonen",
title = "An Implementation Guide to a Proposed Standard for
Floating-Point Arithmetic",
journal = j-COMPUTER,
volume = "13",
number = "1",
pages = "68--79",
month = jan,
year = "1980",
CODEN = "CPTRB4",
DOI = "https://doi.org/10.1109/MC.1980.1653344",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Sun May 02 09:17:48 1999",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See errata in \cite{Coonen:1981:EIG}. See
\cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
acknowledgement = ack-nj,
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@Article{Dao:1980:CNA,
author = "T. T. Dao and M. Davio and C. Gossart",
title = "Complex Number Arithmetic with Odd-Valued Logic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-29",
number = "7",
pages = "604--611",
month = jul,
year = "1980",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1980.1675631",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 19:15:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675631",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{DeVaal:1980:SZI,
author = "C. {De Vaal} and R. Nouta",
title = "On the suppression of zero-input parasitic
oscillations in floating point wave digital filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "27",
number = "2",
pages = "144--145",
month = feb,
year = "1980",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "Fettweis [1] has given a condition which guarantees,
if satisfied, the absence of zero-input parasitic
oscillations in wave digital filters. In this paper a
method is given which can be used to implement this
condition in the case of floating point \ldots{}",
}
@Article{Etzel:1980:RRN,
author = "M. Etzel and W. Jenkins",
title = "Redundant residue number systems for error detection
and correction in digital filters",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "28",
number = "5",
pages = "538--545",
month = oct,
year = "1980",
CODEN = "IETABA",
DOI = "https://doi.org/10.1109/TC.1979.1675263",
ISSN = "0096-3518",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26148",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
keywords = "residue arithmetic; residue number system",
summary = "In spite of rapid advances during the last few years
in the design and realization of digital filters, very
little attention has been given to the problems of
error detection and correction in digital filters. This
paper describes how redundant \ldots{}",
}
@InProceedings{Farrell:1980:PFP,
author = "L. Farrell",
title = "8232: a Peripheral for Floating-Point Arithmetic",
crossref = "IEEE:1980:PMA",
pages = "13--18",
year = "1980",
bibdate = "Wed Sep 07 22:25:18 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Unpublished{Fraley:1980:PSB,
author = "R. A. Fraley and J. S. Walther",
title = "A Proposed Standard for Binary Floating-Point
Arithmetic, Alternative 3, Draft 1",
day = "4",
month = jan,
year = "1980",
bibdate = "Thu Nov 25 10:19:54 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Cited in \cite{Payne:1980:VFPb}.",
acknowledgement = ack-nhfb,
}
@InProceedings{Fraley:1980:STO,
author = "R. A. Fraley and J. S. Walther",
title = "Safe Treatment of Overflow and Underflow Conditions",
crossref = "Electro:1980:ECR",
pages = "18/2/1--5",
year = "1980",
bibdate = "Wed Sep 07 21:38:30 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Gajski:1980:PC,
author = "D. D. Gajski",
title = "Parallel Compressors",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-29",
number = "5",
pages = "393--398",
month = may,
year = "1980",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1980.1675589",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 10:56:18 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Gargantini:1980:PSR,
author = "Irene Gargantini",
title = "Parallel Square-Root Iterations for Multiple Roots",
journal = j-COMPUT-MATH-APPL,
volume = "6",
number = "3",
pages = "279--288",
month = "????",
year = "1980",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 18:51:19 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122180900358",
acknowledgement = ack-jr # " and " # ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221/",
}
@Article{Ginsberg:1980:MFE,
author = "Myron Ginsberg",
title = "Monitoring floating-point error propagation in
scientific computation",
journal = j-COMPUT-MATH-APPL,
volume = "6",
number = "1",
pages = "23--43",
year = "1980",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
MRclass = "65G10 (65-04)",
MRnumber = "82a:65031",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
xxnote = "Special Issue",
}
@Article{Ginsberg:1980:MFP,
author = "Myron Ginsberg",
title = "Monitoring Floating-Point Error Propagation in
Scientific Computation",
journal = j-COMPUT-MATH-APPL,
volume = "6",
number = "1",
pages = "23--43",
month = "????",
year = "1980",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
MRclass = "65G10 (65-04)",
MRnumber = "82a:65031",
bibdate = "Wed Mar 1 18:51:18 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122180900577",
acknowledgement = ack-jr # " and " # ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221/",
xxnote = "Special Issue",
}
@Article{Goodwin:1980:PNU,
author = "D. T. Goodwin",
title = "Partial Non-Underflow and Non-Overflow of an
Arithmetic Stack",
journal = j-COMP-J,
volume = "23",
number = "2",
pages = "153--160",
month = may,
year = "1980",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/23.2.153",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "68B20",
MRnumber = "81i:68039",
bibdate = "Tue Dec 4 14:48:08 MST 2012",
bibsource = "Compendex database;
http://comjnl.oxfordjournals.org/content/23/2.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/23/2/153.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/153.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/154.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/155.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/156.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/157.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/158.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/159.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/160.tif",
acknowledgement = ack-nhfb,
classcodes = "C6150J (Operating systems)",
classification = "723",
corpsource = "Department of Computer Sci., University of Keele,
Newcastle-under-Lyme, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "arithmetic stack; computer programming; high level
language compile time; overflow; stack; storage
allocation; underflow",
reviewer = "K. S. Fu",
treatment = "P Practical",
}
@Book{Gosling:1980:DAU,
author = "John B. Gosling",
title = "Design of Arithmetic Units for Digital Computers",
publisher = pub-MAC,
address = pub-MAC:adr,
pages = "x + 139",
year = "1980",
ISBN = "0-387-91171-5, 0-333-26397-9, 0-333-26398-7",
ISBN-13 = "978-0-387-91171-7, 978-0-333-26397-6,
978-0-333-26398-3",
LCCN = "QA76.6.G668, TK7888.3 .G64 1980",
bibdate = "Wed Sep 07 20:43:22 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
tableofcontents = "Front Matter / iii--x \\
Preliminary Notes / 1--5 \\
Addition / 6--21 \\
Multiplication / 22--38 \\
Negative Numbers and Their Effect on Arithmetic /
39--54 \\
Division / 55--73 \\
Floating Point Operation / 74--104 \\
Other Functions of the Arithmetic Unit / 105--114 \\
Practical Design Problems / 115--119 \\
Mathematical Functions and Array Processing / 120--129
\\
Back Matter / 130--139",
}
@Article{Grappel:1980:IZP,
author = "R. Grappel and J. Hemenway",
title = "Increase {Z8000} power with floating-point routines",
journal = j-EDN,
volume = "25",
number = "8",
pages = "179--185",
month = apr,
year = "1980",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:06 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@Book{Gregory:1980:ECW,
author = "Robert Todd Gregory",
title = "Error-Free Computation: Why it is Needed and Methods
for Doing it",
publisher = pub-R-E-KRIEGER,
address = pub-R-E-KRIEGER:adr,
pages = "vi + 152",
year = "1980",
ISBN = "0-89874-240-4",
ISBN-13 = "978-0-89874-240-4",
LCCN = "QA297.5 .G73",
MRclass = "65G05",
MRnumber = "MR586772 (83f:65061)",
bibdate = "Sat Sep 03 10:09:50 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Approximation theory --- Data processing;
Floating-point arithmetic",
tableofcontents = "1: Mathematics vs. Numerical Mathematics \\
2: Ill-Conditioned Problems vs. Numerically Unstable
Algorithms \\
3: A Scaling Problem \\
4: ?? \\
5: ?? \\
Index",
}
@Article{Gruner:1980:IUC,
author = "K. Gr{\"u}ner",
title = "Implementation of Universal Computer Arithmetic with
Optimal Accuracy",
journal = j-COMPUTING,
volume = "24",
number = "2--3",
pages = "181--193",
year = "1980",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G99 (68A05)",
MRnumber = "83c:65118",
bibdate = "Tue Jan 2 17:40:54 MST 2001",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date); MathSciNet
database",
acknowledgement = ack-nhfb,
affiliation = "University of Karlsruhe, Karlsruhe, West Germany",
classification = "C4240",
description = "computational complexity",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Computing (Vienna/New York)",
keywords = "computer arithmetic; computer programming; fast
algorithms; intervals; mapping properties; matrices;
numerical computations; universal computer arithmetic;
vectors; word length",
}
@TechReport{Hamacher:1980:DCV,
author = "V. Carl Hamacher",
title = "Design of a {CPU} for variable precision, decimal
arithmetic",
type = "Technical Report",
number = "ABC",
institution = "Department of Electrical Engineering, University of
Toronto",
address = "Toronto, ON, Canada",
month = "????",
year = "1980",
bibdate = "Sun Dec 30 15:37:50 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal arithmetic",
}
@Article{Havender:1980:DBF,
author = "J. W. Havender",
title = "Decimal-to-binary floating point number conversion
mechanism",
journal = j-IBM-TDB,
volume = "23",
number = "2",
pages = "706--708",
month = jul,
year = "1980",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Floating point numbers may be converted from decimal
to binary using a high speed natural logarithm and
exponential function calculation mechanism and a fixed
point divide/multiply unit.\par
The problem solved is to convert numbers expressed in a
radix 10 floating point form to numbers expressed in a
radix 2 floating point form.",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
keywords = "decimal floating-point arithmetic",
}
@Article{Havender:1980:DBN,
author = "J. W. Havender",
title = "Decimal-to-binary Number Conversion",
journal = j-IBM-TDB,
volume = "23",
number = "3",
pages = "1126--1127",
month = aug,
year = "1980",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
keywords = "decimal floating-point arithmetic",
}
@Article{Haviland:1980:CAP,
author = "G. L. Haviland and A. A. Tuszynski",
title = "A {CORDIC} Arithmetic Processor Chip",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-29",
number = "2",
pages = "68--79",
month = feb,
year = "1980",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1980.1675529",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 08 00:47:17 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Head:1980:MM,
author = "A. K. Head",
title = "Multiplication modulo $n$",
journal = j-BIT,
volume = "20",
number = "1",
pages = "115--116",
month = mar,
year = "1980",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01933594",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "68-04 (65G10)",
MRnumber = "81g:68001",
MRreviewer = "K. Kilberth",
bibdate = "Wed Jan 4 18:52:16 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=20&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=20&issue=1&spage=115",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Hehner:1980:CNR,
author = "E. C. R. Hehner and R. N. S. Horspool",
title = "Corrigendum: {``A new representation of the rational
numbers for fast easy arithmetic'' [SIAM J. Comput.
{\bf 8} (1979), no. 2, 124--134, MR 80h:68027]}",
journal = j-SIAM-J-COMPUT,
volume = "9",
number = "1",
pages = "217--217",
month = "????",
year = "1980",
CODEN = "SMJCAT",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
MRclass = "68C05 (10A30)",
MRnumber = "81f:68044",
bibdate = "Mon Nov 29 10:59:12 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/9/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Hehner:1979:NRR}.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
}
@Article{Henrich:1980:FPA,
author = "C. J. Henrich",
title = "Floating-point arithmetic: can it be trusted?",
journal = j-MINI-MICRO-SYSTEMS,
volume = "13",
number = "11",
pages = "143--151",
month = nov,
year = "1980",
CODEN = "XWJXEH",
ISSN = "1000-1220",
bibdate = "Wed Sep 14 19:14:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Mini-Micro Systems",
}
@InProceedings{Henrici:1980:MPR,
author = "Peter Henrici",
booktitle = "Interval mathematics, 1980 ({Freiburg}, 1980)",
title = "A model for the propagation of rounding error in
floating arithmetic",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "49--73",
year = "1980",
DOI = "https://doi.org/10.1016/B978-0-12-518850-0.50009-3",
ISBN = "0-12-518850-1",
ISBN-13 = "978-0-12-518850-0",
MRclass = "65G05",
MRnumber = "651358",
bibdate = "Mon Jan 28 07:08:10 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/B9780125188500500093",
abstract = "The subject of propagation of rounding error, while of
undisputed importance in numerical analysis, is
notorious for the difficulties that it presents when it
is to be taught in the classroom in such a manner that
the student is neither insulted by lack of mathematical
content nor bored by lack of transparence and clarity.
On examination of some classical approaches, it appears
that the effect of tedium is often achieved by the
attempt of being absolutely rigorous. Absolute rigor in
error analysis is a triviality. Perhaps, what is
required in error analysis is not so much rigor but
rather an understanding why some algorithms work and
others do not. This chapter presents a model for the
propagation of rounding error in floating arithmetic
that aims at such an understanding. To bring to light
the essential consequences of floating arithmetic, the
model makes certain idealizing or simplifying
assumptions that are not always satisfied on real-life
computers. The model nevertheless furnishes realistic
descriptions of the numerical performance of a large
class of algorithms that can be described in terms of
operations on real numbers.",
acknowledgement = ack-nhfb,
author-dates = "Peter Karl Henrici (13 September 1923--13 March
1987)",
}
@PhdThesis{Holm:1980:FAP,
author = "John Erick Holm",
title = "Floating-point arithmetic and program correctness
proofs",
type = "Thesis ({Ph.D.})",
school = "Cornell University",
address = "Ithaca, NY, USA",
pages = "vii + 133",
month = aug,
year = "1980",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.",
}
@Article{Horna:1980:FAC,
author = "O. A. Horna",
title = "Fast algorithms for the computation of binary
logarithms",
journal = "COMSAT Technical Review",
volume = "10",
number = "1",
pages = "91--101",
month = "Spring",
year = "1980",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Hough:1980:APS,
author = "D. Hough",
title = "Applications of a Proposed Standard for Floating-Point
Arithmetic",
crossref = "Electro:1980:ECR",
pages = "18/3/1--6",
year = "1980",
bibdate = "Wed Sep 07 21:39:26 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@TechReport{Hull:1980:PPI,
author = "Thomas E. Hull and Christian H. Reinsch and John R.
Rice",
title = "Principles, Preferences and Ideals for Computer
Arithmetic",
type = "Technical report",
number = "TR-339",
institution = inst-CS-PURDUE,
address = inst-CS-PURDUE:adr,
pages = "13",
day = "1",
month = jun,
year = "1980",
bibdate = "Sun Dec 30 13:46:29 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-339.pdf",
abstract = "This paper presents principles and preferences for the
implementation of computer arithmetic and ideals for
the arithmetic facilities in future programming
languages. The implementation principles and
preferences are for the current approaches to the
design of arithmetic units. The ideals are for the long
term development of programming languages, with the
hope that arithmetic units will be built to support the
requirements of programming languages.",
acknowledgement = ack-nhfb,
author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022)",
keywords = "decimal floating-point arithmetic",
}
@Article{Jenkins:1980:CRN,
author = "W. K. Jenkins",
title = "Complex residue number arithmetic for high-speed
signal processing",
journal = j-ELECT-LETTERS,
volume = "16",
number = "17",
pages = "660--661",
day = "14",
month = aug,
year = "1980",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:19800468",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
MRclass = "94A05",
MRnumber = "MR583226 (81h:94003)",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4244229",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "residue arithmetic; residue number system",
summary = "Complex residue number arithmetic is developed for
high-speed processing of complex waveforms. An
important feature of complex residue arithmetic is that
complex multiplication can be implemented by a real
index calculus, thereby providing a highly \ldots{}",
}
@Article{Johannes:1980:DSE,
author = "J. D. Johannes and C. Dennis Pegden and F. E. Petry",
title = "Decimal Shifting for an Exact Floating Point
Representation",
journal = j-COMPUT-ELECTR-ENG,
volume = "7",
number = "3",
pages = "149--155",
month = sep,
year = "1980",
CODEN = "CPEEBQ",
ISSN = "0045-7906 (print), 1879-0755 (electronic)",
ISSN-L = "0045-7906",
bibdate = "Fri Nov 28 11:42:59 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computers and Electrical Engineering",
keywords = "decimal floating-point arithmetic",
}
@Article{Johnson:1980:DQS,
author = "E. L. Johnson",
title = "A Digital Quarter Square Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-29",
number = "3",
pages = "258--261",
month = mar,
year = "1980",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1980.1675558",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 19:15:24 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675558",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Jullien:1980:IMM,
author = "G. A. Jullien",
title = "Implementation of Multiplication, Modulo a Prime
Number, with Applications to Number Theoretic
Transforms",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-29",
number = "10",
pages = "899--905",
month = oct,
year = "1980",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1980.1675473",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 19:15:29 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675473",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kahan:1980:HCE,
author = "William M. Kahan",
title = "Handheld Calculator Evaluates Integrals",
journal = j-HEWLETT-PACKARD-J,
volume = "31",
number = "8",
pages = "23--32",
month = aug,
year = "1980",
CODEN = "HPJOAX",
ISSN = "0018-1153",
MRclass = "65-04 (65D30)",
MRnumber = "MR590837 (82d:65001)",
MRreviewer = "S. Dubuc",
bibdate = "Tue Mar 25 14:12:15 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/hpj.bib",
note = "Lecture notes for Math 128.",
URL = "http://www.cs.berkeley.edu/~wkahan/Math128/INTGTkey.pdf",
acknowledgement = ack-nhfb,
classcodes = "C4160 (Numerical integration and differentiation);
C5230 (Digital arithmetic methods)",
corpsource = "Hewlett--Packard Co., Palo Alto, CA, USA",
fjournal = "Hewlett--Packard Journal",
keywords = "34C; digital arithmetic; handheld calculator; HP;
integrals; integration; numerical integration;
numerical methods",
reviewer = "S. Dubuc",
treatment = "G General Review; P Practical",
}
@Unpublished{Kahan:1980:SPI,
author = "W. Kahan",
title = "Software $ \sqrt x $ for the Proposed {IEEE}
Floating-Point Standard",
institution = inst-BERKELEY-CS,
address = inst-BERKELEY-CS:adr,
day = "25",
month = aug,
year = "1980",
bibdate = "Mon Apr 25 18:24:02 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Manuscript",
acknowledgement = ack-nhfb,
}
@InProceedings{Kleinsteiber:1980:IHM,
author = "James R. Kleinsteiber",
title = "{IBM} 4341 hardware/microcode trade-off decisions",
crossref = "Johnson:1980:MPA",
pages = "190--192",
year = "1980",
bibdate = "Thu Aug 07 18:22:42 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The design of IBM's 4341 Processor, as with other
processors, involved many cost/performance tradeoffs.
The designer is continually under pressure to increase
processor speed without increasing cost or to decrease
processor cost without decreasing performance. This
paper will examine some of the engineering decisions
that were made in the attempt to make the 4341 a
high-performing yet low cost processor. These decisions
include searching for, or developing, algorithms that
make the best use of hardware properties, such as data
path width, arithmetic/logical operations and special
functions. Functions were sought such that a small
amount of added hardware would go a long way towards
improving system performance. Hardware designers,
microcoders and performance analysis people worked
together to implement instructions, functions and
algorithms with the proper mixture of hardware
functions and microcode in order to build a viable
processor. Some specific functions will be covered to
examine a few of the decisions. The TEST UNDER MASK
performance problem will be discussed with its
resulting implementation decision. The method of using
EXCLUSIVE OR to clear storage and the resulting
algorithm design will be shown. Other topics to be
discussed include multiple hardware functions and the
resulting effect on floating point, fixed point and
decimal multiply; the divide function and its effect on
floating point and fixed point divide; and the effect
of an 8-byte data path for decimal arithmetic.",
acknowledgement = ack-nhfb,
keywords = "decimal arithmetic",
}
@InProceedings{Kulisch:1980:AOI,
author = "U. W. Kulisch and W. L. Miranker",
title = "Arithmetic Operations in Interval Spaces",
crossref = "Alefeld:1980:FNC",
pages = "51--67",
year = "1980",
bibdate = "Tue Oct 23 08:17:48 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "interval arithmetic",
}
@Article{Ladner:1980:PPC,
author = "Richard E. Ladner and Michael J. Fischer",
title = "Parallel Prefix Computation",
journal = j-J-ACM,
volume = "27",
number = "4",
pages = "831--838",
month = oct,
year = "1980",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/322217.322232",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Wed Oct 26 22:55:08 1994",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Par.Arch.Indep.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jacm.bib",
abstract = "The prefix problem is to compute all the products $
x_1 * x_2 * \cdots * x_k $ for $ 1 \leq k \leq n $,
where $*$ is an associative operation. A recursive
construction is used to obtain a product circuit for
solving the prefix problem which has depth exactly $
\lceil \log n \rceil $ and size bounded by $ 4 n $ An
application yields fast, small Boolean circuits to
simulate finite-state transducers. By simulating a
sequential adder, a Boolean circuit which has depth $ 2
\lceil \log_2 n \rceil + 2 $ and size bounded by $ 14 n
$ is obtained for $n$-bit binary addition. The size can
be decreased significantly by permitting the depth to
increase by an additive constant.",
acknowledgement = ack-nhfb,
ajournal = "J. Assoc. Comput. Mach.",
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "https://dl.acm.org/loi/jacm",
}
@Article{Lemaire:1980:INR,
author = "C. A. Lemaire and J. C. Svercek",
title = "Improved Non-restoring Division",
journal = j-IBM-TDB,
volume = "23",
number = "3",
pages = "1149--1151",
month = aug,
year = "1980",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Book{Levy:1980:CPA,
author = "Henry M. Levy and Richard H. {Eckhouse, Jr.}",
title = "Computer Programming and Architecture --- the
{VAX-11}",
publisher = pub-DP,
address = pub-DP:adr,
pages = "xxi + 407",
year = "1980",
ISBN = "0-932376-07-X",
ISBN-13 = "978-0-932376-07-7",
LCCN = "QA76.8 .V37 L48 1980",
bibdate = "Wed Dec 15 10:38:14 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Part 1: The user architecture \\
Architecture and implementation \\
Computer structures and elementary AX-11 programming \\
Instruction and addressing fundamentals \\
More advanced programming techniques \\
Data types and data structures \\
Comparative architectures \\
Part 2: The system architecture \\
Physical input and output \\
The support of an operating system \\
The structure of a VAX-11 operating system \\
The operating system interface \\
The efficient implementation of an architecture",
}
@MastersThesis{Macke:1980:DMF,
author = "Edward T. Macke",
title = "Design of a modular floating point arithmetic unit",
type = "Thesis ({M.S.})",
school = "Washington University, Department of Electrical
Engineering",
address = "St. Louis, MO, USA",
pages = "ix + 174",
year = "1980",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Microprocessors --- Design
and construction.",
}
@InProceedings{Matula:1980:FFP,
author = "D. W. Matula",
title = "Foundations of Finite Precision Rational Arithmetic",
crossref = "Alefeld:1980:FNC",
pages = "85--111",
year = "1980",
bibdate = "Tue Oct 23 08:17:48 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "interval arithmetic; rational arithmetic",
}
@InProceedings{McMinn:1980:IND,
author = "C. McMinn",
title = "The {Intel 8087}: a Numeric Data Processor",
crossref = "Electro:1980:ECR",
pages = "14/5/1--8",
year = "1980",
bibdate = "Mon Sep 12 08:30:36 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Book{Mead:1980:IVS,
author = "Carver Mead and Lynn Conway",
title = "Introduction to {VLSI} Systems",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xvi + 396",
year = "1980",
ISBN = "0-201-04358-0",
ISBN-13 = "978-0-201-04358-7",
LCCN = "TK7874 .M371",
bibdate = "Mon Sep 16 16:25:00 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
tableofcontents = "MOS devices and circuits \\
Integrated system fabrication \\
Data and control flow in systematic structures \\
Implementing integrated system designs: from circuit
topology to patterning geometry to wafer fabrication
\\
Overview of an LSI computer system, and the design of
the OM2 data path chip \\
Architecture and design of system controllers, and the
design of the OM2 controller chip \\
System timing \\
Highly concurrent systems \\
Physics of computational systems",
}
@Article{Meinardus:1980:OPN,
author = "G{\"u}nter Meinardus and G. D. Taylor",
title = "Optimal Partitioning of {Newton}'s Method for
Calculating Roots",
journal = j-MATH-COMPUT,
volume = "35",
number = "152",
pages = "1221--1230",
month = oct,
year = "1980",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65H05 (41A30)",
MRnumber = "81j:65069",
MRreviewer = "Derek W. Arthur",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Fachbereich Math., University of Siegen, Siegen, West
Germany",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "cube root; domain interval; function approximation;
iterative methods; method; Newton; optimal
partitioning; reciprocal square root; square root;
subinterval",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Metropolis:1980:SIN,
author = "N. Metropolis",
title = "Summation of imprecise numbers",
journal = j-COMPUT-MATH-APPL,
volume = "6",
number = "3",
pages = "297--299",
year = "1980",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(80)90037-1",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
MRclass = "65U05",
MRnumber = "MR604094 (82d:65092)",
bibdate = "Sat Feb 8 10:29:40 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0458.65029",
abstract = "An algorithm is presented for computer summation of
imprecise numbers that may have quite disparate
magnitudes and variances. Each number is represented by
its expected value and variance. Exact numbers form a
subset and are treated in a consistent manner.
Cancellation effects are minimized.",
acknowledgement = ack-nhfb,
fjournal = "Computers \& Mathematics with Applications. An
International Journal",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Moore:1980:MIA,
author = "R. E. Moore",
title = "Microprogrammed interval arithmetic",
journal = j-SIGNUM,
volume = "15",
number = "2",
pages = "30--30",
month = jun,
year = "1980",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:08 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@InProceedings{Nave:1980:NDP,
author = "R. Nave and J. Palmer",
title = "A numeric data processor",
crossref = "IEEE:1980:IIS",
pages = "108--109",
year = "1980",
bibdate = "Wed Sep 07 22:22:14 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{North:1980:BRS,
author = "J. D. North",
title = "Book Review: a {Sixteenth Century} Polymath,
{{\booktitle{Wilhelm Schickard, 1592--1635: Astronom,
Geograph, Orientalist, Erfinder der Rechenmaschine}}}",
journal = j-J-HIST-ASTRON,
volume = "11",
number = "2",
pages = "138--140",
month = jun,
year = "1980",
CODEN = "JHSAA2",
DOI = "https://doi.org/10.1177/002182868001100210",
ISSN = "0021-8286 (print), 1753-8556 (electronic)",
ISSN-L = "0021-8286",
bibdate = "Mon Sep 29 17:17:57 MDT 2014",
bibsource = "http://jha.sagepub.com/content/11/2.toc;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jhistastron.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal for the History of Astronomy",
journal-URL = "https://journals.sagepub.com/home/JHA",
}
@InProceedings{Oberaigner:1980:AMG,
author = "W. Oberaigner",
title = "Algorithms for Multiplication with Given Precision",
crossref = "Alefeld:1980:FNC",
pages = "121--129",
year = "1980",
bibdate = "Tue Oct 23 08:17:48 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "interval arithmetic",
}
@InProceedings{Palmer:1980:IND,
author = "J. Palmer",
title = "The {Intel} 8087 Numeric Data Processor",
crossref = "Anonymous:1980:CPA",
pages = "174--181",
year = "1980",
bibdate = "Mon Sep 12 08:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Palmer:1980:LIN,
author = "J. Palmer",
title = "An {LSI} Implementation of a New System for
Floating-Point Arithmetic",
crossref = "Electro:1980:ECR",
pages = "18/4/1--8",
year = "1980",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Misc{Palmer:1980:UND,
author = "John F. Palmer and Bruce W. Ravenel and Rafi Nave",
title = "{US4338675}: Numeric data processor",
howpublished = "U.S. Patent",
day = "13",
month = feb,
year = "1980",
bibdate = "Sat Nov 09 10:23:07 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Published July 6, 1982. This patent was reissued on
July 2, 1991 as patent USRE33629.",
abstract = "A floating point, integrated, arithmetic circuit is
organized around a file format having a floating point
numeric domain exceeding that of any single or double
precision floating point numbers, long or short integer
words or BCD data upon which it must operate. As a
result the circuit has a greater reliability, range and
precision than ever previously achieved without
entailing additional circuit complexity. Reliability is
further enhanced by a systematic three bit rounding
field, and by including means for detecting every error
or exception condition with an optional expected
response provided thereto by hardware. As a result of
such organization, an unexpected increase of capacity
is achieved wherein transcendental functions can be
computed totally in hardware, and whereby mixed mode
arithmetic can be implemented without difficulty. The
numeric processor also includes a programmable shifter
capable of arbitrary numbers of bit and byte shifts in
a single clock cycle, as well as an arithmetic unit
capable of implementing multiplication, division,
modulo reduction and square roots directly in
hardware.",
acknowledgement = ack-nhfb,
}
@InProceedings{Payne:1980:VFPa,
author = "M. Payne and D. Bhandarkar",
title = "{VAX} Floating Point: a Solid Foundation for Numerical
Computation",
crossref = "Electro:1980:ECR",
pages = "18/1/1--12",
year = "1980",
bibdate = "Wed Sep 07 21:37:14 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://dl.acm.org/doi/pdf/10.1145/641845.641849",
abstract = "[From the first paragraph of the introduction] This
paper describes the environment provided by the
recently announced enhanced VAX floating point
architecture and compares it with the features
described in various proposals for an IEEE Floating
Point Standard. The IEEE Standards Committee created a
Working Group on Floating Point Arithmetic late in
1977. Four formal proposals for a floating point
standard have been submitted to the Working Group. Of
these, three have received extensive discussion. The
fourth describes a floating point system in which range
and precision are dynamically traded off against each
other in order to avoid overflow and underflow; it was
submitted after agreement had already been reached on
the basic specifications for a floating point
representation, and never received serious
consideration. The other three proposals are in
substantial agreement on the representation and
arithmetic for ordinary floating point numbers. There
has, however, been sharp disagreement on the handling
of exceptions and on how extra precision should be made
available for ``critical'' calculations.",
acknowledgement = ack-nj,
}
@Article{Payne:1980:VFPb,
author = "Mary Payne and Dileep Bhandarkar",
title = "{VAX} floating point: a solid foundation for numerical
computation",
journal = j-COMP-ARCH-NEWS,
volume = "8",
number = "4",
pages = "22--33",
month = jun,
year = "1980",
CODEN = "CANED2",
DOI = "https://doi.org/10.1145/641845.641849",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Sat Jun 24 12:02:21 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{Pedersen:1980:HBM,
author = "P. W. Pedersen",
title = "Hvordan beregner man kvadratroden? \toenglish {How do
you calculate the square root?} \endtoenglish",
journal = "Elektronik (Denmark)",
volume = "??",
number = "4",
pages = "18--21",
month = apr,
year = "1980",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Purtilo:1980:IAP,
author = "Jim Purtilo",
title = "On implementing arbitrary precision arithmetic in
{NIL}: an exercise in data abstraction",
journal = j-SIGSAM,
volume = "14",
number = "1",
pages = "14--18",
month = feb,
year = "1980",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Wed Oct 5 08:31:56 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIGSAM Bulletin",
issue = "??",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@Article{Rallapalli:1980:CMF,
author = "K. Rallapalli and J. Kroeger",
title = "Chips make fast math a snap for microprocessors",
journal = j-ELECTRONICS,
volume = "53",
number = "10",
pages = "153--157",
month = apr,
year = "1980",
ISSN = "0883-4989",
bibdate = "Wed Sep 07 22:27:11 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronics",
journal-URL = "https://www.mdpi.com/journal/electronics",
}
@Article{Reid:1980:CDP,
author = "John Reid",
title = "Complex double precision in association with {Fortran
77}",
journal = j-SIGNUM,
volume = "15",
number = "1",
pages = "16--17",
month = mar,
year = "1980",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:08 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C6140D (High level languages)",
corpsource = "Computer Sci. and Systems Div., AERE Harwell, UK",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "compilers; complex double precision arithmetic;
digital arithmetic; FORTRAN; FORTRAN 77; portability",
treatment = "P Practical",
}
@Article{Reid:1980:FMF,
author = "J. K. Reid",
title = "Functions for manipulating floating-point numbers",
journal = j-SIGPLAN,
volume = "15",
number = "6",
pages = "68--76",
month = jun,
year = "1980",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sat Apr 25 11:46:37 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
corpsource = "Computer Sci. and Systems Div., AERE, Harwell, Didcot,
UK",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "complete computer programs; digital arithmetic;
floating point numbers; function manipulation;
portability; software portability",
treatment = "T Theoretical or Mathematical",
}
@Article{Rink:1980:CPS,
author = "R. Rink",
title = "Correction to {``Performance of state regulator
systems with floating-point computation''}",
journal = j-IEEE-TRANS-AUTOMAT-CONTR,
volume = "25",
number = "3",
pages = "612--612",
month = jun,
year = "1980",
CODEN = "IETAA9",
ISSN = "0018-9286 (print), 1558-2523 (electronic)",
ISSN-L = "0018-9286",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Rink:1979:PSR}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Automatic Control",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
}
@PhdThesis{Rump:1980:KFM,
author = "Siegfried M. Rump",
title = "{Kleine Fehlerschranken bei Matrixproblemen}.
({German}) [Small error bounds for matrix problems]",
type = "{Ph.D.} Thesis",
school = "Institut f{\"u}r Angewandte Mathematik der
Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "vi + 131 + 49",
year = "1980",
bibdate = "Fri Jan 06 07:57:41 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ti3.tuhh.de/rump/Research/topics.php#PhD",
acknowledgement = ack-nhfb,
keywords = "accurate dot products; accurate floating-point
summation; long accumulator",
language = "German",
}
@InProceedings{Scherer:1980:SNR,
author = "R. Scherer and K. Zeller",
title = "Shorthand Notation for Rounding Errors",
crossref = "Alefeld:1980:FNC",
pages = "165--168",
year = "1980",
bibdate = "Tue Oct 23 08:17:48 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "interval arithmetic; rounding error",
}
@Manual{SOITA:1980:AIE,
key = "SOITA",
title = "{Applesoft II}: extended floating-point {BASIC}: quick
reference guide",
organization = "Southwestern Ohio Instructional Television
Association",
address = "Oxford, OH, USA",
year = "1980",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "1 pamphlet",
series = "SOITA \#2008",
acknowledgement = ack-nhfb,
keywords = "Apple II (Computer) --- Programming; BASIC (Computer
program language)",
}
@Article{Speiser:1980:RCZ,
author = "A. P. Speiser",
title = "The Relay Calculator {Z4}",
journal = j-ANN-HIST-COMPUT,
volume = "2",
number = "3",
pages = "242--245",
month = jul # "\slash " # sep,
year = "1980",
CODEN = "AHCOE5",
DOI = "https://doi.org/10.1109/MAHC.1980.10026",
ISSN = "0164-1239",
ISSN-L = "0164-1239",
bibdate = "Fri Nov 1 15:29:17 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://dlib.computer.org/an/books/an1980/pdf/a3242.pdf;
http://www.computer.org/annals/an1980/a3242abs.htm",
acknowledgement = ack-nhfb,
fjournal = "Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}
@Article{Stevenson:1980:RPI,
author = "David Stevenson",
title = "A report on the proposed {IEEE Floating Point Standard
(IEEE task p754)}",
journal = j-COMP-ARCH-NEWS,
volume = "8",
number = "5",
pages = "11--12",
month = aug,
year = "1980",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Wed Nov 24 10:59:34 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Book{Stone:1980:ICA,
editor = "Harold S. Stone and Tien Chi Chen and Michael J. Flynn
and Samuel H. Fuller and others",
title = "Introduction to Computer Architecture",
publisher = "Science Research Associates",
address = "Chicago, IL, USA",
edition = "Second",
pages = "673",
year = "1980",
ISBN = "0-574-21225-6",
ISBN-13 = "978-0-574-21225-2",
LCCN = "QA76.9.A73 I57 1980",
bibdate = "Fri Nov 9 19:22:07 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
price = "US\$16.95 (est.)",
series = "The SRA computer science series",
acknowledgement = ack-nhfb,
subject = "Computer architecture",
tableofcontents = "Part I: Basic computer architecture \\
Introduction / Harold S. Stone \\
Data representation / Herschel H. Loomis, Jr. \\
Microprocessor architecture / Thomas M. Whitney \\
Introduction to microcomputers / K. B. Magleby \\
Memory and storage / Richard E. Matick \\
Input/output processing / William G. Lane \\
Part II: Advanced topics \\
Stack computers / William M. McKeeman \\
Parallel computers / Harold S. Stone \\
Overlap and pipeline processing / Tien Chi Chen \\
Interpretation, microprogramming, and the control of a
computer / Michael J. Flynn \\
Performance evaluation / Samuel H. Fuller \\
Operating systems and computer architecture / Richard
L. Sites",
}
@InProceedings{Stone:1980:TFP,
author = "H. S. Stone",
title = "Towards a Floating-Point Standard",
crossref = "Electro:1980:ECR",
pages = "18/0/1--5",
year = "1980",
bibdate = "Wed Sep 07 21:33:52 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Stummel:1980:REA,
author = "F. Stummel",
title = "Rounding Error Analysis of Elementary Numerical
Algorithms",
crossref = "Alefeld:1980:FNC",
pages = "169--195",
year = "1980",
bibdate = "Tue Aug 28 06:19:13 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "interval arithmetic; rounding error",
}
@Article{Swartzlander:1980:AUH,
author = "E. E. {Swartzlander, Jr.} and B. K. Gilbert",
title = "Arithmetic for Ultra-High-Speed Tomography",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-29",
number = "5",
pages = "341--353",
month = may,
year = "1980",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1980.1675584",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 19:15:25 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675584",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Swartzlander:1980:CA,
editor = "Earl E. {Swartzlander, Jr.}",
title = "Computer Arithmetic",
publisher = pub-DOWDEN,
address = pub-DOWDEN:adr,
pages = "xiii + 378",
year = "1980",
ISBN = "0-87933-350-2",
ISBN-13 = "978-0-87933-350-8",
LCCN = "QA76.6 .C633",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Benchmark papers in electrical engineering and
computer science; 21",
acknowledgement = ack-nj # " and " # ack-nhfb,
keywords = "Computer arithmetic; Electronic digital computers ---
Programming; Floating-point arithmetic",
tableofcontents = "Arithmetic operations in a binary computer \\
High-speed arithmetic in binary computers \\
Fast carry logic for digital computers \\
A logic for high-speed addition \\
Conditional-sum addition logic \\
An evaluation of several two-summand binary \\
Adder with distributed control \\
Multiple addition by residue threshold, functions and
their representation by Array logic \\
Counting responders in an associative memory \\
Parallel counters \\
A signed binary multiplication technique \\
Multiplying made easy for digital assemblies \\
A binary multiplication scheme based on squaring \\
A suggestion for a fast multiplier \\
Some schemes for parallel multipliers \\
On parallel digital multipliers \\
A compact high-speed parallel multiplication scheme \\
A two' complement parallel array multiplication
algorithm \\
Comments on ``A two's complement parallel array
multiplication algorithm'' \\
The quasi-serial multiplier \\
The two's complement quasi-serial multiplier \\
Division \\
A new class of digital division methods \\
An algorithm for rapid binary \\
Higher-radix division using estimates of the divisor
and partial remainders \\
An algorithm for division \\
A division method using a parallel multiplier \\
On division by functional iteration \\
Logarithms \\
Computation of the base two logarithm of binary
logarithms and elementary \\
A note on base-2 logarithm computations \\
Digital filtering using \\
The sign / logarithm number system \\
Elementary functions \\
The CORDIC trigonometric computing technique \\
Digit-by-digit transcendental-function computation \\
A unified algorithm for elementary functions \\
Some properties of iterative square-rooting methods
using high-speed multiplication \\
Radix-16 evaluation of certain elementary functions \\
Floating-point arithmetic \\
On the distribution of numbers \\
An analysis of floating-point addition \\
The IBM System/360 Model 91: floating-point execution
unit \\
Design of large high-speed floating-point-arithmetic
units \\
Analysis of rounding methods in floating-point
arithmetic",
}
@Article{Swartzlander:1980:MA,
author = "E. E. {Swartzlander, Jr.}",
title = "Merged Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-29",
number = "10",
pages = "946--950",
month = oct,
year = "1980",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1980.1675482",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 19:31:28 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675482",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Thornton:1980:CP,
author = "James E. Thornton",
title = "The {CDC 6600} Project",
journal = j-ANN-HIST-COMPUT,
volume = "2",
number = "4",
pages = "338--348",
month = oct # "\slash " # dec,
year = "1980",
CODEN = "AHCOE5",
DOI = "https://doi.org/10.1109/MAHC.1980.10044",
ISSN = "0164-1239",
bibdate = "Fri Nov 1 15:29:17 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://dlib.computer.org/an/books/an1980/pdf/a4338.pdf;
http://www.computer.org/annals/an1980/a4338abs.htm",
abstract = "This article is an account of the development of the
Control Data 6600 computer first developed in 1964. Of
historical interest is the design team approach adopted
by Control Data in which a small staff of engineers was
isolated from the main operations of the company. Some
review is made of the design process as well as the
unique features of the machine. The article also
includes some comments in retrospect about the results
of certain of the initial design objectives.",
acknowledgement = ack-nhfb,
fjournal = "Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}
@MastersThesis{Ting:1980:MCU,
author = "I-chyng Ting",
title = "A microprocessor-based controller using floating-point
arithmetic",
type = "Thesis ({M.S.})",
school = "Auburn University",
address = "Auburn, AL, USA",
pages = "ix + 167",
year = "1980",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Microprocessors.",
}
@MastersThesis{Tucker:1980:IAD,
author = "Richard Wesley Tucker",
title = "Implementation of arithmetic for the data flow machine
processing unit",
type = "Thesis ({B.S.})",
school = "Massachusetts Institute of Technology. Dept. of
Electrical and Engineering and Computer Science",
address = "Cambridge, MA, USA",
pages = "i + 58",
year = "1980",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supervised by Jack B. Dennis.",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Microprocessors ---
Programming.; Val (Computer program language).",
}
@InProceedings{Ulrich:1980:IMS,
author = "Ch. Ulrich",
title = "Iterative Methods in the Spaces of Rounded
Computations",
crossref = "Alefeld:1980:FNC",
pages = "197--209",
year = "1980",
bibdate = "Tue Oct 23 08:17:48 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "interval arithmetic; rounding error",
}
@InProceedings{Undheim:1980:CFP,
author = "T. Undheim",
title = "Combinatorial Floating Point Processor as an Integral
Part of the Computer",
crossref = "Electro:1980:ECR",
pages = "14/1/1--6",
year = "1980",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Verma:1980:MPF,
author = "S. B. Verma and Maithili Sharan",
title = "Multiple Precision Floating-point Computation in
{FORTRAN}",
journal = j-SPE,
volume = "10",
number = "3",
pages = "163--173",
month = mar,
year = "1980",
CODEN = "SPEXBL",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Thu Sep 8 08:20:53 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}
@TechReport{Virkkunen:1980:UAF,
author = "V.-E. Juhani Virkkunen",
title = "A unified approach to floating-point rounding with
applications to multiple-precision summation",
type = "{Diss. Helsingfors}",
institution = "Department of Computer Science, University of
Helsinki",
address = "Helsinki, Finland",
pages = "66",
year = "1980",
ISBN = "951-45-1948-5",
ISBN-13 = "978-951-45-1948-2",
bibdate = "Thu May 09 08:25:02 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@PhdThesis{vonGudenberg:1980:EAR,
author = "J. Wolff {von Gudenberg}",
title = "{Einbettung allgemeiner Rechnerarithmetik in Pascal
mittels eines Operatorkonzepts und Implementierung der
Standardfunktionen mit optimaler Genauigkeit}
\toenglish {Embedding a General Computer Arithmetic in
Pascal by Means of an Operator Concept and the
Implementation of Elementary Functions with Optimal
Accuracy} \endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "??",
year = "1980",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Waldecker:1980:NSR,
author = "D. E. Waldecker",
title = "Nonrestoring Square Root with Simplified Answer
Generation",
journal = j-IBM-TDB,
volume = "22",
number = "11",
pages = "4807--4808",
month = apr,
year = "1980",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Article{Waser:1980:EGP,
author = "S. Waser",
title = "{Entwicklung von Gleitkomma-Prozessoren} \toenglish
{Development of Floating-Point Processors}
\endtoenglish",
journal = j-ELECTRONIK,
volume = "29",
number = "9",
pages = "50--54",
month = apr,
year = "1980",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronik",
}
@MastersThesis{Watkins:1980:MFU,
author = "Timothy Ervin Watkins",
title = "A microprogrammed {FFT} utilizing floating point
hardware",
type = "Thesis ({M.S.})",
school = "UCLA",
address = "Los Angeles, CA, USA",
pages = "v + 56",
year = "1980",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Fourier transformations
--- Computer programs.; Microprogramming.",
}
@MastersThesis{Wong:1980:IOF,
author = "Clement Sau-Fai Wong",
title = "Input\slash output and floating-point arithmetic
package",
type = "Thesis ({M.S.})",
school = "University of Tennessee, Knoxville",
address = "Knoxville, TN, USA",
pages = "vi + 61",
year = "1980",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer input-output equipment.; Electronic digital
computers --- Programming.; Floating-point arithmetic.;
Microcomputers.",
}
@InProceedings{Yohe:1980:FPE,
author = "J. M. Yohe",
title = "Floating point exception handling for interval
arithmetic",
crossref = "Nickel:1980:IMP",
pages = "547--554",
year = "1980",
MRclass = "65G10",
MRnumber = "83c:65115",
bibdate = "Fri Dec 08 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Yohe:1980:PSI,
author = "J. M. Yohe",
title = "Portable Software for Interval Arithmetic",
crossref = "Alefeld:1980:FNC",
pages = "211--229",
year = "1980",
bibdate = "Tue Oct 23 08:17:48 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A portable multiple precision interval arithmetic
package for FORTRAN has been developed by substituting
the multiple precision arithmetic package of Richard P.
Brent for the underlying arithmetic in the author's
earlier single precision interval arithmetic package.
This package, like the earlier version, offers a
complete range of operations and functions for interval
calculations.\par
In this paper, we outline the design philosophy of the
earlier package and show how this design facilitated
the incorporation of the Brent package. We discuss
several desirable host system features and possible
adaptations of the interval package, and explain how
the design of the package would allow it to serve in
differing environments with only relatively minor
changes.\par
Since the package may be of direct use to many
individuals, we also discuss its installation on other
host systems and its use via the AUGMENT precompiler
for Fortran.",
acknowledgement = ack-nhfb,
keywords = "interval arithmetic; multiple precision arithmetic",
}
@Article{Zeman:1980:HSM,
author = "J. Zeman and H. T. {Nagle, Jr.}",
title = "A High-Speed Microprogrammable Digital Signal
Processor Employing Distributed Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-29",
number = "2",
pages = "134--144",
month = feb,
year = "1980",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1980.1675537",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 19:15:24 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675537",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Agrawal:1981:NAM,
author = "D. P. Agrawal and R. C. Joshi",
title = "Negabinary Addition and Multiplication Using Binary
Circuits",
crossref = "IEEE:1981:PSC",
pages = "270--273",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Agrawal_Joshi.pdf",
abstract = "This paper deals with design techniques that allow
adoption of off-the-shelf binary arithmetic circuits to
perform multi-operand addition and multiplication of
negabinary numbers. The multiple operands could be
easily added with augmented binary adders connected in
the form of a tree. The same hardware could be used to
perform multiplication. But, from an LSI implementation
viewpoint, the use of cellular array structures is
explored and necessary challenges to design a combined
binary/negabinary multiplier unit, are also outlined.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Andrews:1981:EFM,
author = "M. Andrews and D. Jaeger and S. F. McCormick and G. D.
Taylor",
title = "Evaluation of Functions on Microcomputers: $ \exp (x)
$",
journal = j-COMPUT-MATH-APPL,
volume = "7",
number = "6",
pages = "503--508",
year = "1981",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Thu Sep 15 18:40:45 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
xxmonth = "(none)",
}
@MastersThesis{Arnold:1981:PFP,
author = "Jeffrey M. Arnold",
title = "{PSI}, a floating point processor for the {NU}
Computer",
type = "Thesis ({B.S.})",
school = "Massachusetts Institute of Technology. Dept. of
Electrical and Engineering and Computer Science",
address = "Cambridge, MA, USA",
pages = "42",
year = "1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supervised by Stephen A. Ward.",
acknowledgement = ack-nhfb,
keywords = "Computer architecture.; Floating-point arithmetic.;
Intel 8086 (Microprocessor); Microprocessors --- Design
and construction.",
}
@InProceedings{Arora:1981:CSR,
author = "R. K. Arora and Saroj Kaushik",
title = "Conversion Scheme in Residue Code",
crossref = "IEEE:1981:PSC",
pages = "152--156",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Arora_Kaushik.pdf",
abstract = "In this paper, an implementation scheme involving
decoders and residue adders has been suggested to
convert input data in fixed radix representation to
residue representation. A method dealing with the
reverse process is also demonstrated. A comparison has
been made with the methods known hitherto.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5; residue number system",
}
@InProceedings{Atkins:1981:FIS,
author = "D. E. Atkins and K. S. Trivedi",
title = "The {Fifth IEEE Symposium on Computer Arithmetic}:
Foreword",
crossref = "IEEE:1981:PSC",
pages = "iv--iv",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Trivedi_Atkins.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Avizienis:1981:LCR,
author = "Algirdas Avi{\v{z}}ienis",
title = "Low-Cost Residue and Inverse Residue Error-Detecting
Codes for Signed-Digit Arithmetic",
crossref = "IEEE:1981:PSC",
pages = "165--168",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Avizienis.pdf",
abstract = "Low-cost residue and inverse residue codes for error
detection in signed-digit arithmetic are defined in
this paper. Checking algorithms are presented for both
digit-serial and parallel computation of the residues.
Residue digit operations are defined for two-operand
addition, multi-operand addition, multiplication,
conversion, and reconversion algorithms. All algorithms
employ the same Arithmetic Building Element ``ABE''
that has been previously developed for signed-digit
arithmetic.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Banerji:1981:HSD,
author = "Dilip K. Banerji and To-Yat Cheung and V. Ganesan",
title = "A High-Speed Division Method in Residue Arithmetic",
crossref = "IEEE:1981:PSC",
pages = "158--164",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Banerji_Cheung_Ganesan.pdf",
abstract = "This paper is concerned with the operation of division
in residue number systems. Residue codes are introduced
and the basic residue arithmetic operations are
defined. Previous results on residue division are
outlined. A well-known integer division algorithm is
used and adapted for residue division. A new method is
proposed for choosing an approximate divisor,
approximate dividends, and the partial quotients. The
proposed method yields correct quotients faster than
the existing methods and is general in its application
i.e., it is not restricted by the choice of moduli as
long as they are relatively prime.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Barlow:1981:DAA,
author = "Jesse Barlow",
title = "On the Distribution af Accumulated Roundoff Error in
Floating Point Arithmetic",
crossref = "IEEE:1981:PSC",
pages = "100--105",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Barlow.pdf",
abstract = "This paper discusses longstanding problems in the
probabilistic error analysis of numerical algorithms
when they are performed in floating point
arithmetic.\par
Local roundoff error in floating point addition is
characterized and its mean and variance are
approximated. We apply these results to finding
distributions for the roundoff error accumulated in
sums and long inner products.\par
We state theorems which resolve questions left open in
Bustoz et al. [5] and Hamming [11]. These theorems are
proven in [3].",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@PhdThesis{Barlow:1981:PEA,
author = "Jesse Louis Barlow",
title = "Probabilistic error analysis of floating point and
{CRD} arithmetics",
type = "{Ph.D.} (Electrical Engineering and Computer
Science)",
school = "Northwestern University",
address = "Evanston, IL, USA",
pages = "????",
year = "1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Bashe:1981:AIE,
author = "C. J. Bashe and W. Buchholz and G. V. Hawkins and J.
J. Ingram and N. Rochester",
title = "The Architecture of {IBM}'s Early Computers",
journal = j-IBM-JRD,
volume = "25",
number = "5",
pages = "363--375",
month = sep,
year = "1981",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Mon Jan 24 21:36:17 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@MastersThesis{Benjamin:1981:FPF,
author = "Bruce P. Benjamin",
title = "Fixed point to floating point converter",
type = "{Master of Science, Plan II}",
school = "University of California, Berkeley. Dept. of
Electrical Engineering and Computer Sciences",
address = "Berkeley, CA, USA",
pages = "60",
year = "1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bhuyan:1981:MAP,
author = "L. Bhuyan and D. P. Agrawal",
title = "Multiple Addition and Parallel Counter in Generalized
Binary and Negabinary Systems",
crossref = "IEEE:1981:PSC",
pages = "264--269",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Bhuyan_Agrawal.pdf",
abstract = "This paper explores the possibility of utilizing
counters for reducing the partial products generated
from multiplication of two numbers represented in a
generalized binary system. Algorithm for multi operand
addition of Koren's generalized number system are
worked out. A carry look-ahead adder is developed and
hardware aspects of possible counters for this class of
binary number system are discussed. Negabinary counters
are also introduced in line with those proposed for
binary multiplication by Stenzel et al.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Bice:1981:AAS,
author = "P. K. Bice",
title = "Algorithm adds square root to micro's arithmetic
capability",
journal = j-ELECTRONIC-DESIGN,
volume = "29",
number = "11",
pages = "146",
month = may,
year = "1981",
CODEN = "ELODAW",
ISSN = "0013-4872 (print), 1944-9550 (electronic)",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
}
@Article{Blikle:1981:CTI,
author = "Andrzej Blikle",
title = "The Clean Termination of Iterative Programs",
journal = j-ACTA-INFO,
volume = "16",
number = "2",
pages = "199--217",
month = oct,
year = "1981",
CODEN = "AINFA2",
ISSN = "0001-5903 (print), 1432-0525 (electronic)",
ISSN-L = "0001-5903",
MRclass = "68B10",
MRnumber = "83c:68015",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
ftp://ftp.ira.uka.de/pub/bibliography/Misc/HBP/ACTAI.bib;
ftp://ftp.ira.uka.de/pub/bibliography/Misc/leavens.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
catcode = "D.2; D.2.4; F.3",
content = "Most correctness proofs assume that elementary
instructions represent total functions. In fact this is
not always the case: for instance, in dealing with real
numbers, Brown's model of floating point computation
[1], a model which has been accepted by the designers
of ADA, uses interval analysis. If the interval of x
overlaps the interval of y, the Boolean value of x r y
is not well defined.\par
In this paper the author studies the clean termination
(i.e., without abortion) of iterative programs, not
supposing that the test functions are total. The
relational approach to computing, which the author has
largely worked out (cf. Sanderson [2] for an account
from the starting point) is very well suited for that
design. A general theorem links the ``global
correctness'' of a program with a ``well-founded''
breakdown of the program relation. Next the author
gives new validation rules, in which a Z b depart from
the usual meaning. Last (but not least) one finds an
exhaustive study of the integer square root in a
realistic arithmetic.\par
Due to the great significance of the matter, we must
call attention to this paper. \par
M. F. Aribaud, Paris, France \par
REFERENCES \par
[1] BROWN, W. S. A simple but realistic model of
floating-point computation, ACM Trans. Math. Softw. 7
(1981), 445 480. \par
[2] SANDERSON, J. G. A relational theory of computing,
Lecture Notes in Computer \ldots{}",
CRclass = "D.2.4 Program Verification; D.2.4 Program
Verification; D.2.4 Correctness proofs; F.3.1
Specifying and Verifying and Reasoning about Programs",
CRnumber = "39409",
descriptor = "Software, SOFTWARE ENGINEERING, Program Verification;
Software, SOFTWARE ENGINEERING, Program Verification,
Correctness proofs; Theory of Computation, LOGICS AND
MEANINGS OF PROGRAMS, Specifying and Verifying and
Reasoning about Programs",
fjournal = "Acta Informatica",
genterm = "LANGUAGES; RELIABILITY; THEORY; VERIFICATION",
journal-URL = "http://www.springerlink.com/content/0001-5903",
reviewer = "M. F. Aribaud",
subject = "D. Software; D.2 SOFTWARE ENGINEERING; D. Software;
D.2 SOFTWARE ENGINEERING; F. Theory of Computation; F.3
LOGICS AND MEANINGS OF PROGRAMS",
}
@TechReport{Brent:1981:MUG,
author = "Richard P. Brent",
title = "{MP} User's Guide",
number = "TR-CS-81-08",
institution = "Department of Computer Science, Australian National
University",
address = "Canberra, ACT, Australia",
edition = "Fourth",
pages = "73",
month = jun,
year = "1981",
bibdate = "Fri Nov 28 15:59:05 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "MP is a multiple-precision floating-point arithmetic
package. It is almost completely machine-independent,
and should run on any machine with an ANSI Standard
Fortran (ANS X3.9-1966) compiler, sufficient memory,
and a wordlength (for integer arithmetic) of at least
16 bits. A precompiler (Augment) which facilitates the
use of the MP package is available.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@InProceedings{Bridge:1981:AAA,
author = "Carol L. Bridge and P. David Fisher and Robert G.
Reynolds",
title = "Asynchronous Arithmetic Algorithms for Data-Driven
Machines",
crossref = "IEEE:1981:PSC",
pages = "56--62",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Bridge_Fisher_Reynolds.pdf",
abstract = "With data-driven machines a statement associated with
a given processing element fires the moment its input
operands become available. In order to take full
advantage of this computer structure and achieve
maximum throughput, the processing elements themselves
should also be asynchronous; i.e., instruction
execution times should be data dependent to minimize
overall delays. Five general procedures are described
that may be used to design self-timing processing
units: task completion prediction, task completion
detection, operand preprocessing, pre-estimation of
input operand values, and significance control.
Analysis and simulations suggest that the greatest
potential for speed improvement over synchronous
counterparts comes with self-timing algorithms for both
division and the evaluation of special functions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Brown:1981:SRM,
author = "W. S. Brown",
title = "A Simple but Realistic Model of Floating-Point
Computation",
journal = j-TOMS,
volume = "7",
number = "4",
pages = "445--480",
month = dec,
year = "1981",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355972.355975",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Aug 29 23:03:20 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib;
https://www.math.utah.edu/pub/tex/bib/unix.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "computer arithmetic; environment parameters; error
analysis; Euclidean norm; floating-point arithmetic;
software portability",
}
@MastersThesis{Cariker:1981:RFM,
author = "Earnest Allan Cariker",
title = "A rapid-approximation floating-point mathematics
package for the {INTEL} 8080 microprocessor",
type = "Computing Science Thesis ({M.S.})",
school = "Texas A\&M University",
address = "College Station, TX, USA",
pages = "viii + 152",
year = "1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Mathematical analysis.; Microprocessors.; Programming
(Electronic computers); Programming languages
(Electronic computers)",
}
@MastersThesis{Cary:1981:BFP,
author = "David A. Cary",
title = "The {Berkeley} floating point project",
type = "{Master of Science, Plan II}",
school = "University of California, Berkeley. Dept. of
Electrical and Engineering and Computer Sciences",
address = "Berkeley, CA, USA",
pages = "107",
year = "1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Noted as posthumous in \cite{Aspinwall:1985:RVM}.",
}
@Article{Ceruzzi:1981:ECK,
author = "Paul E. Ceruzzi",
title = "The Early Computers of {Konrad Zuse}, 1935 to 1945",
journal = j-ANN-HIST-COMPUT,
volume = "3",
number = "3",
pages = "241--262",
month = jul # "\slash " # sep,
year = "1981",
CODEN = "AHCOE5",
ISSN = "0164-1239",
bibdate = "Fri Nov 1 15:29:18 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://dlib.computer.org/an/books/an1981/pdf/a3241.pdf;
http://www.computer.org/annals/an1981/a3241abs.htm",
acknowledgement = ack-nhfb,
fjournal = "Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}
@Manual{Cheng:1981:AAF,
author = "Steven Cheng",
title = "{Am9511A\slash Am9512} floating point processor
manual",
organization = "Advanced Micro Devices",
address = "Sunnyvale, CA, USA",
pages = "55",
year = "1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units.; Floating-point
arithmetic.",
}
@InProceedings{Chow:1981:PDA,
author = "P. Chow and Z. G. Vranesic and J. L. Yen",
title = "A Pipelined Distributed Arithmetic {PFFT} Processor",
crossref = "IEEE:1981:PSC",
pages = "198--206",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Chow_Vranesic_Yen.pdf",
abstract = "Previous experience i,n implementing the Prime Factor
Fourier Transform showed that it was much more
difficult to do than the FFT because of its complicated
structure. In most FFT implementations the
``butterfly'' structure is the basic arithmetic unit
implemented. It is much simpler than the equivalent
PFFT unit.\par
This paper describes a different architecture for
implementing PFFT machines using distributed arithmetic
and ROM's to perform the computations. It is found to
be much simpler and more modular than a design which
uses multipliers and adders. The implementation of a
PFFT processor with a throughput of 104 kHz for complex
data points is described.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5; Prime Factor Fourier Transform (PFFT)",
}
@Article{Chroust:1981:MAD,
author = "G. Chroust",
title = "Method of Adding Decimal Numbers by Means of Binary
Arithmetic",
journal = j-IBM-TDB,
volume = "23",
number = "10",
pages = "4525--4526",
month = mar,
year = "1981",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
keywords = "decimal floating-point arithmetic",
}
@InProceedings{Ciminiera:1981:AAF,
author = "L. Ciminiera and A. Serra",
title = "Arithmetic Array for Fast Inner Product Evaluation",
crossref = "IEEE:1981:PSC",
pages = "207--214",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Ciminiera_Serra.pdf",
abstract = "The paper presents a new fast arithmetic array,
suitable for VLSI implementation, which computes the
inner product of two vectors. The operands and the
result are expressed using the 2's complement notation,
which is the most general and flexible one. Cells
performing the $ 2 \times 2 $ bit full multiplication
are used for obtaining a reduction of the operation
time.\par
A particular pipelining scheme, with different degrees
of latching, is used in order to implement parallel
computations with a moderate cost increase. Graphs
showing the characteristics and the advantage domain of
the proposed array are presented. An IC implementation
of the proposed array could have a speed from 5 to 10
times greater than the multiplier-accumulator circuits
currently available.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Ciminiera:1981:FAM,
author = "L. Ciminiera and A. Serra and A. Valenzano",
title = "{Fast and Accurate Matrix Triangularization Using an
Iterative Structure}",
crossref = "IEEE:1981:PSC",
pages = "215--221",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Ciminiera_Serra_Valenzano.pdf",
abstract = "The paper presents a new iterative array, which
performs the triangularization of a dense matrix, using
the Givens rotation algorithm. Two slightly different
arrays are presented: the first one performs the
factorization of a single matrix; the second one
performs the recursive triangularization. The
implementation of the cell in the array is based on the
on-line arithmetic, which allows us to obtain high
performances. Furthermore, the cell implementation
requires only three types of arithmetic units
(multiplication\slash addition, square root, division)
and shift registers for data buffering and for
generating the timing signals.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Cody:1981:APF,
author = "William J. {Cody, Jr.}",
title = "Analysis of Proposals for the Floating-Point
Standard",
journal = j-COMPUTER,
volume = "14",
number = "3",
pages = "63--68",
month = mar,
year = "1981",
CODEN = "CPTRB4",
DOI = "https://doi.org/10.1109/C-M.1981.220379",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Sat Sep 24 09:21:33 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
note = "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Computer",
URL = "https://ethw.org/w/images/f/fb/Analysis_of_Proposals_Cody.pdf",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@InProceedings{Cohen:1981:CAU,
author = "M. Cohen and V. C. Hamacher and T. E. Hull",
title = "{CADAC}: An Arithmetic Unit for Clean Decimal
Arithmetic and Controlled Precision",
crossref = "IEEE:1981:PSC",
pages = "106--112",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Cohen_Hamacher_Bull.pdf",
abstract = "This paper describes the design of an arithmetic unit
called CADAC (Clean Arithmetic with Decimal base And
Controlled Precision). A brief indication of
programming language specifications for carrying out
``ideal'' floating-point arithmetic is given. These
specifications include detailed requirements for
precision control and exception handling at the level
of a programming language such as Fortran. CADAC is an
arithmetic unit which performs the four floating-point
operations add\slash subtract \slash multiply\slash
divide on decimal base numbers in accordance with the
language requirements. A three-level pipeline is used
to overlap 2-digit-at-a-time (``double digit'') serial
processing of the partial products\slash remainders.
Although the logic design is relatively complex, the
performance is efficient and the advantages gained by
implementing programmer-controlled precision directly
in the hardware are significant.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Coonen:1981:EIG,
author = "Jerome T. Coonen",
title = "Errata: {An Implementation Guide to a Proposed
Standard for Floating Point Arithmetic}",
journal = j-COMPUTER,
volume = "14",
number = "3",
pages = "62--62",
month = mar,
year = "1981",
CODEN = "CPTRB4",
DOI = "https://doi.org/10.1109/C-M.1981.220378",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Wed Sep 14 21:15:55 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See
\cite{Coonen:1980:IGP,IEEE:1985:AIS,IEEE:1985:ASI}.",
acknowledgement = ack-nj,
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@Article{Coonen:1981:UDN,
author = "Jerome T. Coonen",
title = "Underflow and the Denormalized Numbers",
journal = j-COMPUTER,
volume = "14",
number = "3",
pages = "75--87",
month = mar,
year = "1981",
CODEN = "CPTRB4",
DOI = "https://doi.org/10.1109/C-M.1981.220382",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Fri Sep 2 23:38:17 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
acknowledgement = ack-nj,
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@MastersThesis{Curley:1981:PPN,
author = "A. Curley",
title = "{PNCL}: a Prototype Numerical Computation Language",
type = "{M.Sc.} thesis",
school = "Department of Computer Science, University of
Toronto",
address = "Toronto, ON, Canada",
year = "1981",
bibdate = "Sun Dec 30 15:41:22 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Davis:1981:EFA,
author = "Diane F. Davis",
title = "Elementary Functions on an Array Processor",
crossref = "IEEE:1981:PSC",
pages = "170--178",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Davis.pdf",
abstract = "The algorithms used for elementary functions on the
FPS-164 array processor are described. In each case,
the choice of the algorithm depends on the parallel
hardware, the capability of the instruction word, and
the precision desired. For some, the choice depends on
the version, either scalar or vector. Algorithms for
the divide, square root, cosine\slash sine,
exponential, and logarithm are discussed. Those for
arctangent, tangent, arc-cosine\slash sine, cosh, sinh,
and tanh are summarized.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5; Floating-Point Systems FPS-164",
}
@Manual{DECESD:1981:VIS,
author = "{Digital Equipment Corporation.Educational Services
Dept}",
title = "{VAX-11} instruction set",
organization = "Digital Equipment Corporation",
address = "Maynard, MA, USA",
edition = "Revised",
pages = "various",
year = "1981",
bibdate = "Sun May 02 09:19:03 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "VAX-11 (Computer) --- Programming.",
remark = "In container. Student guide --- Programming examples
--- Character string instructions --- Instruction
formats and addressing modes --- Variable bit field
instructions --- Stack and address instructions ---
Integer, logical and branch instructions --- Floating
point instructions --- Decimal string instructions
--Procedure and subroutine instructions --- Special
instructions --- Module tests --- Evaluation sheets ---
Selected tables.",
}
@InProceedings{Demmel:1981:EUS,
author = "James Demmel",
title = "Effects of Underflow on Solving Linear Systems",
crossref = "IEEE:1981:PSC",
pages = "113--119",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Demmel.pdf",
abstract = "Software to solve systems of linear equations by
Gaussian elimination has in the past ignored the
effects of underflow. But when underflows are replaced
by zeroes, this software can give spurious though
plausible results much worse than would be blamed on
roundoff. When underflow is gradual, as in the proposed
IEEE standard for floating point arithmetic, the same
software gives provably more reliable results. To
achieve the same reliability without gradual underflow,
but with underflows set to zero, complicated tests must
be inserted into the software.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Efe:1981:MOA,
author = "Kemal Efe",
title = "Multi-Operand Addition with Conditional Sum Logic",
crossref = "IEEE:1981:PSC",
pages = "251--255",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Efe.pdf",
abstract = "Column-wise addition schemes involve counting the
number of 1's in a column and representing this number
in binary weighted form. In Conditional Sum Logic
(CSL), partial results are first generated for every
column, then one of these results is selected depending
on the incoming carry value. A compact scheme for
counting the number of 1's and generating partial
results for all possible distributions of incoming
carries is introduced. Application of such counters to
CSL yields a high speed in multi-operand addition.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@TechReport{Eide:1981:FPA,
author = "Vigleik Eide",
title = "Floating-point arithmetic on a micro-computer",
type = "Hovedoppgave i informatikk (cand. real)",
institution = "Universitetet i Oslo",
address = "Oslo, Norway",
pages = "71",
year = "1981",
bibdate = "Thu May 09 08:12:55 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@PhdThesis{Farmwald:1981:DHP,
author = "P. M. Farmwald",
title = "On the Design of High Performance Digital Arithmetic
Units",
type = "Thesis ({Ph.D.})",
school = "Stanford University",
address = "Stanford, CA, USA",
pages = "????",
month = aug,
year = "1981",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@InProceedings{Farmwald:1981:HBE,
author = "P. Michael Farmwald",
title = "High bandwidth evaluation of certain elementary
functions",
crossref = "IEEE:1981:PSC",
pages = "139--142",
year = "1981",
bibdate = "Mon May 20 05:27:32 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Farmwald.pdf",
abstract = "Among the requirements currently being imposed on
high-performance digital computers to an increasing
extent are the high-bandwidth computations of
elementary functions, which are relatively
time-consuming procedures when conducted in software.
In this paper, we elaborate on a technique for
computing piecewise quadratic approximations to many
elementary functions. This method permits the effective
use of large RAMs or ROMs and parallel multipliers for
rapidly generating single-precision floating-point
function values (e.g., 30-45 bits of fraction, with
current RAM and ROM technology). The technique, based
on the use of Taylor series, may be readily pipelined.
Its use for calculating values for floating-point
reciprocal, square root, sine, cosine, arctangent,
logarithm, exponential and error functions is
discussed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Fredette:1981:RES,
author = "G. Fredette",
title = "68000 routine extracts square roots",
journal = j-EDN,
volume = "26",
number = "16",
pages = "185--194",
month = aug,
year = "1981",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@Article{Ganesan:1981:GSC,
author = "K. Ganesan and A. Augustine",
title = "8086 generates sines and cosines",
journal = j-EDN,
volume = "26",
number = "6",
pages = "186--188",
month = mar,
year = "1981",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@Book{Glaser:1981:HBO,
author = "Anton Glaser",
title = "History of Binary and Other Nondecimal Numeration",
publisher = pub-TOMASH,
address = pub-TOMASH:adr,
edition = "Revised",
pages = "xiii + 218",
year = "1981",
ISBN = "0-938228-00-5",
ISBN-13 = "978-0-938228-00-4",
LCCN = "QA141.2 .G55 1981",
bibdate = "Fri Mar 17 08:12:27 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "See also original edition \cite{Glaser:1971:HBO}.",
acknowledgement = ack-nhfb,
author-dates = "1924--",
remark = "Based on the author's thesis (Ph.D.--Temple
University), presented under the title: History of
modern numeration systems.",
subject = "Numeration; History; 31.14 number theory; 15.00
history: general; Numeration; Dualsystem; Geschichte;
Talstelsels; History; Num{\'e}ration; Histoire;
Dualsystem; Geschichte.",
}
@Book{Gorin:1981:IDA,
author = "Ralph E. Gorin",
title = "Introduction to {DECSYSTEM-20} Assembly Language
Programming",
publisher = pub-DP,
address = pub-DP:adr,
pages = "xxx + 545",
year = "1981",
ISBN = "0-932376-12-6",
ISBN-13 = "978-0-932376-12-1",
LCCN = "QA76.8.D17 .G67",
bibdate = "Tue Dec 14 22:54:14 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$40.00",
acknowledgement = ack-nhfb,
}
@InProceedings{Gorji-Sinaki:1981:DDS,
author = "A. Gorji-Sinaki and M. D. Ercegovac",
title = "Design of a Digit-Slice On-Line Arithmetic Unit",
crossref = "IEEE:1981:PSC",
pages = "72--80",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_GorjiSinaki_Ercegovac.pdf",
abstract = "A gate level design of a digit-slice on-line
arithmetic unit is presented. This unit is designed as
a set of basic modules Processing Elements (PE), each
of which operates on a single digit of the operands and
the results. It is capable of executing four basic
operations of addition\slash subtraction,
multiplication and division in an on-line manner. The
results are generated during the digit-serial input of
the operands, beginning always with the most
significant digit. A general (with respect to radix)
analysis of the cost and speed of the proposed unit is
also given.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Gosling:1981:CSH,
author = "J. B. Gosling and J. H. P. Zurawski and D. B. G.
Edwards",
title = "A Chip-Set for a High-Speed Low-cost Floating-Point
Unit",
crossref = "IEEE:1981:PSC",
pages = "50--55",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Gosling_Zurawski_Edwards.pdf",
abstract = "Although the advent of microprocessors has put
considerable computing power in the hands of large
numbers of users, there is still an important group who
have yet to benefit fully from large scale
integration., As a step in the direction of rectifying
this situation, a highly flexible chip set is being
designed, with a view to reducing the cost of a
powerful floating point processor by a factor of about
4. Processing speed will be up to twice that of an
equivalent unit built from MSI devices, before
allowance is made for savings on wiring delays. It will
be possible to construct a unit satisfying all
published standards, proposed and existing (de facto),
as well as permitting a number of extensions not
specifically in these standards. At a cost between 100
and 150 ICs, and with a floating-point add time of
around 120ns, the proposed unit is cost-effective
compared to currently available coprocessors.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Grappel:1981:RDB,
author = "R. D. Grappel",
title = "68000 routine divides 32-bit numbers",
journal = j-EDN,
volume = "26",
number = "5",
pages = "161--162",
month = mar,
year = "1981",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@InProceedings{Gregory:1981:RAR,
author = "R. T. Gregory",
title = "Residue Arithmetic with Rational Operands",
crossref = "IEEE:1981:PSC",
pages = "144--145",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Gregory.pdf",
abstract = "A method is described for doing residue arithmetic
when the operands are rational numbers. A rational
operand $ a / b $ is mapped onto the integer $ a
b^{-1}|_p $ and the arithmetic is performed in $
\mathrm {GF}(p) $. A method is given for taking an
integer result and finding its rational equivalent (the
one which corresponds to the correct rational
result).",
acknowledgement = ack-nhfb,
keywords = "ARITH-5; residue number system",
}
@Article{Griffiths:1981:BDC,
author = "L. K. Griffiths",
title = "Binary-to-Decimal Conversion",
journal = j-IBM-TDB,
volume = "24",
number = "1A",
pages = "237--238",
month = jun,
year = "1981",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Fri Nov 28 17:04:53 2003",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Binary to decimal conversion can be achieved by
multiplying $ 1 / 10 $ as $ 51 / 512 \times 256 / 255 $
and using the fact that $ 256 / 255 = 1 + 1 / 256 + 1 /
256^2 + \cdots $, i.e., $ 256 / 255 = 257 - 256 $
rounded up.\par
This method can be performed efficiently on short word
computers with only adding and shifting operations,
i.e., first multiplying by $ 51 / 512 $ and then
correcting by multiplying by $ 256 / 255 $.",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
keywords = "decimal floating-point arithmetic",
}
@Article{Grote:1981:CIS,
author = "H. Grote",
title = "Code improves on a square-root routine",
journal = j-EDN,
volume = "26",
number = "11",
pages = "198--200",
month = may,
year = "1981",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@MastersThesis{Hazlerig:1981:CES,
author = "Steven Jackson Hazlerig",
title = "Comparison and evaluation of several floating-point
schemes for the {Motorola} 68000 microprocessor",
type = "Thesis ({M.S.})",
school = "Massachusetts Institute of Technology. Dept. of
Electrical and Engineering and Computer Science",
address = "Cambridge, MA, USA",
pages = "103",
year = "1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supervised by Richard E. Zippel.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
keywords = "Floating-point arithmetic.; Microprocessors ---
Programming.; Microprogramming.",
}
@TechReport{Hendra:1981:FPS,
author = "R. G. Hendra",
title = "A floating point software package for use on {LSI-11}
computers at {SLAC}",
type = "Technical note",
number = "SLAC TN 81-3",
institution = "SLAC",
address = "Stanford, CA, USA",
pages = "8",
month = jun,
year = "1981",
bibdate = "Fri May 25 05:50:26 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0046833",
acknowledgement = ack-nhfb,
}
@Article{Hough:1981:API,
author = "David Hough",
title = "Applications of the Proposed {IEEE-754} Standard for
Floating Point Arithmetic",
journal = j-COMPUTER,
volume = "14",
number = "3",
pages = "70--74",
month = mar,
year = "1981",
CODEN = "CPTRB4",
DOI = "https://doi.org/10.1109/C-M.1981.220381",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Fri Sep 2 23:38:14 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
acknowledgement = ack-nhfb # " and " # ack-nj,
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@Article{Huang:1981:IFD,
author = "Chao Huang and D. Peterson and H. Rauch and J. Teague
and D. Fraser",
title = "Implementation of a fast digital processor using the
residue number system",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "28",
number = "1",
pages = "32--38",
month = jan,
year = "1981",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1049/el:19800468",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23509",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "This paper contains a description of a special purpose
digital processor which has been implemented using
residue arithmetic. The processor does two-dimensional
pulse matching by convolving a two-dimensional
five-by-five filter with the Incoming data \ldots{}",
}
@MastersThesis{Hwang:1981:CFF,
author = "Shu-Hwa Hwang",
title = "Computation in a finite field using rational
operands",
type = "Thesis ({M.S.})",
school = "University of Tennessee, Knoxville",
address = "Knoxville, TN, USA",
pages = "v + 80",
year = "1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Algorithms.; Floating-point arithmetic.; Modular
arithmetic.; Programming (Electronic computers)",
}
@InProceedings{Hwang:1981:PAV,
author = "Kai Hwang and Yen-Heng Cheng",
title = "Partitioned Algorithms and {VLSI} Structures for
Large-Scale Matrix Computations",
crossref = "IEEE:1981:PSC",
pages = "222--232",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Hwang_Cheng.pdf",
abstract = "VLSI modular arithmetic structures and new partitioned
matrix algorithms are developed in this paper to
perform hardware matrix computations in solving
large-scale linear system of equations. Gaussian
elimination and inversion of triangular matrices are
shown systematically partitionable. All the partitioned
algorithms being developed can achieve linear
computation time $ O(n) $, where $n$ is the order of
the linear system. The partitioned matrix computations
are feasible for modular VLSI implementation with
constrained I/O terminals. Performance analysis and
design tradeoffs of the partitioned VLSI arithmetic
structures are also provided.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Irwin:1981:RAP,
author = "Mary Jane Irwin and Dwight R. Smith",
title = "A Rational Arithmetic Processor",
crossref = "IEEE:1981:PSC",
pages = "241--245",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Irwin_Smith.pdf",
abstract = "An arithmetic processor based upon a rational
representation scheme is examined. The key feature of
this rational processor is its ability to efficiently
reduce a result ratio to its irreducible form (the
greatest common divisor of the numerator and
denominator is unity). The reduction algorithm
presented generates the reduced ratio in parallel with
the evaluation of the ratio's greatest common divisor.
Hardware designs for the reduction algorithm and the
basic arithmetic operations are given.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Jenkins:1981:CSP,
author = "W. K. Jenkins and M. H. Etzel",
title = "Correction to {``Special} properties of complement
codes for redundant residue number systems''",
journal = j-PROC-IEEE,
volume = "69",
number = "8",
pages = "1086--1086",
month = aug,
year = "1981",
CODEN = "IEEPAD",
DOI = "https://doi.org/10.1049/el:19800468",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Jenkins:1981:SPC}.",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=31304",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
keywords = "residue arithmetic; residue number system",
}
@Article{Jenkins:1981:SPC,
author = "W. K. Jenkins and M. H. Etzel",
title = "Special properties of complement codes for redundant
residue number systems",
journal = j-PROC-IEEE,
volume = "69",
number = "1",
pages = "132--133",
month = jan,
year = "1981",
CODEN = "IEEPAD",
DOI = "https://doi.org/10.1049/el:19800468",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See correction \cite{Jenkins:1981:CSP}.",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=31297",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
keywords = "residue arithmetic; residue number system",
summary = "Redundant residue number systems are of interest
because they have properties that are useful for error
control and failure recovery in digital processors.
This letter shows how complement coding interferes with
error detection in redundant residue \ldots{}",
}
@TechReport{Kahan:1981:WDW,
author = "W. Kahan",
title = "Why Do We Need a Floating-Point Arithmetic Standard?",
type = "Technical Report",
institution = inst-BERKELEY,
address = inst-BERKELEY:adr,
pages = "41",
day = "12",
month = feb,
year = "1981",
bibdate = "Fri Apr 7 12:22:17 GMT 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Available in a retypeset version
\cite{Kahan:2001:WDW}.",
}
@Article{Karplus:1981:ASI,
author = "W. J. Karplus and D. Cohen",
title = "Architectural and Software Issues in the Design of
Peripheral Array Processors",
journal = j-COMPUTER,
volume = "??",
number = "??",
pages = "??--??",
month = sep,
year = "1981",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Fri Nov 09 19:01:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@InProceedings{Kaushik:1981:SDS,
author = "Saroj Kaushik and R. K. Arora",
title = "Sign Detection in the Symmetric Residue Number
System",
crossref = "IEEE:1981:PSC",
pages = "146--150",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Kaushik_Arora.pdf",
abstract = "This paper is concerned with the algebraic sign
detection of a number in the Symmetric Residue Number
System. A new approach has been suggested which
completely avoids the time consuming process of the
Symmetric Mixed Radix Conversion (SMRC). An algorithm
based on the above approach implementable in parallel
for sign detection is also presented. The hardware
representation of the above algorithm is shown. The
time and hardware complexity required for the process
have also been computed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Kielbasinski:1981:IRL,
author = "Andrzej Kie{\l}basi{\'n}ski",
title = "Iterative refinement for linear systems in
variable-precision arithmetic",
journal = j-BIT,
volume = "21",
number = "1",
pages = "97--103",
month = mar,
year = "1981",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01934074",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65G05",
MRnumber = "83a:65042",
bibdate = "Wed Jan 4 18:52:17 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=21&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=21&issue=1&spage=97",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; variable-precision
arithmetic",
}
@Book{Knuth:1981:SA,
author = "Donald E. Knuth",
title = "Semi\-nu\-mer\-i\-cal Algorithms",
volume = "2",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Second",
pages = "xi + 624",
year = "1981",
ISBN = "0-201-03822-6",
ISBN-13 = "978-0-201-03822-4",
LCCN = "QA76.6 .K64",
bibdate = "Wed Dec 15 15:47:38 1993",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$19.75",
series = "The Art of Computer Programming",
acknowledgement = ack-nj,
}
@InProceedings{Kobayashi:1981:FMO,
author = "Hideaki Kobayashi",
title = "A Fast Multi-Operand Multiplication Scheme",
crossref = "IEEE:1981:PSC",
pages = "246--250",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Kobayashi.pdf",
abstract = "Recent developments in integrated circuit technology
have made efficient schemes for computer arithmetic
possible. This paper discusses a generation-summation
scheme for fast multi-operand multiplication. Synthesis
of three-operand multipliers utilizing a single type of
standard LSI device is also discussed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Book{Kogge:1981:APC,
author = "Peter M. Kogge",
title = "The Architecture of Pipelined Computers",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xii + 334",
year = "1981",
ISBN = "0-07-035237-2",
ISBN-13 = "978-0-07-035237-7",
LCCN = "QA76.5 .K587",
bibdate = "Wed Dec 15 10:37:46 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Introduction \\
Hardware design and stage cascading \\
Timing, control, and performance \\
Static pipelined systems: vector processors \\
The programming of pipelined vector processors \\
Pipelining in SISD machine designs \\
Future trends \\
Appendix: Collision vector characteristics",
}
@Article{Koren:1981:CPN,
author = "I. Koren and Y. Maliniak",
title = "On Classes of Positive, Negative, and Imaginary Radix
Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "30",
number = "5",
pages = "212--317",
month = may,
year = "1981",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1981.1675788",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Aug 22 09:00:57 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A unified approach to a broad class of finite number
representation systems is proposed. This class contains
aDl positive and negative radix systems and other
well-known number systems. In addition, it can be
extended to include imaginary radix number systems. The
proposed approach enables us to develop a single set of
algorithms for arithmetic operations.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Kornerup:1981:IRA,
author = "Peter Kornerup and David W. Matula",
title = "An Integrated Rational Arithmetic Unit",
crossref = "IEEE:1981:PSC",
pages = "233--240",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Kornerup_Matula.pdf",
abstract = "Based on the classical Euclidian Algorithm, we develop
the foundations of an arithmetic unit performing Add,
Subtract, Multiply and Divide on rational operands. The
unit uses one unified algorithm for all operations,
including rounding. A binary implementation, based on
techniques known from the SRT division, is described.
Finally, a hardware implementation using ripple-free,
carry-save addition is analyzed, and adapted to a
floating-slash representation of the rational
operands.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Book{Kulisch:1981:CAT,
author = "Ulrich W. Kulisch and Willard L. Miranker",
title = "Computer Arithmetic in Theory and Practice",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xiii + 249",
year = "1981",
ISBN = "0-12-428650-X",
ISBN-13 = "978-0-12-428650-4",
LCCN = "QA162 .K84",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Computer science and applied mathematics",
acknowledgement = ack-nhfb,
keywords = "Algebra, Abstract.; Computer arithmetic.;
Floating-point arithmetic.; Interval analysis
(Mathematics)",
remark = "See \cite[pp. 1.10--1.11]{Coonen:1984:CPS} for
negative comments about the floating-point model in
this book, and the impracticality of implementing it in
early-1980s technology. Coonen comments: ``their scheme
is {\em sufficient\/} to perform reliable computation,
aided by devious algorithms; there is no evidence that
their scheme is {\em necessary}. nor that the
deviousness of their algorithms is unavoidable.''",
}
@Article{Kunz:1981:QZ,
author = "W. Kunz",
title = "{Quadratwurzel mit dem $ \mu $P Z80} \toenglish
{Square Roots with the Z80 Microprocessor}
\endtoenglish",
journal = j-ELECTRONIK,
volume = "7",
pages = "109--110",
year = "1981",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronik",
}
@InProceedings{Ligomenides:1981:CRF,
author = "P. Ligomenides and R. Newcomb",
title = "Complement Representations in the {Fibonacci}
Computer",
crossref = "IEEE:1981:PSC",
pages = "6--9",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Ligomenides_Newcomb.pdf",
abstract = "Two complement representations and a sign-magnitude
one are introduced which allow for handling negative
numbers using only binary coefficients in Fibonacci
base expansions. These are developed for practical
implementation in Fibonacci computers.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Ling:1981:HSB,
author = "Huey Ling",
title = "High-speed binary adder",
journal = j-IBM-JRD,
volume = "25",
number = "2/3",
pages = "156--166",
month = may # "\slash " # jun,
year = "1981",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Mar 25 14:26:59 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C5120 (Logic and switching circuits)",
corpsource = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "adders; fewer logic levels; high; neighbouring bit;
new carry propagation; new scheme; pairs; reduced
component count; speed binary adder; uniform fanin
loading; uniform fanout loading",
treatment = "N New Development",
}
@Article{Linnainmaa:1981:CEU,
author = "Seppo Linnainmaa",
title = "Combatting the effects of underflow and overflow in
determining real roots of polynomials",
journal = j-SIGNUM,
volume = "16",
number = "2",
pages = "11--16",
month = jun,
year = "1981",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:09 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@Article{Linnainmaa:1981:SDP,
author = "Seppo Linnainmaa",
title = "Software for Doubled-Precision Floating-Point
Computations",
journal = j-TOMS,
volume = "7",
number = "3",
pages = "272--283",
month = sep,
year = "1981",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355958.355960",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "68B99 (65G99 68C05)",
MRnumber = "82h:68041",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://doi.acm.org/10.1145/355958.355960",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "accurate floating-point summation; exact
multiplication; floating-point arithmetic; rounding
errors; software portability",
}
@Article{Louie:1981:APS,
author = "T. Louie",
title = "Array Processors: a Selected Bibliography",
journal = j-COMPUTER,
volume = "??",
number = "??",
pages = "??--??",
month = sep,
year = "1981",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Fri Nov 09 19:04:04 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@InProceedings{Markov:1981:IAA,
author = "Svetoslav Markov",
title = "On an Interval Arithmetic and Its Applications",
crossref = "IEEE:1981:PSC",
pages = "274--278",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Markov.pdf",
abstract = "It is our point of view that familiar interval
arithmetic defined by $ A*B = \{ a * b : a \in A, b \in
B \} $, $ * \in \{ +, -, \times, : \} $ is inefficient
in certain respects. For instance, it is not in a
position to produce exact representations of sets of
the form $ \{ f(x, y, \ldots {}, z) : x \in X. y \in Y,
\ldots {}, z \in Z \} $ even for simple functions $f$
of one variable. We make use of another interval
arithmetic which is very convenient for computer
computations and for construction of interval
algorithms. As an example we consider a method for the
construction of interval expressions for sets of the
form $ \{ f(x) : x \in [x_1, x_2] \} $, where $f$ is an
elementary function.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5; interval arithmetic",
}
@Article{Maron:1981:IAP,
author = "N. Maron and T. A. Brengle",
key = "Maron \& Brengle",
title = "Integrating an Array Processor into a Scientific
Computing System",
journal = j-COMPUTER,
volume = "14",
number = "9",
pages = "41--44",
month = sep,
year = "1981",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Parallel/Multi.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@Article{Matsui:1981:OUF,
author = "S. Matsui and M. Iri",
title = "An overflow\slash underflow-free floating-point
representation of numbers",
journal = j-J-INF-PROCESS,
volume = "4",
number = "3",
pages = "123--133",
year = "1981",
CODEN = "JIPRDE",
ISSN = "0387-6101",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.0",
content = "The authors propose a floating-point number
representation whereby the allocation of digits between
exponent and mantissa would vary with the size of the
number. In extreme cases in which the entire word is
not long enough to contain the exponent, they move to a
different ``level'' and work with exponents of
exponents. They have implemented the scheme in
software, and they claim that a hardware implementation
is possible without loss of efficiency. Their examples
include Graeffe's method, which seems to survive better
in their environment than in a conventional
floating-point environment, and Racah symbols, which
are functions of factorials.\par
The examples are not totally convincing.
Polynomial-factoring is not a computational bottleneck.
The Racah symbols would indeed cause trouble if
computed in a direct manner in conventional floating
point; however, the use of a log-gamma function would
largely eliminate the problem.\par
By using certain bit-configurations to denote
``nonnumbers'' the authors make good their claim of
overflow-free arithmetic. The system clearly has the
merit of convenience. In the absence of a formal error
analysis it is not yet clear what price has to be paid
for the convenience. \par
A. C. R. Newbery, Lexington.",
CRclass = "G.1.0 General; G.1.0 Computer arithmetic",
CRnumber = "40691",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic",
fjournal = "Journal of Information Processing",
genterm = "DESIGN; PERFORMANCE",
reviewer = "A. C. R. Newbery; Newbery, A. C. R",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Miller:1981:RGU,
author = "W. Miller",
title = "A Remark on Gradual Underflow",
journal = j-COMPUTING,
volume = "27",
number = "3",
pages = "217--225",
year = "1981",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Oct 12 16:33:42 MDT 1999",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "Univ of Ariz, Tucson, USA",
classification = "723",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Computing (Vienna/New York)",
keywords = "computer arithmetic; computer metatheory;
floating-point arithmetic; IEEE 754 arithmetic",
}
@Article{Mitra:1981:CRA,
author = "D. Mitra and V. Lawrence",
title = "Controlled rounding arithmetics, for second-order
direct-form digital filters, that eliminate all
self-sustained oscillations",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "28",
number = "9",
pages = "894--905",
month = sep,
year = "1981",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "Quantization often allows a recursive second-order
filter to oscillate even when the underlying linear
model is absolutely stable and there is no external
signal present to excite the filter. One of the
significant innovative ideas recently \ldots{}",
}
@Article{Munson:1981:FPR,
author = "David C. {Munson, Jr.} and Bede Liu",
title = "Floating point roundoff error in the prime factor
{FFT}",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "29",
number = "4",
pages = "877--882",
month = aug,
year = "1981",
CODEN = "IETABA",
ISSN = "0096-3518",
MRclass = "65R10 (94A05)",
MRnumber = "82f:65132",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The prime factor fast Fourier transform (PF FFT),
developed by Kolba and Parks, makes use of recent
computational complexity results by Winograd to compute
the DFT with a fewer number of multiplications than
that required by the FFT. Patterson and McClellan have
derived an expression for the mean squared error (MSE)
in the PF FFT, assuming finite precision fixed point
arithmetic. In this paper, we derive an expression for
the MSE in the PF FFT, assuming floating point
arithmetic. This expression is quite complicated, so an
upper bound on the MSE is also derived which is easier
to compute. Simulation results are presented comparing
the error in the PF FFT with both the derived bound and
the error observed in a radix-2 FFT.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
}
@InProceedings{Nguyen:1981:SAD,
author = "Diem Dinh Nguyen",
title = "A Systematic Approach to the Design of Structures for
Addition and Subtraction --- Case of Radix $ r = m^k
$",
crossref = "IEEE:1981:PSC",
pages = "42--49",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Nguyen.pdf",
abstract = "The results of Robertson concerning a systematic
approach to the design of Adder\slash Subtracter
structures of radix $ r = 2^k $, $ k \geq I $ are
generalised to cover all structures of radix $ r = m^k
$, $ k \geq I $ and $ m \geq 2 $. The use of
quasibinary representations help reduce the number of
types of fundamental structures required. In addition
to the types encountered in the earlier case, only one
new type of fundamental structure called Radix-$m$
Carry Generator is needed. Examples in the particular
case of Decimal Adder\slash Subtracter structures are
used to illustrate the results.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Ong:1981:TQC,
author = "S. Ong and D. E. Atkins",
title = "Towards Quantitative Comparison of Computer Number
Systems",
crossref = "IEEE:1981:PSC",
pages = "21--33",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Ong_Atkins.pdf",
abstract = "This paper describes an evolving Arithmetic Design
System (ADS) to support the quantitative evaluation of
alternate number systems with respect to a given
application and realization technology. In computer
arithmetic we are concerned with establishing a
correspondence between abstract quantities (numbers)
and some physical representation (symbols), and with
simulating the operations on these symbols. The ADS is
intended to help study the cost and performance of
alternate simulations. A finite number system is a
triple consisting of a symbol set (elements are called
``digit-vectors''), an interpretation set, a mapping
between these two sets, and a set of operators
(digit-vector algorithms) defined on its symbol set. A
set of these digit vector algorithms are proposed for
conducting arithmetic design. A number system matrix
defines the digit vector algorithm for numerous number
systems and a method for computing time and space
complexity of compositions of these algorithms is
proposed. An example of how the system could be used to
compare addition, with and without overflow detection,
for three number systems is given.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Owens:1981:CAD,
author = "Robert Michael Owens",
title = "Compound Algorithms for Digit On-Line Arithmetic",
crossref = "IEEE:1981:PSC",
pages = "64--71",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Owens.pdf",
abstract = "This paper describes a systematic method which has
been. successfully used to create several digit online
algorithms. Basically, the method entails converting in
a systematic way a known continued sums\slash products
algorithm and combining the converted form of the
continued sums\slash product algorithm with a
generalized digitization algorithm. Not only does the
method seem to have wide applicability in the creation
of digit online algorithms for many elementary
functions but the algorithms which have resulted from
this method themselves have several desirable
properties.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Padegs:1981:SB,
author = "A. Padegs",
title = "{System\slash 360} and Beyond",
journal = j-IBM-JRD,
volume = "25",
number = "5",
pages = "377--390",
month = sep,
year = "1981",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Sat Jan 29 17:56:34 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Pan:1981:BCA,
author = "V. Pan",
title = "The bit-complexity of arithmetic algorithms",
journal = j-J-ALG,
volume = "2",
number = "2",
pages = "144--163",
month = jun,
year = "1981",
CODEN = "JOALDV",
DOI = "https://doi.org/10.1016/0196-6774(81)90016-X",
ISSN = "0196-6774 (print), 1090-2678 (electronic)",
ISSN-L = "0196-6774",
bibdate = "Tue Dec 11 09:13:49 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jalg.bib",
URL = "http://www.sciencedirect.com/science/article/pii/019667748190016X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Algorithms",
journal-URL = "http://www.sciencedirect.com/science/journal/01966774",
}
@InProceedings{Papachristou:1981:APA,
author = "C. A. Papachristou",
title = "Algorithms for Parallel Addition and Parallel
Polynomial Evaluation",
crossref = "IEEE:1981:PSC",
pages = "256--263",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Papachristou.pdf",
abstract = "This paper presents two related algorithms for
implementing parallel $n$-bit binary addition and
evaluating $n$-th degree polynomials, respectively. The
approach taken makes use of an iterative construction,
the computation tree. The algorithms are particularly
effective for moderate values of $n$ and are in accord
with well-known asymptotic bounds. In the case of
$n$-bit addition, the implementations constitute
lookahead tree circuits of $r$-input standard logic
elements. Extensions to modular tree structures for
lookahead adders are also considered. In the case of
parallel polynomial evaluation, the operations of
ordinary addition and multiplication are assumed with
the capability to employ $r$ arguments
simultaneously.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Peng:1981:AES,
author = "Hong Peng",
title = "Algorithms for extracting square roots and cube
roots",
crossref = "IEEE:1981:PSC",
pages = "121--126",
year = "1981",
bibdate = "Thu Sep 01 11:37:17 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Peng.pdf",
abstract = "This paper describes a kind of algorithms for fast
extracting square roots and cube roots, their
mathematical proofs, their revised algorithm formulae,
and hardware implementation of the square root
algorithm. These algorithms may be of no significance
for large scale computer with fast division. But I am
sure that it is effective and economical to apply these
algorithms to the circuit designs of some mini- and
microcomputers with general multiplication and
division, such as nonrestoring division.",
acknowledgement = ack-nj,
keywords = "ARITH-5",
}
@Article{Peters:1981:EFB,
author = "James V. Peters",
title = "An Equivalent Form of {Benford's Law}",
journal = j-FIB-QUART,
volume = "19",
number = "1",
pages = "74--75",
month = feb,
year = "1981",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:59:53 MDT 2011",
bibsource = "http://www.fq.math.ca/19-1.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/19-1/peters.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@InProceedings{Raghavendra:1981:SLA,
author = "C. S. Raghavendra and M. D. Ercegovac",
title = "A Simulator for On-Line Arithmetic",
crossref = "IEEE:1981:PSC",
pages = "92--98",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Raghavendra_Ercegovac.pdf",
abstract = "On-line arithmetic is a special class of serial
arithmetic where algorithms produce results with the
most significant digit first during the serial input of
the operands. Speedup of computations can be achieved
by overlapping or pipelining successive operations with
small delays. This paper describes the design and
implementation of a simulator for on-line arithmetic
algorithms. The simulator was designed primarily to
serve as\par
(1) an experimental tool for synthesis of on-line
algorithms;\par
(2) a performance evaluation tool of on-line
arithmetic;\par
(3) an on-line calculator in solving some problems
involving linear and non-linear recurrences.\par
The simulator evaluates arithmetic expressions given in
a highly functional form. Presently, the set of
operations supported include addition, subtraction,
multiplication, division, and square root. Several
examples are presented in this paper to illustrate the
usage of the simulator. The simulator package is
implemented in 'C' language on a VAX 11/780 system.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Rao:1981:AFF,
author = "T. R. N. Rao",
title = "Arithmetic of Finite Fields",
crossref = "IEEE:1981:PSC",
pages = "2--5",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Rao.pdf",
abstract = "The arithmetic operations in finite fields and their
implementation are important to the construction of
error detecting and correcting codes. The addition,
multiplication and division in the field $ \mathrm
{GF}(2^m) $ are implemented as polynomial operations
using binary logic of flip-flops and EXOR's. For fields
of nonbinary characteristic, modular arithmetic (with
modulus $p$, a prime) becomes important. This paper
focuses on problems relating to the arithmetic of $
\mathrm {GF}(p) $, and some recent results and new
ideas on this topic are presented here.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Rao:1981:CHC,
author = "T. M. Rao and R. T. Gregory",
title = "The Conversion of {Hensel} Codes to Rational Numbers",
crossref = "IEEE:1981:PSC",
pages = "10--14",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Rao_Gregory.pdf",
abstract = "In a finite-segment p-adic number system one of the
difficult problems is concerned with converting Hensel
codes back into rational numbers. An algorithm for this
conversion is proposed which is based on a
sophisticated table look-up procedure.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Redinbo:1981:SRN,
author = "G. Redinbo and W. Hunnebeck",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '81}",
title = "On the simulation of residue number systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "339--342",
year = "1981",
CODEN = "????",
DOI = "https://doi.org/10.1049/el:19800468",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "It is sometimes difficult to simulate on general
purpose computers the performance of digital systems
that use residue number systems. This paper
demonstrates a new technique that makes effective use
of a Fast Fourier Transform (FFT) to simulate the
\ldots{}",
}
@InProceedings{Robertson:1981:SAD,
author = "J. E. Robertson",
title = "A Systematic Approach to the Design of Structures for
Arithmetic",
crossref = "IEEE:1981:PSC",
pages = "35--41",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Robertson.pdf",
abstract = "A design tool for the decomposition of binary digital
structures for addition and subtraction has been
developed. A simplified theory reduces a complex
structure to a collection of basic structures of one
type, namely, a full adder. The simplified theory is
applicable to the design of parallel counters and array
multipliers. A general theory is used for decomposition
to three types of basic structures, whose complexity is
usually on the order of a half-adder. The general
theory is applicable to redundant array multipliers and
signed-digit adders.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Rodrigues:1981:HEM,
author = "M. R. D. Rodrigues and J. H. P. Zurawski and J. B.
Gosling",
title = "Hardware evaluation of mathematical functions",
journal = j-IEE-PROC-E,
volume = "128",
number = "4",
pages = "155--164",
month = jul,
year = "1981",
CODEN = "IPETD3",
ISSN = "0143-7062",
bibdate = "Thu Sep 1 10:15:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEE proceedings, E: Computers and digital techniques",
}
@InProceedings{Rutenbar:1981:CSV,
author = "R. A. Rutenbar and Y. E. Park",
title = "Case Study of a {VLSI} Design Project: a Simple Inner
Product Machine",
crossref = "IEEE:1981:PSC",
pages = "184--189",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Rutenbar_Park.pdf",
abstract = "We present a case study of the application of recently
evolved structured VLSI design methodologies to the
design and implementation of a simple VLSI quasi-serial
inner product machine.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Schonfelder:1981:ECP,
author = "J. L. Schonfelder and M. Razaz",
title = "Error control with polynomial approximations",
journal = j-IMA-J-NUMER-ANAL,
volume = "1",
number = "1",
pages = "105--114",
year = "1981",
CODEN = "IJNADH",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65D15",
MRnumber = "83d:65043, 607250",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@TechReport{Schryer:1981:TCF,
author = "N. L. Schryer",
title = "A Test of a Computer's Floating-Point Arithmetic
Unit",
number = "Computer Science Technical Report 89",
institution = "AT\&T Bell Laboratories",
pages = "66",
month = feb,
year = "1981",
bibdate = "Fri Nov 30 11:20:24 2001",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://plan9.bell-labs.com/cm/cs/cstr/89.ps.gz;
http://www.bell-labs.com/topic/swdist/",
acknowledgement = ack-nj,
keywords = "floating-point testing",
}
@Article{Schwarz:1981:EYC,
author = "H. R. Schwarz",
title = "The Early Years of Computing in {Switzerland}",
journal = j-ANN-HIST-COMPUT,
volume = "3",
number = "2",
pages = "121--132",
month = apr # "\slash " # jun,
year = "1981",
CODEN = "AHCOE5",
DOI = "https://doi.org/10.1109/MAHC.1981.10013",
ISSN = "0164-1239",
ISSN-L = "0164-1239",
bibdate = "Fri Nov 1 15:29:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/bibnet/authors/r/rutishauser-heinz.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://dlib.computer.org/an/books/an1981/pdf/a2121.pdf;
http://www.computer.org/annals/an1981/a2121abs.htm",
acknowledgement = ack-nhfb,
content = "Schwartz describes two early computers used at the
Swiss Federal Institute of Technology (whose German
acronym is ETH) during the 1950s. Despite the more
general title, he does not mention any non-ETH
computers in this article. According to Schwartz, the
first programmable computer in Switzerland was the Z4
developed by Konrad Zuse in Germany during World War II
and installed at the ETH in 1950. Except for the ERMETH
(also at the ETH), he does not mention any subsequent
Swiss installations during the period, leaving a weak
implication that there were none.\par
The Z4 was an electromechanical machine with a total
data memory of 64 32-bit words and no program memory.
Programs were executed while being read from punched
tape. Conditional test instructions permitted
instructions on the tape to be skipped; other control
instructions caused an alternate tape reader to begin
processing a program (a form of subroutine-call). The
arithmetic unit could perform true floating-point
operations. This arithmetic unit contained built-in
functions for computing squares, reciprocals, and
square roots. (Ten years later, mere integer division
was still optional at an extra cost on the IBM 1401.)
There were special representations for infinity and
``undefined'' so that operations such as division by
zero could continue without interruption but with a
meaningful result.",
CRclass = "K.2.7 ERMETH; K.2 Hardware; K.2 Software",
CRnumber = "39473",
descriptor = "Computing Milieux, HISTORY OF COMPUTING; Computing
Milieux, HISTORY OF COMPUTING, ERMETH; Computing
Milieux, HISTORY OF COMPUTING, Hardware; Computing
Milieux, HISTORY OF COMPUTING, Software",
fjournal = "Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
reviewer = "D. Ross",
subject = "K. Computing Milieux; K.2 HISTORY OF COMPUTING",
subject-dates = "Ambros Speiser (13 November 1922--10 May 2003); Heinz
Rutishauser (30 January 1918--10 November 1970); Eduard
Stiefel (21 April 1909--25 November 1978)",
}
@Article{Smith:1981:ERA,
author = "J. M. Smith and F. W. J. Olver and D. W. Lozier",
title = "Extended-Range Arithmetic and Normalized {Legendre}
Polynomials",
journal = j-TOMS,
volume = "7",
number = "1",
pages = "93--105",
month = mar,
year = "1981",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355934.355940",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D20 (65G05)",
MRnumber = "83a:65017",
bibdate = "Mon Aug 29 22:02:12 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://doi.acm.org/10.1145/355934.355940",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "angular momentum; extended-range arithmetic; Legendre
polynomials; overflow; underflow",
}
@Book{Spaniol:1981:CAL,
author = "Otto Spaniol",
title = "Computer Arithmetic: Logic and Design",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "280",
year = "1981",
ISBN = "0-471-27926-9",
ISBN-13 = "978-0-471-27926-6",
LCCN = "QA76.6 .S6613, TK7888.3.S7",
bibdate = "Thu Sep 01 22:26:58 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "English translation of \cite{Spaniol:1976:AR}.",
acknowledgement = ack-nhfb,
tableofcontents = "Notation \\
Adders \\
Multiplication \\
Division \\
Redundant notation \\
Calculation of special functions \\
Time complexity of arithmetic operations",
}
@Article{Stevenson:1981:ITP,
author = "David Stevenson",
title = "{IEEE Task 754}: a Proposed Standard for Binary
Floating-Point Arithmetic: Draft 8.0",
journal = j-COMPUTER,
volume = "14",
number = "3",
pages = "51--62",
month = mar,
year = "1981",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Thu Sep 1 10:14:17 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
annote = "Offered here for public comment, this proposed
standard facilitates transportation of numerically
oriented programs and encourages development of
high-quality numerical software.",
country = "USA",
date = "30/10/88",
descriptors = "Standardization; computer arithmetic; IEEE 754;
floating point; computation structure; numerical
software",
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@Article{Stevenson:1981:PSBa,
author = "David Stevenson",
title = "A Proposed Standard for Binary Floating-Point
Arithmetic",
journal = j-COMPUTER,
volume = "14",
number = "3",
pages = "51--62",
month = mar,
year = "1981",
CODEN = "CPTRB4",
DOI = "https://doi.org/10.1109/C-M.1981.220377",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Sun May 2 09:21:54 1999",
bibsource = "Distributed/QLD.bib; Distributed/QLD/1981.bib;
https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
acknowledgement = ack-nhfb # " and " # ack-nj,
annote = "Offered here for public comment, this proposed
standard facilitates transportation of numerically
oriented programs and encourages development of
high-quality numerical software.",
country = "USA",
date = "30/10/88",
descriptors = "Standardization; computer arithmetic; IEEE 754;
floating point; computation structure; numerical
software",
enum = "2967",
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
location = "PKI-OG: Li-Ord.Le; RWTH-AC-DFV: Bibl.",
references = "0",
revision = "21/04/91",
}
@Book{Stevenson:1981:PSBb,
author = "David Stevenson",
title = "A proposed standard for binary floating-point
arithmetic: draft 8.0 of {IEEE} Task {P754}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "36",
year = "1981",
bibdate = "Sun May 02 09:22:07 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
acknowledgement = ack-nhfb,
keywords = "Compiling (Electronic computers).; Floating-point
arithmetic.",
remark = "Reprinted from: Computer, v. 14, no. 3 (Mar. 1981):
51--87. Includes articles by W.J. Cody, David Hough,
and Jerome T. Coonen.",
}
@InProceedings{Stummel:1981:PAM,
author = "F. Stummel",
title = "Optimal error estimates for {Gaussian} elimination in
floating-point arithmetic",
crossref = "GAMM:1981:PAM",
journal = j-Z-ANGE-MATH-MECH,
volume = "62",
number = "5",
pages = "T355--T357",
year = "1981",
CODEN = "ZAMMAX",
ISSN = "0044-2267 (print), 1521-4001 (electronic)",
ISSN-L = "0044-2267",
MRclass = "65G05 (65F10)",
MRnumber = "84j:65039",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und
Mechanik}",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
}
@InProceedings{Tan:1981:ADC,
author = "C.-I. Tan and B. C. McInnis",
booktitle = "20th {IEEE} Conference on Decision and Control
including the Symposium on Adaptive Processes",
title = "Adaptive digital control implemented using residue
number systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "808--812",
year = "1981",
CODEN = "????",
DOI = "https://doi.org/10.1109/CDC.1981.269326",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The application of residue number systems for the
implementation of adaptive digital controllers is
presented. Division operations are avoided through the
use of iteration to solve for the value of the control.
Decoding computations are simplified \ldots{}",
}
@InProceedings{Taylor:1981:CHD,
author = "George S. Taylor",
title = "Compatible hardware for division and square root",
crossref = "IEEE:1981:PSC",
pages = "127--134",
year = "1981",
bibdate = "Mon Sep 16 16:30:51 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Taylor.pdf",
abstract = "Hardware for radix four division and radix two square
root is shared in a processor designed to implement the
proposed IEEE floating-point standard. The division
hardware looks ahead to find the next quotient digit in
parallel with the next partial remainder. An 8-bit ALU
estimates the next remainder's leading bits. The
quotient digit look-up table is addressed with a
truncation of the estimate rather than a truncation of
the full partial remainder. The estimation ALU and the
look-up table are asymmetric for positive and negative
remainders. This asymmetry reduces the width of the ALU
and the number of minterms in the logic equations for
the look-up table. The square root algorithm obtains
the correctly rounded result in about two division
times using small extensions to the division
hardware.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5; correct rounding; floating-point arithmetic",
}
@Article{Taylor:1981:FPR,
author = "Fred J. Taylor and Chao H. Huang",
title = "A floating-point residue arithmetic unit",
journal = j-J-FRANKLIN-INST,
volume = "311",
number = "1",
pages = "33--53",
month = jan,
year = "1981",
CODEN = "JFINAB",
ISSN = "0016-0032 (print), 1879-2693 (electronic)",
ISSN-L = "0016-0032",
MRclass = "94A11 (68A05)",
MRnumber = "82a:94013",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "B.2; G.1.0",
content = "This paper describes the logical design of a floating
point arithmetic unit using a hybrid residue number
system. Mantissas of numbers are operated in a residue
system while the exponents are in binary. Some basic
operations, such as scaling and underflow/overflow
detection, are described, and circuit implementation
using ROMs indicated. ``For example, let m(z)` be a
2N-bit work in integer form and H_0 and H_1 represent
the two following hypotheses. If m(z`) e H_1, then
m(z`) W 1-2- 2^2N = 2^2N 1. If m(z)` e H_0, then m(z)`
< 1-2- 2^2N = 2^2N 1. The hypothesis testing is
accomplished by comparing each of the mixed-radix
digits of m(z)` to that of 2^2N 1 through L independent
binary comparators.'' Circuits for multiplication,
addition, and subtraction are derived. The procedures
seem reasonable and the proofs rigorous. Table look up
cycle times and memory requirements for different
implementation of the arithmetic units are estimated.
These are comparable with corresponding times and
memory needs for PDP/11. Use in algorithms such as FFT
is argued for.\par
The exposition is somewhat difficult. As with many
logical designs one is not sure whether the approach
given is optimum (for any sense of the word
``optimum''). In the absence of a working system one
can not be sure",
CRclass = "B.2.1 Design Styles; G.1.0 General; G.1.0 Computer
arithmetic",
CRnumber = "39211",
descriptor = "Hardware, ARITHMETIC AND LOGIC STRUCTURES, Design
Styles; Mathematics of Computing, NUMERICAL ANALYSIS,
General, Computer arithmetic",
fjournal = "Journal of {The Franklin Institute}",
genterm = "DESIGN",
journal-URL = "http://www.sciencedirect.com/science/journal/00160032",
reviewer = "B. Hazeltine; Hazeltine, B",
subject = "B. Hardware; B.2 ARITHMETIC AND LOGIC STRUCTURES; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@InProceedings{Taylor:1981:VHP,
author = "George S. Taylor and David A. Patterson",
title = "{VAX} Hardware for the Proposed {IEEE} Floating-Point
Standard",
crossref = "IEEE:1981:PSC",
pages = "190--196",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Taylor_Patterson.pdf",
abstract = "The proposed IEEE floating-point standard has been
implemented in a substitute floating-point accelerator
for the VAX-11/760. We explain how features of the
proposed standard influenced the design of the new
processor. By comparing it with the original VAX
accelerator, we illustrate the differences between
hardware for the proposed standard and hardware for a
more traditional floating-point architecture.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Todericiu:1981:AOBb,
author = "Doru Todericiu",
title = "Analyses d'ouvrages: {{\booktitle{Whilhelm Schickard
(1592--1635), Astronom, Geograph, Orientalist, Erfinder
der Rechenmaschine}} par Friedrich Seck}",
journal = j-REV-HIST-SCI,
volume = "34",
number = "3--4",
pages = "374--374",
month = "juillet--octobre",
year = "1981",
CODEN = "RHSAAM",
DOI = "https://doi.org/10.2307/23632469",
ISSN = "0151-4105 (print), 1969-6582 (electronic)",
ISSN-L = "0048-7996",
bibdate = "Tue Jun 16 11:06:47 MDT 2015",
bibsource = "http://www.jstor.org/stable/i23631674;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/revhistsci.bib",
URL = "http://www.jstor.org/stable/23632469",
acknowledgement = ack-nhfb,
ajournal = "Rev. hist. sci.",
fjournal = "Revue d'Histoire des Sciences",
journal-URL = "http://www.jstor.org/journals/00487996.html;
http://www.persee.fr/collection/rhs",
language = "French",
}
@Book{Tyner:1981:GDP,
author = "Paul Tyner",
title = "{iAPX} 432 General Data Processor Architecture
Reference Manual",
publisher = pub-INTEL,
address = pub-INTEL:adr,
pages = "various",
year = "1981",
LCCN = "TK7895.M5 T85 1981",
bibdate = "Fri Dec 08 13:03:20 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
xxISBN = "(none)",
}
@Manual{vonGudenberg:1981:GAP,
author = "J. Wolff von Gudenberg",
title = "{Gesamte Arithmetik des Pascal-SC Rechners.
Benutzerhandbuch}. ({German}) [{Complete} Arithmetic of
the {Pascal-SC} Computer: User Handbook]",
organization = "Institute for Applied Mathematics, University of
Karlsruhe",
address = "Karlsruhe, West Germany",
pages = "????",
year = "1981",
bibdate = "Wed Oct 13 22:27:27 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@InProceedings{Walker:1981:EMA,
author = "Gregory Walker",
title = "Extension of the {MC68000} Architecture to Include
Standard Floating-Point Arithmetic",
crossref = "IEEE:1981:PSC",
pages = "179--182",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Walker.pdf",
abstract = "The synthetic aspect of designing a computer
architecture is particularly evident when the design is
highly constrained from two independent directions.
Floating-point extensions of the MC68000 architecture
incorporate the IEEE Proposed Floating-point Standard
into the existing MC68000 architecture.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Washington:1981:BLF,
author = "Lawrence C. Washington",
title = "{Benford's Law} for {Fibonacci} and {Lucas} Numbers",
journal = j-FIB-QUART,
volume = "19",
number = "2",
pages = "175--176",
month = apr,
year = "1981",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:59:55 MDT 2011",
bibsource = "http://www.fq.math.ca/19-2.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/19-2/washington.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@TechReport{Watanuki:1981:FOAa,
author = "Osaaki Watanuki",
title = "Floating-point on-line arithmetic for highly
concurrent digit-serial computation: application to
mesh problems",
institution = "Computer Science Dept. Research Laboratory",
address = "Los Angeles, CA, USA",
pages = "xvi + 149",
year = "1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "UCLA-ENG; 8107 ReRport [sic] / UCLA Computer Science
Department; no. CSD 810529 Report (University of
California, Los Angeles. Computer Science Dept.); no.
CSD-810529",
acknowledgement = ack-nhfb,
keywords = "Differential equations, Partial.; Floating-point
arithmetic.",
remark = "Consists of the author's thesis ({Ph.D.})--UCLA, 1981.
Bibliography: p. 146-149.",
}
@PhdThesis{Watanuki:1981:FOAb,
author = "Osaaki Watanuki",
title = "Floating-point on-line arithmetic for highly
concurrent digit-serial computation: application to
mesh problems",
type = "Thesis ({Ph.D.})",
school = "UCLA",
address = "Los Angeles, CA, USA",
pages = "xvi + 149",
year = "1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Differential equations, Partial.; Floating-point
arithmetic.",
}
@InProceedings{Watanuki:1981:FPLa,
author = "O. Watanuki and M. D. Ercegovac",
title = "Floating-point On-Line Arithmetic: Algorithms",
crossref = "IEEE:1981:PSC",
pages = "81--86",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Watanuki_Ercegovac_a.pdf",
abstract = "For effective application of on-line arithmetic to
practical numerical problems, floating-point algorithms
for on-line addition\slash subtraction and
multiplication have been implemented by introducing the
notion of quasi-normalization. Those proposed are
normalized fixed-precision FLPOL (floating-point
on-line) algorithms.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Watanuki:1981:FPLb,
author = "O. Watanuki and M. D. Ercegovac",
title = "Floating-point On-Line Arithmetic: Error Analysis",
crossref = "IEEE:1981:PSC",
pages = "87--91",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Watanuki_Ercegovac_b.pdf",
abstract = "The properties of redundant number system in mantissa
representation are studied and the range of the
redundant mantissa is derived. From the range of the
mantissa and the absolute error of on-line operations,
the MRRE (maximum relative representation error) is
defined and analyzed for redundant floating-point
numbers.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Wehringer:1981:FSA,
author = "A. Wehringer",
title = "{Flie{\ss}komma-Arithmetik} \toenglish {Floating-point
Arithmetic} \endtoenglish",
journal = "Elektronikschau",
volume = "5",
pages = "34--36",
year = "1981",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Wehringer:1981:SBM,
author = "A. Wehringer",
title = "{Schnelle 16-bit-Multiplikation und Division}
\toenglish {Fast 16-bit Multiplication and Division}
\endtoenglish",
journal = "Elektronikschau",
volume = "10",
pages = "36--37",
year = "1981",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Manual{Weinreb:1981:LMM,
author = "Daniel Weinreb and David Moon",
title = "{LISP} Machine Manual",
organization = "MIT Artificial Intelligence Laboratory",
address = "Cambridge, MA, USA",
edition = "Third",
month = mar,
year = "1981",
bibdate = "Wed Jan 29 17:08:51 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "From \cite{Steele:2004:RHP}: ``The number of digits
printed is the `correct' number; no information present
in the flonum is lost, and no extra trailing digits are
printed that do not represent information in the
flonum. Feeding the [printed representation] of a
flonum back to the reader is always supposed to produce
an equal flonum.''",
}
@InProceedings{Willoner:1981:AME,
author = "Robert Willoner and I-Ngo Chen",
title = "An Algorithm for Modular Exponentiation",
crossref = "IEEE:1981:PSC",
pages = "135--138",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Willoner_Chen.pdf",
abstract = "The best known algorithm for {\em modular
exponentiation}, $ M^e \bmod t $ for arbitrary $M$,
$e$, and $t$ is of $ O(n^3) $ where $n$ is the number
ot bits in the largest of $M$, $e$ and $t$. This paper
presents an $ O(n) $ algorithm for the problem where $
M^e \bmod t $ is required for many values of $M$ and
$e$ with constant $t$. Some preprocessing is done on
$t$, and the results are applied repeatedly to
different values of $M$ and $e$. The main algorithm
involves {\em on-line} arithmetic in a {\em redundant}
number system. An immediate application is in
encoding\slash decoding of messages in an RSA-based
{\em public-key cryptosystem}.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Zurawski:1981:DHS,
author = "J. H. P. Zurawski and J. B. Gosling",
title = "Design of High-Speed Digital Divider Units",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-30",
number = "9",
pages = "691--699",
month = sep,
year = "1981",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1981.1675869",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 18:45:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675869",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InCollection{Aiken:1982:ASC,
author = "Howard H. Aiken and Grace M. Hopper",
title = "The Automatic Sequence Controlled Calculator (1946)",
crossref = "Randell:1982:ODC",
pages = "203--222",
year = "1982",
bibdate = "Sun Nov 03 08:36:11 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Andrews:1982:MMS,
author = "M. Andrews",
title = "Mathematical Microprocessor Software: a $ \sqrt (x) $
Comparison",
journal = j-IEEE-MICRO,
volume = "2",
number = "3",
pages = "63--79",
month = jul # "\slash " # sep,
year = "1982",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1982.290970",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Article{Andrews:1982:SRX,
author = "M. Andrews",
title = "Square-Root-{X} Comparison --- New Results Discovered
--- Reply",
journal = j-IEEE-MICRO,
volume = "2",
number = "4",
pages = "5--6",
month = oct # "\slash " # dec,
year = "1982",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1982.291010",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Dec 14 06:08:58 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Science Citation Index database (1980--2000)",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Article{Anonymous:1982:ARBf,
author = "Anonymous",
title = "Article Review: {{\booktitle{Ada model arithmetic:
costs and benefits}}: Wallis, P. J. L. \booktitle{IEE
Proc.-E Comput. Dig. Tech.} Vol 129 No 2 (March 1982)
pp 75--80}",
journal = j-MICROPROC-MICROSYS,
volume = "6",
number = "9",
pages = "497--498",
month = nov,
year = "1982",
CODEN = "MIMID5",
DOI = "https://doi.org/10.1016/0141-9331(82)90515-4",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Mon Jan 14 21:50:13 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0141933182905154",
acknowledgement = ack-nhfb,
fjournal = "Microprocessors and Microsystems",
}
@TechReport{Anonymous:1982:MKF,
author = "Anonymous",
title = "{Materialiensammlung zum 5. Kolloquium (mit Floating
Point Systems) Neue Rechnerarchitekturen:
Anwendungsgebiete und Realisierungen: Hannover, (18.Mai
1982)}",
type = "{Bericht}",
number = "30",
institution = "Regionales Rechenzentrum f{\"u}r Niedersachsen bei der
Universit{\"a}t Hannover",
address = "Hannover, Germany",
pages = "58",
year = "1982",
bibdate = "Thu May 09 09:13:36 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Anonymous:1982:NPAa,
author = "Anonymous",
title = "New product applications: Array processor performs 5
million floating-point operations per second, has
200-ns operation time",
journal = j-IEEE-SPECTRUM,
volume = "19",
number = "1",
pages = "104--118",
month = jan,
year = "1982",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1982.6366777",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Sat Jan 18 16:51:45 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "Algorithms; Arrays; Microcomputers; Microprocessors;
Process control; Speech; Standards",
}
@MastersThesis{Arnold:1982:EPS,
author = "Mark Gordon Arnold",
title = "Extending the Precision of the Sign Logarithm Number
System",
type = "{M.S.} Thesis",
school = "University of Wyoming",
address = "Laramie, WY, USA",
year = "1982",
bibdate = "Fri Jun 24 16:06:13 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Bairstow:1982:FPP,
author = "R. Bairstow and J. Barlow and M. Jires and M. Waters",
title = "A floating point processor for {Intel 8080A}
microprocessor systems",
type = "Technical report",
number = "RL 82-020",
institution = "Rutherford Appleton Lab.",
address = "Harwell, Oxon, UK",
pages = "44",
month = mar,
year = "1982",
bibdate = "Fri May 25 05:47:40 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0050018",
acknowledgement = ack-nhfb,
}
@InProceedings{Baraniecki:1982:QEL,
author = "A. Baraniecki and G. Jullien",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '82}",
title = "Quantization error and limit cycles analysis in
residue number system coded recursive filters",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "52--55",
year = "1982",
CODEN = "????",
DOI = "https://doi.org/10.1049/el:19820632",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The paper discusses the Residue Number System (RNS)
implementation of second order recursive digital filter
sections. The RNS offers the advantage of using integer
based arithmetic operations and a simple hardware
realization involving arrays of \ldots{}",
}
@Article{Barnes:1982:RNI,
author = "C. Barnes and T. Miyawaki",
title = "Roundoff Noise Invariants in Normal Digital Filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "29",
number = "4",
pages = "251--256",
month = apr,
year = "1982",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "The unit noise gains for optimal and parallel normal
realizations of digital filters can be expressed in
terms of a set of noise gain parameters that are simply
related to the pole locations and pole residues. These
noise gain parameters are shown \ldots{}",
}
@Article{Bernhard:1982:CCS,
author = "R. Bernhard",
title = "Computers: Computing at the speed limit: Computers
1000 times faster than today's supercomputers would
benefit vital scientific applications",
journal = j-IEEE-SPECTRUM,
volume = "19",
number = "7",
pages = "26--31",
month = jul,
year = "1982",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1982.6366940",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Sat Jan 18 16:51:45 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib;
https://www.math.utah.edu/pub/tex/bib/super.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "Computational modeling; Computer architecture;
computer industry; Computers; Educational institutions;
engineering applications; floating-point operations per
second; flops; Program processors; scientific
applications; Solid modeling; special purpose
computers; very large-scale integration; VLSI",
}
@Article{Bernhard:1982:GSP,
author = "R. Bernhard",
title = "Giants in small packages [array processors]",
journal = j-IEEE-SPECTRUM,
volume = "19",
number = "2",
pages = "39--44",
month = feb,
year = "1982",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1982.6366796",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Sat Jan 18 16:51:45 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "architecture; array processor; Arrays; arrays of
numbers; computer; computer architecture; digital
arithmetic; digital computers; Hardware; matrices;
Microcomputers; Pipelines; Program processors;
repetitive arithmetic operations; Vectors; vectors",
}
@Article{Bohannan:1982:MAP,
author = "J. W. Bohannan and D. J. Bradley and D. A. Kummer and
J. A. Saenz",
title = "Multiplication Algorithm for Packed {BCD} Numbers",
journal = j-IBM-TDB,
volume = "25",
number = "4",
pages = "2225",
month = sep,
year = "1982",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Article{Bohlender:1982:ROA,
author = "G. Bohlender and K. Gr{\"u}ner and J. Wolff {von
Gudenberg}",
title = "{Realisierung einer optimalen Arithmetik} \toenglish
{Realization of Optimal Arithmetic} \endtoenglish",
journal = j-ELEK-RECHENANLAGEN,
volume = "24",
number = "2",
pages = "68--72",
month = apr,
year = "1982",
CODEN = "ELRAA4",
ISSN = "0013-5720",
bibdate = "Sat Feb 10 12:41:07 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronische Rechenanlagen",
}
@Article{Brent:1982:RLP,
author = "R. P. Brent and H. T. Kung",
title = "A regular layout for parallel adders",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-31",
number = "??",
pages = "260--264",
year = "1982",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1982.1675982",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Sep 16 16:06:24 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Brooks:1982:OCL,
author = "R. A. Brooks and R. P. Gabriel and G. L. {Steele
Jr.}",
title = "An optimizing compiler for lexically scoped {LISP}",
journal = j-SIGPLAN,
volume = "17",
number = "6",
pages = "261--275",
month = jun,
year = "1982",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sat Apr 25 11:46:37 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C6140D (High level languages); C6150C (Compilers,
interpreters and other processors)",
conflocation = "Boston, MA, USA; 23--25 June 1982",
conftitle = "Proceedings of the SIGPLAN '82 Symposium on Compiler
Construction",
corpsource = "MIT, Cambridge, MA, USA",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "BLISS-11; complex numbers; floating-point; FORTRAN;
lexically scoped LISP; LISP; list manipulation;
multiprocessing supercomputer; optimizing compiler;
PASCAL; PQCC compiler; program compilers; S-1 PASCAL;
stable-driven; symbolic processing; TNBIND technique;
vectors",
sponsororg = "ACM",
treatment = "P Practical",
}
@Article{Burr:1982:CCR,
author = "S. A. Burr",
title = "Computing cube roots when a fast square root is
available",
journal = j-COMPUT-MATH-APPL,
volume = "8",
number = "3",
pages = "181--183",
month = "????",
year = "1982",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(82)90041-4",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 18:51:22 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122182900414",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221/",
}
@Article{Cassola:1982:FPA,
author = "R. L. Cassola",
title = "Floating Point Algorithm Design",
journal = j-COMP-DESIGN,
volume = "21",
number = "6",
pages = "107--114",
month = jun,
year = "1982",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Design",
}
@Article{Cassola:1982:FPM,
author = "R. L. Cassola",
title = "A Floating Point Module for Military Computers",
journal = j-COMP-DESIGN,
volume = "21",
number = "2",
pages = "67--76",
month = feb,
year = "1982",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Design",
}
@MastersThesis{Cavanagh:1982:DCA,
author = "Joseph J. F. Cavanagh",
title = "Digital computer arithmetic: design and
implementation",
type = "Thesis ({M.S.})",
school = "University of Santa Clara",
address = "Santa Clara, CA, USA",
pages = "vii + 503",
year = "1982",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units.; Floating-point
arithmetic.",
}
@InProceedings{Cody:1982:BCC,
author = "W. J. Cody",
title = "Basic concepts for computational software",
crossref = "Messina:1982:PMM",
pages = "1--23",
year = "1982",
DOI = "https://doi.org/10.1007/3-540-11603-6_1",
bibdate = "Fri Sep 23 23:12:32 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Cody:1982:FPM,
author = "W. J. Cody",
title = "Floating-point parameters, models, and standards",
crossref = "Reid:1982:RBN",
pages = "51--69",
year = "1982",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.0; D.3.0",
CRclass = "G.1.0 General; G.1.0 Computer arithmetic; D.3.0
General; D.3.0 Standards",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic; Software, PROGRAMMING LANGUAGES,
General, Standards",
genterm = "THEORY; STANDARDIZATION",
guideno = "10367",
keywords = "languages; standardization",
review = "ACM CR 8402-0092",
reviewer = "Hansen, E",
subject = "D.3.0 Software, PROGRAMMING LANGUAGES, General,
Standards \\ G.1.0 Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic; G. Mathematics
of Computing; G.1 NUMERICAL ANALYSIS; D. Software; D.3
PROGRAMMING LANGUAGES",
}
@TechReport{Cody:1982:GPI,
author = "W. J. Cody",
title = "A Generalization of the Proposed {IEEE} Standard for
Floating-Point Arithmetic",
type = "Technical Report",
number = "??",
institution = inst-ANL,
address = inst-ANL:adr,
pages = "20",
year = "1982",
bibdate = "Thu Nov 17 10:40:11 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Republished in \cite{Cody:1983:GPI}.",
acknowledgement = ack-nhfb,
}
@InProceedings{Cody:1982:ITF,
author = "W. J. Cody",
title = "Implementation and Testing of Function Software",
crossref = "Messina:1982:PMM",
pages = "24--47",
year = "1982",
DOI = "https://doi.org/10.1007/3-540-11603-6_1",
bibdate = "Sat Sep 24 01:18:12 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "range reduction",
}
@Article{Corbett:1982:EAF,
author = "R. P. Corbett",
title = "Enhanced arithmetic for {Fortran}",
journal = j-SIGPLAN,
volume = "17",
number = "12",
pages = "41--48",
month = dec,
year = "1982",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sat Apr 25 11:46:37 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C6140D (High level languages)",
corpsource = "Department of Computer Sci., University of California,
Berkeley, CA, USA",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "accuracy; arithmetic; digital arithmetic; efficiency;
FORTRAN; Fortran; programmers; speed; widest need
evaluation",
treatment = "P Practical",
}
@InProceedings{Dao:1982:KCA,
author = "T. T. Dao",
editor = "{IEEE}",
booktitle = "Proceedings of the 12th International Symposium on
Multiple-Valued Logic, May 1982",
title = "{Knuth}'s Complex Arithmetic with Quaternary
Hardware",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "94--98",
month = may,
year = "1982",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Aug 22 09:14:13 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Dekker:1982:PCM,
author = "T. J. Dekker",
editor = "Paul C. Messina and Almerico Murli",
booktitle = "Problems and Methodologies in Mathematical Software
Production",
title = "Program Correctness and Machine Arithmetic",
volume = "142",
publisher = pub-SV,
address = pub-SV:adr,
pages = "48--80",
year = "1982",
bibdate = "Sat May 1 15:24:45 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
}
@Book{DeSautels:1982:ALP,
author = "Edouard J. DeSautels",
title = "Assembly language programming for {PDP-11} and
{LSI-11} computers: an introduction to computer
organization",
publisher = "William C. Brown Co. Publ.",
address = "Dubuque, IA",
pages = "xviii + 574",
year = "1982",
ISBN = "0-697-08164-8",
ISBN-13 = "978-0-697-08164-3",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$21.95",
acknowledgement = ack-nhfb,
catcode = "A; C.1.1; D.3; D.3.2; D.3.2",
content = "The author has provided material on the Assembler
language for the PDP-11 or LSI-11 computers in an
original and comprehensive manner. Users of this
Assembler or even of this computer should find this
text especially valuable as a student text or as a
permanent reference. Much of the material in the
PDP-11, MACRO-11 Reference Manual, Processor Handbook,
Peripheral Handbook, and Terminals and Communications
Handbook is organized in this book in a readable,
step-by-step manner. Required is access to a PDP-11 (or
LSI-11) and some knowledge of programming in a
high-level language.\par
Topics include the following: \par
* Very accessible and detailed material on introduction
to computers and programming. It is unlikely that a
reader would require much if any prior knowledge of
computers.\par
* An early introduction to machine language to explain
the functioning of a computer, and then a lead-in into
Assembler language.\par
* Development of the use of registers, Assembler
Directives, indexing, immediate operands, arithmetic
for signed and unsigned data, subroutines, stacks,
passing parameters, input/output, floating-point
arithmetic, and more.\par
* An interesting chapter, ``Selected Topics,'' covering
such subjects as tables, lists, queues, trees, threaded
code, and reentrant co",
CRclass = "C.1.1 Single Data Stream Architectures; C.1.1 PDP-11;
D.3.2 Language Classifications; D.3.2 Language
Classifications; D.3.2 Macro and assembly languages;
D.3.2 Language Classifications; D.3.2 PDP-11 assembly
language",
CRnumber = "40452",
descriptor = "General Literature, INTRODUCTORY AND SURVEY; Computer
Systems Organization, PROCESSOR ARCHITECTURES, Single
Data Stream Architectures, PDP-11; Software,
PROGRAMMING LANGUAGES, Language Classifications;
Software, PROGRAMMING LANGUAGES, Language
Classifications, Macro and assembly languages;
Software, PROGRAMMING LANGUAGES, Language
Classifications, PDP-11 assembly language",
genterm = "LANGUAGES",
pubname = "William C. Brown Co. Publ., Dubuque, IA",
reviewer = "P. Abel; Abel, P",
subject = "A. General Literature; A.1 INTRODUCTORY AND SURVEY; C.
Computer Systems Organization; C.1 PROCESSOR
ARCHITECTURES; D. Software; D.3 PROGRAMMING LANGUAGES;
D. Software; D.3 PROGRAMMING LANGUAGES; D. Software;
D.3 PROGRAMMING LANGUAGES",
}
@InCollection{Dreyer:1982:ACI,
author = "H.-J. Dreyer and A. Walther",
title = "The Automatic Calculator {IPM} (1946)",
crossref = "Randell:1982:ODC",
pages = "155--161",
year = "1982",
bibdate = "Sun Nov 03 08:36:11 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Epstein:1982:UAF,
author = "C. Epstein and W. L. Miranker and T. J. Rivlin",
title = "Ultra-arithmetic {I}: function data types",
journal = j-MATH-COMP-SIM,
volume = "24",
number = "1",
pages = "1--18",
month = feb,
year = "1982",
CODEN = "MCSIDR",
ISSN = "0378-4754 (print), 1872-7166 (electronic)",
ISSN-L = "0378-4754",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "G.1; G.1.2; G.1.2",
CRclass = "G.1.5 Roots of Nonlinear Equations; G.1.2
Approximation; G.1.2 Chebyshev approximation and
theory; G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
Nonlinear Equations; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Chebyshev
approximation and theory; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation",
fjournal = "Mathematics and Computers in Simulation",
genterm = "algorithms",
guideno = "09324",
journal-URL = "http://www.sciencedirect.com/science/journal/03784754",
jrldate = "Feb. 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Epstein:1982:UAI,
author = "C. Epstein and W. L. Miranker and T. J. Rivlin",
title = "Ultra-arithmetic {II}: intervals of polynomials",
journal = j-MATH-COMP-SIM,
volume = "24",
number = "1",
pages = "19--29",
month = feb,
year = "1982",
CODEN = "MCSIDR",
ISSN = "0378-4754 (print), 1872-7166 (electronic)",
ISSN-L = "0378-4754",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2; G.1.1; G.1.0",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.1 Interpolation; G.1.1 Spline and
piecewise polynomial interpolation; G.1.0 General;
G.1.0 Error analysis",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Interpolation, Spline and piecewise polynomial
interpolation; Mathematics of Computing, NUMERICAL
ANALYSIS, General, Error analysis",
fjournal = "Mathematics and Computers in Simulation",
genterm = "algorithms",
guideno = "09325",
journal-URL = "http://www.sciencedirect.com/science/journal/03784754",
jrldate = "Feb. 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Fateman:1982:HLL,
author = "Richard J. Fateman",
title = "High-Level Language Implications of the Proposed
{IEEE} Floating-Point Standard",
journal = j-TOPLAS,
volume = "4",
number = "2",
pages = "239--257",
month = apr,
year = "1982",
CODEN = "ATPSDT",
DOI = "https://doi.org/10.1145/357162.357168",
ISSN = "0164-0925 (print), 1558-4593 (electronic)",
ISSN-L = "0164-0925",
bibdate = "Thu Nov 8 14:50:28 2007",
bibsource = "Compiler/bevan.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An IEEE Computer Society working group on
floating-point arithmetic has recommended a standard
for binary floating-point number formats, operations,
and semantics. This paper, which has evolved in part
during the deliberations of that committee, describes
the significance to languages and, in particular, to
FORTRAN and its variants, of various novel features of
the recommended standard.",
acknowledgement = ack-pb,
checked = "19940302",
fjournal = "ACM Transactions on Programming Languages and
Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J783",
keywords = "computer arithmetic; control structures; data types
and structures; error handling and recovery;
floating-point arithmetic; FORTRAN; run-time
environments",
source = "Dept. Library",
}
@TechReport{Feldstein:1982:EPI,
author = "A. Feldstein and R. Goodman",
title = "The evaluation of probability integrals for the loss
of significance in floating point subtraction and
addition",
type = "Technical report",
institution = "Department of Mathematics, Arizona State University",
address = "Tempe, AZ, USA",
year = "1982",
bibdate = "Tue Oct 09 09:50:41 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Feldstein:1982:LSF,
author = "A. Feldstein and R. Goodman",
title = "Loss of Significance in Floating Point Subtraction and
Addition",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-31",
number = "4",
pages = "328--335",
month = apr,
year = "1982",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1982.1676002",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We study the loss of significant $ \beta $ its (base $
\beta $ digits) in floating point addition or
subtraction. To do this, we calculate the conditional
probability of a post-arithmetic normalization shift of
$m$ $ \beta $ its, given an exponent difference of $k$
$ \beta $ its. The study is done for various bases $
\beta $, under two different assumptions---that the
operands are selected at random from the logarithmic
distribution or from the uniform distribution.",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Fulton:1982:BJB,
author = "T. A. Fulton and L. N. Dunkleberger",
title = "{B.S.T.J.} Briefs: a {Josephson} Parallel Multiplier",
journal = j-BELL-SYST-TECH-J,
volume = "61",
number = "5",
pages = "931--933",
month = may # "--" # jun,
year = "1982",
CODEN = "BSTJAN",
ISSN = "0005-8580",
bibdate = "Tue Nov 9 11:15:56 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1982/BSTJ.1982.6105.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol61/bstj61-5-931.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Gerrity:1982:CRR,
author = "G. W. Gerrity",
title = "Computer Representation of Real Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-31",
number = "8",
pages = "709--714",
month = aug,
year = "1982",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1982.1676076",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:33:14 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676076",
abstract = "Hwang's model for the computer representation of real
numbers is extended to explicitly distinguish between
the representational system used to denote real numbers
and the internal encoding of the digits of the
representation in the computer memory. The encoding
function can then be chosen to preserve certain
properties of the real number system and to optimize
the computer arithmetic in a sense to be described
herein. Two examples of optimal computer arithmetics
are discussed.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Goodrich:1982:VEP,
author = "J. L. Goodrich",
title = "Very efficient 8080 program multiplies and divides",
journal = j-ELECTRONICS,
volume = "55",
number = "4",
pages = "144--145",
month = feb,
year = "1982",
ISSN = "0883-4989",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronics",
journal-URL = "https://www.mdpi.com/journal/electronics",
}
@InProceedings{Gordon:1982:BFS,
author = "E. Gordon and C. Hastings",
booktitle = "Conference Record, {SOUTHCON, 1982}",
title = "Big, Fast and Simple Algorithms, Architecture and
Components for High-end Minis",
publisher = "????",
address = "????",
pages = "????",
year = "1982",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri Nov 09 18:54:03 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Paper 21/3.",
acknowledgement = ack-nhfb,
}
@Article{Hantler:1982:ESS,
author = "S. L. Hantler and A. H. Karp",
title = "Exponential by Sequential Squaring",
journal = j-IBM-TDB,
volume = "25",
number = "1",
pages = "171--173",
month = jun,
year = "1982",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@InProceedings{Hull:1982:PCE,
author = "T. E. Hull",
title = "Precision Control, Exception Handling and a Choice of
Numerical Algorithms",
crossref = "Watson:1982:NAP",
pages = "169--178",
year = "1982",
DOI = "https://doi.org/10.1007/BFb0093156",
bibdate = "Sat Feb 8 10:29:52 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "Proposes precision control as later provided in
Numerical Turing.",
}
@InProceedings{Hull:1982:UCP,
author = "T. E. Hull",
title = "The uses of controlled precision",
crossref = "Reid:1982:RBN",
pages = "71--82",
year = "1982",
bibdate = "Fri Jan 04 12:57:37 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
xxpages = "71--84",
}
@Article{Hwang:1982:PMA,
author = "Kai Hwang and Yeng-Heng Cheng",
title = "Partitioned Matrix Algorithms for {VLSI} Arithmetic
Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-31",
number = "12",
pages = "1215--1224",
month = dec,
year = "1982",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1982.1675945",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:33:17 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675945",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Jenkins:1982:FRD,
author = "W. Jenkins",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '82}",
title = "Failure resistant digital filters based on residue
number system product codes",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "60--63",
year = "1982",
CODEN = "????",
DOI = "https://doi.org/10.1049/el:19820632",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Residue number system product codes are proposed for
the design of self-checking digital filters. It is
shown that product codes require redundancy that is
similar to, but slightly less than that of systematic
codes for simultaneous overflow \ldots{}",
}
@Article{Jenkins:1982:RNS,
author = "W. K. Jenkins",
title = "Residue number system error checking using expanded
projection",
journal = j-ELECT-LETTERS,
volume = "18",
number = "21",
pages = "927--928",
day = "14",
month = oct,
year = "1982",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:19820632",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4246948",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "residue arithmetic; residue number system",
summary = "A new concept called expanded projection is presented
that simplifies the process of error detection and
location in redundant residue number codes. Expanded
projection simplifies the circuit complexity of the
error checker, resulting in a structure \ldots{}",
}
@InProceedings{Kahan:1982:NOS,
author = "W. Kahan and Jerome T. Coonen",
title = "The Near Orthogonality of Syntax, Semantics, and
Diagnostics in Numerical Programming Environments",
crossref = "Reid:1982:RBN",
pages = "103--115",
year = "1982",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "D.3; G.1.0; F.3.2; D.2.5; D.2; D.3",
content = "Programmers of early computers had to content
themselves with what the machine designers offered and
be glad that the hardware worked at all. Later, with
the introduction of higher-level languages, the
computing environment was modified by the language
designers who attempted to resolve a three-cornered
tug-of-war among implementation efficiency, program
portability, and usefulness to the programmer. The
conflict between the first two resulted in languages
that reflected the least common denominator of
available hardware, since language designers were
disinclined to mention any capability not available on
all computers. A case in point is floating-point
arithmetic, where the subtleties of overflow,
underflow, and rounding are generally well beyond the
control of the programmer in a high-level language. The
new standard for binary floating-point arithmetic that
has been proposed by IEEE Computer Society's
Floating-Point Committee, Task P754 [1], makes an
attempt to escape from this situation. It represents
the Committee's view of the floating-point requirements
of the \ldots{}",
CRclass = "D.3.1 Formal Definitions and Theory; G.1.0 General;
G.1.0 Computer arithmetic; F.3.2 Semantics of
Programming Languages; F.3.2 Algebraic approaches to
semantics; D.2.5 Testing and Debugging; D.2.5
Diagnostics; D.2.6 Programming Environments; D.3.3
Language Constructs",
CRnumber = "8401-0021",
descriptor = "Software, PROGRAMMING LANGUAGES, Formal Definitions
and Theory; Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic; Theory of
Computation, LOGICS AND MEANINGS OF PROGRAMS, Semantics
of Programming Languages, Algebraic approaches to
semantics; Software, SOFTWARE ENGINEERING, Testing and
Debugging, Diagnostics; Software, SOFTWARE ENGINEERING,
Programming Environments; Software, PROGRAMMING
LANGUAGES, Language Constructs",
genterm = "LANGUAGES; STANDARDIZATION",
keywords = "floating-point arithmetic; rounding errors",
remark = "This article forms the body of \cite[Chapter
3]{Coonen:1984:CPS}.",
reviewer = "M. Marcotty; Marcotty, M",
source = "in the relationship between numerical computation and
programming languages. Proc. IFIP TC2 working
conference (Boulder, CO, Aug. 3--7, 1981) J. K. Reid
(Ed.) Elsevier North-Holland, Inc., New York, 1982",
subject = "D. Software; D.3 PROGRAMMING LANGUAGES; G. Mathematics
of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of
Computation; F.3 LOGICS AND MEANINGS OF PROGRAMS; D.
Software; D.2 SOFTWARE ENGINEERING; D. Software; D.2
SOFTWARE ENGINEERING; D. Software; D.3 PROGRAMMING
LANGUAGES",
}
@Book{Katzan:1982:IAA,
author = "Harry Katzan",
title = "Invitation to {Ada} and {Ada} reference manual ({July
1980})",
publisher = "PBI",
address = "New York, NY, USA",
pages = "xi + 429",
year = "1982",
ISBN = "0-89433-132-9",
ISBN-13 = "978-0-89433-132-9",
LCCN = "QA76.73.A35 K37 1982",
bibdate = "Wed Oct 13 06:37:40 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "See \cite[p. 1.10]{Coonen:1984:CPS} for negative
comments about the floating-point model for Ada in this
book.",
subject = "Ada (computer program language)",
}
@InProceedings{Kerkhoff:1982:LDM,
author = "H. G. Kerkhoff and H. A. J. Robroek",
editor = "{IEEE}",
booktitle = "Proceedings of the 12th International Symposium on
Multiple-Valued Logic, May 1982",
title = "The Logic Design of Multiple-valued Logic Functions
Using {CCD}'s",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "35--44",
year = "1982",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Aug 22 09:16:45 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Korn:1982:EDF,
author = "G. A. Korn",
title = "{EARLY DESIRE}: a floating-point equation language
simulation system for minicomputers and
microcomputers",
journal = j-SIMULATION,
volume = "38",
number = "5",
pages = "151--159",
month = may,
year = "1982",
CODEN = "SIMUA2",
ISSN = "0037-5497 (print), 1741-3133 (electronic)",
ISSN-L = "0037-5497",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "I.6; G; D.4.7",
CRclass = "I.6.2 Simulation Languages; D.4.7 Organization and
Design; D.4.7 Interactive systems",
descriptor = "Computing Methodologies, SIMULATION AND MODELING,
Simulation Languages; Mathematics of Computing,
MISCELLANEOUS; Software, OPERATING SYSTEMS,
Organization and Design, Interactive systems",
fjournal = "Simulation",
genterm = "DESIGN; LANGUAGES",
guideno = "08785",
journal-URL = "http://sim.sagepub.com/content/by/year",
subject = "I. Computing Methodologies; I.6 SIMULATION AND
MODELING; G. Mathematics of Computing; G.m
MISCELLANEOUS; D. Software; D.4 OPERATING SYSTEMS",
}
@Article{Leuprecht:1982:PAR,
author = "H. Leuprecht and W. Oberaigner",
title = "Parallel Algorithms for the Rounding-Exact Summation
of Floating-Point Numbers",
journal = j-COMPUTING,
volume = "28",
number = "2",
pages = "89--104",
month = "????",
year = "1982",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "68A05 (65G05)",
MRnumber = "83c:68009",
bibdate = "Fri Dec 08 11:53:42 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
keywords = "accurate floating-point summation",
}
@Article{McCormick:1982:EFM,
author = "S. F. McCormick and G. D. Taylor and D. V. Pryor",
title = "Evaluation of Functions on Microcomputers: $ \ln (x)
$",
journal = j-COMPUT-MATH-APPL,
volume = "8",
number = "5",
pages = "389--392",
year = "1982",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Thu Sep 15 18:41:01 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
xxmonth = "(none)",
}
@Article{McPherson:1982:LSG,
author = "John C. McPherson and Frank E. Hamilton and Robert R.
{Seeber, Jr.}",
title = "A Large-Scale, general-Purpose Electronic Digital
calculator: The {SSEC}",
journal = j-ANN-HIST-COMPUT,
volume = "4",
number = "4",
pages = "313--326",
month = oct # "\slash " # dec,
year = "1982",
CODEN = "AHCOE5",
ISSN = "0164-1239",
ISSN-L = "0164-1239",
bibdate = "Fri Nov 1 15:29:19 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://dlib.computer.org/an/books/an1982/pdf/a4313.pdf;
http://www.computer.org/annals/an1982/a4313abs.htm",
acknowledgement = ack-nhfb,
fjournal = "Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}
@Article{Monroe:1982:FFP,
author = "Alfred J. Monroe",
title = "{Forth} Floating Point Package",
journal = j-DDJ,
volume = "7",
number = "9",
pages = "16--??",
month = sep,
year = "1982",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Oklobdzija:1982:LSR,
author = "V. G. Oklobdzija and M. D. Ercegovac",
title = "An On-Line Square Root Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-31",
number = "1",
pages = "70--75",
month = jan,
year = "1982",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1982.1675887",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:33:09 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675887",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Palmer:1982:VRN,
author = "J. F. Palmer",
title = "{VLSI} and the Revolution in Numeric Computation",
crossref = "Ruschitzka:1982:IWC",
pages = "339--341",
year = "1982",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InCollection{Phillips:1982:BC,
author = "E. William Phillips",
title = "Binary Calculation",
crossref = "Randell:1982:ODC",
pages = "303--314",
year = "1982",
bibdate = "Wed Oct 13 09:51:37 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "The 1936 epigraph credited to this author in
\cite[Chapter 7]{Coonen:1984:CPS} says: ``The ultimate
aim is to persuade all of the civilized world to
abandon the decimal numeration and to use octonal in
its place; to discontinue counting in tens and to count
in eights instead. However, it seems unlikely that the
whole civilized world will be persuaded to complete
this change during the next twelve months, having
previously declined similar invitations.''",
}
@InProceedings{Rall:1982:ACA,
author = "L. B. Rall",
editor = "Anonymous",
booktitle = "{Proceedings of the 1982 Army Numerical Analysis and
Computers Conference}",
title = "Accurate computer arithmetic for scientific
computation",
volume = "82--83",
publisher = "US Army Research Office",
address = "Research Triangle Park, NC, USA",
bookpages = "xiv + 606",
pages = "343--356",
month = aug,
year = "1982",
bibdate = "Wed Oct 13 21:52:01 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Two volumes.",
URL = "http://books.google.com/books?id=pFb-QQAACAAJ",
abstract = "The operations of accurate arithmetic can be
implemented easily on a microcomputer or a computer
with microprogrammable arithmetic operations. In
addition, for accurate final results, a compiler is
necessary which will select the appropriate operations.
A language of this type (PASCAL-SC) was developed.
Along with accurate real arithmetic, this compiler
provides accurate complex arithmetic, real and complex
interval arithmetic, and vector and matrix arithmetic
over these data types. Some features of PASCAL-SC
related to scientific and engineering computation are
described. In most cases, the operations of accurate
arithmetic are performed at the same speed as ordinary
(uncontrolled) floating-point arithmetic.",
acknowledgement = ack-nhfb,
keywords = "analysis (mathematics); arithmetic; computation;
microcomputers; microprogramming; Pascal (programming
language)",
meetingname = "Army Numerical Analysis and Computers Conference (1982
: Vicksburg, Miss.)",
remark = "The theme of the 1982 Conference was Grid Techniques
for Partial Differential Equations.",
subject = "Numerical analysis; Computer programs; Congresses;
Numerical Mathematics. Computer Hardware. Computers.
Partial differential equations. Symposia. Numerical
analysis. Grids. Computations. Methodology.
Mathematical programming. Finite difference theory.
Finite element analysis. Boundaries. Hydrodynamics. Gas
dynamics. Interior ballistics. Autofrettage. Land
mines. Blast loads. Conduction(heat transfer) Magnet
coils. Water waves. Currents",
xxtitle = "Accurate arithmetic for scientific computation",
xxvolume = "82-3",
}
@InProceedings{Ramnarayan:1982:AER,
author = "R. Ramnarayan and F. Taylor",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '82}",
title = "Analysis of errors in residue number system ({RNS})
based {IIR} digital filters",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "56--59",
year = "1982",
CODEN = "????",
DOI = "https://doi.org/10.1049/el:19820632",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The problem of analyzing errors in Residue Number
System (RNS) based IIR Digital filters is considered in
this paper. There are basically three types of errors
in RNS based digital filters, They are coefficient
quantization errors(1), scaling errors \ldots{}",
}
@Article{Rix:1982:UQA,
author = "P. Rix",
title = "{Universeller Quad\-rat\-wurz\-el-Al\-go\-rith\-mus}
\toenglish {Universal Square Root Algorithms}
\endtoenglish",
journal = j-ELECTRONIK,
volume = "23",
pages = "81--82",
year = "1982",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronik",
}
@Article{Rump:1982:CR,
author = "Siegfried M. Rump",
title = "{Computer und Rechengenauigkeit} \toenglish {Computer
and Computational Precision} \endtoenglish",
journal = j-ELEK-RECHENANLAGEN,
volume = "24",
number = "6",
pages = "268--277",
month = dec,
year = "1982",
CODEN = "ELRAA4",
ISSN = "0013-5720",
bibdate = "Sat Feb 10 12:41:06 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronische Rechenanlagen",
}
@Article{Sacks-Davis:1982:ARN,
author = "R. Sacks-Davis",
title = "Applications of Redundant Number Representations to
Decimal Arithmetic",
journal = j-COMP-J,
volume = "25",
number = "4",
pages = "471--477",
month = nov,
year = "1982",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compendex database;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/471.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/472.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/473.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/474.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/475.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/476.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/477.tif",
abstract = "A decimal arithmetic unit is proposed for both integer
and floating-point computations. To achieve comparable
speed to a binary arithmetic unit, the decimal unit is
based on a redundant number representation. With this
representation no loss of compactness is made relative
to binary coded decimal (BCD) form. In this paper the
hardware required for the implementation of the basic
operations of addition, subtraction, multiplication and
division are described and the properties of
floating-point arithmetic based on a redundant number
representation are investigated.",
acknowledgement = ack-nhfb,
classcodes = "C5260 (Digital signal processing)",
classification = "721; 723",
corpsource = "Department of Computer Sci., Monash University,
Clayton, Vic., Australia",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "addition; binary; binary arithmetic unit; coded
decimal; computers, digital; decimal floating-point
arithmetic; digital arithmetic; division; floating
point arithmetic; floating-point; integer;
multiplication; redundant number representations;
subtraction",
remark = "The redundant number representation postpones the need
to carry during add, subtract, multiply, and divide,
delaying it until the final rounding step in a store
instruction. See
\cite{Fahmy:2003:CRF,Fahmy:2003:RDF}.",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Samsen:1982:AFP,
author = "G. R. Samsen",
title = "An Advanced Floating Point Processor to Enhance Speed
of Mathematical Processing",
crossref = "Southcon:1982:SCR",
pages = "16/1/1--3",
year = "1982",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Sasaki:1982:EGE,
author = "T. Sasaki and H. Murao",
key = "Symbolic_determinant; Symbolic_linear_systems;
Gaussian_elimination",
title = "Efficient {Gaussian} elimination method for symbolic
determinants and linear systems",
journal = j-TOMS,
volume = "8",
number = "3",
pages = "277--289",
month = sep,
year = "1982",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/356004.356007",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "F.2; G.1.3; I.1.2",
content = "The computation of the solution of a linear system
whose entries are indeterminates or polynomials is of
interest both for theoretic and practical reasons. The
similar problem of computing the determinant is
important because of the relationship of the
determinant and resultant to factorization, polynomial
greatest-common-divisor calculations, and computation
with algebraic functions. Engineering application areas
of this material include the analysis of electrical or
other networks.\par
These computation problems are quite distinct from
others which would appear to be superficially similar,
namely numerical linear algebra problems. The result of
computing a numerical determinant is a floating point
number with an associated error. The result of
computing an exact algebraic determinant is, typically,
a large expression whose terms may be rearranged into
various ``factored'' forms for savings in computation
time and space. This answer has no error
whatsoever.\par
Clever and efficient programs in each domain have been
shown to be disastrous in the other. Thus one of the
best algebraic techniques for determinant calculations
for ``sparse polynomial'' matrices is expansion by
minors [1]; whereas Gaussian elimination is far
superior \ldots{}",
CRclass = "F.2.1 Numerical Algorithms and Problems; G.1.3
Numerical Linear Algebra; G.1.3 Linear systems (direct
and iterative methods); I.1.2 Algorithms; I.1.2
Algebraic algorithms",
CRnumber = "40106",
descriptor = "Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems;
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra, Linear systems (direct and iterative
methods); Computing Methodologies, ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
genterm = "ALGORITHMS; PERFORMANCE",
journal-URL = "https://dl.acm.org/loi/toms",
reviewer = "R. J. Fateman; Fateman, R. J",
subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1
ALGEBRAIC MANIPULATION",
}
@Article{Sasaki:1982:PFM,
author = "T. Sasaki and Y. Kanada",
title = "Practically Fast Multiple Precision Evaluation of
{LOG} ($ {X} $)",
journal = j-INFO-PROC,
volume = "5",
number = "4",
pages = "247--250",
month = "????",
year = "1982",
bibdate = "Thu Sep 8 08:20:54 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Schatte:1982:FPF,
author = "P. Schatte",
title = "The Frequency of Postshifts in Floating-Point
Multiplication",
journal = "Elektronische Informationsverarbeitung und
Kybernetik",
volume = "18",
number = "9",
pages = "523--526",
month = "????",
year = "1982",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Sewell:1982:RLT,
author = "B. T. Sewell",
title = "A Rapid Lookup Table Method for Trigonometric
Functions",
journal = j-SPE,
volume = "12",
number = "10",
pages = "885--887",
month = oct,
year = "1982",
CODEN = "SPEXBL",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
keywords = "algorithms",
subject = "G Mathematics of Computing, MISCELLANEOUS \\ J.2
Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Chemistry",
}
@InCollection{Sheldon:1982:ICP,
author = "John W. Sheldon and Liston Tatum",
title = "The {IBM} Card-Programmed Electronic Calculator
(1951)",
crossref = "Randell:1982:ODC",
pages = "233--239",
year = "1982",
bibdate = "Sun Nov 03 08:36:11 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Sippel:1982:FRI,
author = "Timothy N. Sippel",
title = "Floating {RISCS}: implementation and analysis of
floating point on {RISC} {I}",
type = "Electrical Engineering and Computer Sciences Master of
Science Report",
school = "University of California, Department of Electrical
Engineering and Computer Sciences",
address = "Berkeley, CA, USA",
pages = "various",
year = "1982",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Sips:1982:CPM,
author = "H. J. Sips",
title = "Comments on {``An $ O(n) $ Parallel Multiplier with
Bit-Sequential Input and Output''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-31",
number = "4",
pages = "325--327",
month = apr,
year = "1982",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1982.1676000",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:33:11 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676000",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Strader:1982:CBS,
author = "N. R. Strader and V. T. Rhyne",
title = "A Canonical Bit-Sequential Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-31",
number = "8",
pages = "791--795",
month = aug,
year = "1982",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1982.1676085",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:33:14 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676085",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Tan:1982:ADC,
author = "Chung-I Tan and B. McInnis",
title = "Adaptive digital control implemented using residue
number systems",
journal = j-IEEE-TRANS-AUTOMAT-CONTR,
volume = "27",
number = "2",
pages = "499--502",
month = apr,
year = "1982",
CODEN = "IETAA9",
DOI = "https://doi.org/10.1109/CDC.1981.269326",
ISSN = "0018-9286 (print), 1558-2523 (electronic)",
ISSN-L = "0018-9286",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See comments \cite{Pei:1984:CAD}.",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=24189",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Automatic Control",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
keywords = "residue arithmetic; residue number system",
summary = "The application of residue number systems for the
implementation of adaptive digital controllers is
presented. Division operations are avoided through the
use of iteration to solve for the value of the control.
Decoding computations are simplified \ldots{}",
}
@Article{Taylor:1982:ARM,
author = "F. J. Taylor and C. H. Huang",
title = "An Autoscale Residue Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-31",
number = "4",
pages = "321--325",
month = apr,
year = "1982",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1982.1675999",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:30:01 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Taylor:1982:VRA,
author = "F. J. Taylor",
title = "A {VLSI} Residue Arithmetic Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-31",
number = "6",
pages = "540--546",
month = jun,
year = "1982",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1982.1676036",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:33:12 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676036",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Teachey:1982:SRX,
author = "R. D. Teachey",
title = "Square-Root-{X} Comparison --- New Results
Discovered",
journal = j-IEEE-MICRO,
volume = "2",
number = "4",
pages = "5--5",
month = oct # "\slash " # dec,
year = "1982",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1982.290929",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Dec 14 06:08:58 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Science Citation Index database (1980--2000)",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@InCollection{TorresyQuevedo:1982:EAD,
author = "Leonardo {Torres y Quevedo}",
title = "Essays on Automatics --- Its Definitions ---
Theoretical Extent of its Applications (1914)",
crossref = "Randell:1982:ODC",
pages = "89--107",
year = "1982",
bibdate = "Sun Nov 03 08:36:11 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "This translation and reprint contains a description of
what is believed to be the first design, albeit purely
theoretical, and for an electromechanical device, of
floating-point arithmetic. See, however, the
independent work, and first practical implementation of
floating-point arithmetic of Zuse
\cite{Zuse:1982:MAE,Zuse:1982:OCD}.",
}
@Article{Turner:1982:DLS,
author = "Peter R. Turner",
title = "The distribution of leading significant digits",
journal = j-IMA-J-NUMER-ANAL,
volume = "2",
number = "4",
pages = "407--412",
year = "1982",
CODEN = "IJNADH",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65G99 (60E05)",
MRnumber = "84f:65038",
MRreviewer = "Seppo Linnainmaa",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Velasevic:1982:RLC,
author = "Dusan M. Velasevi{\'c}",
title = "Right-to-Left Code Generation for Arithmetic
Expressions",
journal = j-COMP-J,
volume = "25",
number = "3",
pages = "316--326",
month = aug,
year = "1982",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/25.3.316",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:48:13 MST 2012",
bibsource = "Compendex database;
http://comjnl.oxfordjournals.org/content/25/3.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/;
https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/25/3/316.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/316.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/317.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/318.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/319.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/320.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/321.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/322.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/323.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/324.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/325.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/326.tif",
acknowledgement = ack-nhfb,
classcodes = "C6110 (Systems analysis and programming); C6120 (File
organisation)",
classification = "723",
corpsource = "Faculty of Electrical Engng., University of Belgrade,
Belgrade, Yugoslavia",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "arithmetic; automatic programming; binary tree
structure; code generator; codes, symbolic; data
structures; expressions; FORTRAN; notation; postfix;
right-to-left code generation; translation grammar;
vector-generatrice",
treatment = "P Practical",
}
@Article{Ware:1982:BMF,
author = "F. A. Ware and W. H. McAllister and J. R. Carlson and
D. K. Sun and R. J. Vlach",
title = "64 Bit Monolithic Floating Point Processors",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "SC-17",
number = "5",
pages = "898--907",
month = oct,
year = "1982",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "Describes a set of three processor chips capable of
performing 32 and 64 bit floating point add/subtract,
multiply, and divide operations. The chips can perform
over one million scalar floating point operations per
second, and over four million vector \ldots{}",
}
@Book{Waser:1982:IAD,
author = "Shlomo Waser and Michael J. Flynn",
title = "Introduction to Arithmetic for Digital Systems
Designers",
publisher = pub-HRW,
address = pub-HRW:adr,
pages = "xvii + 308",
year = "1982",
ISBN = "0-03-060571-7",
ISBN-13 = "978-0-03-060571-0",
LCCN = "TK7895 A65 W37 1982",
bibdate = "Sat Sep 03 09:25:17 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Master copy output on Alphatype CRS high-resolution
phototypesetter. This book went to press while the IEEE
754 Floating-Point Standard was still in development;
consequently, some of the material on that system was
invalidated by the final Standard (1985)
\cite{IEEE:1985:AIS}.",
acknowledgement = ack-nj # " and " # ack-nhfb,
tableofcontents = "Preface\\
Acknowledgments\\
Abbreviations and Symbols\\
1. Numeric Data Representation\\
2. Residue Numbers and the Limits of Fast Arithmetic\\
3. Addition and Subtraction\\
4. Multiplication\\
5. Division\\
6. Pipelining of Arithmetic Operations\\
Appendix.\\
References.\\
Index.",
}
@Book{Wilkes:1982:PPE,
author = "M. V. (Maurice Vincent) Wilkes and David J. Wheeler
and Stanley Gill",
title = "The Preparation of Programs for an Electronic Digital
Computer: with Special Reference to the {EDSAC} and the
Use of a Library of Subroutines",
volume = "1",
publisher = pub-TOMASH,
address = pub-TOMASH:adr,
pages = "xxxi + 167",
year = "1982",
ISBN = "0-262-23118-2 (MIT Press 1984), 0-938228-03-X",
ISBN-13 = "978-0-262-23118-3 (MIT Press 1984),
978-0-938228-03-5",
LCCN = "QA76.6 .W545 1982",
bibdate = "Mon Feb 10 11:33:59 MST 2020",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "With a new introduction by Martin Campbell-Kelly.",
series = "Charles Babbage Institute reprint series for the
history of computing",
acknowledgement = ack-nhfb,
}
@InCollection{Wilson:1982:PC,
author = "Kenneth G. Wilson",
title = "Experiences with a floating point systems array
processor",
crossref = "Rodrigue:1982:AC",
pages = "279--314",
year = "1982",
MRclass = "65W05",
MRnumber = "759 559",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Wu:1982:DFA,
author = "Market Wen-Han Wu",
title = "Design of a fast addressable hardware floating-point
arithmetic package for small computer",
type = "Thesis ({M.S.})",
school = "Tufts University. Department of Engineering",
address = "Boston, MA, USA",
pages = "iii + 102",
year = "1982",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Microcomputers ---
Programming.",
}
@InCollection{Zuse:1982:MAE,
author = "Konrad Zuse",
title = "Method for Automatic Execution of Calculations with
the aid of Computers (1936)",
crossref = "Randell:1982:ODC",
pages = "163--170",
year = "1982",
bibdate = "Sun Nov 03 08:36:11 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "This translation and reprint of a German patent
application of 11 April 1936 briefly describes the
floating-point system that was first successfully
implemented in a digital computer, the Zuse Z3, in
1941.",
}
@InProceedings{Agrawal:1983:DPV,
author = "Dharma P. Agrawal and Girish C. Pathak and Nikunja K.
Swain and Shuwan K. Agrawal",
title = "On Design and Performance of {VLSI} Based Parallel
Multiplier",
crossref = "IEEE:1983:PSC",
pages = "17--21",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Agrawal_Pathak_Swain_Agrawal.pdf",
abstract = "This paper introduces the VLSI design and layout of a
$ (\log^2 n) $ time $n$-bit binary parallel multiplier
for two unsigned operands. Proposed design consists of
partitioning the multiplier and multiplicand bits into
four groups of $ n / 4 $ bits each and then reducing
the matrix of sixteen product terms using three to two
parallel counters and Brent-Kung $ (\log n) $ time
parallel adder. Area-time performance of the present
scheme has been compared with the existing schemes for
parallel multipliers. Regular and recursive design of
the multiplier is shown to be suitable for VLSI
implementation and an improved table look up multiplier
has been used to form the basis of the recursive design
scheme.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@Article{Agrawal:1983:ICA,
author = "D. P. Agrawal and T. R. N. Rao",
title = "Introduction: Computer Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "4",
pages = "329--330",
month = apr,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676232",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676232",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Akamine:1983:SMQ,
author = "Masami Akamine and Tatsuo Higuchi",
title = "Synthesis of minimum quantization error digital
filters using floating-point arithmetic",
journal = j-ELECTRON-COMMUN-JPN,
volume = "66",
number = "10",
pages = "29--38",
year = "1983",
CODEN = "ECOJAL",
ISSN = "0424-8368",
MRclass = "94A12",
MRnumber = "85k:94010",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics and communications in Japan",
}
@InProceedings{Annaratone:1983:MME,
author = "M. Annaratone and R. Stefanelli",
title = "A Multiplier with Multiple Error Correction
Capability",
crossref = "IEEE:1983:PSC",
pages = "44--51",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Annaratone_Stefanelli.pdf",
abstract = "This paper presents a technique for increasing the
reliability of arithmetic units. An error model is then
presented: this model well represents the faulty
behavior of many arithmetic units. The Residue Number
System and its related properties are used in order to
obtain a simple architecture (called Reliability
Network, R-Net). The main characteristics of the
presented technique are a significant reduction in the
number of gates and a limited increase of global
execution times. The extensive use of combinational
logic makes it possible to implement the R-Net almost
completely by means of Programmable Logic Arrays
(PLA's). Finally, both the intrinsic regularity of the
R-Net and its simple internal interconnection scheme
make this approach suitable for a practical VLSI
implementation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@Article{Armer:1983:DCR,
author = "Paul Armer",
title = "11. The {Defense Calculator} at the {Rand
Corporation}",
journal = j-ANN-HIST-COMPUT,
volume = "5",
number = "2",
pages = "202--202",
month = apr # "\slash " # jun,
year = "1983",
CODEN = "AHCOE5",
ISSN = "0164-1239",
ISSN-L = "0164-1239",
bibdate = "Fri Nov 1 15:29:20 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://dlib.computer.org/an/books/an1983/pdf/a2202a.pdf;
http://www.computer.org/annals/an1983/a2202aabs.htm",
acknowledgement = ack-nhfb,
fjournal = "Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}
@Article{Asai:1983:CPI,
author = "H. Asai",
title = "A Consideration of a Practical Implementation For a
New Convergence Division",
journal = j-INFO-PROC-LETT,
volume = "17",
number = "5",
pages = "273--281",
month = dec,
year = "1983",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@Article{Asai:1983:SOM,
author = "Hitohisa Asai and C. K. Cheng",
title = "Speeding Up an Overrelaxation Method of Division in
Radix-$ 2^n $ Machine",
journal = j-CACM,
volume = "26",
number = "3",
pages = "216--220",
year = "1983",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:22:06 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm26.html#AsaiC83;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "arithmetic",
oldlabel = "AsaiC83",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/AsaiC83",
}
@MastersThesis{Aspinwall:1983:IIF,
author = "David Brian Masters Aspinwall",
title = "An implementation of the {IEEE} floating point
standard on a {VAX-11\slash 780}",
type = "Thesis ({M.S.})",
school = "San Francisco State University",
address = "San Francisco, CA, USA",
pages = "ix + 138",
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer architecture.; Floating-point arithmetic.;
Microprogramming.; VAX-11 (Computer) --- Programming.",
}
@Article{Aspinwall:1983:MVM,
author = "David B. Aspinwall and Yale N. Patt",
title = "Modifications to the {VAX-11\slash 780}
microarchitecture to support {IEEE} floating point
arithmetic",
journal = j-SIGMICRO,
volume = "14",
number = "4",
pages = "61--69",
month = dec,
year = "1983",
CODEN = "SIGMDJ",
DOI = "https://doi.org/10.1145/1096419.1096429",
ISSN = "0163-5751, 1050-916X",
ISSN-L = "0163-5751",
bibdate = "Fri Apr 16 10:27:31 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
URL = "https://dl.acm.org/doi/10.1145/1096419.1096429",
abstract = "The VAX-11/780 was designed specifically to implement
the VAX architecture. As such, it does not support the
IEEE standard for floating point arithmetic. A project
was undertaken to provide this support by modifying the
11/780 microarchitecture. Our objective was to produce
a microengine that would efficiently execute a modified
VAX instruction set, in particular, one that executes
VAX floating point instructions consistent with the
IEEE standard. We made minimal changes to the 11/780
hardware, relying primarily on changes to the
microcode. This paper describes the work of this
project.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMICRO Newsletter",
journal-URL = "https://dl.acm.org/loi/sigmicro",
}
@InProceedings{Avizienis:1983:AAE,
author = "Algirdas Avizienis and C. S. Raghavendra",
title = "Applications for Arithmetic Error Codes in Large,
High-Performance Computers",
crossref = "IEEE:1983:PSC",
pages = "169--173",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Avizienis_Raghavendra.pdf",
abstract = "Large, high-performance computers are too costly to
allow full replication for fault detection and error
correction in the communication and processing of
numerical information. For this reason more
cost-effective arithmetic error code applications offer
an attractive alternative.\par
Part I of this paper presents a generalization of
low-cost inverse residue codes into two-dimensional
encodings. Error detecting and error correcting
properties of two-dimensional inverse residue codes are
discussed.\par
Part II discusses a multi-phase application of inverse
residue codes in which the form of encoding is altered
and additional time is allocated after faults occur.
The goal is to defer repair and to continue operation
at a slower speed until scheduled maintenance can take
place.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@Article{Bandeira:1983:TCA,
author = "N. Bandeira and K. Vaccaro and J. A. Howard",
title = "A Two's Complement Array Multiplier Using True Values
of the Operands",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "8",
pages = "745--747",
month = aug,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676312",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:11 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676312",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Banerji:1983:RPF,
author = "D. K. Banerji and S. Kaushik",
title = "Representation and Processing of Fractions in a
Residue System",
crossref = "IEEE:1983:PSC",
pages = "29--36",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Banerji_Kaushik.pdf",
abstract = "This paper proposes a scheme for the representation
and processing of fractions in a residue system. The
scheme is based on a mixed radix representation of a
fraction in a residue system. The algorithms for basic
arithmetic operations of addition, subtraction, and
multiplication involving fractions are developed and
are shown to provide some improvement over an existing
method. Application of these algorithms to division of
two integers in the residue system has been shown.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; residue number systems",
}
@Article{Baxter:1983:CRS,
author = "I. Baxter",
title = "Code replication speeds multiplication",
journal = j-EDN,
volume = "28",
number = "4",
pages = "261--262",
month = feb,
year = "1983",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@InProceedings{Bayoumi:1983:MVI,
author = "M. A. Bayoumi and G. A. Jullien and W. C. Miller",
title = "Models for {VLSI} Implementation of Residue Number
System Arithmetic Modules",
crossref = "IEEE:1983:PSC",
pages = "174--183",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Bayoumi_Jullien_Miller.pdf",
abstract = "This paper discusses the implementation of RNS
arithmetic modules using VLSI technology. The modules
are based on the interconnection of readonly memory
look-up tables. The paper first outlines a memory model
for a single look-up table which allows the selection
of the most efficient layout for memories which do not
have power of $2$ dimensions. The paper then discusses
various examples of interconnected memory modules with
associated optimizing layout algorithms. Finally, an
example is given of the application of one of the
modules to a large prime modulus multiplier.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; residue number systems",
}
@InProceedings{Bhat:1983:HPF,
author = "J. Bhat",
title = "High Performance Floating Point Co-Processor for
Protected Multi-User Systems",
crossref = "Mini-Micro:1983:MMN",
pages = "7/2/1--5",
year = "1983",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Blakley:1983:MAI,
author = "G. R. Blakley and I. Borosh",
title = "Modular arithmetic of iterated powers",
journal = j-COMPUT-MATH-APPL,
volume = "9",
number = "4",
pages = "567--581",
month = "????",
year = "1983",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 18:51:24 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122183901141",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221/",
}
@InProceedings{Boney:1983:FPPa,
author = "J. Boney and V. Shahan",
title = "Floating-point Power for the {M68000} Family",
crossref = "Mini-Micro:1983:MMN",
pages = "7/3/1--9",
year = "1983",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Boney:1983:FPPb,
author = "J. Boney and V. Shahan",
title = "Floating-point Power for the {M68000} Family",
crossref = "Mini-Micro:1983:MMW",
pages = "16/5/1--10",
year = "1983",
bibdate = "Mon Sep 12 22:01:17 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Brown:1983:NEA,
author = "W. S. Brown and C. S. Wetherell",
title = "A Numeric Error Algebra",
crossref = "IEEE:1983:PSC",
pages = "86--93",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Brown_Wetherell.pdf",
abstract = "Wetherell recently described an algebra of error
values that could be added to the ordinary arithmetic
of a programming language. Along with ordinary
arithmetic values, error values were included in the
set of computational quantities. The error values could
participate in all arithmetic operations and return
meaningful results. Unfortunately, the definitions of
the error values were not precise enough. Using Brown's
model of computer arithmetic, we supply precise
definitions for the error values, define the
fundamental arithmetic operations on the new values,
comment on their properties, and discuss briefly how
they might be used and implemented. We also compare our
model to the error handling features of the proposed
IEEE floating point standard",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@Article{Bushard:1983:MTS,
author = "L. B. Bushard",
title = "A Minimum Table Size Result for Higher Radix
Nonrestoring Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "6",
pages = "521--526",
month = jun,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676273",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:09 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676273",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Caraiscos:1983:REA,
author = "C. Caraiscos and Bede Liu",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP '83}",
title = "A round-off error analysis of the {LMS} adaptive
algorithm",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "29--32",
year = "1983",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The steady state output error of the Least Mean Square
(LMS) Adaptive Algorithm due to the finite precision
arithmetic of a digital processor is analyzed. It is
found to consist of three terms: (1) the error due to
the input data quantization, (2) \ldots{}",
}
@Article{Chamrad:1983:FFP,
author = "V. Chamrad",
title = "A Fast Floating-Point Square-Rooting Routine for the
8080\slash 8085 Microprocessors",
journal = j-KYBERNETIKA,
volume = "19",
number = "4",
pages = "335--344",
month = "????",
year = "1983",
CODEN = "KYBNAI",
ISSN = "0023-5954",
bibdate = "Wed Sep 14 20:24:32 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Kybernetika",
}
@Article{Chan:1983:ACS,
author = "Tony F. Chan and Gene H. Golub and Randall J.
LeVeque",
title = "Algorithms for computing the sample variance: Analysis
and recommendations",
journal = j-AMER-STAT,
volume = "37",
number = "3",
pages = "242--247",
month = aug,
year = "1983",
CODEN = "ASTAAJ",
DOI = "https://doi.org/10.2307/2683386",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
MRclass = "62-04",
MRnumber = "84k:62003",
bibdate = "Mon May 5 09:19:29 MDT 1997",
bibsource = "Distributed/QLD.bib; Distributed/QLD/1983.bib;
ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jstor.org/stable/2683386",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
country = "USA",
date = "13/05/93",
descriptors = "Simulation; statistics; numeric calculation",
enum = "7109",
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
location = "SEL: Wi",
references = "0",
revision = "16/01/94",
}
@Article{Chang:1983:HSN,
author = "Tung-Liang Chang and P. Fisher",
title = "High-speed normalization and rounding circuits for
pipelined floating-point processors",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "31",
number = "6",
pages = "1403--1408",
month = dec,
year = "1983",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "A fast leading/trailing-zero detection circuit
(LZDC/TZDC) is described, and then applied to the
design of a pipelined floating-point (FLP) processor.
This circuit has a total delay of 5{\Delta} and a
hardware complexity of(m + 1)(3 log_{2}(p) + 4
\ldots{}).",
}
@Article{Chow:1983:PDA,
author = "P. Chow and Z. Vranesic and Jui Lin Yen",
title = "A Pipelined Distributed Arithmetic {PFFT} Processor",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "12",
pages = "1128--1136",
month = dec,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676173",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:13 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
note = "See correction \cite{Anonymous:1984:CPD}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676173",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Ciminiera:1983:FIM,
author = "L. Ciminiera and A. Serra",
title = "Fast Iterative Multiplying Array",
crossref = "IEEE:1983:PSC",
pages = "60--66",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ciminiera_Serra.pdf",
abstract = "A high speed multiplying array is presented. It is
based on a new cell, which is able to generate and add
a rectangular block of elementary products. A careful
design of the cell allows us to obtain a small delay
for the signals which should be propagated through the
whole array. This feature leads to a remarkable
improvement in the array speed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@Article{Cloutier:1983:PAR,
author = "Mark J. Cloutier and Matthew J. Friedman",
title = "Precision Averaging for Real-Time Analysis",
journal = j-CACM,
volume = "26",
number = "7",
pages = "525--529",
year = "1983",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:31:47 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm26.html#CloutierF83;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "CloutierF83",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/CloutierF83",
}
@InProceedings{Cody:1983:GPI,
author = "W. J. Cody",
title = "A generalization of the proposed {IEEE} standard for
floating-point arithmetic",
crossref = "Gentle:1983:CSS",
pages = "133--139",
year = "1983",
bibdate = "Thu Nov 17 10:41:05 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Republication of \cite{Cody:1982:GPI}.",
acknowledgement = ack-nhfb,
keywords = "standardization",
subject = "G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS,
General, Computer arithmetic \\ K.7 Computing Milieux,
THE COMPUTING PROFESSION, Miscellaneous \\ K.1
Computing Milieux, THE COMPUTER INDUSTRY, Standards",
}
@Article{Cohen:1983:CCP,
author = "Marty S. Cohen and T. E. Hull and V. Carl Hamacher",
title = "{CADAC}: a Controlled-Precision Decimal Arithmetic
Unit",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "4",
pages = "370--377",
month = apr,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676238",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676238",
abstract = "This paper describes the design of an arithmetic unit
called CADAC (clean arithmetic with decimal base and
controlled precision). Programming language
specifications for carrying out `ideal' floating-point
arithmetic are described first. These specifications
include detailed requirements for dynamic precision
control and exception handling, along with both complex
and interval arithmetic at the level of a programming
language such as Fortran or PL/I.\par
CADAC is an arithmetic unit which performs the four
floating-point operations add\slash subtract\slash
multiply\slash divide on decimal numbers in such a way
as to support all the language requirements
efficiently. A three-level pipeline is used to overlap
two-digit-at-a-time serial processing of the partial
products\slash remainders. Although the logic design is
relatively complex, the performance is efficient, and
the advantages gained by implementing
programmer-controlled precision directly in the
hardware are significant.",
acknowledgement = ack-nhfb # "\slash " # ack-jr,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "decimal floating-point arithmetic",
remark = "From MFC: Normalized decimal floating-point. Need for
variable precision (intermediate > final, increasing
precision, etc.). Base representation is BCD (2-32
digits). Hardware prototype built",
}
@Article{Collis:1983:MSZ,
author = "B. Collis",
title = "Macros speed 8080, {Z80} multiplication",
journal = j-EDN,
volume = "28",
number = "24",
pages = "225",
month = nov,
year = "1983",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@Article{Corbett:1983:EAF,
author = "Robert Paul Corbett",
title = "Enhanced arithmetic for {Fortran}",
journal = j-SIGNUM,
volume = "18",
number = "1",
pages = "24--28",
month = jan,
year = "1983",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:11 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@Article{Coupe:1983:SPZ,
author = "B. Coupe",
title = "Superefficient programs for 8080 and {Z80} multiply",
journal = j-ELECTRONICS,
volume = "56",
number = "6",
pages = "142--143",
month = mar,
year = "1983",
ISSN = "0883-4989",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronics",
journal-URL = "https://www.mdpi.com/journal/electronics",
}
@InProceedings{Dadda:1983:SSF,
author = "Luigi Dadda",
title = "Some Schemes for Fast Serial Input Multipliers",
crossref = "IEEE:1983:PSC",
pages = "52--59",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Dadda.pdf",
abstract = "The design of fast multipliers for binary numbers
represented in serial form is considered according to a
general scheme composed by an array generator and a
summator. The bits of the product are generated with
the least delay with respect to the operators bits. The
array generator computes the elements of the multiplier
array. The summator computes the sum of the array
elements in order to generate the product bits. The
array elements can be generated according to two
different general schemes: the first computes all the
new array elements at each step (arranged on a diagonal
and on a row of the multiplier array), the second
computes the multiplier array elements column by
column. Several schemes of array generators are given
and compared, and for each of them a suitable summator
using parallel counters is illustrated.",
acknowledgement = ack-nhfb,
author-dates = "29 April 1923--26 October 2012",
keywords = "ARITH-6",
}
@InProceedings{Dao:1983:QCA,
author = "T. T. Dao",
editor = "{IEEE}",
booktitle = "Proceedings of the 13th International Symposium on
Multiple-valued Logic, May 1983",
title = "A Quaternary Cellular Array Complex Number
Multiplier",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "255--262",
year = "1983",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Aug 22 09:15:45 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Davis:1983:HSD,
author = "George R. Davis and Thomas M. King",
title = "A High-Speed Digital Divider",
journal = j-IEEE-TRANS-INSTRUM-MEAS,
volume = "IM-32",
number = "2",
pages = "309--312",
month = jun,
year = "1983",
CODEN = "IEIMAO",
DOI = "https://doi.org/10.1109/TIM.1983.4315069",
ISSN = "0018-9456 (print), 1557-9662 (electronic)",
ISSN-L = "0018-9456",
bibdate = "Tue Jan 08 22:43:51 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper describes an efficient method for
generating the quotient of two binary numbers at speeds
comparable to existing multiplier chips. A digital
divider is designed using the BEST LINE segmentation
approximation. The reciprocal curve is subdivided into
small sections, and a least squares straight line
approximation is used to recreate each section. An
analysis is presented to determine the segmentation
granularity and the binary word length of constants
needed to closely approximate the curve. A compromise
design based on statistical performance as well as the
complexity of the hardware requirements are
evaluated.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Instrument \& Measurement",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=19",
}
@Article{Demsky:1983:MMC,
author = "J. Demsky and M. Schlesinger and R. D. Kent",
title = "Micro/mini computer program for calculating the square
root of rationals at arbitrary precision",
journal = j-COMP-PHYS-COMM,
volume = "29",
number = "3",
pages = "237--244",
month = may,
year = "1983",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(83)90004-8",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:28:04 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465583900048",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Dietrich:1983:VQF,
author = "D. Dietrich",
title = "{Verfahren zur L{\"o}sung von Quadratwurzeln f{\"u}r
Mikrorechnerprozeduren} \toenglish {Methods for the
Solution of Square Roots for Microprocessor
Subroutines} \endtoenglish",
journal = j-ELEKTRONIKER,
volume = "8",
pages = "EL-1--EL-6",
year = "1983",
CODEN = "ELKRBL",
ISSN = "0531-9218",
bibdate = "Fri Dec 08 13:05:49 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektroniker (Switzerland)",
}
@InProceedings{Donthi:1983:BSM,
author = "Ravindra V. Donthi and Mohammed Saleem and Harpreet
Singh",
title = "On Bit Sequential Multipliers",
crossref = "IEEE:1983:PSC",
pages = "104--108",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Donthi_Saleem_Singh.pdf",
abstract = "Recently bit sequential multiplier algorithms have
been found more useful in the area of interconnection
of multiple processors within a VLSI structure [1],
[2]. The object of the present paper is to suggest
modified bit sequential algorithms to achieve more
speed and to attain its conformity with other
algorithms such as division, square-rooting, etc. with
a view to utilize them in future arithmetic arrays. In
the present paper the following has been taken up: (a)
Bit sequential multiplier using carry look-ahead
technique, (b) Bit sequential multiplier using most
significant bit first,and (c) Negabinary bit sequential
multiplier.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@Article{Dubrulle:1983:CNM,
author = "Augustin A. Dubrulle",
title = "Class of Numerical Methods for the Computation of
{Pythagorean} Sums",
journal = j-IBM-JRD,
volume = "27",
number = "6",
pages = "582--589",
month = nov,
year = "1983",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Mar 25 14:26:59 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Moler:1983:RSR} and generalization
\cite{Jamieson:1989:SNR}.",
abstract = "Moler and Morrison have described an iterative
algorithm for the computation of the Pythagorean sum
(a**2 plus b**2)** one-half of two real numbers a and
b. This algorithm is immune to unwarranted
floating-point overflows, has a cubic rate of
convergence, and is easily transportable. This paper,
which shows that the algorithm is essentially Halley's
method applied to the computation of square roots,
provides a generalization to any order of convergence.
Formulas of orders 2 through 9 are illustrated with
numerical examples. The generalization keeps the number
of floating-point divisions constant and should be
particularly useful for computation in high-precision
floating-point arithmetic.",
acknowledgement = ack-nhfb,
classcodes = "C4190 (Other numerical methods); C5230 (Digital
arithmetic methods)",
classification = "723; 921",
corpsource = "IBM Sci. Centre, Palo Alto, CA, USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
journalabr = "IBM J Res Dev",
keywords = "computer programming; digital arithmetic;
floating-point divisions; Halley's method;
high-precision floating-point arithmetic; iterative
algorithm; iterative methods; mathematical techniques
--- Numerical Methods; Pythagorean sums; rate of
convergence; square roots",
treatment = "T Theoretical or Mathematical",
}
@Article{Dyer:1983:ZRP,
author = "D. C. Dyer",
title = "{Z80} routine performs 16-bit multiply",
journal = j-EDN,
volume = "28",
number = "5",
pages = "144",
month = mar,
year = "1983",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@InProceedings{Ercegovac:1983:HRD,
author = "Milo{\v{s}} D. Ercegovac",
title = "A Higher-Radix Division with Simple Selection of
Quotient Digits",
crossref = "IEEE:1983:PSC",
pages = "94--98",
month = jun,
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ercegovac.pdf",
abstract = "A higher-radix division algorithm with simple
selection of quotient digits is described. The proposed
scheme is a combination of the multiplicative
normalization used in the continued-product algorithms
and the recursive division algorithm. The scheme
consists of two parts: in the first part, the divisor
and the dividend are transformed into the range which
allows the quotient digits to be selected by rounding
partial remainders to the most significant radix-$r$
digit in the second part. Since the selection requires
only the most significant part of the partial
remainder, limited carry-propagation adders can be used
to form the partial remainders. The divisor and
dividend transformations are performed in three steps
using multipliers of the form $ 1 + s_k r^{-k} $ as in
the continued product algorithm. The higher radix of
the form $ r = 2^k, k = 2, 4, 8, \ldots {} $ can be
used to reduce the number of steps while retaining the
simple quotient selection rules.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; division",
}
@InProceedings{Ferguson:1983:DTE,
author = "Joel Ferguson and John Paul Shen",
title = "The Design of Two Easily-Testable {VLSI} Array
Multipliers",
crossref = "IEEE:1983:PSC",
pages = "2--9",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ferguson_Shen.pdf",
abstract = "Array multipliers are well-suited for VLSI
implementation because of the regularity in their
iterative structure. However, most VLSI circuits are
very difficult to test. This paper shows that, with
appropriate cell design, array multipliers can be
designed to be very easily-testable. An array
multiplier is called C-testable if all its adder cells
can be exhaustively tested while requiring only a
constant number of test patterns. The testability of
two well-known array multiplier structures are [sic]
studied. The conventional design of the carry-save
array multiplier is shown to be not C-testable.
However, a modified design, using a modified adder
cell, is generated and shown to be C-testable and
requires only 16 test patterns. Similar results are
obtained for the Baugh--Wooley two's complement array
multiplier. A modified design of the Baugh--Wooley
array multiplier is shown to be C-testable and requires
55 test patterns. The implementation of a practical
C-testable $ 16 \times 16 $ array multiplier is also
presented.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@InProceedings{Fraenkel:1983:SN,
author = "A. S. Fraenkel",
title = "Systems of Numeration",
crossref = "IEEE:1983:PSC",
pages = "37--42",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Fraenkel.pdf",
abstract = "A numeration system is a set of integers (basis
elements) such that every integer can be represented
uniquely over the set using integer digits of bounded
size. Such systems are scattered in many fields in
mathematics and computer science. Many of the known
ones and new ones are unified and derived from a basic
result on recursively defined basis elements.
Applications are indicated.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; number systems",
}
@Article{Gaitanis:1983:NPC,
author = "N. Gaitanis and C. Halatsis",
title = "Near-Perfect Codes for Binary-Coded Radix-$r$
Arithmetic Units",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "5",
pages = "494--497",
month = may,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676261",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:09 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676261",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Galand:1983:FD,
author = "C. Galand",
title = "Fast Division",
journal = j-IBM-TDB,
volume = "26",
number = "3B",
pages = "1537--1539",
month = aug,
year = "1983",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Article{Gavrielov:1983:CSF,
author = "M. Gavrielov and A. Kaminker and Y.-T. Sidi",
title = "Coprocessors Speed Floating Point Calculations",
journal = j-COMP-DESIGN,
volume = "22",
number = "11",
pages = "197--204",
month = oct,
year = "1983",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Sun Sep 11 11:55:54 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Design",
}
@Article{Gnanasekaran:1983:BSI,
author = "R. Gnanasekaran",
title = "On a Bit-Serial Input and Bit-Serial Output
Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "9",
pages = "878--880",
month = sep,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676341",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:12 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676341",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Gosling:1983:STF,
author = "J. B. Gosling",
title = "Some Tricks of the (Floating-Point) Trade",
crossref = "IEEE:1983:PSC",
pages = "218--220",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Gosling.pdf",
abstract = "In designing a floating-point arithmetic unit there
are a number of places where the characteristics of the
operations and the operands permit simplifications in
the logical design. These have not been well
documented, with the result that each new generation of
designers has made the same mistakes as their
predecessors. This paper describes some of these
simplifications as they affect the mantissa section of
a floating-point addition and subtraction unit. The
areas covered include normalisation and rounding.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@Article{Grappel:1983:FPP,
author = "R. D. Grappel",
title = "Floating-point-processing unit improves 16-bit-$ \mu
{P} $ performance",
journal = j-EDN,
volume = "28",
number = "19",
pages = "181--188",
month = sep,
year = "1983",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@InProceedings{Grnarov:1983:LMN,
author = "A. L. Grnarov and M. D. Ercegovac",
title = "On-line multiplicative normalization",
crossref = "IEEE:1983:PSC",
pages = "151--155",
year = "1983",
bibdate = "Tue Nov 13 15:44:54 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Grnarov_Ercegovac.pdf",
abstract = "In this article we describe a derivation and an
algorithm for on-line multiplicative normalization of
fractions. The algorithm is a variation of the
continued product normalization algorithm and it is
used for on-line evaluation of elementary functions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; elementary functions; on-line arithmetic",
}
@InProceedings{Guibas:1983:FBA,
author = "L. Guibas and J. E. Vuillemin",
title = "On Fast Binary Addition in {MOS} Technologies",
crossref = "IEEE:1983:PSC",
pages = "22--23",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Guibas_Vuillemin.pdf",
acknowledgement = ack-nhfb,
keywords = "addition; ARITH-6",
remark = "Paper did not arrive in time for the proceedings.",
}
@Article{Halatsis:1983:ECC,
author = "C. Halatsis and N. Gaitanis and M. Sigala",
title = "Error-Correcting Codes in Binary-Coded Radix-$r$
Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "3",
pages = "326--328",
month = mar,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676227",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676227",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Hamada:1983:UUR,
author = "H. Hamada",
title = "{URR}: Universal representation of real numbers",
journal = j-NEW-GEN-COMP,
volume = "1",
number = "2",
pages = "205--209",
month = jun,
year = "1983",
CODEN = "NGCOE5",
DOI = "https://doi.org/10.1007/BF03037427",
ISSN = "0288-3635 (print), 1882-7055 (electronic)",
ISSN-L = "0288-3635",
bibdate = "Thu Dec 14 16:45:14 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "New Generation Computing",
journal-URL = "https://dl.acm.org/loi/newg",
}
@Article{Heninger:1983:ZZF,
author = "A. Heninger",
title = "{Zilog}'s {Z8070} Floating Point Processor",
crossref = "Mini-Micro:1983:MMN",
pages = "16/2/1--7",
year = "1983",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InCollection{HP:1983:CDR,
author = "{Hewlett Packard}",
booktitle = "Software Internal Design Specification for the
{HP-71}, Vol. 1",
title = "Chapter 13: Data Representations",
publisher = "Hewlett Packard Company",
address = "Palo Alto, CA, USA",
pages = "13.1--13.17",
month = dec,
year = "1983",
bibdate = "Fri Nov 28 17:17:29 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Part \#00071-90068. Manual available from {\em The
Museum of HP Calculators}.",
URL = "http://www.hpmuseum.org/",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@Article{Huang:1983:FPM,
author = "C. H. Huang",
title = "A Fully Parallel Mixed-Radix Conversion Algorithm for
Residue Number Applications",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "4",
pages = "398--402",
month = apr,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676242",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676242;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35226",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "A new, fully parallel mixed-radix conversion (MRC)
algorithm which utilizes the maximum parallelism that
exists in the residues (RNS) to mixed-radix (MR) digits
conversion to achieve high throughput rate and very
short conversion time is presented. \ldots{}",
}
@Article{Huntsman:1983:MFP,
author = "Clayton Huntsman and Duane Cawthron",
title = "The {MC68881} Floating-Point Coprocessor",
journal = j-IEEE-MICRO,
volume = "3",
number = "6",
pages = "44--54",
month = nov # "\slash " # dec,
year = "1983",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1983.291185",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Dec 14 06:08:58 MST 2000",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Science Citation Index database (1980--2000)",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5230 (Digital arithmetic
methods)",
classification = "714; 723; 902",
corpsource = "Motorola Inc., Austin, TX, USA",
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
keywords = "arithmetic; computer architecture; computers;
coprocessor; digital arithmetic; floating-point;
floating-point arithmetic; IEEE arithmetic; IEEE
standard; integrated circuits, VLSI --- Applications;
M68000 family; M68000 microprocessor; MC68881
floating-point processor; microprocessor chips;
real-number computations; satellite; standards",
treatment = "P Practical; T Theoretical or Mathematical",
}
@Article{Iffrig:1983:ULC,
author = "L. D. Iffrig",
title = "Use less code for fast 8080 multiply",
journal = j-EDN,
volume = "28",
number = "13",
pages = "293",
month = jun,
year = "1983",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@TechReport{Ingram:1983:ACW,
author = "Windell F. Ingram and Radhakrishnan, N. (Narayanswamy)
and Deborah F. Dent",
title = "Accuracy considerations when using some minicomputers
for scientific and engineering problems",
institution = "U.S. Army Engineer Waterways Experiment Station;
available from National Technical Information Service",
address = "Vicksburg, MS, USA",
pages = "76 + 6 + 3",
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Technical report; K-83-2 Technical report (U.S. Army
Engineer Waterways Experiment Station); K-83-2.",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Minicomputers.;
Programming (Electronic computers).",
remark = "Cover title. ``September 1983.'' ``Prepared for
Office, Chief of Engineers, U.S. Army.'' Funded by
Office, Chief of Engineers.",
}
@Book{Intel:1983:HRM,
author = "Intel",
title = "The {iAPX} 286 Hardware Reference Manual",
publisher = pub-INTEL,
address = pub-INTEL:adr,
year = "1983",
LCCN = "QA76.8.I264 I14 1983",
bibdate = "Wed Feb 9 09:02:53 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "The definitive statement of the 80286 and 80287
hardware at a strongly technical level. Not an
instruction set reference, but does contain instruction
timing tables. See also \cite{Intel:1985:PRM}.",
acknowledgement = ack-nhfb,
}
@InProceedings{Irwin:1983:NLD,
author = "Mary Jane Irwin and Robert Michael Owens",
title = "Numerical Limitation on the Design of Digit On-Line
Networks",
crossref = "IEEE:1983:PSC",
pages = "156--161",
year = "1983",
bibdate = "Tue Nov 13 15:50:08 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Owens_Irwin.pdf",
abstract = "A fully digit online arithmetic unit generates at
least the $i$ most (least) significant digits of the
result after having been supplied no more than the $ (i
+ k) $ most (least) significant digits of each operand,
where $k$ is a small constant. This digit serial
property can be used to reduce the aggregate fill and
flush times of a chained array of digit online
arithmetic units and to reduce their VLSI
interconnection complexity. However, because of this
digit serial property, unique and inherent limitations
may have to be imposed on any arithmetic unit which
performs digit online operations. For some
calculations, these limitations may be so severe as to
make digit online evaluation virtually impossible. We
show several important signal processing problems where
these limitations have either been avoided or their
effect greatly reduced.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; on-line arithmetic",
}
@Article{James:1983:RDB,
author = "F. V. James",
title = "An 8085 routine divides 32-bit unsigned numbers",
journal = j-ELECTRONICS,
volume = "56",
number = "22",
pages = "163--165",
month = nov,
year = "1983",
ISSN = "0883-4989",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronics",
journal-URL = "https://www.mdpi.com/journal/electronics",
}
@Article{Jankowski:1983:NFS,
author = "M. Jankowski and A. Smoktunowicz and H.
Wo{\'z}niakowski",
title = "A note on floating-point summation of very many
terms",
journal = "Elektron. Informationsverarb. Kybernet.",
volume = "19",
number = "9",
pages = "435--440",
year = "1983",
MRclass = "65V05",
MRnumber = "85c:65161",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
altjournal = "Journal of Information Processing and Cybernetics ---
EIK",
keywords = "accurate floating-point summation",
}
@Article{Jenkins:1983:DEC,
author = "W. K. Jenkins",
title = "The Design of Error Checkers for Self-Checking Residue
Number Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "4",
pages = "388--396",
month = apr,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676240",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676240;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35226",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "During the last few years residue number (RNS)
arithmetic has gained increasing importance for
providing high speed fault tolerant performance in
dedicated digital signal processors. One factor that
has limited the use of redundant RNS theory in
\ldots{}",
}
@InProceedings{Johnsen:1983:IFP,
author = "K. Johnsen",
title = "An {IEEE} Floating Point Arithmetic Implementation",
crossref = "IEEE:1983:PSC",
pages = "130--135",
year = "1983",
bibdate = "Tue Nov 13 15:50:08 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Johnsen.pdf",
abstract = "This article describes some of the methods and
algorithms used in an implementation of floating point
arithmetic following (almost) the IEEE standard defined
in (1). The description is more directly
algorithm-oriented than the `Implementation Guide' for
this standard (2), since the latter does not treat an
actual implementation. The article consists of two
parts. One concerns the problem of getting the
preliminary result from each of the arithmetic
operations, this result is the basis for a correct
rounding. The other part treats the multiword
arithmetic, i.e., the routines to perform an $ m \times
n $ bit operation, using the corresponding $n$ bit
operation supplied by the hardware. Only multiplication
and division are described, since the add\slash
subtract routines are trivial. For division also a
method for getting an $n$ bit inverse is included,
since the hardware in the case had no division
operation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; correct rounding; floating-point arithmetic;
IEEE 754",
}
@MastersThesis{Jung:1983:BRR,
author = "C. Jung",
title = "{Berechnung der reellen und reellintervallwertigen
Standard- funktionen mit maximaler Genauigkeit in einem
hexadezimalen Gleitkommaformat} \toenglish {Computation
of the Real and Real Interval Valued Standard Functions
with Maximal Accuracy in a Hexadecimal Floating-Point
Format} \endtoenglish",
type = "{Diplomarbeit}",
school = "Institut f{\"u}r Angewandte Mathematik,
Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "??",
month = sep,
year = "1983",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@TechReport{Kahan:1983:M,
author = "W. Kahan",
title = "Minimizing $ q {\rm *} m - n $",
institution = "Department of Mathematics and Department of Electrical
Engineering and Computer Science, University of
California, Berkeley",
address = "Berkeley, CA, USA",
month = mar,
year = "1983",
bibdate = "Fri May 03 12:26:29 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/testpi/nearpi.c",
acknowledgement = ack-nhfb,
remark = "Nearpi, a C program to exhibit large floating-point
numbers $ Z = m * 2^L $ very close to integer multiples
of $ \pi / 2 $.",
}
@InProceedings{Kahan:1983:MWS,
author = "W. Kahan",
title = "Mathematics Written in Sand --- The {HP-15C}, {Intel
8087}, etc.",
crossref = "Anonymous:1983:PSC",
bookpages = "vi + 344",
pages = "12--26",
year = "1983",
bibdate = "Fri May 03 12:02:15 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/MathSand.pdf",
acknowledgement = ack-nhfb,
remark = "The original published version was a photoreduction of
dot-matrix printer output; the URL points to a cleaner
version.",
}
@TechReport{Kanada:1983:CDP,
author = "Y. Kanada and Y. Tamura and S. Yoshino and Y. Ushiro",
title = "Calculation of $ \pi $ to 10,013,395 Decimal Places
Based on the {Gauss--Legendre} Algorithm and {Gauss}
Arctangent Relation",
type = "Technical report",
number = "CCUT-TR-84-01",
institution = "Computer Centre, University of Tokyo",
address = "Bunkyo-ky, Yayoi 2-11-16, Tokyo 113, Japan",
month = dec,
year = "1983",
bibdate = "Mon Jul 18 17:50:42 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaushik:1983:SDN,
author = "S. Kaushik",
title = "Sign Detection in Non-Redundant Residue Number System
with Reduced Information",
crossref = "IEEE:1983:PSC",
pages = "24--28",
year = "1983",
bibdate = "Tue Nov 13 15:50:08 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Kaushik.pdf",
abstract = "A necessary and sufficient condition for sign
detection in Non-Redundant Residue Number System by
reducing the information of a residue digit has been
obtained. The function to reduce the information of a
residue digit $ x_p $ corresponding to a modulus $ m_p
$ has been assumed to be periodic with the period
length $ \hat {m}_p $, where $ \hat {m}_p = M / m_p $
and $ M = \prod_{i = 1}^n m_i $. A sequential method
for determining the sign of a number is shown to
demonstrate the applicability of the results thus
proved.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; residue number systems",
}
@MastersThesis{Kirk:1983:MFP,
author = "Patrick Donald Kirk",
title = "Microcomputer and floating point firmware design",
type = "Thesis ({M.S.})",
school = "California State University, Long Beach",
address = "Long Beach, CA, USA",
pages = "2 + xi + 237",
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Microcomputers ---
Programming.",
}
@InProceedings{Kobayashi:1983:AHS,
author = "Hideaki Kobayashi and Ronald D. Bonnell",
title = "Arithmetic for a High-Speed Adaptive Learning Network
Element",
crossref = "IEEE:1983:PSC",
pages = "164--168",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Kobayashi_Bonnel.pdf",
abstract = "This paper presents a novel arithmetic scheme for a
high-speed adaptive learning network (ALN) element. An
ALN is a self-organizing scheme for implementing the
Kolmogorov--Gabor (K-G) polynomial which maps an input
vector $X$ into an output scalar $Y$. In the first
layer of an ALN there are $ n(n - 1) / 2 $ elements. In
the next layer the number of elements needed depends
upon the number of outputs that are propagated from the
first layer. In this paper only the design of a single
element is considered. An array of memories (RAMs) and
a parallel adder are used to perform multinomial
arithmetic for the element. The memory array contains
subfunction values which are calculated by an external
host computer and downloaded to the memory array. All
the memories operate on the input variables
concurrently via a common address bus. The subfunction
values from the memory array are then summed by a
parallel adder to obtain the output of the element.
complete ALN implemented with the proposed ALN elements
has advantages in operation speed and less hardware.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@Article{Kornerup:1983:FPR,
author = "Peter Kornerup and David W. Matula",
title = "Finite precision rational arithmetic: An arithmetic
unit",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "4",
pages = "378--388",
month = apr,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676239",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676239",
abstract = "The foundations of an arithmetic unit performing the
add, subtract, multiply, and divide operations on
rational operands are developed. The unit uses the
classical Euclidean algorithm as one unified algorithm
for all the arithmetic operations, including rounding.
Binary implementations are discussed, based on
techniques known from SRT division, and utilizing
ripple-free borrow-save and carry-save addition.
Average time behavior is investigated.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Krishnamurthy:1983:FID,
author = "E. V. Krishnamurthy and V. K. Murthy",
title = "Fast Iterative Division of $p$-adic Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "4",
pages = "396--398",
month = apr,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676241",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676241",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Lastman:1983:DFP,
author = "G. J. Lastman",
title = "Determination of Floating Point Characteristics for a
Personal Computer",
crossref = "IEEE:1983:IEE",
pages = "424--427",
year = "1983",
bibdate = "Thu Sep 01 12:11:33 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Linnainmaa:1983:ELE,
author = "Seppo Linnainmaa",
title = "Error linearization as an effective tool for
experimental analysis of the numerical stability of
algorithms",
journal = j-BIT,
volume = "23",
number = "3",
pages = "346--359",
month = sep,
year = "1983",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01934463",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65G05 (65J05)",
MRnumber = "85e:65020",
bibdate = "Wed Jan 4 18:52:18 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=23&issue=3;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=23&issue=3&spage=346",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Lozier:1983:UFP,
author = "Daniel W. Lozier",
title = "The use of floating-point and interval arithmetic in
the computation of error bounds",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "4",
pages = "411--417",
month = apr,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676245",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "65G05",
MRnumber = "85f:65042",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676245",
abstract = "Three forms of interval floating-point arithmetic are
defined in terms of absolute precision, relative
precision, and combined absolute and relative
precision. The absolute-precision form corresponds to
the centered form of conventional rounded-interval
arithmetic. The three forms are compared on the basis
of the number of floating-point operations needed to
generate error bounds for inner-product accumulation.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
catcode = "G.1.0",
CRclass = "G.1.0 General; G.1.0 Error analysis",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
genterm = "ALGORITHMS; PERFORMANCE",
guideno = "06575",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
reviewer = "N. N. Abdelmalek",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@InProceedings{Majerski:1983:SRA,
author = "Stanislaw Majerski",
title = "Square-Root Algorithms for High-Speed Digital
Circuits",
crossref = "IEEE:1983:PSC",
pages = "99--102",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Majerski.pdf",
abstract = "Two binary algorithms for the square rooting of a sum
of two numbers are presented. They are designed for
high-speed digital circuits and are based on the
classical nonrestoring method. The main difference lies
in the replacement of subtractions and additions by the
parallel reduction of three summands to two, their sum
being unchanged to eliminate a carry propagation. The
term ``parallel reduction'' is introduced here for the
carry-save addition of three summands, positive and
negative as well. The two result summands form a
successive partial remainder. Their most significant
three-bit groups are used to determine the ``digits''
$1$, $0$, $ + 1 $ of the square root in a redundant
notation. These digits are transformed into the
conventional-notation bits, which are used in the
further steps of the square-rooting process",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; square root",
}
@Article{Maric:1983:PBC,
author = "I. Maric and L. Cucancic",
title = "On the Possibilities of the {BCD} Code Application in
the Floating-Point Arithmetic Algorithms",
journal = j-INT-J-MINI-MICROCOMPUTERS,
volume = "5",
number = "2",
pages = "19--22",
month = "????",
year = "1983",
CODEN = "IJMMDE",
ISSN = "0702-0481",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "International Journal of Mini and Microcomputers",
}
@InProceedings{Markov:1983:NAF,
author = "Svetoslav Markov",
title = "On the Numerical Algorithms Formulated in Computer
Arithmetic",
crossref = "IEEE:1983:PSC",
pages = "82--85",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Markov.pdf",
abstract = "We discuss some mathematical tools and techniques
supporting the construction of rigorous bounds
producing, numerically convergent algorithms, which are
formulated in terms of computer arithmetic operations.
Two important computer-arithmetic effects are
considered and their application as stopping criteria
is illustrated.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@InProceedings{Martin:1983:FPS,
author = "G. R. Martin",
title = "Floating Point Support for the {NS16000} Family -- The
{NS16081}",
crossref = "Mini-Micro:1983:MMW",
pages = "16/3/1--3",
year = "1983",
bibdate = "Wed Sep 07 22:33:22 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Matula:1983:OPF,
author = "David W. Matula and Peter Kornerup",
title = "An Order Preserving Finite Binary Encoding of the
Rationals",
crossref = "IEEE:1983:PSC",
pages = "201--209",
year = "1983",
bibdate = "Tue Nov 13 15:50:08 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Matula_Kornerup.pdf",
abstract = "We describe a new binary encoding for numbers termed
lexicographic continued fraction (LCF) representation
that provides a one-to-one order preserving finite bit
string representation for every rational. Conversion
either way between binary integer numerator-denominator
pair representation and LCF representation is shown
feasible in time linear with bit string length, given
registers of length sufficient to hold the numerator
and denominator. LCF bit string length is about $ 2
\max \{ \log_2 P, \log_2 q \} $ for the irreducible
fraction $ p / q $. Realization of arithmetic $ ( +, -,
\times, \divide) $ on LCF bit string encoded operands
is shown feasible. Some relations between the theory of
best rational approximation and the values represented
by truncated LCF bit strings are noted to assess the
feasibility of a finite precision arithmetic based on
LCF representation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; lexicographic continued fraction (LCF);
rational arithmetic",
}
@Article{McCool:1983:NDC,
author = "Thomas E. McCool",
title = "4. {NSA}'s {Defense Calculator}, 1952--1953",
journal = j-ANN-HIST-COMPUT,
volume = "5",
number = "2",
pages = "186--187",
month = apr # "\slash " # jun,
year = "1983",
CODEN = "AHCOE5",
ISSN = "0164-1239",
ISSN-L = "0164-1239",
bibdate = "Fri Nov 1 15:29:20 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://dlib.computer.org/an/books/an1983/pdf/a2186.pdf;
http://www.computer.org/annals/an1983/a2186abs.htm",
acknowledgement = ack-nhfb,
fjournal = "Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}
@Article{McGuire:1983:PCB,
author = "D. W. McGuire",
title = "8048 program computes 16-by-8-bit quotient",
journal = j-ELECTRONICS,
volume = "56",
number = "10",
pages = "152--153",
month = may,
year = "1983",
ISSN = "0883-4989",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronics",
journal-URL = "https://www.mdpi.com/journal/electronics",
}
@TechReport{Midttun:1983:FMP,
author = "G. Midttun",
title = "A fast micro-programmable floating point processor",
type = "Technical report",
number = "CERN DD 83-16",
institution = "CERT",
address = "Geneva, Switzerland",
pages = "31",
month = sep,
year = "1983",
bibdate = "Fri May 25 05:43:42 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0058382",
acknowledgement = ack-nhfb,
keywords = "emulation; MICE; microcode; PDP11",
}
@Article{Mikov:1983:PAFa,
author = "A. I. Mikov",
title = "Probabilistic analysis of floating-point addition
({Russian})",
journal = "Kibernetika (Kiev)",
volume = "3",
pages = "87--93",
year = "1983",
MRclass = "60K99 (65G05)",
MRnumber = "85h:60154",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "English translation in \cite{Mikov:1983:PAFb}.",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Mikov:1983:PAFb,
author = "A. I. Mikov",
title = "Probabilistic analysis of floating-point addition",
journal = j-CYBER,
volume = "19",
number = "3",
pages = "401--410",
month = may,
year = "1983",
CODEN = "CYBNAW",
DOI = "https://doi.org/10.1007/BF01072156",
ISSN = "0011-4235 (print), 2375-0189 (electronic)",
MRclass = "60K99 (65G05)",
MRnumber = "85h:60154",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Translated from \cite{Mikov:1983:PAFa}.",
URL = "http://link.springer.com/article/10.1007/BF01072156",
acknowledgement = ack-nhfb,
fjournal = "Cybernetics",
journal-URL = "http://link.springer.com/journal/10559",
}
@Article{Miller:1983:RNS,
author = "D. D. Miller and J. N. Polky",
title = "A Residue Number System Implementation of the {LMS}
Algorithm Using Optical Waveguide Circuits",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "11",
pages = "1013--1028",
month = nov,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676152",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:12 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676152;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35222",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "A detailed design of a real-time data processor based
on the residue number system is presented which uses
near-term optical waveguide devices and concepts. The
optical computational units consist of cascaded,
mask-programmable arrays of total \ldots{}",
}
@InProceedings{Miola:1983:UVA,
author = "A. Miola",
title = "A Unified View of Approximate Rational Arithmetic and
Rational Interpolation",
crossref = "IEEE:1983:PSC",
pages = "210--215",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Miola.pdf",
abstract = "In this paper we cover the problem of approximation of
numbers and of functions by presenting some well known
results in a unified view that could help in better
understanding the algebraic bases of the problem. In
fact, the Extended Euclid's algorithm happens to be the
unique and common tool solving the approximation
problems both for numbers and for functions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; rational arithmetic; rational interpolation",
}
@Article{Moler:1983:RSR,
author = "Cleve B. Moler and Donald Morrison",
title = "Replacing Square Roots by {Pythagorean} Sums",
journal = j-IBM-JRD,
volume = "27",
number = "6",
pages = "577--581",
month = nov,
year = "1983",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Dubrulle:1983:CNM} and generalization
\cite{Jamieson:1989:SNR}.",
URL = "http://www.research.ibm.com/journal/rd/276/ibmrd2706P.pdf",
abstract = "An algorithm is presented for computing a 'Pythagorean
sum' a(+)b= square root a/sup 2/+b/sup 2/ directly from
a and b without computing their squares or taking a
square root. No destructive floating point overflows or
underflows are possible. The algorithm can be extended
to compute the Euclidean norm of a vector. The
resulting subroutine is short, portable, robust, and
accurate, but not as efficient as some other
possibilities. The algorithm is particularly attractive
for computers where space and reliability are more
important than speed",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C4190 (Other numerical methods); C5230 (Digital
arithmetic methods)",
corpsource = "Department of Computer Sci., University of New Mexico,
Albuquerque, NM, USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "algorithms; digital arithmetic; Euclidean norm;
floating-point arithmetic; iterative methods;
performance; Pythagorean sums; subroutine; vector",
review = "ACM CR 8406-0463",
subject = "G.1 Mathematics of Computing, NUMERICAL ANALYSIS,
Roots of Nonlinear Equations \\ F.2.1 Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials \\ F.2.2 Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Geometrical problems and computations",
treatment = "T Theoretical or Mathematical",
}
@Article{Moran:1983:BRB,
author = "Bruce T. Moran",
title = "Book Review: {{\booktitle{Wissenschaftsgeschichte um
Wilhelm Schickard: Vortr{\"a}ge bei dem Symposion der
Universitat T{\"u}bingen im 500 Jahr ihres Bestehens am
24. und 25. Juni 1977}} by Friedrich Seck}",
journal = j-ISIS,
volume = "74",
number = "3",
pages = "448--449",
month = sep,
year = "1983",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:22:47 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i211164;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1980.bib",
URL = "http://www.jstor.org/stable/232640",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@InProceedings{Morrison:1983:EHL,
author = "R. Morrison and A. J. Cole and P. J. Bailey and M. A.
Wolfe and M. Shearer",
title = "Experience with a High Level Language that Supports
Interval Arithmetic",
crossref = "IEEE:1983:PSC",
pages = "74--78",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Morrison_Cole_Bailey_Wolfe_Shearer.pdf",
abstract = "An extension of the language S-algol called Triplex
which facilitates the use of interval arithmetic and
which is similar to triplex algol 60 is described.
Experience in the use of Triplex is reported. In
particular, a Triplex program corresponding to a
triplex algol 60 program of Nickel is given, together
with numerical results.",
acknowledgement = ack-nhfb,
keywords = "Algol 60; ARITH-6; interval arithmetic; S-Algol;
Triplex (Algol)",
}
@Article{Murugesan:1983:ACF,
author = "S. Murugesan and V. K. Agrawal",
title = "Algorithm converts fractions to {BCD}",
journal = j-EDN,
volume = "28",
number = "19",
pages = "245--246",
month = sep,
year = "1983",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@Article{Nagpal:1983:PAT,
author = "H. K. Nagpal and G. A. Jullien and W. C. Miller",
title = "Processor Architectures for Two-Dimensional Convolvers
Using a Single Multiplexed Computational Element with
Finite Field Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "11",
pages = "989--1001",
month = nov,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676150",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:12 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676150",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Nave:1983:ITF,
author = "R. Nave",
title = "Implementation of Transcendental Functions on a
Numerics Processor",
journal = j-MICROPROC-MICROPROG,
volume = "11",
number = "3--4",
pages = "221--225",
month = mar # "--" # apr,
year = "1983",
CODEN = "MMICDT",
ISSN = "0165-6074 (print), 1878-7061 (electronic)",
ISSN-L = "0165-6074",
bibdate = "Fri Dec 08 13:05:28 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Microprocessing and Microprogramming",
}
@InProceedings{Ni:1983:VRM,
author = "Lionel M. Ni and Kai Hwang",
title = "Vector Reduction Methods for Arithmetic Pipelines",
crossref = "IEEE:1983:PSC",
pages = "144--150",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ni_Hwang.pdf",
abstract = "Vector reduction arithmetic accepts a vector as input
and produces a scalar output. This class of vector
operations forms the basis of many scientific
computations. In a pipelined processor, a feedback loop
is required to reduce vectors. Since the output of the
pipeline depends on previous outputs, improper control
of the feedback loop will destroy the benefit from
pipelining. A generalized computing model is proposed
to schedule the activities in a vector reduction
pipeline. Two new vector reduction methods, symmetric
and asymmetric, are proposed and analyzed for pipelined
processing. These two methods compare favorably with
the known recursive reduction method in achieving
higher pipeline utilization and in eliminating large
memory for intermediate results. An interleaving method
is proposed to reduce multiple vectors to multiple
scalars in a single arithmetic pipeline. The pipeline
can be fully utilized by interleaved multiple vector
processing.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@InProceedings{Ohlsson:1983:MML,
author = "Lennart Ohlsson and Bertil Svensson",
title = "Matrix Multiplication on {LUCAS}",
crossref = "IEEE:1983:PSC",
pages = "116--122",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ohlsson_Svensson.pdf",
abstract = "Multiplication of two $N$ by $N$ matrices involves $
N^3 $ multiplications of elements. The task allows a
large amount of parallelism to be utilized, indicating
that it can be efficiently executed on a parallel
computer. This paper describes how matrix
multiplication is performed on LUCAS, an SIMD type
parallel processor with bit-serial processing elements.
The interconnection network is of Perfect Shuffle\slash
Exchange type. The case of study is when the number of
processing elements is between $ N^2 $ and $ N^3 $. The
algorithm presented can be applied to any computer with
the same interconnection structure. Formulas showing
how the execution time depends on data length and
matrix size are presented together with measured values
from execution on LUCAS.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; LUCAS (Lund University Content Addressable
System)",
}
@InProceedings{Ong:1983:CAS,
author = "Shauchi Ong and D. E. Atkins",
title = "A Comparison of {ALU} Structures for {VLSI}
Technology",
crossref = "IEEE:1983:PSC",
pages = "10--16",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ong_Atkins.pdf",
abstract = "Although many of the basic techniques of computer
arithmetic have been known since the earliest days of
electronic computing, there is a continuing need to
re-evaluate them in the context of developments in VLSI
circuit technology. Furthermore, recent work in
complexity of algorithms, particularly the solution of
recurrence relations, suggests new candidate structures
for generating the carry vector and raises the
questions as to their practicality in modern logic
design practice.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@Article{Owens:1983:TRI,
author = "R. M. Owens",
title = "Techniques to Reduce the Inherent Limitations of Fully
Digit On-Line Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "4",
pages = "406--411",
month = apr,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676244",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676244",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Ozawa:1983:AIK,
author = "K. Ozawa",
title = "Analysis and Improvement of {Kahan}'s Summation
Algorithm",
journal = j-INFO-PROC,
volume = "6",
number = "4",
pages = "226--230",
year = "1983",
bibdate = "Mon Sep 12 08:06:17 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
keywords = "accurate floating-point summation",
}
@InProceedings{Palmer:1983:VSN,
author = "J. F. Palmer",
title = "{VLSI} starts a numeric revolution",
crossref = "IEEE:1983:PII",
pages = "186--189",
year = "1983",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Pan:1983:ALC,
author = "V. Ya Pan",
title = "The additive and logical complexities of linear and
bilinear arithmetic algorithms",
journal = j-J-ALG,
volume = "4",
number = "1",
pages = "1--34",
month = mar,
year = "1983",
CODEN = "JOALDV",
DOI = "https://doi.org/10.1016/0196-6774(83)90031-7",
ISSN = "0196-6774 (print), 1090-2678 (electronic)",
ISSN-L = "0196-6774",
bibdate = "Tue Dec 11 09:14:02 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jalg.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0196677483900317",
acknowledgement = ack-nhfb,
fjournal = "Journal of Algorithms",
journal-URL = "http://www.sciencedirect.com/science/journal/01966774",
}
@Article{Patel:1983:CED,
author = "J. H. Patel and L. Y. Fung",
title = "Concurrent Error Detection in Multiply and Divide
Arrays",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "4",
pages = "417--422",
month = apr,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676246",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676246",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Payne:1983:DRT,
author = "M. H. Payne and R. N. Hanek",
title = "Degree Reduction for Trigonometric Functions",
journal = j-SIGNUM,
volume = "18",
number = "2",
pages = "18--19",
month = apr,
year = "1983",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/1057605.1057606",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This report is a companion to Reference 1 on radian
reduction. As in Reference 1 \cite{Payne:1983:RRT}, the
motivation arises from a desire to eliminate messages
like ``argument too large'' in trigonometric function
routines. The presence of very large arguments in the
VAX H format, on the Cray 1, and on an IEEE machine
with extended registers, make this a real problem. As
for the radian reduction algorithm, the degree
algorithm will reduce any argument, however large, so
long as it is representable; its speed is nearly
independent of the size of the argument to be reduced;
and full accuracy is maintained in the neighborhoods of
the zeros of the desired function. We believe that the
approach is new and represents a significant
improvement over procedures currently in use. A variant
of the procedure is used in Version 3 of the VAX Math
Library.",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "range reduction",
}
@Article{Payne:1983:RRT,
author = "M. H. Payne and R. N. Hanek",
title = "Radian Reduction for Trigonometric Functions",
journal = j-SIGNUM,
volume = "18",
number = "1",
pages = "19--24",
month = jan,
year = "1983",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/1057600.1057602",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An accurate reduction poses little difficulty for
arguments of a few radians. However for, say, a CRAY 1,
H format on the VAX, or double extended in the proposed
IEEE standard, the maximum argument which might be
presented for reduction is of the order of $ 2^{16000}
$ radians. Accurate reduction of such an argument would
require storage of $ \pi $ (or its reciprocal) to over
16,000 bits. Direct reduction by division (or
multiplication) then requires generation of a somewhat
larger number of bits in the result in order to
guarantee the accuracy of the reduction. Of these bits
only the low few bits of the integer part of the
quotient (product) and enough bits to correctly round
the remainder are relevant; the rest will be
discarded.",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "correct rounding; floating-point arithmetic; range
reduction",
}
@Article{Preparata:1983:MCA,
author = "F. P. Preparata",
title = "A Mesh-Connected Area-Time Optimal {VLSI} Multiplier
of Large Integers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "2",
pages = "194--198",
month = feb,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676203",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:07 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676203",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Prosser:1983:NCS,
author = "C. J. Prosser",
title = "A note on computing the square root of an integer",
journal = j-COMP-J,
volume = "26",
number = "2",
pages = "187--188",
month = may,
year = "1983",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/187.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/188.tif",
acknowledgement = ack-nhfb,
classcodes = "C4190 (Other numerical methods); C7310 (Mathematics
computing)",
corpsource = "Rutherford and Appleton Lab., Chilton, Didcot, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "binary; computer; fixed-point number; integer;
interactive methods; iterative methods; PASCAL; Pascal
implementation; square root; subroutines; successive
subtraction",
treatment = "P Practical",
}
@Article{Prosser:1983:SNN,
author = "C. J. Prosser",
title = "Short Notes: a Note on Computing the Square Root of an
Integer",
journal = j-COMP-J,
volume = "26",
number = "2",
pages = "187--188",
month = may,
year = "1983",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/26.2.187",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:48:14 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/26/2.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/26/2/187.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/187.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/188.tif",
acknowledgement = ack-nhfb,
classcodes = "C4190 (Other numerical methods); C7310 (Mathematics
computing)",
corpsource = "Rutherford and Appleton Lab., Chilton, Didcot, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "binary; computer; fixed-point number; integer;
iterative methods; PASCAL; Pascal implementation;
square root; subroutines; successive subtraction",
treatment = "P Practical",
}
@Article{Quinn:1983:EPR,
author = "Kevin Quinn",
title = "Ever Had Problems Rounding Off Figures? {This} Stock
Exchange Has",
journal = j-WALL-ST-J,
volume = "??",
number = "??",
pages = "37--37",
day = "8",
month = nov,
year = "1983",
CODEN = "WSJOAF",
ISSN = "0099-9660",
bibdate = "Thu Oct 17 06:28:35 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Wall Street Journal",
}
@Article{Rall:1983:BRB,
author = "L. B. Rall",
title = "Book Review: {{\booktitle{Computer Arithmetic in
Theory and Practice}} (Ulrich W. Kulisch and Willard L.
Miranker)}",
journal = j-SIAM-REVIEW,
volume = "25",
number = "4",
pages = "585--588",
month = "????",
year = "1983",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1025138",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:53:41 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/25/4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "October 1983",
}
@Article{Rall:1983:CAT,
author = "L. B. Rall",
title = "Computer Arithmetic in Theory and Practice ---
{Kulisch, U. W., Miranker, W. L.}",
journal = j-SIAM-REVIEW,
volume = "25",
number = "4",
pages = "585--588",
month = "????",
year = "1983",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1025138",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Ramachandran:1983:SRE,
author = "V. Ramachandran",
title = "Single Residue Error Correction in Residue Number
Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "5",
pages = "504--507",
month = may,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676264",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:09 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676264;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35227",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "We present a new method to correct single errors in an
n-residue number system through the use of r redundant
moduli. The method requires {\lceil}2n/r{\rceil} + 2
recombinations of n residues in the worst case. This is
of lower complexity than any \ldots{}",
}
@InProceedings{Rao:1983:ICS,
author = "T. R. N. Rao and P. Kornerup",
title = "{IEEE Computer Society Sixth Symposium on Computer
Arithmetic}",
crossref = "IEEE:1983:PSC",
pages = "1--1",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Rao_Kornerup.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@InProceedings{Robertson:1983:CDM,
author = "James E. Robertson",
title = "Conditions for the Distributivity of Multiplication
with Respect to Set Addition and Their Effect on the
Design of Array Multipliers",
crossref = "IEEE:1983:PSC",
pages = "67--71",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Robertson.pdf",
abstract = "Some conditions for distributivity of multiplication
with respect to set addition are determined. In
particular, distributivity holds if positive numbers
are used, but does not hold for negative numbers in
radix complement form. Use of simple recoding methods
to achieve distributivity is not helpful, since costs
of elementary multipliers and summing networks are
increased. Distributivity does hold for the digit sets
used for signed-digit arithmetic, and the requirement
for distributivity provides guidance for the design of
elementary multipliers.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@Article{Robison:1983:USF,
author = "A. D. Robison",
title = "Use Squares for Fast Multiplication",
journal = j-EDN,
volume = "28",
number = "21",
pages = "263, 267",
month = oct,
year = "1983",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@MastersThesis{Rosenblum:1983:IIS,
author = "David Samuel Rosenblum",
title = "An implementation of the {IEEE} standard for binary
floating-point arithmetic for the {Motorola} 6809
microprocessor",
type = "Thesis ({M.S.})",
school = "North Texas State University",
address = "Denton, TX, USA",
pages = "vi + 83",
month = aug,
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic.; Microprocessors ---
Programming.",
}
@InProceedings{Rump:1983:SAP,
author = "Siegfried M. Rump",
title = "Solving algebraic problems with high accuracy",
crossref = "Kulisch:1983:NAS",
pages = "51--120",
year = "1983",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "G.1; G.1.3; G.1.0; G.1.0",
content = "Numerical methods for the following applications are
surveyed in this paper: solving systems of linear
algebraic equations; obtaining the inverse of a given
matrix; finding zeros of functions and polynomials;
computing eigenvalues and eigenvectors of a matrix;
treating linear, quadratic and convex programming
problems; and calculating the values of arithmetic
expressions. Both the case where the coefficient matrix
is square and the case where the coefficient matrix is
rectangular are handled in connection with the solution
of systems of linear algebraic equations. Moreover,
methods for the special, but important, cases where the
coefficient matrix of a system of linear algebraic
equations is band or sparse are given. (In the latter
case, it is assumed that the system is solved by
iterative processes.) The common feature of all these
methods is that by studying carefully the basic
properties of the computer arithmetic (sketched in the
beginning of the paper), one can avoid the round-off
errors and, thus, achieve a high degree of accuracy. If
the data are exactly representable on the computer
under consideration, \ldots{}",
CRclass = "G.1.3 Numerical Linear Algebra; G.1.3 Numerical Linear
Algebra; G.1.3 Sparse and very large systems; G.1.0
General; G.1.0 Computer arithmetic; G.1.0 General;
G.1.0 Error analysis",
CRnumber = "8503-0216",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Numerical Linear Algebra; Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse
and very large systems; Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic;
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis",
genterm = "ALGORITHMS; PERFORMANCE",
reviewer = "Z. Zlatev; Zlatev, Z",
source = "in A new approach to scientific computation. Proc. of
the symposium on a new approach to scientific
computation (Yorktown Heights, NY, August 3, 1982), U.
Kulisch and W. Miranker (Eds.), Academic Press, Inc.,
New York, NY, 1983",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@InProceedings{Sand:1983:DIP,
author = "J. R. Sand and J. O. Bumgarner",
title = "{Dysan IEEE P-754} Binary Floating Point
Architecture",
crossref = "Ranocchia:1983:RFA",
pages = "185--194",
year = "1983",
bibdate = "Sat Nov 12 21:59:00 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Sandesara:1983:ZZF,
author = "S. Sandesara",
title = "{Zilog}'s {Z8070} Floating-Point Processor",
crossref = "Mini-Micro:1983:MMN",
pages = "7/4/1--3",
year = "1983",
bibdate = "Mon Sep 12 08:05:44 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Schelin:1983:CFA,
author = "Charles W. Schelin",
title = "Calculator function approximation",
journal = j-AMER-MATH-MONTHLY,
volume = "90",
number = "5",
pages = "317--325",
month = may,
year = "1983",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2975781",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "65D15 (65-03 65-04)",
MRnumber = "84h:65021",
MRreviewer = "J. Albrycht",
bibdate = "Wed Dec 3 17:17:33 MST 1997",
bibsource = "http://www.jstor.org/journals/00029890.htm;
https://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.jstor.org/stable/2975781",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
keywords = "Computer Function Evaluation; CORDIC Scheme; tabular
function values",
}
@InProceedings{Scherson:1983:MOA,
author = "Isaac Scherson and Smil Ruhman",
title = "Multi-operand Associative Arithmetic",
crossref = "IEEE:1983:PSC",
pages = "123--129",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Scherson_Ruhman.pdf",
abstract = "Multi-operand associative techniques attain their full
power in algorithms where the data may be recast into
disjoint data sets, all acted upon concurrently, each
by a different operand common to the set. But the
multi-operand approach can also serve to enhance
arithmetic operations significantly. The speed-up of
associative multiplication by handling a number of
multiplier bits at a time is described and analyzed,
including an effective algorithm for a limited sum of
products. The most complex process treated is
convolution, which serves to illustrate the enhancement
of an extended sum of products. Any number of vectors
stored in memory can be convolved simultaneously by a
common filter vector. Execution time is 45 milliseconds
for 1024 element data and filter vectors, 2048 element
results, and 16-bit precision.",
acknowledgement = ack-nhfb,
}
@Book{Schmid:1983:DC,
author = "Hermann Schmid",
title = "Decimal Computation",
publisher = pub-R-E-KRIEGER,
address = pub-R-E-KRIEGER:adr,
pages = "xi + 266",
year = "1983",
ISBN = "0-89874-318-4",
ISBN-13 = "978-0-89874-318-0",
LCCN = "QA75 .S34 1983",
bibdate = "Thu Sep 1 10:14:05 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprint of \cite{Schmid:1974:DC}.",
acknowledgement = ack-nhfb,
keywords = "binary-coded decimal system; calculators--circuits;
decimal floating-point arithmetic",
}
@InProceedings{Seidensticker:1983:CFH,
author = "R. B. Seidensticker",
title = "Continued Fractions For High-Speed and High-Accuracy
Computer Arithmetic",
crossref = "IEEE:1983:PSC",
pages = "184--193",
year = "1983",
bibdate = "Tue Nov 13 15:50:08 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Seidensticker.pdf",
abstract = "Continued fraction representation has many advantages
for fast and high-accuracy computation when compared
with positional notation. A continued fraction is a
number of the form\par
$$ p_1 + q_1 / (p_2 + q_2 / (p_3 + \cdots {}))
$$,\par
\noindent where $p$ and $q$ are integers. Some of the
benefits of continued fraction representation for
computer arithmetic are: faster multiply and divide
than with positional notation, fast evaluation of
trigonometric, logarithmic, and other unary functions,
easy extension to infinite-precision arithmetic,
infinite-precision representation of many
transcendental numbers, no roundoff or truncation
errors, and improved software transportability because
accuracy is not hardware dependent. A unified system
for continued fraction arithmetic is given along with
an outline of a hardware architecture for evaluating
these functions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; continued fractions",
}
@MastersThesis{Shah:1983:FPP,
author = "Kamalesh Ramanlal Shah",
title = "Floating point processor for {STOIC} instrumentation",
type = "Thesis ({M.S. in Engineering})",
school = "University of Texas at Austin",
address = "Austin, TX, USA",
pages = "xi + 188",
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Medical electronics.; Medical instruments and
apparatus --- Design and construction.;
Microprocessors.",
}
@Article{Smith:1983:FPA,
author = "Burks Smith",
title = "Floating Point Arithmetic and Numeric Representation
in Computers [letter] in {DDC}",
journal = j-DDJ,
volume = "8",
number = "2",
pages = "55--??",
month = feb,
year = "1983",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Soderstrand:1983:IRN,
author = "M. Soderstrand and C. Vernia and Jui-Hua Chang",
title = "An improved residue number system digital-to-analog
converter",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "30",
number = "12",
pages = "903--907",
month = dec,
year = "1983",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1049/el:19820632",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23540",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "A new technique for Residue Number System (RNS)
Digital-to-Binary or Digital-to-Analog conversion based
on the Chinese Remainder Theorem allows conversion with
only one level of ROM and one level of Adders. The
ROM's are small (e.g., 256 x 8) and \ldots{}",
}
@TechReport{Spafford:1983:RAP,
author = "Eugene Howard Spafford",
title = "A report on the accuracy of {PRIME} computers'
floating point software and hardware and the {SWT} math
library user's guide",
type = "{GIT-ICS}",
number = "83/09",
institution = "School of Information and Computer Science, Georgia
Institute of Technology",
address = "Atlanta, GA, USA",
pages = "v + 57",
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computers.",
}
@Article{Speiser:1983:SFP,
author = "Jeffrey Speiser",
title = "{Savage} Floating Point Benchmark in {PASCAL} in
{16BST}",
journal = j-DDJ,
volume = "8",
number = "11",
pages = "112--??",
month = nov,
year = "1983",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@TechReport{Springer:1983:FP,
author = "Charles Towne Springer",
title = "Floating point",
institution = "Mountain View Pr.",
address = "Mountain View, CA, USA",
pages = "22",
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "MVP-FORTH series; v. 3",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.; FORTH (Computer program
language)",
remark = "Title on cover: FORTH floating point.
``Pre-publication.''",
}
@Article{Swartzlander:1983:SLA,
author = "E. E. {Swartzlander, Jr.} and D. V. Satish Chandra and
H. T. {Nagle, Jr.} and S. A. Starks",
title = "Sign\slash Logarithm Arithmetic for {FFT}
Implementation",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "6",
pages = "526--534",
month = jun,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676274",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:09 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
note = "See comments \cite{Hongyuan:1986:CSL}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676274",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Takefuji:1983:FMS,
author = "Yoshiyasu Takefuji and Takakazu Kurokawa and Hideo
Aiso",
title = "Fast Matrix Solver in {$ \mathrm {GF}(2) $}",
crossref = "IEEE:1983:PSC",
pages = "138--143",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Takefuji_Kurokawa_Aiso.pdf",
abstract = "In this paper a parallel and pipelined fast matrix
equation solver in $ \mathrm {GF}(2) $ is proposed
where the elements are 0s or 1s. The solver employing
the iterative logic circuits which are suitable for
VLSI implementation can be realized by the conventional
Gauss--Jordan Elimination Method. $ O(n) $ gate stages
in the pipeline and $ O(n^2) $ total gates are required
for solving $ A X = b $ where $A$ is a matrix of $ n
\times n $, $X$ and $b$ are vectors respectively. The
organization of the solver is discussed in this
paper.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@TechReport{Tamura:1983:CDB,
author = "Y. Tamura and Y. Kanada",
title = "Calculation of $ \pi $ to 4,194,293 Decimals Based on
the {Gauss--Legendre} Algorithm",
type = "Technical report",
number = "CCUT-TR-83-01",
institution = "Computer Centre, University of Tokyo",
address = "Tokyo, Japan",
month = may,
year = "1983",
bibdate = "Mon Jul 18 17:46:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Taylor:1983:AE,
author = "George S. Taylor",
title = "Arithmetic on the {ELXSI 6400}",
crossref = "IEEE:1983:PSC",
pages = "110--115",
year = "1983",
bibdate = "Tue Nov 13 15:50:05 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Taylor.pdf",
abstract = "The ELXSI System 6400 is a new 64-bit general-purpose
mainframe computer [1]. This paper describes its
arithmetic instruction set architecture and the
organization of the arithmetic processor. The ELXSI
instruction set supports a complete implementation of
the proposed IEEE floating point standard [2], plus
integer and decimal arithmetic. The System 6400
arithmetic processor uses ECL gate arrays to execute
these instructions at high speed using a single board
of hardware.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; ELXSI 6400",
}
@Article{Taylor:1983:OFR,
author = "F. J. Taylor",
title = "An Overflow-Free Residue Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "5",
pages = "501--504",
month = may,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676263",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:09 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676263",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@MastersThesis{Thomas:1983:HLM,
author = "James W. Thomas",
title = "High-level language management of the {IEEE}
floating-point environment: research project",
type = "Thesis ({M.S. in Electrical Engineering})",
school = "University of California, Berkeley. Dept. of
Electrical Engineering and Computer Sciences",
address = "Berkeley, CA, USA",
pages = "27",
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Tseng:1983:FIP,
author = "Yeong-Jeng Tseng",
title = "A floating-point inner product step processor for use
in a {VLSI} Systolic array",
type = "Thesis ({M.S.})",
school = "Michigan State University",
address = "East Lansing, MI 48824, USA",
pages = "ix + 63",
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units; Electronic
digital computers --- Circuits; Floating-point
arithmetic; Integrated circuits --- Very large scale
integration.",
}
@Article{Ulman:1983:SDI,
author = "Z. D. Ulman",
title = "Sign Detection and Implicit-Explicit Conversion of
Numbers in Residue Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "6",
pages = "590--594",
month = jun,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676282",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:10 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676282",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Voelz:1983:CAE,
author = "H. V{\"o}lz",
title = "{CORDIC und {\"a}hnliche Algorithmen der elementaren
Funktionen mit besonderer Eignung f{\"u}r Mikrorechner}
\toenglish {CORDIC and Similar Algorithms for
Elementary Functions with Particular Aptitude for
Microcomputers} \endtoenglish",
journal = j-NACH-ELEK,
volume = "33",
number = "12",
pages = "506--510",
month = "????",
year = "1983",
CODEN = "NTELAP",
ISSN = "0323-4657",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Nachrichtentechnik Elektronik",
}
@Article{Vogt:1983:AFM,
author = "R. Vogt and R. Waser",
title = "{Arithmetikroutinen f{\"u}r die
Me{\ss}\-dat\-en\-ver\-ar\-beit\-ung} \toenglish
{Arithmetic Routines for Measurement Applications}
\endtoenglish",
journal = j-ELECTRONIK,
volume = "20",
pages = "85--92",
year = "1983",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronik",
}
@InProceedings{Wallis:1983:AFP,
author = "Peter J. L. Wallis",
title = "{Ada} Floating-Point Arithmetic as a Basis for
Portable Numerical Software",
crossref = "IEEE:1983:PSC",
pages = "79--81",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Wallis.pdf",
abstract = "Ada supports two different schemes for floating-point
arithmetic portability -- one based on the use of the
underlying machine arithmetic and the other based on
the `model arithmetic' that the underlying machine
supports, Features of both schemes are explained in the
context of their suitability as bases for the
production of portable numerical software.",
acknowledgement = ack-nhfb,
keywords = "Ada; ARITH-6",
}
@MastersThesis{Walsh:1983:FGE,
author = "Edmund John Walsh",
title = "Floating gatefield effect transistor operating point
changes: causes, characterization, and effect on
electric field measurement by the device",
type = "Thesis ({M.S.})",
school = "Boston University",
address = "Boston, MA, USA",
pages = "v + 121",
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Boston University. --- College of Engineering ---
Theses.",
}
@Article{Watanuki:1983:EAC,
author = "Osaaki Watanuki and Milo{\v{s}} D. Ercegovac",
title = "Error analysis of certain floating-point on-line
algorithms",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "4",
pages = "352--358",
month = apr,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676236",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "65G05",
MRnumber = "85h:65099",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676236",
abstract = "he properties of redundant number system in
significand (mantissa) representation are studied and
the range of redundant significand is derived. From the
range of the redundant significand and the absolute
error of on-line operations, the MRRE (maximum relative
representation error) is defined and analyzed for
floating-point on-line addition and multiplication.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
catcode = "G.1.0; G.1.0",
CRclass = "G.1.0 General; G.1.0 Error analysis; G.1.0 General;
G.1.0 Parallel algorithms",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis; Mathematics of Computing, NUMERICAL
ANALYSIS, General, Parallel algorithms",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
guideno = "06565",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
reviewer = "Oliver, J",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@MastersThesis{Williams:1983:BFP,
author = "Bertrand Jeffery Williams",
title = "A bit-serial floating point multiply\slash add
architecture for signal processing applications",
type = "Electrical Engineering Thesis ({M.S.})",
school = "Texas A\&M University",
address = "College Station, TX, USA",
pages = "x + 97",
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer architecture.; Floating-point arithmetic.;
Signal processing.",
}
@Article{Wingert:1983:ITA,
author = "J. A. Wingert",
title = "Improved Table-assisted Addition and Multiplication
Methods",
journal = j-IBM-TDB,
volume = "25",
number = "9",
pages = "4742--4743",
month = feb,
year = "1983",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@InProceedings{Yoshida:1983:FPR,
author = "Kaoru Yoshida",
title = "Floating-Point Recurring Rational Arithmetic System",
crossref = "IEEE:1983:PSC",
pages = "194--200",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Yoshida.pdf",
abstract = "Major computer arithmetic systems are based on the
concept of realizing only terminate rationals in
positional notation. This paper proposes a new
arithmetic scheme of indicating periodicity in the
radix representation of a mantissa to realize recurring
rationals as well as terminate rationals. A new
arithmetic system adopting the scheme, called the
``FLP/R* arithmetic system'', is proposed. Properties
of the FLP/R* numbers and the procedure of the FLP/R*
arithmetic are described.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; rational arithmetic",
}
@Article{Ypma:1983:ERE,
author = "T. J. Ypma",
title = "The effect of rounding errors on {Newtonlike}
methods",
journal = j-IMA-J-NUMER-ANAL,
volume = "3",
number = "1",
pages = "109--118",
year = "1983",
CODEN = "IJNADH",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65G05 (65H05)",
MRnumber = "84h:65047",
MRreviewer = "Ren{\'e} Alt",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@InProceedings{Abruzzo:1984:ACA,
author = "J. Abruzzo",
title = "Applicability of {CORDIC} Algorithm to Arithmetic
Processing",
crossref = "Kirk:1984:CRE",
pages = "79--86",
year = "1984",
bibdate = "Thu Sep 01 11:21:05 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Agrawal:1984:ACB,
author = "V. K. Agrawal and S. Murugesan",
title = "Algorithm converts {BCD} fractions to binary",
journal = j-EDN,
volume = "29",
number = "13",
pages = "278--280",
month = jun,
year = "1984",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@Article{Alia:1984:VAD,
author = "G. Alia and E. Martinelli",
title = "A {VLSI} algorithm for direct and reverse conversion
from weighted binary number system to residue number
system",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "31",
number = "12",
pages = "1033--1039",
month = dec,
year = "1984",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1109/TC.1984.1676355",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23552",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "Residue Number Systems (RNS) are proved to be useful
in many applications, as for example in signal
processing. In this paper, a VLSI computing
architecture is proposed for converting an integer
number N from the weighted binary representation into
\ldots{}",
}
@InProceedings{Ancona:1984:PET,
author = "M. Ancona and G. Dodero and F. Ricci",
title = "A portable environment for teaching mathematical
software development",
crossref = "Ford:1984:TML",
pages = "135--145",
year = "1984",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See main entry CR, Rev. 8508--0689.",
acknowledgement = ack-nhfb,
content = "ALGORITHMS; DESIGN; LANGUAGES; STANDARDIZATION",
procloc = "Proceedings paper",
subject = "G. Mathematics of Computing; G.4 MATHEMATICAL
SOFTWARE; K. Computing Milieux; K.6 MANAGEMENT OF
COMPUTING AND INFORMATION SYSTEMS; D. Software; D.2
SOFTWARE ENGINEERING; K. Computing Milieux; K.3
COMPUTERS AND EDUCATION",
subjects = "mathematics of computing, mathematical software,
portability; computing milieux, management of computing
and information systems, software management, software
development; software, software engineering,
distribution and maintenance, portability; computing
milieux, computers and education, computer and
information science education, computer science
education",
wsub = "A. C. R. Newbery",
}
@Article{Anonymous:1984:CPD,
author = "Anonymous",
title = "Correction to {``A Pipelined Distributed Arithmetic
PFFT Processor''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-33",
number = "3",
pages = "288--288",
month = mar,
year = "1984",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1984.1676429",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 09:22:50 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
note = "See \cite{Chow:1983:PDA}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676429",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Bell:1984:RMR,
author = "M. {Bell, Jr.} and W. Jenkins",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '84}",
title = "A residue to mixed radix converter and error checker
for a five-moduli residue number system",
volume = "??",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "242--245",
year = "1984",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A design is presented for an experimental device which
converts data from residue representation to mixed
radix representation while simultaneously checking for
single digit errors. The experimental system has a high
speed pipelined architecture and \ldots{}",
}
@Article{Black:1984:NIS,
author = "Cheryl M. Black and Robert P. Burton and Thomas M.
Miller",
title = "The Need for an Industry Standard of Accuracy for
Elementary-Function Programs",
journal = j-TOMS,
volume = "10",
number = "4",
pages = "361--366",
month = dec,
year = "1984",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2701.356101",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sun Sep 04 20:32:29 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Bollen:1984:NSD,
author = "J. A. M. Bollen",
title = "Numerical Stability of Descent Methods for Solving
Linear Equations",
journal = j-NUM-MATH,
volume = "43",
number = "3",
pages = "361--377",
year = "1984",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65G05 (65F10)",
MRnumber = "85f:65041",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "B0290B (Error analysis in numerical methods); C4110
(Error analysis in numerical methods)",
corpsource = "Department of Appl. Maths., Twente University of
Technol., Enschede, Netherlands",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "descent methods; digital arithmetic; error analysis;
floating point arithmetic; Gauss-Southwell method;
gradient method; linear differential equations; linear
equations; linear systems; numerical stability;
roundoff error analysis; stability",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Boney:1984:GTD,
author = "J. Boney",
title = "Goals and tradeoffs in the design of the {MC68881}
floating point coprocessor",
crossref = "NCC:1984:ACP",
pages = "107--113",
year = "1984",
bibdate = "Wed Sep 7 22:31:45 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Borwein:1984:AGM,
author = "J. M. Borwein and P. B. Borwein",
title = "The Arithmetic-Geometric Mean and Fast Computation of
Elementary Functions",
journal = j-SIAM-REVIEW,
volume = "26",
number = "3",
pages = "351--366",
month = jul,
year = "1984",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1026073",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65D20 (26A09)",
MRnumber = "86d:65029",
MRreviewer = "S. Conde",
bibdate = "Sat Mar 29 09:53:48 MDT 2014",
bibsource = "Compendex database;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://epubs.siam.org/toc/siread/26/3;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
abstract = "We produce a self contained account of the
relationship between the Gaussian arithmetic-geometric
mean iteration and the fast computation of elementary
functions. A particularly pleasant algorithm for pi is
one of the by-products.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliationaddress = "Dalhousie Univ, Halifax, NS, Can",
classification = "723; 921",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
journalabr = "SIAM Rev",
keywords = "AGM (Arithmetic-Geometric Mean); arithmetic-geometric
mean; calculation of pi; computational methods;
elliptic functions; Iterative Methods; mathematical
techniques; numerical mathematics",
onlinedate = "July 1984",
}
@InProceedings{Braddock:1984:ASP,
author = "M. Braddock and V. Shahan",
title = "Amplifying System Performance in Floating-point
Intensive Applications with the {MC68881}",
crossref = "Mini-Micro:1984:MMS",
pages = "6/2/1--7",
year = "1984",
bibdate = "Wed Sep 7 22:31:45 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Butterfield:1984:MT,
author = "J. Butterfield",
title = "Math and Tables",
journal = j-COMPUTE,
volume = "6",
number = "9",
pages = "134--135",
month = sep,
year = "1984",
CODEN = "COMPER",
ISSN = "0194-357X",
bibdate = "Thu Sep 1 10:15:30 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Compute",
}
@Article{Caraiscos:1984:REA,
author = "C. Caraiscos and Bede Liu",
title = "A roundoff error analysis of the {LMS} adaptive
algorithm",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "32",
number = "1",
pages = "34--41",
month = feb,
year = "1984",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "The steady state output error of the least mean square
(LMS) adaptive algorithm due to the finite precision
arithmetic of a digital processor is analyzed. It is
found to consist of three terms: (1) the error due to
the input data quantization, (2) the \ldots{}",
}
@Book{Cavanagh:1984:DCA,
author = "Joseph J. F. Cavanagh",
title = "Digital Computer Arithmetic: Design and
Implementation",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xi + 468",
year = "1984",
ISBN = "0-07-010282-1",
ISBN-13 = "978-0-07-010282-8",
LCCN = "QA76.9.C62 C38 1984",
bibdate = "Sat May 18 14:16:35 2002",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$21.95",
acknowledgement = ack-nj,
}
@MastersThesis{Cheng:1984:FPC,
author = "Doreen Y. Cheng",
title = "A floating point coprocessor for the {Butterfly}
multiprocessor system: research project",
type = "Thesis ({M.S. in Electrical Engineering})",
school = "University of California, Berkeley. Dept. of
Electrical Engineering and Computer Sciences",
address = "Berkeley, CA, USA",
pages = "51 + 38",
month = may,
year = "1984",
bibdate = "Wed Nov 25 08:35:11 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Clarke:1984:AAR,
author = "M. R. Clarke",
title = "An Analytical Approach to Rounding",
journal = j-J-APPL-STAT,
volume = "11",
number = "1",
pages = "12--20",
year = "1984",
CODEN = "????",
DOI = "https://doi.org/10.1080/02664768400000003",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Tue Sep 6 11:15:48 MDT 2011",
bibsource = "http://www.tandf.co.uk/journals/routledge/02664763.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
onlinedate = "28 Jul 2006",
}
@Article{Clenshaw:1984:BFP,
author = "C. W. Clenshaw and F. W. J. Olver",
title = "Beyond Floating Point",
journal = j-J-ACM,
volume = "31",
number = "2",
pages = "319--328",
month = apr,
year = "1984",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/62.322429",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "65G05",
MRnumber = "819 141",
bibdate = "Wed Jan 15 18:12:53 MST 1997",
bibsource = "Compendex database;
ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jacm.bib",
abstract = "A new number system is proposed for computer
arithmetic based on iterated exponential functions. The
main advantage is to eradicate overflow and underflow,
but there are several other advantages and these are
described and discussed.",
acknowledgement = ack-nhfb,
affiliationaddress = "Univ of Lancaster, Dep of Mathematics,
Lancaster, Engl",
classification = "723",
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
journalabr = "J Assoc Comput Mach",
keywords = "computer arithmetic; computer metatheory; error
analysis; mathematical techniques --- Digital
Arithmetic; overflow; rounding error; underflow",
}
@Article{Cody:1984:PRW,
author = "William J. {Cody, Jr.} and Jerome T. Coonen and David
M. Gay and K. Hanson and David Hough and W. Kahan and
R. Karpinski and John F. Palmer and F. N. Ris and D.
Stevenson",
title = "A Proposed Radix- and Word-length-independent Standard
for Floating-Point Arithmetic",
journal = j-IEEE-MICRO,
volume = "4",
number = "4",
pages = "86--100",
month = jul # "\slash " # aug,
year = "1984",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1984.291224",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Nov 8 14:50:28 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@PhdThesis{Coonen:1984:CPS,
author = "Jerome Toby Coonen",
title = "Contributions to a Proposed Standard for Binary
Floating-Point Arithmetic",
type = "Thesis ({Ph.D.} in Mathematics)",
school = "Department of Mathematics, University of California at
Berkeley",
address = "Berkeley, CA, USA",
pages = "320",
day = "18",
month = dec,
year = "1984",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In the fall of 1977 the Institute of Electrical and
Electronics Engineers commissioned working group 754 to
draft a standard for binary floating-point arithmetic.
It was intended to prevent the proliferation of
disparate arithmetics in the new microprocessor
industry. At that time there were so many different
flavors of arithmetic available on mainframes and
minicomputers that the cost of reconciling their
differences in numerical software had become, and
remains, staggering. Now, more than five years later,
draft 10.0 of the proposed standard has been voted out
of the working group for IEEE approval.\par
This thesis consists of a set of ``footnotes'' to the
proposed standard. The first of them, an implementation
guide published in January 1980, served as a working
draft of the standard for over a year. The remaining
chapters unfolded as the proposed standard did. They
include an analysis of gradual underflow, the most
controversial feature of the standard; an exhaustive
discussion of radix conversion, which has been
specified in the proposed standard only up to a
worst-case error bound; and a revised version of the
arithmetic test suite which has been available in
machine-readable form from the working group.",
acknowledgement = ack-nj # " and " # ack-nhfb,
advisor = "William M. Kahan",
remark = "Doctoral degree conferred December 18, 1984.",
}
@InCollection{Corliss:1984:AGT,
author = "George F. Corliss and Louis B. Rall",
title = "Automatic generation of {Taylor} series in
{Pascal-SC}: {Basic} operations and applications to
differential equations",
crossref = "Anonymous:1984:TFA",
pages = "177--209",
year = "1984",
bibdate = "Fri Dec 8 13:09:09 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Pascal-SC supports user-defined data types,
user-defined operators, and accurate floating point and
interval arithmetic for numerical computations. The
authors implement data types TAYLOR and ITAYLOR
(Interval Taylor) with operators $+$, $-$, $*$, $/$, $
** $, and the functions SQR, SQRT, EXP, SIN, COS,
ARCTAN, and LN. An initial value problem $ y' = y^2 $,
$ y(0) = 1 $, is solved with TAYLOR and with ITAYLOR
types to show that the series generation exhibits a
mild instability which has no significant effect on the
values of the solution computed by analytic
continuation.",
acknowledgement = ack-nj,
comment = "Also appeared as {\sl MRC Technical Summary Report No.
2497}, Mathematics Research Center, University of
Wisconsin-Madison, 1983.",
keywords = "automatic differentiation; stability.; Taylor series",
}
@Article{Cowlishaw:1984:DRL,
author = "M. F. Cowlishaw",
title = "The Design of the {REXX} Language",
journal = j-IBM-SYS-J,
volume = "23",
number = "4",
pages = "326--335",
year = "1984",
CODEN = "IBMSA7",
ISSN = "0018-8670",
bibdate = "Wed Jan 08 16:35:07 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "First published as IBM Hursley Technical Report
TR12.223, October 1983.",
abstract = "One way of classifying computer languages is by two
classes: languages needing skilled programmers, and
personal languages used by an expanding population of
general users. REstructured eXtended eXecutor (REXX) is
a flexible personal language designed with particular
attention to feedback from its users. It has proved to
be effective and easy to use, yet it is sufficiently
general and powerful to fulfill the needs of many
demanding professional applications. REXX is system and
hardware independent, so that it has been possible to
integrate it experimentally into several operating
systems. Here REXX is used for such purposes as command
and macro programming, prototyping, education, and
personal programming. This study introduces REXX and
describes the basic design principles that were
followed in developing it.",
acknowledgement = ack-nhfb,
affiliation = "IBM UK Ltd, Scientific Cent, Winchester, Engl",
affiliationaddress = "IBM UK Ltd, Scientific Cent, Winchester, Engl",
classification = "723",
fjournal = "IBM Systems Journal",
journalabr = "IBM Syst J",
keywords = "command program interpreters; computer operating
systems; computer programming languages; decimal
floating-point arithmetic; language concepts; personal
language; REXX language",
remark = "REXX supports arbitrary precision arithmetic with up
to $ 10^9 $ digits, and an exponent range of $ \pm 10^9
$. This capability was added to REXX in 1981.",
}
@Article{Demmel:1984:URN,
author = "James Demmel",
title = "Underflow and the reliability of numerical software",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "5",
number = "4",
pages = "887--919",
month = dec,
year = "1984",
CODEN = "SIJCD4",
ISSN = "0196-5204",
MRclass = "65G05",
MRnumber = "85m:65035",
MRreviewer = "G. Alefeld",
bibdate = "Tue Apr 29 19:18:28 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
corpsource = "Div. of Computer Science, California University,
Berkeley, CA, USA",
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
keywords = "codes; digital arithmetic; eigenvalue calculation;
Gaussian elimination; gradual underflow; numerical
software; polynomial evaluation; reliability; roundoff;
roundoff errors; store zero; uncertainty; underflow
mechanisms",
treatment = "T Theoretical or Mathematical",
}
@Article{Demsky:1984:MMC,
author = "J. Demsky and M. Schlesinger and R. D. Kent",
title = "Micro/mini computer program for calculating the square
root of rationals at arbitrary precision",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-877",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)82981-1",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:58 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584829811",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Dietrich:1984:FPR,
author = "D. Dietrich and R. Fischer",
title = "{Floating-Point-Routinen, entwickelt f{\"u}r
Mikrorechner} \toenglish {Floating-point Routines
Developed for Microcomputers} \endtoenglish",
journal = j-ELEKTRONIKER,
volume = "8",
pages = "49--54",
year = "1984",
CODEN = "ELKRBL",
ISSN = "0531-9218",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektroniker (Switzerland)",
}
@Article{Duncan:1984:FSF,
author = "Ray Duncan and Martin Tracy",
title = "The {FVG} Standard Floating-Point Extension",
journal = j-DDJ,
volume = "9",
number = "9",
pages = "110--??",
month = sep,
year = "1984",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
xxnote = "??Check author order??",
}
@Article{Dunford:1984:SFPa,
author = "Christopher J. Dunford",
title = "{Savage} floating-point benchmark in 8088\slash 8087
assembly language in {16BST}",
journal = j-DDJ,
volume = "9",
number = "7",
pages = "116--??",
month = jul,
year = "1984",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Dunford:1984:SFPb,
author = "Christopher J. Dunford",
title = "{Savage} floating-point benchmark in {Modula-2} in
{16BST}",
journal = j-DDJ,
volume = "9",
number = "8",
pages = "106--??",
month = aug,
year = "1984",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Ercegovac:1984:LAO,
author = "Milo{\v{s}} D. Ercegovac",
title = "On-line arithmetic: An overview",
journal = j-SPIE,
volume = "495",
pages = "86--93",
year = "1984",
bibdate = "Fri Nov 30 06:32:39 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Real Time Signal Processing VII.",
acknowledgement = ack-nhfb,
}
@Article{Ferguson:1984:SFP,
author = "Kenneth M. Ferguson",
title = "{Savage} floating-point benchmark deficiencies of in
{16BST}",
journal = j-DDJ,
volume = "9",
number = "8",
pages = "107--??",
month = aug,
year = "1984",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Fisher:1984:UAP,
author = "Gerry Fisher",
title = "Universal Arithmetic Packages",
journal = j-SIGADA-LETTERS,
volume = "3",
number = "6",
pages = "30--47",
month = may # "\slash " # jun,
year = "1984",
CODEN = "AALEE5",
DOI = "https://doi.org/10.1145/998388.998389",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Thu Sep 28 07:33:23 MDT 2000",
bibsource = "ftp://ftp.uu.net/library/bibliography;
http://www.adahome.com/Resources/Bibliography/articles.ref;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
note = "See erratum \cite{Froggatt:2015:EAU}.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "universal integer, universal real, rational
arithmetic",
}
@InCollection{Gautschi:1984:QNC,
author = "Walter Gautschi",
title = "Questions of numerical condition related to
polynomials",
crossref = "Golub:1984:SNA",
volume = "24",
pages = "140--177",
year = "1984",
MRclass = "65F35 (65H05)",
MRnumber = "925213",
bibdate = "Fri Feb 9 15:28:14 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@PhdThesis{Gleditsch:1984:FTR,
author = "Torstein Gleditsch",
title = "Forslag til rask prosessor for flerformat
floating-point aritmetikk. ({Norwegian}) [{Proposal}
for a fast processor for multiformat floating-point
arithmetic]",
type = "Hovedoppgave i informatikk (cand.scient)",
school = "Universitetet i Oslo",
address = "Oslo, Norway",
year = "1984",
bibdate = "Thu May 09 08:19:32 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Norwegian",
}
@Article{Goldberg:1984:LVS,
author = "Morton Goldberg",
title = "{LISP} Version of the {Savage} Floating Point
Benchmark in {16BST}",
journal = j-DDJ,
volume = "9",
number = "6",
pages = "82--??",
month = jun,
year = "1984",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Book{Gregory:1984:MAE,
author = "Robert Todd Gregory and E. V. Krishnamurthy",
title = "Methods and Applications of Error-Free Computation",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xii + 194",
year = "1984",
ISBN = "0-387-90967-2",
ISBN-13 = "978-0-387-90967-7",
LCCN = "QA297.5 .G735 1984",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Texts and monographs in computer science",
acknowledgement = ack-nhfb,
keywords = "Approximation theory --- Data processing.;
Floating-point arithmetic.",
shorttableofcontents = "Glossary of Notation / xi \\
I: Residue or Modular Arithmetic / 1 \\
II: Finite-Segment p-adic Arithmetic / 63 \\
III: Exact Computation of Generalized Inverses / 109
IV: Integer Solutions to Linear Equations / 134 \\
V: Iterative Matrix Inversion and the Iterative
Solution of Linear Equations / 162 \\
VI: The Exact Computation of the Characteristic
Bibliography / 186 \\
Index / 191",
tableofcontents = "Glossary of Notation / xi \\
I: Residue or Modular Arithmetic / 1 \\
1. Introduction / 1 \\
2. Single-Modulus Residue Arithmetic / 3 \\
3. Multiple-Modulus Residue Arithmetic / 11 \\
4. Mapping Standard Residue Representations onto
Integers / 17 \\
5. Single-Modulus Residue Arithmetic with Rational
Numbers / 23 \\
6. The Forward Mapping and the Inverse Mapping / 31 \\
7. Multiple-Modulus Residue Arithmetic with Rational
Numbers / 49 \\
II: Finite-Segment p-adic Arithmetic / 63 \\
1. Introduction / 63 \\
2. The Field of p-adic Numbers / 63 \\
3. Arithmetic in QP / 73 \\
4. A Finite-Segment p-adic Number System / 79 \\
5. Arithmetic Operations on Hensel Codes / 90 \\
6. Removing a Leading Zero from a Hensel Code / 99 \\
7. Mapping a Hensel Code onto a Unique Order-N Farey
Fraction / 100 \\
III: Exact Computation of Generalized Inverses / 109
\\
1. Introduction / 109 \\
2. Properties of g-inverses / 110 \\
3. Applications of g-inverses / 116 \\
4. Exact Computation of A+ if A Is a Rational Matrix /
118 \\
5. Failures of Residue Arithmetic and Precautionary
Measures / 131 \\
IV: Integer Solutions to Linear Equations / 134 \\
1. Introduction / 134 \\
2. Theoretical Background / 135 \\
3. The Matrix Formulation of Chemical Equations / 138
\\
4. Solving the Homogeneous System / 140 \\
5. Solving a Non-Homogeneous System / 148 \\
6. Solving Interval Linear Programming Problems / 150
\\
7. The Solution of Systems of Mixed-Integer Linear
Equations / 155 \\
V: Iterative Matrix Inversion and the Iterative
Solution of Linear Equations / 162 \\
1. Introduction / 162 \\
2. The Newton--Schultz Method for the Matrix Inverse /
163 \\
3. Iterative Solution of a Linear System / 169 \\
4. Iterative Computation of g-inverses / 174 \\
VI: The Exact Computation of the Characteristic
Polynomial of a Matrix / 180 \\
1. Introduction / 180 \\
2. The Algorithm Applied to Lower Hessenberg Matrices /
181 \\
Bibliography / 186 \\
Index / 191",
}
@Article{Guest:1984:RNS,
author = "C. C. Guest and M. M. Mirsalehi and T. K. Gaylord",
title = "Residue Number System Truth-Table Look-Up Processing
--- Moduli Selection and Logical Minimization",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-33",
number = "10",
pages = "927--931",
month = oct,
year = "1984",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1984.1676355",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 09:22:55 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676355;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35232",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "Truth table look-up processing using binary coded
residue numbers is investigated for full-precision
addition and multiplication for implementations using
either electronic or optical technologies. The
logically minimized numbers of input \ldots{}",
}
@Book{Hamacher:1984:CO,
author = "V. Carl Hamacher and Zvonko G. Vranesic and Safwat G.
Zaky",
title = "Computer organization",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
edition = "Second",
pages = "xvi + 590",
year = "1984",
ISBN = "0-07-025683-7",
ISBN-13 = "978-0-07-025683-5",
LCCN = "QA76.9.A73 H351 1984",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$34.95",
series = "McGraw-Hill series in computer organization and
architecture",
acknowledgement = ack-nhfb,
catcode = "C; B",
content = "The reviewer recommends this book to those who are
interested in learning the basics of computer
organization, particularly at the hardware and device
level. This book does not deal with the concepts
related to computer organization from an abstract,
mathematical level. It also does not attempt to
describe the computer organization using a high-level
language. Instead, the authors concentrate on
uniprocessing systems, with a large number of examples
drawn from VAX-11, IBM 370, and HP 3000. The book does
not cover multiprocessors.\par
The organization of the book is summarized here.
Chapter 1 introduces a number of terms. Chapters 2 and
3 concentrate in detail (a total of 101 pages) on the
addressing methods and instruction sets, with examples
taken primarily from the above mentioned machines.
Chapters 4 and 5 (a total of 50 pages) deal with the
control unit for the instruction fetch and execute,
with Chapter 5 being devoted to microprogrammed control
and bit slice designs. In Chapter 6 (a total of 64
pages) the authors cover Input/Output organization,
which includes a good deal about the
synchronous/asynchronous I/O operations, I/O
interfaces, etc. Chapter 7 presents the usual material
on the fixed- and floating-point arithmetic. \ldots{}",
CRnumber = "8509-0786",
descriptor = "Computer Systems Organization, GENERAL; Hardware,
GENERAL",
genterm = "DESIGN",
reviewer = "A. Deb",
subject = "C. Computer Systems Organization; C.0 GENERAL; B.
Hardware; B.0 GENERAL",
tableofcontents = "Basic structure of computers \\
Addressing methods and machine program sequencing \\
Instruction sets \\
The processing Unit \\
Microprogrammed control \\
Input--output organization- \\
Arithmetic \\
The main memory \\
Computer peripherals and work stations \\
Software \\
Microprocessors \\
Computer communications",
}
@Article{Honma:1984:IAE,
author = "Hitoshi Honma and Masahiko Sagawa",
title = "Improving the accuracy and error analysis in
floating-point {FFT} computation",
journal = j-ELECTRON-COMMUN-JPN,
volume = "67",
number = "11",
pages = "9--18",
year = "1984",
CODEN = "ECOJAL",
ISSN = "0424-8368",
MRclass = "65T05 (65G05 94A11)",
MRnumber = "86g:65238",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics and communications in Japan",
}
@TechReport{IBM:1984:ISR,
author = "{IBM Corporation}",
title = "{IBM System\slash 370 RPQ}. High Accuracy Arithmetic",
type = "Technical report",
number = "SA22-7093-0",
institution = pub-IBM,
address = pub-IBM:adr,
month = jan,
year = "1984",
bibdate = "Wed Oct 04 09:39:49 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bitsavers.trailing-edge.com/pdf/ibm/370/princOps/SA22-7093-0_High_Accuracy_Arithmetic_Jan84.pdf",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point dot product; accurate
floating-point summation; ACRITH",
remark = "According to IBM Web pages, ACRITH was withdrawn in
1991, and replaced by ACRITH XSC; however, I have yet
to be able to find online documentation for that
system.",
tableofcontents = "HIGH-ACCURACY-ARITHMETIC FACILITY / 1 \\
Floating-Point Instructions With Rounding Options / 1
\\
Normalization / 2 \\
Rounding / 2 \\
Rounding Modes / 2 \\
Guard Digit, Rounding Digit, and Sticky Bit / 3 \\
Arithmetic Exceptions / 4 \\
Default Result for Exponent Underflow / 5 \\
Floating-Point Accumulator / 5 \\
Vectors / 5 \\
Accumulator Layout / 6 \\
Accumulator Status Area / 8 \\
Accumulator Overflow / 9 \\
Storage-Operand Consistency / 9 \\
Instructions / 10 \\
ADD ACCUMULATOR TO ACCUMULATOR / 11 \\
ADD TO ACCUMULATOR / 12 \\
ADD WITH ROUNDING / 12 \\
CLEAR ACCUMULATOR / 13 \\
DIVIDE WITH ROUNDING / 13 \\
LOAD WITH ROUNDING / 14 \\
MULTIPLY AND ACCUMULATE / 15 \\
MULTIPLY WITH ROUNDING / 17 \\
ROUND FROM ACCUMULATOR / 17 \\
SUBTRACT ACCUMULATOR FROM ACCUMULATOR / 18 \\
SUBTRACT FROM ACCUMULATOR / 18 \\
SUBTRACT WITH ROUNDING / 19 \\
INDEX / 21",
}
@Book{ISO:1984:IID,
author = "{International Organization for Standardization}",
key = "ISO",
title = "{ISO\slash IEC DIS 10858}: {Information} technology
--- {Radix-independent} floating-point arithmetic",
publisher = pub-ISO,
address = pub-ISO:adr,
pages = "????",
year = "1984",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri May 28 21:52:25 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.iso.ch/cate/d18890.html",
acknowledgement = ack-nhfb,
}
@Article{Jones:1984:SRM,
author = "Christopher B. Jones",
title = "A Significance Rule for Multiple-Precision
Arithmetic",
journal = j-TOMS,
volume = "10",
number = "1",
pages = "97--107",
month = mar,
year = "1984",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/356068.356076",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65G05 (65G10)",
MRnumber = "86e:65063",
bibdate = "Sun Sep 04 20:02:26 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Multiple-precision arithmetic overcomes the round-off
error incurred in conventional floating-point
arithmetic, at the cost of increased processing
overhead. Significance arithmetic takes into account
the inexactness of the operands of a calculation, but
can lead to loss of significant digits after a long
series of operations. A new technique is described
which alleviates the overhead of multiple-precision
arithmetic by allowing nonsignificant digits to be
discarded, while limiting the significance loss per
operation to a controllable and acceptable rate. The
technique is based on storing an inexact number
interval, using a criterion of significance to
determine the precision with which the limits of
interval should be stored. A procedure referred to as a
significance rule uses this criterion to remove some of
the nonsignificant digits from the limits of an
interval prior to storage. A certain number of
nonsignificant digits are retained as guard digits.
Calculations are performed using exact interval
arithmetic and the significance-rule procedure is
invoked after each operation to remove superfluous
digits. Round-off in the procedure causes a slight
increase in the interval width on each operation. This
results in a cumulative loss of significance at a rate
related to the number of guard digits.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Karp:1984:ELS,
author = "A. H. Karp",
title = "Exponential and Logarithm by Sequential Squaring",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-33",
number = "5",
pages = "462--464",
month = may,
year = "1984",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1984.1676464",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Katzan:1984:IA,
author = "Harry Katzan",
title = "Invitation to {Ada}",
publisher = "PBI",
address = "New York, NY, USA",
pages = "x + 173",
year = "1984",
ISBN = "0-89433-239-2 (paperback)",
ISBN-13 = "978-0-89433-239-5 (paperback)",
LCCN = "QA76.73.A35 K36 1984",
bibdate = "Wed Oct 13 06:37:40 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$14.95",
series = "Petrocelli invitation to series",
acknowledgement = ack-nhfb,
remark = "See \cite[p. 1.10]{Coonen:1984:CPS} for negative
comments about the floating-point model for Ada in the
predecessor of this book \cite{Katzan:1982:IAA}.",
subject = "Ada (Computer program language)",
}
@Article{Kawabata:1984:SFP,
author = "Hugh M. Kawabata",
title = "{Savage} Floating Point Benchmark in {Fortran} in
{16BST}",
journal = j-DDJ,
volume = "9",
number = "1",
pages = "83--??",
month = jan,
year = "1984",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Book{Koopman:1984:FFP,
author = "Philip J. Koopman",
title = "{FORTH} floating point",
publisher = "Mountain View Pr.",
address = "Mountain View, CA, USA",
edition = "Second",
pages = "346",
year = "1984",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "MVP-FORTH series; v. 3",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.; FORTH (Computer program
language)",
}
@Article{Korn:1984:ISD,
author = "G. A. Korn",
title = "Interactive simulation with a direct-executing,
floating-point equation language",
journal = j-SYS-ANA-MODEL-SIM,
volume = "1",
number = "1",
pages = "45--54",
year = "1984",
CODEN = "SAMSEC",
ISSN = "0232-9298",
ISSN-L = "0232-9298",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "The University of Arizona, Tucson",
bibno = "43792",
catcode = "I.6.2; I.6.3",
CRclass = "I.6.2 Simulation Languages; I.6.3 Applications",
descriptor = "Computing Methodologies, SIMULATION AND MODELING,
Simulation Languages; Computing Methodologies,
SIMULATION AND MODELING, Applications",
fjournal = "Systems analysis, modelling, simulation",
genterm = "THEORY; DESIGN; LANGUAGES",
guideno = "1988-14427",
journalabbrev = "Syst. Anal. Model. Simul.",
subject = "I. Computing Methodologies; I.6 SIMULATION AND
MODELING; I. Computing Methodologies; I.6 SIMULATION
AND MODELING",
}
@Article{Kornerup:1984:CFP,
author = "Peter Kornerup and David W. Matula",
title = "Correction to `{`Finite Precision Rational Arithmetic:
An Arithmetic Unit''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-33",
number = "7",
pages = "682--682",
month = jul,
year = "1984",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1984.5009346",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 09:22:53 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009346",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Lin:1984:DSD,
author = "Ming-Liang Lin and Ernst Leiss and Bayliss McInnis",
title = "Division and sign detection algorithms for residue
number systems",
journal = j-COMPUT-MATH-APPL,
volume = "10",
number = "4--5",
pages = "331--342",
month = "????",
year = "1984",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:00:50 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122184900610",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@InProceedings{Ling:1984:NAS,
author = "Fuyun Ling and J. Proakis",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP '84}",
title = "Numerical accuracy and stability: Two problems of
adaptive estimation algorithms caused by round-off
error",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "571--574",
year = "1984",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "This paper investigates the numerical accuracy and the
numerical stability of adaptive estimation algorithms.
A feedback system model is provided to investigate the
numerical stability of the algorithms. Simulation
results on the comparison of \ldots{}",
}
@Article{Longo:1984:CFU,
author = "S. A. Longo",
title = "Calculating Functions using {Ada}",
journal = j-J-PAS-ADA,
volume = "3",
number = "4",
pages = "34--36",
month = jul # "--" # aug,
year = "1984",
ISSN = "0735-1232",
bibdate = "Fri Dec 08 13:05:34 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Journal of Pascal and Ada",
}
@InProceedings{Look:1984:CSH,
author = "H. W. Look",
title = "Compatible software and hardware implementations
permitted by {IEEE} standards for binary floating-point
arithmetic",
crossref = "NCC:1984:ACP",
pages = "101--105",
year = "1984",
bibdate = "Wed Sep 7 22:31:45 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Lorenz:1984:MIL,
author = "E. Lorenz and R. Sandau",
title = "{M{\"o}glichkeiten der Implementierung
leistungsf{\"a}higer Multiplikationsprogramme in
Mikrorechnersystemen} \toenglish {Possibilities of the
Implementation of Efficient Multiplication Instructions
in Microcomputer Systems} \endtoenglish",
journal = j-NACH-ELEK,
volume = "34",
number = "8",
pages = "288--290",
month = "????",
year = "1984",
CODEN = "NTELAP",
ISSN = "0323-4657",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Nachrichtentechnik Elektronik",
}
@TechReport{Mackin:1984:FFG,
author = "Michael A. Mackin and James F. Soeder",
title = "Floating-point function generation routines for 16-bit
microcomputers",
institution = "National Aeronautics and Space Administration",
address = "Washington DC, USA",
pages = "????",
year = "1984",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "NASA technical memorandum; 83783",
acknowledgement = ack-nhfb,
govtdocnumber = "NAS 1.15:83783 830-D (MF)",
keywords = "Microcomputers --- Programming.",
remark = "Distributed to depository libraries in microfiche.
Microfiche. [Washington, D.C.?: National Aeronautics
and Space Administration], 1984. 1 microfiche.",
}
@Article{Mactaggart:1984:SCR,
author = "I. Ross Mactaggart and Mervyn A. Jack",
title = "A single chip radix-$2$ {FFT} butterfly architecture
using parallel data distributed arithmetic",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "SC-19",
number = "3",
pages = "368--373",
month = jun,
year = "1984",
CODEN = "IJSCBC",
DOI = "https://doi.org/10.1109/JSSC.1984.1052151",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Thu Jul 07 10:57:50 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
}
@Article{Mansfield:1984:CAC,
author = "Richard Mansfield",
title = "A Complete Axiomatization of Computer Arithmetic",
journal = j-MATH-COMPUT,
volume = "42",
number = "166",
pages = "623--635",
month = apr,
year = "1984",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65G99 (03B70 03C70 68Q40)",
MRnumber = "85k:65040",
MRreviewer = "R. P. Brent",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Department of Math., Pennsylvania State University,
University Park, PA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "axiom system; complete axiomatization; computer
arithmetic; digital arithmetic; multiplication; rounded
addition; rounded arithmetic",
treatment = "T Theoretical or Mathematical",
}
@Article{Miller:1984:ILA,
author = "D. Miller and J. Polky",
title = "An implementation of the {LMS} algorithm in the
residue number system",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "31",
number = "5",
pages = "452--461",
month = may,
year = "1984",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1109/TC.1984.1676355",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23556",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "The Residue Arithmetic Adaptive Filter (RAAF)
processor performs the least mean square (LMS)
algorithm using 60 ns discrete PROM-latch combinations
for the residue operations. Parallel and pipeline
techniques are used throughout. Since the LMS
\ldots{}",
}
@Article{Moran:1984:SST,
author = "Thomas W. Moran",
title = "Some Spreadsheet Tests of the {Savage} Floating-Point
Benchmark in {16BST}",
journal = j-DDJ,
volume = "9",
number = "8",
pages = "106--??",
month = aug,
year = "1984",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@InCollection{Munzel:1984:RAE,
author = "Georg M{\"u}nzel",
booktitle = "Parallel computing 83 (Berlin, 1983)",
title = "Residue arithmetic for exact calculations on the
{DAP}",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "199--204",
year = "1984",
MRclass = "65W05",
MRnumber = "MR809397 (86k:65141)",
bibdate = "Thu Nov 8 14:50:29 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Murray:1984:SFA,
author = "J. T. Murray",
title = "Sin\slash Cos Functions via Approximations Plus Error
Compensation",
journal = j-IBM-TDB,
volume = "26",
number = "10A",
pages = "4967--4968",
month = mar,
year = "1984",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Misc{OliverWhiteheadQuintet:1984:FN,
author = "Oliver Whitehead Quintet",
title = "Free for now",
publisher = "Justin Time Records",
address = "????",
year = "1984",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "1 sound disc",
acknowledgement = ack-nhfb,
keywords = "Jazz --- 1981-1990.",
remark = "Brief record. Free for now --- Six-string waltz ---
Old friend --- Invention; Excuses, excuses --- Getting
away --- Woman in blue --- Floating point --- Crazy
season --- Do it with your socks on. Performed by the
Oliver Whitehead Quintet. JUST 4; Justin Time Records",
}
@Book{Palmer:1984:P,
author = "John F. Palmer and Stephen P. Morse",
title = "The 8087 Primer",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "viii + 182",
year = "1984",
ISBN = "0-471-87569-4",
ISBN-13 = "978-0-471-87569-7",
LCCN = "QA76.8.I2923 P34 1984",
bibdate = "Wed Dec 15 10:40:38 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Excellent coverage of the 8087 numeric coprocessor by
the chief architects of the Intel 8087 (Palmer) and
8086 (Morse). Contains many candid statements about
design decisions in these processors. A must for
serious assembly language coding of the 8087 and 80287
chips. See also \cite{Intel:1985:PRM}.",
acknowledgement = ack-nhfb,
}
@Article{Parker:1984:CCS,
author = "J. R. Parker",
title = "On Converting Character Strings to Integers",
journal = j-INFO-PROC-LETT,
volume = "19",
number = "1",
pages = "17--19",
day = "26",
month = jul,
year = "1984",
CODEN = "IFPLAT",
DOI = "https://doi.org/10.1016/0020-0190(84)90122-4",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Wed Nov 11 12:16:26 MST 1998",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/infoproc1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0020019084901224",
acknowledgement = ack-nhfb,
classification = "723; C4240 (Programming and algorithm theory)",
corpsource = "Department of Computer Sci., University of Calgary,
Calgary, Alta., Canada",
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
journalabr = "Inf Process Lett",
keywords = "character strings; character to integer conversion;
computer programming; integer overflow; programming
theory",
treatment = "T Theoretical or Mathematical",
}
@Article{Pei:1984:CAD,
author = "Soo-Chang Pei and Kuo-Chih Ho",
title = "Comments on {``Adaptive digital control implemented
using residue number systems''}",
journal = j-IEEE-TRANS-AUTOMAT-CONTR,
volume = "29",
number = "9",
pages = "863--863",
month = sep,
year = "1984",
CODEN = "IETAA9",
DOI = "https://doi.org/10.1109/TC.1984.1676355",
ISSN = "0018-9286 (print), 1558-2523 (electronic)",
ISSN-L = "0018-9286",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Tan:1982:ADC}.",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=24217",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Automatic Control",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
keywords = "residue arithmetic; residue number system",
summary = "The aim of this correspondence is to correct some
errors and modify Tan and McInnis residue number
decoding scheme into a simplified \ldots{}",
}
@Article{Pfenninger:1984:DES,
author = "E. Pfenninger",
title = "{Divisionsalgorithmus -- einfach und schnell}
\toenglish {Division Algorithms -- Simple and Fast}
\endtoenglish",
journal = j-ELEKTRONIKER,
volume = "15",
pages = "62--64",
year = "1984",
CODEN = "ELKRBL",
ISSN = "0531-9218",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektroniker (Switzerland)",
}
@Article{Pountain:1984:PM,
author = "D. Pountain",
title = "{PROLOG} on Microcomputers",
journal = j-BYTE,
volume = "9",
number = "13",
pages = "355--62",
month = dec,
year = "1984",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
LCCN = "QA 76.5 B98",
bibdate = "Thu Nov 8 14:50:29 2007",
bibsource = "/usr/local/src/bib/bibliography/Ai/log.prog.85.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Discusses micro-PROLOG, a dialect of PROLOG originally
written for the z80 microprocessor, which was the first
microcomputer implementation of the language. The
micro-PROLOG language is an interpreted language. A
program consists of a database of facts and rules that
you can query to solve problems. Logical propositions
replace computer-oriented instructions. Micro-PROLOG
has floating point arithmetic.",
acknowledgement = ack-nhfb,
fjournal = "BYTE Magazine",
keywords = "PROLOG",
}
@Article{Prince:1984:SFP,
author = "Thomas Prince",
title = "{Savage} Floating Point Benchmark in Logo in {16BST}",
journal = j-DDJ,
volume = "9",
number = "6",
pages = "82--??",
month = jun,
year = "1984",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@InProceedings{Rauchwerk:1984:MBF,
author = "M. D. Rauchwerk",
title = "A micro\-pro\-cess\-or-based fast floating point
library",
crossref = "IEEE:1984:CPI",
pages = "488--490",
year = "1984",
bibdate = "Thu Sep 01 12:03:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Regener:1984:MID,
author = "Eric Regener",
title = "Multiprecision Integer Division Examples Using
Arbitrary Radix",
journal = j-TOMS,
volume = "10",
number = "3",
pages = "325--328",
month = sep,
year = "1984",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1271.2738",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65V05",
MRnumber = "86g:65241",
bibdate = "Sun Sep 04 20:18:56 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hansen-per-brinch.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See also \cite{BrinchHansen:1994:MLD}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@InCollection{Schryer:1984:DCF,
author = "N. L. Schryer",
title = "Determination of Correct Floating-Point Model
Parameters",
crossref = "Cowell:1984:SDM",
pages = "360--366",
year = "1984",
bibdate = "Thu Sep 08 17:23:39 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Shahan:1984:MIF,
author = "V. Shahan",
title = "The {MC68881}: The {IEEE} Floating Point Standard
Reduced to One {VLSI} Chip",
crossref = "IEEE:1984:ILD",
pages = "172--176",
year = "1984",
bibdate = "Wed Sep 7 22:31:44 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Shen:1984:DET,
author = "J. P. Shen and F. J. Ferguson",
title = "The Design of Easily Testable {VLSI} Array
Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-33",
number = "6",
pages = "554--560",
month = jun,
year = "1984",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1984.1676480",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 09:22:52 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676480",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Shively:1984:CTG,
author = "R. R. Shively and W. V. Robinson and D. E. Orton",
title = "Cascading Transmission Gates to Enhance Multiplier
Performance",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-33",
number = "7",
pages = "677--679",
month = jul,
year = "1984",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1984.5009343",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 09:22:53 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009343",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Sips:1984:BSA,
author = "Henk J. Sips",
title = "Bit-Sequential Arithmetic for Parallel Processors",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-33",
number = "1",
pages = "7--20",
month = jan,
year = "1984",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1984.5009311",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 09:22:49 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009311",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Smoktunowicz:1984:BCI,
author = "Alicja Smoktunowicz and Jolanta Sokolnicka",
title = "Binary cascades iterative refinement in
doubled-mantissa arithmetics",
journal = j-BIT,
volume = "24",
number = "1",
pages = "123--127",
month = mar,
year = "1984",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01934524",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F05 (65G05)",
MRnumber = "85i:65039",
MRreviewer = "A. Bultheel",
bibdate = "Wed Jan 4 18:52:18 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=24&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=24&issue=1&spage=123",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@InProceedings{Soderstrand:1984:AQL,
author = "M. Soderstrand and G. Poe",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '84}",
title = "Application of quadratic-like complex residue number
system arithmetic to ultrasonics",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "484--487",
year = "1984",
CODEN = "ITCOB4",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The concept of a ``Quadratic-Like'' Complex Residue
Number System is introduced in which certain purely
imaginary numbers exist as reals within the system. It
is shown that the desirable properties of a Quadratic
Complex Residue Number System with \ldots{}",
}
@Article{Soderstrand:1984:PRR,
author = "M. Soderstrand and B. Sinha",
title = "A pipelined recursive residue number system digital
filter",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "31",
number = "4",
pages = "415--417",
month = apr,
year = "1984",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1109/TC.1983.1676240",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23555",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "The well-known advantages of pipelining as applied to
Finite Impulse Response (FIR) Residue Number System
(RNS) arithmetic digital filters is extended to the
important area of Infinite Impulse Response (IIR)
digital filters through a new technique \ldots{}",
}
@Book{Steele:1984:CLL,
author = "Guy L. Steele",
title = "{COMMON LISP}: the language",
publisher = pub-DP,
address = pub-DP:adr,
pages = "xii + 465",
year = "1984",
ISBN = "0-932376-41-X (paperback)",
ISBN-13 = "978-0-932376-41-1 (paperback)",
LCCN = "QA76.73.L23S73 1984",
bibdate = "Wed Jan 29 17:05:18 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "With contributions by Scott E. Fahlman and Richard P.
Gabriel and David A. Moon and Daniel L. Weinreb.",
acknowledgement = ack-nhfb,
keywords = "COMMON LISP (Computer program language)",
remark = "From \cite{Steele:2004:RHP}: ``In general,
computations with floating-point numbers are only
approximate.''",
}
@InProceedings{Stetter:1984:SDC,
author = "Hans J. Stetter",
title = "Sequential defect correction for high-accuracy
floating-point algorithms",
crossref = "Griffiths:1984:NAP",
pages = "186--202",
year = "1984",
DOI = "https://doi.org/10.1007/BFb0099525",
MRclass = "65V05 (65B05 65G05)",
MRnumber = "86j:65188",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Stewart:1984:PWG,
author = "R. G. Stewart",
title = "{P854} Working Group Completes Radix-Independent
Floating-Point Draft",
journal = j-IEEE-MICRO,
volume = "4",
number = "1",
pages = "82--83",
month = jan # "\slash " # feb,
year = "1984",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1984.291326",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Dec 14 06:08:58 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib;
Science Citation Index database (1980--2000)",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Article{Takla:1984:MBF,
author = "N. Takla and M. Hecker",
title = "A Monolithic 64 Bit Floating-Point Coprocessor",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "SC-19",
number = "4",
pages = "538--539",
month = aug,
year = "1984",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "A double/single-precision floating-point processor
using a titanium disilicide 3.5-$\mu$m NMOS process
achieves double-precision add/subtract, multiply, and
divide in 2, 8, and 16 $\mu$s respectively. The chip
has about 35K devices and is about \ldots{}",
}
@Article{Taylor:1984:BFP,
author = "F. Taylor",
title = "Block floating-point distributed filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "31",
number = "3",
pages = "300--304",
month = mar,
year = "1984",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "Distributed filters have been shown to offer an
impressive complexity-throughput tradeoff. In this
correspondence, a precision improvement is made in
distributed filtering using block floating-point
arithmetic. Performance improvement is predicted
\ldots{}",
}
@InProceedings{Teufel:1984:HAO,
author = "Thomas Teufel",
title = "A hardware architecture of an optimal
{BCD}-floating-point processor",
crossref = "Feilmeier:1984:PCP",
pages = "553--560",
year = "1984",
MRclass = "65G05",
MRnumber = "86j:65055",
bibdate = "Mon Apr 14 17:57:50 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@PhdThesis{Teufel:1984:OG,
author = "T. Teufel",
title = "{Ein optimaler Gleitkommaprozessor} \toenglish {An
Optimal Floating-Point Processor} \endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "??",
year = "1984",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Tricker:1984:ERM,
author = "A. R. Tricker",
title = "Effects of Rounding on the Moments of a Probability
Distribution",
journal = j-J-R-STAT-SOC-SER-D-STATISTICIAN,
volume = "33",
number = "4",
pages = "381--390",
month = dec,
year = "1984",
CODEN = "????",
DOI = "https://doi.org/10.2307/2987741",
ISSN = "0039-0526 (print), 1467-9884 (electronic)",
ISSN-L = "0039-0526",
bibdate = "Thu Jan 22 18:10:22 MST 2015",
bibsource = "http://www.jstor.org/stable/i349978;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jrss-d-1980.bib",
URL = "http://www.jstor.org/stable/2987741",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society. Series D
(The Statistician)",
journal-URL = "http://www.jstor.org/journals/00390526.html",
}
@MastersThesis{Trivedi:1984:DVF,
author = "Mrugesh Popatlal Trivedi",
title = "Dianostics of {VLSI} floating-point processors",
type = "Thesis ({M.S.})",
school = "The University of Tennessee, Knoxville",
address = "Knoxville, TN, USA",
pages = "viii + 98",
year = "1984",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.",
}
@MastersThesis{Truong:1984:FPP,
author = "Hung Si Truong",
title = "A floating point processor",
type = "Project ({M.S., Electrical and Electronic
Engineering})",
school = "California State University",
address = "Sacramento, CA, USA",
pages = "viii + 81",
year = "1984",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Charles Lytle, Chairperson",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.",
}
@Article{Uya:1984:CFP,
author = "M. Uya and K. Kaneko and J. Yasui",
title = "A {CMOS} floating point multiplier",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "19",
number = "5",
pages = "697--702",
month = oct,
year = "1984",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "A 32-bit CMOS floating-point multiplier is described.
The chip can perform 32-bit floating-point
multiplication (based on the proposed IEEE Standard
format) and 24-bit fixed-point multiplication (two's
complement format) in less than 78.7 and 71.1 ns
\ldots{}",
}
@Article{vonGudenberg:1984:BMG,
author = "J. Wolff von Gudenberg",
title = "{Berechnung maximal genauer Standardfunktionen mit
einfacher Mantissenl{\"a}nge} \toenglish {Computation
of Maximally Accurate Elementary Functions Using Simple
Mantissa Length} \endtoenglish",
journal = j-ELEK-RECHENANLAGEN,
volume = "26",
number = "5",
pages = "230--238",
month = oct,
year = "1984",
CODEN = "ELRAA4",
ISSN = "0013-5720",
bibdate = "Sat Feb 10 12:41:08 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronische Rechenanlagen",
}
@InCollection{Ware:1984:CMC,
author = "F. Ware and W. McAllister",
title = "{C-MOS} chip set streamlines floating-point
processing",
crossref = "Evanczuk:1984:MSS",
pages = "374--377",
year = "1984",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.0; C.5; C.5",
CRclass = "G.1.0 General; G.1.0 Computer arithmetic; C.5.3
Microcomputers; C.5.4 VLSI Systems",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic; Computer Systems Organization,
COMPUTER SYSTEM IMPLEMENTATION, Microcomputers;
Computer Systems Organization, COMPUTER SYSTEM
IMPLEMENTATION, VLSI Systems",
genterm = "DESIGN",
guideno = "00769",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
C. Computer Systems Organization; C.5 COMPUTER SYSTEM
IMPLEMENTATION; C. Computer Systems Organization; C.5
COMPUTER SYSTEM IMPLEMENTATION",
}
@MastersThesis{Wehmeyer:1984:EFF,
author = "Keith R. Wehmeyer",
title = "Effects of fixed and floating point mathematics on
digital filters",
type = "Thesis ({M.S.})",
school = "University of Cincinnati",
address = "Cincinnati, OH, USA",
pages = "vi + 92",
year = "1984",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "University of Cincinnati --- Theses. M.S. (Electrical
and Computer Engineering (1984))",
}
@Article{Wolrich:1984:HPF,
author = "G. Wolrich and E. McLellan and L. Harada and J.
Montanaro and R. A. J. Yodlowski",
title = "A High Performance Floating Point Coprocessor",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "SC-19",
number = "5",
pages = "690--696",
month = oct,
year = "1984",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "A 34000-transistor single-chip floating-point
coprocessor fabricated in 3-$\mu$m double metal NMOS
technology is described. The fraction data path,
including a shifter and 60-bit carry propagate ALU, is
cycled in 100 ns for all operations requiring
\ldots{}",
}
@InCollection{Woo:1984:AMC,
author = "B. Woo and L. Lin and R. E. Owen",
title = "{ALU}, multiplier chips zip through {IEEE}
floating-point operations",
crossref = "Evanczuk:1984:MSS",
pages = "354--359",
year = "1984",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "C.1.2; G.1.0",
CRclass = "C.1.2 Multiple Data Stream Architectures
(Multiprocessors); C.1.2 Pipeline processors; G.1.0
General; G.1.0 Computer arithmetic",
descriptor = "Computer Systems Organization, PROCESSOR
ARCHITECTURES, Multiple Data Stream Architectures
(Multiprocessors), Pipeline processors; Mathematics of
Computing, NUMERICAL ANALYSIS, General, Computer
arithmetic",
genterm = "DESIGN",
guideno = "00766",
subject = "C. Computer Systems Organization; C.1 PROCESSOR
ARCHITECTURES; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS",
}
@Book{Zuse:1984:CML,
author = "Konrad Zuse",
title = "{Der Computer, mein Lebenswerk}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xv + 218",
year = "1984",
ISBN = "0-387-13814-5 (U.S.)",
ISBN-13 = "978-0-387-13814-5 (U.S.)",
LCCN = "TK7885.22.Z87 A33 1984",
bibdate = "Mon Nov 4 07:46:57 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Based on the author's autobiography with the same
title published in 1970.",
acknowledgement = ack-nhfb,
keywords = "computer engineers --- Germany --- biography;
computers --- Germany --- history; Zuse, Konrad",
}
@Article{Aridgides:1985:EIQ,
author = "A. Aridgides and D. Morgan",
title = "Effects of input quantization in floating-point
digital pulse compression",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "33",
number = "2",
pages = "434--435",
month = apr,
year = "1985",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "A computer simulation of an FFT-based digital LFM
pulse compressor using vector floating point arithmetic
is presented, showing the effects of retaining various
number of mantissa bits at the input quantizer. Plots
of the compressed pulse waveforms \ldots{}",
}
@TechReport{Armstrong:1985:PLHa,
author = "Robert Clyde Armstrong",
title = "Procedural layout of a high-speed floating-point
arithmetic unit",
institution = "Massachusetts Institute of Technology, Research
Laboratory of Electronics",
address = "Cambridge, MA, USA",
pages = "116",
year = "1985",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Technical report; no 508 Technical report
(Massachusetts Institute of Technology. Research
Laboratory of Electronics); no. 508.",
acknowledgement = ack-nhfb,
remark = "Originally presented as author's thesis (Electrical
Engineer --- Massachusetts Institute of Technology)
1985. Bibliography: leaf 116. Supported in part by the
U.S. Air Force Office of Scientific Research contract",
}
@PhdThesis{Armstrong:1985:PLHb,
author = "Robert Clyde Armstrong",
title = "Procedural layout of a high-speed floating-point
arithmetic unit",
type = "Thesis ({Elect. E.})",
school = "Massachusetts Institute of Technology. Dept. of
Electrical Engineering and Computer Science",
address = "Cambridge, MA, USA",
pages = "116",
year = "1985",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supervised by Jonathan Allen.",
acknowledgement = ack-nhfb,
}
@Article{Aspinwall:1985:RVM,
author = "D. B. Aspinwall and Y. N. Patt",
title = "Retrofitting the {VAX-11\slash 780} Microarchitecture
for {IEEE} Floating Point Arithmetic --- Implementation
Issues, Measurements, and Analysis",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "8",
pages = "692--708",
month = aug,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676615",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:33:17 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676615",
abstract = "The VAX-11/7801 was designed specifically to implement
the VAX architecture. As such, it does not support the
IEEE standard for floating point arithmetic. A project
was undertaken to provide this support by modifying the
11/780 microarchitecture. Our objective was to produce
a microengine that would efficiently execute the VAX
instruction set, modified to handle VAX floating point
instructions in accordance with the IEEE standard. Our
methodology was to make minimal changes to the 11/780
hardware, relying primarily on changes to the
microcode. This paper describes the modifications
required to implement the IEEE standard, examines the
various design alternatives available to us, presents
measurements of our implementation, and analyzes our
results. We also offer some comments on the matter of
retrofitting an existing architecture to a new
unintended use.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Auzinger:1985:AAR,
author = "W. Auzinger and H. J. Stetter",
title = "Accurate arithmetic results for decimal data on
non-decimal computers",
journal = "Computing (New York)",
volume = "35",
number = "2",
pages = "141--151",
year = "1985",
CODEN = "????",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.0",
content = "One potentially useful feature absent from the High
Accuracy Arithmetic Subroutine Library (ACRITH) is the
generation of tight and guaranteed bounds on the
computed solution of numerical problems in cases where
some of the original data values are not representable
exactly as machine numbers. At present, such data
values must be replaced by enclosing machine intervals;
for ill-conditioned problems, the final interval
defining the solution may be relatively wide.\par
The authors here discuss the implementation of some
earlier ideas of Stetter's [1], relating to the
coupling of a conversion procedure for decimal data to
the evaluation algorithm proper, with the objective of
generating much narrower inclusions. A clear indication
of how this might be done is presented by means of an
illustrative example. A detailed specification is given
for a linear equation solver which should compute last
bit accurate inclusions of the solution for decimal
data using a hexadecimal machine. Also included are
four varied numerical examples, for which the results
are most impressive, and which appear to justify the
authors' claim. \par
-J. Oliver, Essex, UK \par
REFERENCES \par
[1] STETTER, H. J. Sequential defect correction for
high-accuracy floating-point algorithms, in Numerical
analysis, Proc. of the conference (Dundee, 1983),
Springer-Verlag",
CRclass = "G.1.0 General; G.1.0 Computer arithmetic",
CRnumber = "8607-0617",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic",
genterm = "THEORY; ALGORITHMS",
guideno = "04640",
keywords = "decimal floating-point arithmetic",
reviewer = "J. Oliver",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@InProceedings{Avizienis:1985:AAO,
author = "Algirdas Avi{\v{z}}ienis",
title = "Arithmetic Algorithms for Operands Encoded in
Two-Dimensional Low-Cost Arithmetic Error Code",
crossref = "Hwang:1985:PSC",
pages = "285--292",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Avizienis.pdf",
abstract = "A generalization of low-cost residue codes into
two-dimensional encodings was presented and error
detecting and error correcting properties of two
dimensional inverse residue codes were discussed
previously. This paper presents byte-serial checking,
additive inverse (complementation), and addition
algorithms for operands encoded in two-dimensional
residue and inverse residue codes.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Bannur:1985:VIS,
author = "J. Bannur and A. Varma",
title = "The {VLSI} Implementation of a Square Root Algorithm",
crossref = "Hwang:1985:PSC",
pages = "159--165",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Bannur_Varma.pdf",
abstract = "VLSI implementation of a square root algorithm is
studied. Two possible implementations of the basic
nonrestoring algorithm are presented --- the second is
more area-efficient and modular than the first. The
implementations are simple and easy to control, but, at
the same time, are more area-time efficient than many
existing designs. A hardware algorithm suited to
microprogram implementation is also given. Extension of
the algorithms to achieve $ 1 / 2 $-bit precision is
discussed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Barlow:1985:PEA,
author = "J. L. Barlow and E. H. Bareiss",
title = "Probabilistic error analysis of {Gaussian} elimination
in floating point and logarithmic arithmetic",
journal = j-COMPUTING,
volume = "34",
number = "4",
pages = "349--364",
year = "1985",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G05",
MRnumber = "87c:65046",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
reviewer = "N. N. Abdelmalek",
}
@Article{Barlow:1985:RED,
author = "J. L. Barlow and E. H. Bareiss",
title = "On Roundoff Error Distributions in Floating Point and
Logarithmic Arithmetic",
journal = j-COMPUTING,
volume = "34",
number = "4",
pages = "325--347",
month = dec,
year = "1985",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G05",
MRnumber = "87c:65045",
MRreviewer = "N. N. Abdelmalek",
bibdate = "Tue Oct 12 16:33:42 MDT 1999",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
affiliation = "Pennsylvania State Univ, Computer Science Dep,
University Park, PA, USA",
affiliationaddress = "USA",
classification = "723",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Computing (Vienna/New York)",
keywords = "computer arithmetic; computer metatheory; floating
point arithmetic; logarithmic arithmetic; roundoff
error distributions",
}
@Article{Barnes:1985:SFP,
author = "C. Barnes and Boi Tran and Shu Leung",
title = "On the statistics of fixed-point roundoff error",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "33",
number = "3",
pages = "595--606",
month = jun,
year = "1985",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "Roundoff error after fixed-point multiplication is
commonly modeled as uniformly distributed white noise
that is uncorrelated with the signal. This paper
presents a statistical analysis of fixed-point roundoff
error that identifies the conditions \ldots{}",
}
@Article{Bayoumi:1985:HVA,
author = "M. A. Bayoumi and G. A. Jullien and W. C. Miller",
title = "Hybrid {VLSI} architecture of {FIR} filters using
residue number systems",
journal = j-ELECT-LETTERS,
volume = "21",
number = "8",
pages = "358--359",
day = "11",
month = apr,
year = "1985",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:19850252",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4251043",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "residue arithmetic; residue number system",
summary = "An efficient VLSI architecture of FIR filters based on
large moduli set is described. The structure is hybrid,
combining both binary-based elements and look-up
tables. The binary-based section is arranged as a
two-dimensional systolic array using \ldots{}",
}
@Article{Bittner:1985:WPD,
author = "L. Bittner",
title = "{Weiteres {\"u}ber Pseudo-Divisionsverfahren zur
Berechnung der Standardfunktionen und gewisser
Nicht-Stan\-dard\-funk\-tion\-en} \toenglish {Further
Details on Pseudo-Division Procedures for Computation
of Standard Functions and Certain Nonstandard
Functions} \endtoenglish",
journal = j-Z-ANGE-MATH-MECH,
volume = "65",
number = "12",
pages = "605--612",
year = "1985",
CODEN = "ZAMMAX",
ISSN = "0044-2267 (print), 1521-4001 (electronic)",
ISSN-L = "0044-2267",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und
Mechanik}",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
xxmonth = "(none)",
}
@InProceedings{Bleher:1985:AHA,
author = "J. H. Bleher and A. E. Roeder and Siegfried M. Rump",
title = "{ACRITH}: High-accuracy arithmetic, an advanced tool
for numerical computation",
crossref = "Hwang:1985:PSC",
pages = "318--321",
year = "1985",
bibdate = "Sun May 28 18:31:07 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Bleher_Roeder_Rump.pdf",
abstract = "The High-Accuracy Arithmetic Subroutine Library
(ACRITH) is a program product for engineering /
scientific application. It consists of a subroutine
library for solving problems in numerical computation.
All results obtained have algorithmically verified
accuracy.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Bohte:1985:GEF,
author = "Zvonimir Bohte and Marko Petkov{\v{s}}ek",
title = "{Gaussian} elimination in floating-point arithmetic",
crossref = "Vrdoljak:1985:ICA",
pages = "85--91",
year = "1985",
MRclass = "65F05 (65G05)",
MRnumber = "86m:65028",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Brent:1985:SAI,
author = "R. P. Brent and H. T. Kung",
title = "A Systolic Algorithm for Integer {GCD} Computation",
crossref = "Hwang:1985:PSC",
pages = "118--125",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Brent_Kung.pdf",
abstract = "It is shown that the greatest common divisor of two
$n$-bit integers (given in the usual binary
representation) can be computed in time $ O(n) $ on a
linear systolic array of $ O(n) $ identical cells.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Burton:1985:SFE,
author = "C. G. Burton",
title = "The solution of finite element equations on the
floating point systems {FPS-164} attached processor",
journal = j-COMP-PHYS-COMM,
volume = "37",
number = "1-3",
pages = "171--180",
year = "1985",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
MRclass = "65N20 (65W05)",
MRnumber = "817 063",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@InProceedings{Cantoni:1985:PPA,
author = "V. Cantoni and M. Ferretti and S. Levialdi and R.
Stefanelli",
title = "{PAPIA}: {Pyramidal Architecture for Parallel Image
Analysis}",
crossref = "Hwang:1985:PSC",
pages = "237--242",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Cantoni_Ferretti_Levialdi_Stefanelli.pdf",
abstract = "In 1981 a national research program for the design,
simulation and construction of a multiprocessor image
processing system was started. After a first phase
devoted to the comparison of suggested and existing
systems and to the definition of a set of benchmarks
and to the evaluation of the performances of the major
classes of machines, a new system has been defined. The
structure of the new system is based on a pyramid of
processors and many applications in which this machine
may be exploited are highlighted. The multiprocessor
architecture has been fully designed and the chip will
be built by an Italian silicon foundry, the SGS
company, within the framework of the multichip national
project.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Cathey:1985:ISR,
author = "James Cathey",
title = "68000 Integer square root routine in {16BST}",
journal = j-DDJ,
volume = "10",
number = "5",
pages = "118--??",
month = may,
year = "1985",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@MastersThesis{Chen:1985:FPP,
author = "Jen-Chyun Chen",
title = "8087 floating point processor software utilities
development and evaluation",
type = "Thesis ({M.S.E.E.})",
school = "University of Alabama. Graduate School. Dept. of
Electrical and Engineering",
address = "Tuscaloosa, AL, USA",
pages = "x + 128",
year = "1985",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Programming (Electronic computers); Software
compatibility.",
}
@InProceedings{Chen:1985:MRS,
author = "Tien Chi Chen",
title = "Maximal Redundancy Signed-Digit Systems",
crossref = "Hwang:1985:PSC",
pages = "296--300",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Chen.pdf",
abstract = "The maximal redundancy signed-digit (MAXSD) number
system has the highest redundancy within the
carry-absorbing signed-digit number system proposed by
Avizienis in 1961. The digital values for radix R lie
in $ [1 - R, R - 1] $.\par
Its compatibility with both standard nonredundant
systems and binary arithmetic makes it an excellent
choice for multiprecision arithmetic on binary
machines. The representations for finite numbers are
however nonunique and can even be unbounded in
wordlength; this is resolved by algorithms for partial
or complete conversion to standard nonredundant
notation without explicit carry propagation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Cheng:1985:APF,
author = "H. D. Cheng and K. S. Fu",
title = "Algorithm Partition for a Fixed-Size {VLSI}
Architecture Using Space-Time Domain Expansion",
crossref = "Hwang:1985:PSC",
pages = "126--132",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Cheng_Fu.pdf",
abstract = "The space-time domain expansion method has recently
been used to transform a computational task with a
recursive formula into a VLSI architecture. In addition
to its simplicity and completeness, an important
advantage of this method is that it can easily solve
the problem of partitioning an algorithm to fit a fixed
size VLSI architecture. We propose a computational
model and a partition rule which can be easily used to
partition any recursive computation problem suited to
the space-time domain expansion method so it can be
solved on fixed-size VLSI architectures. Several
examples, such as partitioned vector inner product,
partitioned comparators in relational database
management, partitioned matrix multiplications. and
partitioned transitive closure computation, parallel
recognition of general context-free languages, string
matching and dynamic time-warp pattern-matching are
used to illustrate the proposed method.",
acknowledgement = ack-nhfb,
keywords = "algorithm partition; ARITH-7; multiprocessing;
pipelining; recursive task; space-time domain
expansion; very large scale integration (VLSI)",
}
@InProceedings{Chiarulli:1985:DDR,
author = "Donald M. Chiarulli and W. G. Rudd and Duncan A.
Buell",
title = "{DRAFT}: a Dynamically Reconfigurable Processor for
Integer Arithmetic",
crossref = "Hwang:1985:PSC",
pages = "309--317",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Chiarulli_Rudd_Buell.pdf",
abstract = "A special computer for high-precision arithmetic
features an ALU that is dynamically reconfigurable
under program control. The 256-bit ALU consists of 8
32-bit slices each of which has its own ALU operation
code in each microinstruction. The slices can remain
logically separated from each other, or be dynamically
connected to either or both of their neighbors under
control of a segment control code that is part of each
microinstruction. The micro-assembly language designed
for the machine includes special features to assist in
the control of the segmentation, data addressing, and
control sequencing. Estimations of the times required
to execute arithmetic operations on the machine show
that it will be exceptionally fast for problems in
computational number theory and factoring of
integers.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Chow:1985:PFD,
author = "Edward T. Chow and Dan I. Moldovan",
title = "Prime Factor {DFT} Parallel Processor Using Wafer
Scale Integration",
crossref = "Hwang:1985:PSC",
pages = "133--139",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Chow_Moldovan.pdf",
abstract = "A high speed, flexible, simple and regular Discrete
Fourier Transform (DFT) Array Processor architecture
based on the Prime Factor Algorithm (PFA) is presented
in this paper. The array processor is based only on one
type of VLSI cell and can compute an $N$ point DFT in
$N$ clock cycles throughput when $N$ is a composite
number of prime numbers. The high throughput rate is
achieved with only a small number of cells. With a
special indexing scheme presented in this paper, this
processor can use shift registers as the system memory
so that minimum global control and addressing is
achieved. This array processor architecture is also
highly tolerant to both semiconductor processing yield
and processor defects during run time. Thus, it can be
manufactured in large quantity with VLSI technology on
a single wafer and used in hazardous environments. With
these advantages, it is very attractive to satellite,
military and commercial applications.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Ciminiera:1985:ESP,
author = "L. Ciminiera and A. Serra",
title = "Efficient Serial-Parallel Arrays for Multiplikation
and Addition",
crossref = "Hwang:1985:PSC",
pages = "28--35",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Ciminiera_Serra.pdf",
abstract = "Three new arrays for unsigned and signed
multiplication, and for multiplication\slash addition
are presented. It is assumed that the factors are
expressed in 2's complement, while the addend (in the
latter array only) and the result are expressed in a
redundant notation. The arrays operate in
serial-parallel way since one factor is input in
parallel, while the second factor and the addend (in
the case of multiplication\slash addition) are entered
digit by digit starting from the most significant one;
the result is also produced serially with the most
significant digit first. Hence, the arithmetic unit
presented is suitable to be used as basic block of
special purpose processors performing functions such as
non-recursive digital filtering, signal correlation and
matrix multiplication. Indeed, they have the same speed
improvements as other similar units using redundant
representations for the result, with a cost: equivalent
to their counterparts based on full 2's complement
representation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Cody:1985:PRW,
author = "W. J. Cody and J. T. Coonen and D. M. Gay and K.
Hanson and D. Hough and W. Kahan and R. Karpinski and
J. Palmer and F. N. Ris and D. Stevenson",
title = "A Proposed Radix- and Word-length-independent Standard
for Floating-point Arithmetic",
journal = j-SIGNUM,
volume = "20",
number = "1",
pages = "37--51",
month = jan,
year = "1985",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Sep 1 10:14:17 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@InProceedings{Conover:1985:AHS,
author = "B. Conover and D. L. Gustafson",
title = "An Algorithm for High Speed Square Roots",
crossref = "IEEE:1985:ERC",
pages = "19--21",
year = "1985",
bibdate = "Fri Jun 11 18:04:41 1999",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Cozzens:1985:CDF,
author = "J. Cozzens and L. Finkelstein",
title = "Computing the discrete {Fourier} transform using
residue number systems in a ring of algebraic
integers",
journal = j-IEEE-TRANS-INF-THEORY,
volume = "31",
number = "5",
pages = "580--588",
month = sep,
year = "1985",
CODEN = "IETTAW",
DOI = "https://doi.org/10.1109/TIT.1985.1057081",
ISSN = "0018-9448 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=22750",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Information Theory",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
keywords = "residue arithmetic; residue number system",
summary = "A new method is described for computing an $N = R^{m}
= 2^{upsilon m}$-point complex discrete Fourier
transform that uses quantization within a dense ring of
algebraic integers in conjunction with a residue number
system over this ring. The \ldots{}",
}
@Article{Cuyt:1985:REA,
author = "Annie Cuyt and Paul Van der Cruyssen",
title = "Rounding error analysis for forward continued fraction
algorithms",
journal = j-COMPUT-MATH-APPL,
volume = "11",
number = "6",
pages = "541--564",
month = jun,
year = "1985",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:00:53 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122185900379",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@InProceedings{Dadda:1985:FMT,
author = "Luigi Dadda",
title = "Fast Multipliers for Two's-Complement Numbers in
Serial Form",
crossref = "Hwang:1985:PSC",
pages = "57--63",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Dadda.pdf",
abstract = "Schemes for designing multipliers of binary
two's-complement numbers in serial form are considered
with the condition of the least possible delay between
inputs and output.\par
Such schemes are composed by two parts: the first, the
array generator, produces the terms of the multiplier
array; the second, the summer, is fed by the array
generator and produces the product. Two classes of
multipliers are illustrated: the first generating the
multiplier array by diagonals and rows, the second by
columns.\par
The array generators are composed by and\slash or stack
registers and linear arrays of gates; the summer is
shown to be conveniently using parallel counters.",
acknowledgement = ack-nhfb,
author-dates = "29 April 1923--26 October 2012",
keywords = "ARITH-7",
}
@InProceedings{Dadda:1985:SBN,
author = "Luigi Dadda",
title = "Squares for Binary Numbers in Serial Form",
crossref = "Hwang:1985:PSC",
pages = "173--180",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Dadda1.pdf",
abstract = "The problem of designing squarers for binary number[s]
in serial form (with the condition of the least
possible delay between input and output) is
treated.\par
Several schemes are illustrated, derived from fast
multipliers for binary numbers in serial form,
described in a previous paper.\par
It is shown that some of such multipliers offer a
considerable saving in components when they are reduced
to squarers. Some schemes are illustrated, both for
positive and for two's-complement numbers.",
acknowledgement = ack-nhfb,
author-dates = "29 April 1923--26 October 2012",
keywords = "ARITH-7",
}
@InProceedings{DeMori:1985:DRP,
author = "R. {De Mori} and R. Cardin",
title = "Design for a Recursive Parallel Multiplier",
crossref = "Hwang:1985:PSC",
pages = "44--50",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Demori_Cardin.pdf",
abstract = "A network for performing multiplications of two two's
complement number's is proposed. The network can be
implemented in a synchronous or an asynchronous way. If
the factors to be multiplied have $N$ bits, the area
complexity of the network is $ O(N^2) $ for practical
values of $N$ as in the case of cellular multipliers.
Due to the design approach based on a recursive
algorithm, a time complexity $ O(\log N) $ is
achieved.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Dongarra:1985:FAS,
author = "J. J. Dongarra and D. C. Sorensen",
title = "A Fast Algorithm for the Symmetric Eigenvalue
Problem",
crossref = "Hwang:1985:PSC",
pages = "338--342",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Dongarra_Sorensen.pdf",
abstract = "The symmetric eigenvalue problem is one of the most
fundamental problems of computational mathematics. It
arises in many applications, and therefore represents
an important area for algorithmic research. It is also
one of the first eigenvalue problems for which reliable
methods have been obtained. It would be surprising
therefore, if a new method were to be found that would
offer a significant improvement in execution time over
the fundamental algorithms available in standard
software packages such as EISPACK [7]. However, it is
reasonable to expect that eigenvalue calculations might
be accelerated through the use of parallel algorithms
for parallel computers that are emerging. We shall
present such an algorithm in this paper. The algorithm
is able to exploit parallelism at all levels of the
computation and is well suited to a variety of
architectures. However, a pleasant bonus of this
research is that the parallel algorithm, even when run
in serial mode, is significantly faster than the best
sequential algorithm on large problems, and is
effective on moderate size (order $ \geq 30 $) problems
when run in serial mode.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
remark = "Listed in table of contents as 276--277.",
}
@InProceedings{Dunham:1985:PFM,
author = "C. B. Dunham",
title = "Floating point with rounding before normalization",
crossref = "Meek:1985:PFM",
pages = "91--102",
year = "1985",
MRclass = "65G05",
MRnumber = "86f:65089",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Eldon:1985:FCF,
author = "John A. Eldon",
title = "A Family of {CMOS} Floating Point Arithmetic Chips",
crossref = "Hwang:1985:PSC",
pages = "101--109",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Eldon.pdf",
abstract = "Although the advantages of floating point arithmetic
have long been recognized, hardware complexity and
expense have impeded its use in high speed digital
signal processing (DSP). Now, however, the availability
of a growing number of fast dedicated floating point
adder and multiplier chips is spurring renewed interest
in floating point for real time filtering and spectral
analysis.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Enzmann:1985:WDS,
author = "K. Enzmann",
title = "{Wurzelziehen durch sukzessive Approximation}
\toenglish {Root-Finding by Successive Approximation}
\endtoenglish",
journal = j-ELECTRONIK,
volume = "18",
pages = "92",
year = "1985",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronik",
}
@InProceedings{Ercegovac:1985:DAP,
author = "M. D. Ercegovac and T. Lang",
title = "A Division Algorithm with Prediction of Quotient
Digits",
crossref = "Hwang:1985:PSC",
pages = "51--56",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Ercegovac_Lang.pdf",
abstract = "A division algorithm with a simple selection of
quotient digits including prediction is possible if the
divisor is restricted to a suitable range. The
condition that the divisor must satisfy to have the
quotient digit $ q_{i + 1} $ predicted while computing
$ R_{i + 1} $ are determined. Some implementation
considerations are also given.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Book{Ercegovac:1985:DSH,
author = "Milo{\v{s}} D. Ercegovac and Tom{\'a}s Lang",
title = "Digital systems and hardware\slash firmware
algorithms",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xix + 838",
year = "1985",
ISBN = "0-471-88393-X",
ISBN-13 = "978-0-471-88393-7",
LCCN = "TK7868.D5 E73 1985",
bibdate = "Wed Nov 14 14:42:00 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$32.95",
URL = "http://www.loc.gov/catdir/bios/wiley043/84021983.html;
http://www.loc.gov/catdir/description/wiley035/84021983.html;
http://www.loc.gov/catdir/toc/onix06/84021983.html",
acknowledgement = ack-nhfb,
subject = "computer firmware; digital electronics",
}
@InProceedings{Fandrianto:1985:VFP,
author = "Jan Fandrianto and B. Y. Woo",
title = "{VLSI} Floating-Point Processors",
crossref = "Hwang:1985:PSC",
pages = "93--100",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Fandrianto_Woo.pdf",
abstract = "The advance of VLSI technology has been the enabling
factor in the appearance of VLSI circuits handling
floating-point arithmetics. These circuits have found
their way into many number-crunching applications such
as telecommunications, seismic energy exploration,
radar, medical imaging, graphics and simulation.
Because of the different requirements for different
applications, some processors have a rich repertoire of
functions but rather low performance, while some
processors aim at haying the highest throughput for the
most frequent operations such as multiply and add. This
paper will review the architecture, the technology, and
the design techniques for the current VLSI
floating-point processors; and it will also report a
high performance chipset (Weitek WTL1164\slash 1165)
implementing complete basic arithmetic functions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Ferguson:1985:RBA,
author = "Warren E. Ferguson and David W. Matula",
title = "Rationally Biased Arithmetic",
crossref = "Hwang:1985:PSC",
pages = "194--202",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Ferguson_Matula.pdf",
abstract = "One can naively view a computer number system as a
pair $ (F, P) $ consisting of a finite set $F$ of real
numbers and a rounding rule $P$. One such number system
is a hyperbolic rational number system which has as $F$
a finite set of rational numbers and as $P$ the
so-called mediant rounding rule. In this paper we
demonstrate how one can simulate a hyperbolic rational
number system in any high level language that supports
floating point computation. From this simulation we
infer that hyperbolic rational number systems form
viable alternatives to traditional binary floating
point number systems. Many properties of hyperbolic
rational number systems are derived fran the
relationship of their rounding rule to the
well-developed theory of best rational approximation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Book{Froberg:1985:NMT,
author = "Carl Erik Fr{\"o}berg",
title = "Numerical mathematics: theory and computer
applications",
publisher = pub-BENCUM,
address = pub-BENCUM:adr,
pages = "xi + 436",
year = "1985",
ISBN = "0-8053-2530-1",
ISBN-13 = "978-0-8053-2530-0",
LCCN = "QA297 .F6813 1985",
bibdate = "Fri Aug 20 09:03:54 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Revised edition of {\em Introduction to numerical
analysis, second edition, 1969}
\cite{Froberg:1969:INA}",
subject = "Numerical analysis; Data processing",
}
@InProceedings{Gal:1985:CEF,
author = "Shmuel Gal",
title = "Computing Elementary Functions: a New Approach for
Achieving High Accuracy and Good Performance",
crossref = "Miranker:1985:ASC",
pages = "1--16",
year = "1985",
DOI = "https://doi.org/10.1007/3-540-16798-6_1",
bibdate = "Thu Sep 01 12:27:23 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Gannon:1985:SPH,
author = "Dennis Gannon",
title = "{On} the Structure of Parallelism in a Highly
Concurrent {PDE} Solver",
crossref = "Hwang:1985:PSC",
pages = "252--259",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Gannon.pdf",
abstract = "This paper studies a variation of a parallel multigrid
PDE solver originally due to John Van Rosendale. This
paper gives a detailed analysis of the method and
discusses the large scale parallel structure. It will
show that the method can be viewed as a data driven
``large grain'' systolic structure. At a lower level
the algorithm is seen to be built from grid operators
that are, in turn, defined by expressions involving
vector functions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Gnanasekaran:1985:FSP,
author = "R. Gnanasekaran",
title = "A Fast Serial-Parallel Binary Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "8",
pages = "741--744",
month = aug,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676620",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:33:17 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676620",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Gomez:1985:PFA,
author = "Gustavo Rodr{\'\i}guez G{\'o}mez and David {Carrasco
Villareal}",
title = "Problems in floating-point arithmetic, and a method
for obtaining internal characteristics of digital
computers. ({Spanish})",
journal = "Miscel{\'a}nea Mat.",
volume = "15",
pages = "15--25",
year = "1985",
MRclass = "65G05",
MRnumber = "86h:65060",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Spanish",
}
@Article{Goodman:1985:REF,
author = "R. H. Goodman and A. Feldstein and J. Bustoz",
title = "Relative error in floating-point multiplication",
journal = j-COMPUTING,
volume = "35",
number = "2",
pages = "127--139",
year = "1985",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G05",
MRnumber = "87d:65052",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
reviewer = "Luciano Biasini",
}
@MastersThesis{Gooley:1985:DFM,
author = "Markian Myron Gooley",
title = "Design of a floating-point multiplier with a recursive
fraction-unit",
type = "Thesis ({M.S.})",
school = "University of Illinois at Urbana-Champaign",
address = "Urbana-Champaign, IL 61801, USA",
pages = "vi + 54",
year = "1985",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Graham:1985:IFF,
author = "Douglas R. Graham",
title = "Implementation of {FORTH} with floating point
capabilities of an 8085 system",
type = "Thesis ({M.S.})",
school = "Ohio University",
address = "Athens, OH, USA",
pages = "v + 122",
month = mar,
year = "1985",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "FORTH (Computer program language)",
}
@Article{Grappel:1985:FSC,
author = "R. D. Grappel",
title = "Fast subroutine calculates exponentials",
journal = j-EDN,
volume = "30",
number = "10",
pages = "231",
month = may,
year = "1985",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@InProceedings{Gridley:1985:IPS,
author = "Curt Gridley",
title = "Improving the Performance of Scientific Applications
on a Supermicro Using a Custom Floating Point Processor
and An Optimizing Compiler",
crossref = "USENIX:1985:SCP",
pages = "597--610",
year = "1985",
bibdate = "Tue Feb 20 15:42:13 MST 1996",
bibsource = "ftp://ftp.uu.net/library/bibliography;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Massachusetts Computer Corp.",
}
@InProceedings{Gross:1985:FPA,
author = "Thomas Gross",
title = "Floating-Point Arithmetic on a Reduced-Instruction-Set
Processor",
crossref = "Hwang:1985:PSC",
pages = "86--92",
year = "1985",
bibdate = "Thu Sep 01 12:02:04 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Gross.pdf",
abstract = "Current single chip implementations of
reduced-instruction-set processors do not support
hardware floating-point operations. Instead, floating
point operations have to be provided either by a
co-processor or by software. This paper discusses
issues arising from a software implementation of
floating point arithmetic for the MIPS processor, an
experimental VLSI architecture. Measurements indicate
that an acceptable level of performance is achieved.
but this approach is no substitute for a hardware
accelerator if higher precision results are required,
This paper includes instruction profiles for the basic
floating point operations and evaluates the usefulness
of some aspects of the instruction set.",
acknowledgement = ack-nj,
keywords = "ARITH-7",
}
@Article{Gross:1985:SIF,
author = "Thomas Gross",
title = "Software implementation of floating-point arithmetic
on a reduced-instruction-set processor",
journal = j-J-PAR-DIST-COMP,
volume = "2",
number = "4",
pages = "362--375",
month = nov,
year = "1985",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Carnegie-Mellon Univ, Pittsburgh, PA, USA",
classification = "723; C5230 (Digital arithmetic methods); C6130 (Data
handling techniques); C6140B (Machine-oriented
languages)",
corpsource = "Department of Computer Science, Carnegie-Mellon
University, Pittsburgh, PA, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "computer metatheory; computer software; data handling;
digital arithmetic; floating-point arithmetic;
instruction profiles; instruction sets; integrated
circuits, VLSI; million instructions per minute; MIPS
processor; processors; reduced-instruction-set;
reduced-instruction-set processor; RISC; single chip
implementations; single-chip processors; software
implementation; Stanford MIPS processor; VLSI
architecture",
treatment = "P Practical",
}
@InProceedings{Gudenberg:1985:CID,
author = "R. Lohner and J. Wolff V. Gudenberg",
title = "Complex Interval Division with Maximum Accuracy",
crossref = "Hwang:1985:PSC",
pages = "332--336",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Lohner_Gudenberg.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
xxabstract = "n/a",
}
@TechReport{Hack:1985:RPS,
author = "James J. Hack",
title = "The relationship of peak to sustained performance in
highly concurrent vector machine organizations",
type = "Research report",
number = "RC 11094 (\#49829)",
institution = "IBM T.J. Watson Research Center",
address = "Yorktown Heights, NY, USA",
pages = "22",
year = "1985",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Performance.;
Supercomputers.",
}
@Article{Helyer:1985:SCC,
author = "R. Helyer",
title = "Sine and cosine calculations",
journal = j-MICROPROC-MICROSYS,
volume = "2",
number = "5",
pages = "284",
month = oct,
year = "1985",
CODEN = "MIMID5",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Microprocessors and Microsystems",
}
@Article{Hull:1985:NT,
author = "T. E. Hull and A. Abraham and M. S. Cohen and A. F. X.
Curley and C. B. Hall and D. A. Penny and J. T. M.
Sawchuk",
title = "{Numerical Turing}",
journal = j-SIGNUM,
volume = "20",
number = "3",
pages = "26--34",
month = jul,
year = "1985",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Sat Aug 13 17:16:02 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Numerical Turing is an extension of the Turing
programming language. Turing is a Pascal-like language
(with convenient string handling, dynamic arrays,
modules, and more general parameter lists) developed at
the University of Toronto. Turing has been in use since
May, 1983, and is now available on several
machines.\par
The Numerical Turing extension is especially designed
for numerical calculations. The important new features
are: (a) clean decimal arithmetic, along with
convenient functions for directed roundings and
exponent manipulation; (b) complete precision control
of variables and operations.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "decimal floating-point arithmetic; documentation;
languages",
subject = "D.3.3 Software, PROGRAMMING LANGUAGES, Language
Constructs, Procedures, functions, and subroutines \\
D.3.2 Software, PROGRAMMING LANGUAGES, Language
Classifications, SUPERPILOT \\ G.1.0 Mathematics of
Computing, NUMERICAL ANALYSIS, General, Computer
arithmetic",
}
@Article{Hull:1985:PRV,
author = "T. E. Hull and A. Abrham",
title = "Properly Rounded Variable Precision Square Root",
journal = j-TOMS,
volume = "11",
number = "3",
pages = "229--237",
month = sep,
year = "1985",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/214408.214413",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D15 (65G05)",
MRnumber = "87a:65041",
bibdate = "Mon Dec 08 12:36:56 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p229-hull/",
abstract = "The square root function presented here returns a
properly rounded approximation to the square root of
its argument, or it raises an error condition if the
argument is negative. {\em Properly rounded} means
rounded to the nearest, or to nearest even in case of a
tie. It is {\em variable precision} in that it is
designed to return a $p$-digit approximation to a
$p$-digit argument, for any $ p > 0 $. (Precision $p$
means $p$ decimal digits.) The program and the analysis
are valid for all $ p > 0 $, but current
implementations place some restrictions on $p$.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; decimal floating-point arithmetic;
verification",
subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation. {\bf G.4}: Mathematics of Computing,
MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}:
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Certification and testing. {\bf G.4}: Mathematics of
Computing, MATHEMATICAL SOFTWARE, Verification. {\bf
G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS,
General, Error analysis. {\bf G.1.0}: Mathematics of
Computing, NUMERICAL ANALYSIS, General, Numerical
algorithms.",
}
@Book{Hunter:1985:III,
author = "Colin B. Hunter and James F. Ready and Erin Farquhar",
title = "Introduction to the {Intel iAPX 432} Architecture",
publisher = pub-RESTON,
address = pub-RESTON:adr,
pages = "vii + 181",
year = "1985",
ISBN = "0-8359-3222-2",
ISBN-13 = "978-0-8359-3222-6",
LCCN = "QA76.8.I267 H86 1984",
bibdate = "Mon Feb 7 19:14:11 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$16.95",
acknowledgement = ack-nhfb,
}
@Article{Hurson:1985:SMU,
author = "A. R. Hurson and B. Shirazi",
title = "A systolic multiplier unit and its {VLSI} design",
journal = j-COMP-ARCH-NEWS,
volume = "13",
number = "3",
pages = "302--309",
month = jun,
year = "1985",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 12 09:40:54 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@InProceedings{Hwang:1985:MEC,
author = "Kai Hwang and Zhiwei Xu",
title = "Multiprocessors for Evaluating Compound Arithmetic
Functions",
crossref = "Hwang:1985:PSC",
pages = "266--275",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Hwang_Xu.pdf",
abstract = "A dynamic network approach is proposed for designing
multifunctional arithmetic processors to support {\em
complex}, {\em interval}, {\em vector}, {\em matrix},
{\em polynomial}, and other {\em compound arithmetic}
operations. This arithmetic-network approach is
extended from the multipipeline chaining concept
implemented in Cray Research supercomputers. The
proposed design methodology offers a viable way of
developing very powerful and flexible arithmetic
multiprocessors for scientific supercomputing.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Hwang:1985:SIS,
author = "Kai Hwang and Daniel D. Gajski and Ahmed Sameh",
title = "The {Seventh IEEE Symposium on Computer Arithmetic}:
Foreword",
crossref = "Hwang:1985:PSC",
pages = "iii--iii",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_contents.pdf;
http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Hwang_Gajski_Sameh.pdf;
http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_preface.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
xxabstract = "n/a",
}
@Book{IEEE:1985:AIS,
author = "{IEEE Task P754}",
title = "{ANSI\slash IEEE 754-1985, Standard for Binary
Floating-Point Arithmetic}",
publisher = pub-IEEE-STD,
address = pub-IEEE-STD:adr,
pages = "20",
day = "12",
month = aug,
year = "1985",
ISBN = "1-55937-653-8",
ISBN-13 = "978-1-55937-653-2",
bibdate = "Thu Mar 02 09:57:22 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Revised 1990. A preliminary draft was published in the
January 1980 issue of IEEE Computer, together with
several companion articles
\cite{Cody:1981:APF,Coonen:1981:UDN,Coonen:1980:IGP,Coonen:1981:EIG,Hough:1981:API,Stevenson:1981:PSBa,Stevenson:1981:PSBb}.
The final version was republished in
\cite{IEEE:1985:ISBa,IEEE:1985:ISBb}. See also
\cite{Waser:1982:IAD}. Also standardized as {{\em IEC
60559 (1989-01) Binary floating-point arithmetic for
microprocessor systems}}.",
price = "US\$35.00",
URL = "http://ieeexplore.ieee.org/iel1/2355/1316/00030711.pdf;
http://standards.ieee.org/reading/ieee/std/busarch/754-1985.pdf;
http://standards.ieee.org/reading/ieee/std_public/description/busarch/754-1985_desc.html;
http://www.iec.ch/cgi-bin/procgi.pl/www/iecwww.p?wwwlang=E&wwwprog=cat-det.p&wartnum=019113",
acknowledgement = ack-nhfb,
}
@Manual{IEEE:1985:ASI,
author = "{IEEE Task P754}",
title = "{ANSI}\slash {IEEE 754}-1985, Standard for Binary
Floating-Point Arithmetic",
organization = "IEEE, New York",
month = aug # " 12",
year = "1985",
bibdate = "Thu Nov 8 14:50:30 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "A preliminary draft was published in the January 1980
issue of IEEE Computer, together with several companion
articles
\cite{Cody:1981:APF,Coonen:1981:UDN,Coonen:1980:IGP,Coonen:1981:EIG,Hough:1981:API,Stevenson:1981:PSBa,Stevenson:1981:PSBb}.
Available from the IEEE Service Center, Piscataway, NJ,
USA.",
acknowledgement = ack-nj,
}
@Article{IEEE:1985:ISBa,
author = "IEEE",
title = "{IEEE} Standard for Binary Floating-Point Arithmetic",
journal = j-SIGPLAN,
volume = "22",
number = "2",
pages = "9--25",
month = feb,
year = "1985",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun May 02 09:20:35 1999",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{IEEE:1985:AIS}.",
acknowledgement = ack-nj,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
xxnote = "This reference is wrong; the volume 22 is from 1987,
and neither volume 20 (1985) nor 22 have this
article??",
}
@Book{IEEE:1985:ISBb,
author = "{IEEE Computer Society Standards Committee.Working
group of the Microprocessor Standards Subcommittee} and
{American National Standards Institute}",
title = "{IEEE} standard for binary floating-point arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "18",
year = "1985",
bibdate = "Sun May 02 09:20:47 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{IEEE:1985:AIS}.",
series = "ANSI/IEEE Std 754-1985.",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units --- Standards.;
Floating-point arithmetic --- Standards.",
}
@Book{Intel:1985:FPL,
author = "{Intel Staff}",
title = "Floating Point Library for {DOS} 8096 Systems Manual",
publisher = "Intel Corporation",
address = "Santa Clara",
pages = "60",
month = dec,
year = "1985",
ISBN = "0-917017-75-7",
ISBN-13 = "978-0-917017-75-9",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$10.00",
acknowledgement = ack-nhfb,
keywords = "(COMPUTER OPERATING SYSTEM); PC-DOS; TECHNOLOGY ---
COMPUTERS AND COMPUTER TECHNOLOGY",
language = "eng",
}
@Book{Intel:1985:PRM,
author = "Intel",
title = "The {iAPX} 286 Programmer's Reference Manual",
publisher = pub-INTEL,
address = pub-INTEL:adr,
year = "1985",
bibdate = "Sun May 2 09:20:57 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "The definitive statement of what the 80286 and 80287
are. A valuable reference for instruction definitions.
See also \cite{Intel:1983:HRM,Palmer:1984:P}.",
acknowledgement = ack-nhfb,
}
@Manual{IntelCorporation:1985:FAL,
author = "{Intel Corporation}",
title = "The 8096 floating-point arithmetic library user's
guide for {DOS} systems",
organization = "Intel Corporation",
address = "Santa Clara, CA.",
pages = "various",
year = "1985",
ISBN = "0-917017-75-7",
ISBN-13 = "978-0-917017-75-9",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer programs.; Floating-point arithmetic.;
Operating systems (Computers)",
remark = "``Order number: 122366-001.'' On cover: Software
development tools. Cover title: 8096 floating point
library for DOS systems.",
}
@Article{Jankowski:1985:ASC,
author = "M. Jankowski and H. Wo{\'z}niakowski",
title = "The accurate solution of certain continuous problems
using only single precision arithmetic",
journal = j-BIT,
volume = "25",
number = "4",
pages = "635--651",
year = "1985",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65G05 (65L05)",
MRnumber = "87d:65053",
MRreviewer = "E. R. Hansen",
bibdate = "Thu Nov 12 18:12:56 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "accurate floating-point summation",
}
@InProceedings{Jenkins:1985:CDI,
author = "W. Jenkins and E. Davidson and D. Paul",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '85}",
title = "A custom-designed integrated circuit for the
realization of residue number digital filters",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "220--223",
year = "1985",
CODEN = "????",
DOI = "https://doi.org/10.1049/el:19850252",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Results are presented on the design, layout, and
fabrication of a custom-designed integrated circuit for
a residue number system digital filter module. The
architecture is based on a ROM-ACCUMULATOR FIR
structure in which the modular arithmetic for
\ldots{}",
}
@InProceedings{Kahan:1985:AIA,
author = "W. Kahan and E. LeBlanc",
title = "Anomalies in the {IBM ACRITH} Package",
crossref = "Hwang:1985:PSC",
pages = "322--331",
year = "1985",
bibdate = "Thu Sep 08 00:10:49 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Kahan_LeBlanc.pdf",
abstract = "The IBM ACRITH package of numerical software is
advertised as reliable and easy to use; but sometimes
its results must astonish or confuse a naive user. This
report exhibits a few of the surprises. For instance, a
finite continued fraction, easy to evaluate in two
dozen keystrokes on a handheld calculator, causes
ACRITH to overflow either exponent range or 15
Megabytes of virtual memory. Lacking access to source
code, we must speculate to explain the anomalies. Some
seem attributable to small bugs in the code; some to
optimistic claims or oversimplifications in the code's
documentation; some to flaws in the doctrine underlying
the code. We conclude that different techniques than
used by ACRITH might have been about as accurate and
yet more economical, robust and perspicuous.",
acknowledgement = ack-nj,
keywords = "ARITH-7",
}
@Article{Karpinski:1985:PFP,
author = "R. Karpinski",
title = "Paranoia: a Floating-Point Benchmark",
journal = j-BYTE,
volume = "10",
number = "2",
pages = "223--235",
month = feb,
year = "1985",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "BYTE Magazine",
}
@InProceedings{Kaushik:1985:MEC,
author = "Saroj Kaushik",
title = "Multiple Error Correction and Addictive Overflow
Detection with Magnitude Indices in Residue Code",
crossref = "Hwang:1985:PSC",
pages = "278--284",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Kaushik.pdf",
abstract = "A new approach for correcting multiple errors and
detecting an additive overflow in the Residue Number
System (RNS) is suggested. It works with the code whose
redundancy is in the form of magnitude indices. The
residue representation of a number with magnitude index
is reconsidered. The RNS with magnitude index were
first studied by Sasaki [16] and Rao [15] and then by
Barsi and Maestrini [5,6]. The range of a given RNS is
divided into intervals of equal width and the magnitude
of a number X is defined as a integer locating X into
one of such intervals. We have proposed algorithm which
detects and corrects multiple errors in residue number.
The algorithms for special cases viz., single burst
residue error and single residue error are also
suggested. Some of the advantages are pointed out over
the existing approaches.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Klatte:1985:ASS,
author = "R. Klatte and C. P. Ullrich and J. W. {Von
Gudenberg}",
title = "Arithmetic Specification for Scientific Computation in
{ADA}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "11",
pages = "996--1005",
month = nov,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676532",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:33:34 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676532",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Kobayashi:1985:MTC,
author = "Hideaki Kobayashi",
title = "A Multioperand Two's Complement Addition Algorithm",
crossref = "Hwang:1985:PSC",
pages = "16--19",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Kobayashi.pdf",
abstract = "This paper presents a novel algorithm for summing a
set of 2's complement numbers in parallel. The 2's
complement addition is converted to an equivalent
parallel summation of unsigned numbers. The conversion
is performed by simply complementing all the sign bits.
Only a few constant bits are required for sign
correction. This algorithm is suitable for
computer-aided design (CAD) of custom VLSI.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Manual{Koopman:1985:FFP,
author = "Philip J. Koopman",
title = "{FORTH} floating point",
volume = "3",
organization = "Mountain View Press",
address = "Mountain View, CA, USA",
edition = "Revised",
pages = "346",
year = "1985",
ISBN = "0-914699-28-8",
ISBN-13 = "978-0-914699-28-6",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "MVP-FORTH books",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming;
Floating-point arithmetic; FORTH (Computer program
language)",
remark = "Running title: MVP-FORTH integer and floating point
math. A complete glossary of MVP-FORTH math
extensions.",
}
@InProceedings{Kornerup:1985:FPL,
author = "Peter Kornerup and David W. Matula",
title = "Finite Precision Lexicographic Continued Fraction
Number Systems",
crossref = "Hwang:1985:PSC",
pages = "207--214",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Kornerup_Matula.pdf",
abstract = "Lexicographic continued fraction binary (LCF)
representation provides an order preserving bitstring
representation of the non negative real numbers where
every rational number has a finite length bitstring
representation. We investigate the precision of $k$-bit
LCF approximation. The maximum gap size over $ [0, 1) $
for $ (k + 1) $-bit LCF representation is shown to be
less than $ 2^{0.81k} $, comparable to binary coded
decimal in worst case representation efficiency. The
distribution of gap sizes for $ (k + 1) $-bit LCF
representation over $ [0, 1] $ is shown on a
logarithmic scale to be bell shaped between $ 2^{0.81k}
$ and $ 2^{-1.39k} $, becoming more peaked near the
value corresponding to uniform spacing, $ 2^{-k} $,
with increasing $k$.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Krishnan:1985:CDS,
author = "R. Krishnan and G. Jullien and W. Miller",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '85}",
title = "Complex digital signal processing using quadratic
residue number systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "764--767",
year = "1985",
CODEN = "????",
DOI = "https://doi.org/10.1049/el:19850252",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Recently, the Quadratic Residue Number System (QRNS)
has been introduced [4,5,6], which allows the
multiplication of complex integers with two real
multiplications. Restrictions on the form of the moduli
can be removed if an increase in real \ldots{}",
}
@InProceedings{Kurokawa:1985:PT,
author = "Takakazu Kurokawa and Hideo Aiso",
title = "Polynomial Transformer",
crossref = "Hwang:1985:PSC",
pages = "153--158",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Kurokawa_Aiso.pdf",
abstract = "Any relations among finite fields can be transformed
to a unique polynomial of one variable using Galois
Fields. In this paper, we explain the design of a
``Polynomial Transformer'' which executes the
transformation.\par
Polynomial Transformer consists of very simple and
iterative logic, and it is very suitable for parallel
and pipelined VLSI algorithm. Moreover, three
dimensional construction of a Polynomial Transformer is
possible. Thus, it serves as an example of a typical
three dimensional VLSI.\par
Its application can be found in Polynomial
Transformation, disturbance of data and so on.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Kwan:1985:MOW,
author = "Hon Kwan",
title = "A multi-output wave --- digital biquad using magnitude
truncation instead of controlled rounding",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "32",
number = "11",
pages = "1185--1187",
month = nov,
year = "1985",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "The use of magnitude truncation instead of controlled
rounding for the elimination of zero-input and
constant-input oscillations in the wave digital biquad
derived from the feedforwardRC-active configuration is
described. We also describe \ldots{}",
}
@Article{Lang:1985:ICL,
author = "J. H. Lang and C. A. Zukowski and R. O. Lamaire and
Chae Han",
title = "Integrated-Circuit Logarithmic Arithmetic Units",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "5",
pages = "475--483",
month = may,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676588",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:32:33 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676588",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Li:1985:FCD,
author = "S.-Y. R. Li",
title = "Fast Constant Division Routines",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "9",
pages = "866--869",
month = sep,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676646",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:33:33 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676646",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Li:1985:PAC,
author = "Xiaobo Li and Lionel M. Ni",
title = "A Pipeline Architecture for Computing Cumulative
Hypergeometric Distributions",
crossref = "Hwang:1985:PSC",
pages = "166--172",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Li_Ni.pdf",
abstract = "The hypergeometric distribution is a widely used
arithmetic function and is fundamental to many
statistical sampling and statistical pattern
recognition problems. Computation of the cumulative
hypergeometric distribution function, $ H(a) $, is
extremely time-consuming. As a result, many
approximation algorithms have been proposed to evaluate
the cumulative hypergeometric distribution. This paper
describes a two-level pipeline architecture for
computing $ H(a) $ with computation complexity reduced
to $ c + a $, where $c$ is a constant. The main part of
the design is a type of recurrence computation. A
modular and systematic approach is suggested to
implement the recurrence formula. The computation
complexity of the proposed architecture is also
compared with various other known methods. The highly
regular structure of the design can lead to efficient
VLSI implementation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Ling:1985:NFL,
author = "Fuyun Ling and D. Manolakis and J. Proakis",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP '85}",
title = "New forms of {LS} lattice algorithms and an analysis
of their round-off error characteristics",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1739--1742",
year = "1985",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "New formulas are presented for direct updating of the
reflection coefficients in the a priori and a
posteriori forms of the least squares (LS) lattice
algorithms. An analysis of the numerical
characteristics of the new LS lattice forms is given
and \ldots{}",
}
@InProceedings{Liu:1985:DVR,
author = "Wentai Liu and J. C. Duh and Daniel E. Atkins",
title = "The Design of a Vector-Radix {2DFFT} Chip",
crossref = "Hwang:1985:PSC",
pages = "231--236",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Liu_Duh_Atkins.pdf",
abstract = "Architectures based on the vector-radix 2DFFT
algorithm and hence can avoid the matrix transpose
problem have been proposed. The unique feature of the
proposed architectures is that the data can be driven
into the arithmetic processors in a pipeline fashion.
This paper presents a prototype chip, which has been
designed in $ 2 \mu $ m NMOS technology, for the
generalized butterfly unit. The chip is a two-stage
pipelined processor. The design experience, timing
information, and the chip features including four
multipliers, one adder\slash subtracter and PLA
controllers are presented.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Lohninger:1985:GF,
author = "H. Lohninger",
title = "{Gleitkommaarithmetik f{\"u}r den 68000} \toenglish
{Floating-point Arithmetic for the 68000}
\endtoenglish",
journal = j-MC,
volume = "2",
pages = "58--64",
year = "1985",
ISSN = "0720-4442, 0941-777x , 0943-5409",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "MC: Die Mikrocomputer-Zeitschrift",
}
@Article{Lorenz:1985:AIP,
author = "E. Lorenz",
title = "{Aspekte der Implementierung eines Programmpaketes zur
schnellen und flexiblen Ausf{\"u}hrung von
arithmetischen Operationen mit dem U880} \toenglish
{Aspects of the Implementation of a Software Package
for Fast and Flexible Execution of Arithmetic
Operations on the U880} \endtoenglish",
journal = j-NACH-ELEK,
volume = "35",
number = "5",
pages = "179--181",
month = "????",
year = "1985",
CODEN = "NTELAP",
ISSN = "0323-4657",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "The U880 is a Z80 clone microprocessor that was built
in the GDR (East Germany).",
acknowledgement = ack-nj,
fjournal = "Nachrichtentechnik Elektronik",
}
@InProceedings{Luk:1985:PMC,
author = "Franklin T. Luk",
title = "A Parallel Method for Computing the Generalized
Singular Value Decomposition",
crossref = "Hwang:1985:PSC",
pages = "260--265",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Luk.pdf",
abstract = "We describe a new parallel algorithm for computing the
generalized singular value decomposition of two $ n
\times n $ matrices, one of which is nonsingular. Our
procedure requires $ O(n) $ e time and one triangular
array of $ O(n^2) $ processors.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Majerski:1985:SRA,
author = "S. Majerski",
title = "Square-Rooting Algorithms for High-Speed Digital
Circuits",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "8",
pages = "724--733",
month = aug,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676618",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:33:17 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676618",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Matula:1985:FPR,
author = "David W. Matula and Peter Kornerup",
title = "Finite Precision Rational Arithmetic: Slash Number
Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "1",
pages = "3--18",
month = jan,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676511",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 30 06:21:13 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Fraction number systems characterized by fixed-slash
and floating-slash formats are specified. The structure
of arithmetic over such systems is prescribed by the
rounding obtained from ``best rational approximation.''
Multitiered precision hierarchies of both the
fixed-slash and floating-slash type are described and
analyzed with regards to their support of both exact
rational and approximate real computation.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Manual{ME:1985:FPS,
title = "Floating point and string listing",
organization = "Microprocessor Engineering",
address = "Southampton, UK",
edition = "Second",
pages = "36",
year = "1985",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.",
}
@Article{Mithani:1985:ASN,
author = "D. Mithani and S. Iyer",
title = "Algorithm speeds nonrestoring division in
microprogrammed systems",
journal = j-EDN,
volume = "30",
number = "4",
pages = "199--208",
month = feb,
year = "1985",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 15 18:42:21 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@Article{Modi:1985:AIS,
author = "J. J. Modi and J. S. Rollett",
title = "An algorithm for inverse square-roots",
journal = j-PARALLEL-COMPUTING,
volume = "2",
number = "1",
pages = "69--71",
month = mar,
year = "1985",
CODEN = "PACOEJ",
DOI = "https://doi.org/10.1016/0167-8191(85)90018-3",
ISSN = "0167-8191 (print), 1872-7336 (electronic)",
ISSN-L = "0167-8191",
MRclass = "65W05 (65D15)",
MRnumber = "86j:65195",
bibdate = "Mon Apr 14 12:07:40 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An algorithm is presented for finding $ x^{ 1 / 2} $,
given $x$. The algorithm is designed to be particularly
suited for parallel computation, in which
floating-point multiplication, floating-point addition
and fixed-point arithmetic can be performed
simultaneously.",
acknowledgement = ack-nhfb,
classification = "C4290 (Other computer theory)",
corpsource = "Department of Eng., Cambridge University, UK",
fjournal = "Parallel Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/01678191",
keywords = "fixed-point arithmetic; floating-point addition;
floating-point multiplication; inverse square roots
algorithm; parallel computation; parallel processing",
treatment = "T Theoretical or Mathematical",
}
@Article{Moharir:1985:ESG,
author = "P. S. Moharir",
title = "Extending the Scope of {Golub}'s Method Beyond Complex
Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "5",
pages = "484--487",
month = may,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676590",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:32:33 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676590",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Montgomery:1985:MMT,
author = "Peter L. Montgomery",
title = "Modular Multiplication Without Trial Division",
journal = j-MATH-COMPUT,
volume = "44",
number = "170",
pages = "519--521",
month = apr,
year = "1985",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Y16",
MRnumber = "86e:11121",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2007970",
abstract = "Let $ N > 1 $. We present a method for multiplying two
integers (called $N$-residues) modulo $N$ while
avoiding division by $ N. N $-residues are represented
in a nonstandard way, so this method is useful only if
several computations are done modulo one $N$. The
addition and subtraction algorithms are unchanged.",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "C1160 (Combinatorial mathematics); C5230 (Digital
arithmetic methods); C6130 (Data handling techniques)",
corpsource = "Syst. Dev. Corp., Santa Monica, CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "digital arithmetic; integer; integer arithmetic;
modular arithmetic; modular multiplication;
multiplication; N-residue; N-residue arithmetic; number
theory",
treatment = "T Theoretical or Mathematical",
}
@Manual{Motorola:1985:MFC,
title = "{MC68881} floating-point coprocessor user's manual",
organization = "Motorola, Inc.",
address = "Phoenix, AZ, USA",
pages = "various",
year = "1985",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Microprocessors --- Handbooks, manuals, etc.",
remark = "Spine title: MC68881 user's manual. ``MC68881
UM/AD''--Cover.",
}
@Book{Motorola:1985:MFP,
author = "Motorola",
title = "{MC68881} Floating-Point Coprocessor User's Manual",
publisher = pub-MOTOROLA,
address = pub-MOTOROLA:adr,
edition = "Second",
year = "1985",
bibdate = "Fri Sep 02 23:38:03 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Muller:1985:DBC,
author = "Jean-Michel Muller",
title = "Discrete basis and computation of elementary
functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "9",
pages = "857--862",
month = sep,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676643",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "65D20 (65V05)",
MRnumber = "87e:65016",
MRreviewer = "D. Zwick",
bibdate = "Sun Jul 10 08:33:33 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676643",
abstract = "We give necessary and sufficient conditions in order
that the infinite product or sum of the terms of a
positive decreasing sequence generates the reals in a
given interval.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Naseem:1985:MCA,
author = "Asif Naseem and P. David Fisher",
title = "The Modified {CORDIC} Algorithm",
crossref = "Hwang:1985:PSC",
pages = "144--152",
year = "1985",
bibdate = "Wed Sep 14 20:50:04 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Naseem_Fisher.pdf",
abstract = "A Modified CORDIC Algorithm (MCA) has been developed
for the evaluation of elementary arithmetic functions.
MCA incorporates increased parallelism over the
original CORDIC algorithm, thus, resulting in an
enhanced speed of computation. This has been
accomplished by decoupling the CORDIC iteration
equations, and transforming the sequential nature of
these equations. $n$-bit fixed point data operands are
assumed and the parameter $k$ relates to the level of
parallelism in the algorithm. The modified algorithm
employs a $ [k + 1]n^2 $-bit ROM for lookup tables that
enable elementary arithmetic functions to be evaluated
in no more than $ [3 n + 2] $ and no less than $2$ time
steps. The two bounds correspond to a pipelined and a
parallel implementation, respectively. The formulation
of the MCA can be manipulated to obtain implementations
with various speed\slash cost characteristics. This
compares to $ n(3 n + 1) / 2 $ time steps for the
original CORDIC algorithm. For example, 32-bit ALU has
$ k = 12 $ and $ n = 32 $; so, a 13,312-bit ROM is
required to store the lookup tables, and the
computation requires 98 time steps for a pipelined
implementation.",
acknowledgement = ack-nj,
keywords = "ARITH-7",
}
@Article{Neumaier:1985:IPR,
author = "A. Neumaier",
title = "Inner Product Rounding Error Analysis in the Presence
of Underflow",
journal = j-COMPUTING,
volume = "34",
number = "4",
pages = "365--373",
year = "1985",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G05",
MRnumber = "86j:65054",
bibdate = "Tue Oct 12 16:33:42 MDT 1999",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
affiliation = "Univ Freiburg, Inst f{\"u}r Angewandte Mathematik,
Freiburg, West Germany",
classification = "723; 921",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Computing (Vienna/New York)",
keywords = "computer metatheory; inner product rounding error
analysis; inner products; mathematical techniques ---
error analysis; underflow",
}
@InProceedings{Ngai:1985:RAT,
author = "Tin-Fook Ngai and Mary Jane Irwin",
title = "Regular, area-time efficient carry-lookahead adders",
crossref = "Hwang:1985:PSC",
pages = "9--15",
year = "1985",
bibdate = "Fri Nov 16 10:05:44 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Ngai_Irwin.pdf",
abstract = "For fast binary addition, a carrylookahead (CLA)
design is the obvious choice [OnAt83, BaJM83]. However,
the direct implementation of a CLA adder in VLSI faces
some undesirable limitations. Either the design lacks
regularity, thus increasing the design and
implementation costs, or the interconnection wires are
too long, thus causing area-time inefficiency and
limits on the size of addition. Brent and Kung solved
the regularity problem by reformulating the carry chain
computation [BrKu82]. They showed that an $n$-bit
addition can be performed in time $ O(\log n) $, using
area $ O(n \log n) $ with maximum interconnection wire
length $ O(n) $. In this paper, we give an alternative
$ \log n $ stage design which is nearly optimum with
respect to regularity, area-time efficiency, and
maximum interconnection wire length.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Ni:1985:VRT,
author = "L. M. Ni and Kai Hwang",
title = "Vector-Reduction Techniques for Arithmetic Pipelines",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "5",
pages = "404--411",
month = may,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676580",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:32:26 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676580",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Ohhashi:1985:HSC,
author = "M. Ohhashi and R. E. Schneider",
title = "High-Speed Computation of Unary Functions",
crossref = "Hwang:1985:PSC",
pages = "82--85",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Ohhashi_Schneider.pdf",
abstract = "This paper presents an architecture for fast
evaluation of unary functions such as reciprocal,
square root and reciprocal square root. The theory
behind the architecture has been presented in [1]. The
paper shows the results of extensive simulation that
have allowed us to implement the architecture with
minimum chip count and maximum accuracy. The accuracy
is about 8\% error rate in the LSB of the chosen
representation (IEEE 32-bit floating point format).
This architecture allows the computation of unary
functions in less than 200 nsec.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Oklobdzija:1985:SOS,
author = "Vojin G. Oklobdzija and Earl R. Barnes",
title = "Some Optimal Schemes for {ALU} Implementations in
{VLSI} Technology",
crossref = "Hwang:1985:PSC",
pages = "2--8",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Oklobdzija_Barnes.pdf",
abstract = "An efficient scheme for carry propagation in an ALU
implemented in n-MOS technology is presented. An
algorithm that determines the optimum division of the
carry chain of a parallel adder for various data path
sizes is developed. This yields an implementation of a
fast ALU which due to its regular structure occupies a
modest amount of silicon. The speed of the
implementation described is comparable to the carry
look-ahead scheme. Our method is based on the
optimization of the carry path implemented in n-MOS
technology but the results can be applied to other
technologies.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Book{Palmer:1985:MGN,
author = "John F. Palmer and Stephen P. Morse",
title = "{Die mathematischen Grundlagen der Numerik-Prozessoren
8087\slash 80287}",
publisher = pub-TEWI,
address = pub-TEWI:adr,
pages = "240",
year = "1985",
ISBN = "3-921803-33-0",
ISBN-13 = "978-3-921803-33-2",
LCCN = "????",
bibdate = "Wed Sep 07 21:14:32 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "German translation of {\em The 8087 Primer}
\cite{Palmer:1984:P}.",
acknowledgement = ack-nj,
}
@InProceedings{Papachristou:1985:MIR,
author = "Christos A. Papachristou",
title = "Multi-Input Residue Arithmetic Utilizing Read-Only
Associate Memory",
crossref = "Hwang:1985:PSC",
pages = "182--188",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Papachristou.pdf",
abstract = "In this paper an approach to residue arithmetic is
presented using Read-Only-Associative Memories (ROAMs),
such as PLAs. These memories have considerable
advantages for table lookup arithmetic processing over
the conventional ROMs in terms of their storage and
time efficiency. In residue arithmetic, the ROAM
storage required largely depends on the residue
recurrences in arithmetic tables modulo $M$. After
reviewing recent results on the computation of
recurrences, a scheme is proposed for implementing
residue arithmetic based on ROAMs. The efficiency of
the scheme is established by comparison to conventional
ROM-based table lookup techniques. Applications to
residue-to-binary number system conversion are also
discussed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Parker:1985:GCI,
author = "J. R. Parker",
title = "A General Character to Integer Conversion Method",
journal = j-SPE,
volume = "15",
number = "8",
pages = "761--766",
month = aug,
year = "1985",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.4380150804",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Sat May 31 13:36:16 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/spe.bib",
acknowledgement = ack-nhfb,
fjournal = "Software --- Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
keywords = "algorithms; integer overflow detection; languages;
programming techniques; type conversion",
review = "ACM CR 8603-0209",
subject = "D.1.m Software, PROGRAMMING TECHNIQUES,
Miscellaneous",
}
@InProceedings{Pellegrino:1985:RNS,
author = "J. M. Pellegrino and B. M. Sadler and S. D. Casey",
editor = "Bruce Ronald McAvoy",
booktitle = "{IEEE 1985 Ultrasonics Symposium: proceedings, October
16--18, 1985, Cathedral Hill Hotel, Van Ness at Geary,
San Francisco, CA}",
title = "A Residue Number System for Wideband Acousto-Optic
Spectrum Analysis",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "385--390",
year = "1985",
CODEN = "????",
DOI = "https://doi.org/10.1049/el:19850252",
ISSN = "????",
LCCN = "A367 .U46 1985eb",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 85CH2209-5.",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
}
@PhdThesis{Peralta:1985:TRN,
author = "Rene Caupolican Peralta",
title = "Three results in number theory and cryptography: a new
algorithm to compute square roots modulo a prime
number; On the bit complexity of the discrete
logarithm; {A} framework for the study of
cryptoprotocols",
type = "Thesis ({Ph.D.})",
school = "Department of Computer Science, University of
California, Berkeley",
address = "Berkeley, CA, USA",
pages = "52",
month = dec,
year = "1985",
LCCN = "????",
bibdate = "Sat Oct 17 16:25:07 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "dissertations; dissertations, academic --- UCB ---
computer science --- 1981--1990; University of
California, Berkeley. computer science division --",
}
@Article{Raimi:1985:FDP,
author = "Ralph A. Raimi",
title = "The First Digit Phenomenon Again",
journal = j-PROC-AMER-PHIL-SOC,
volume = "129",
number = "2",
pages = "211--219",
month = jun,
year = "1985",
CODEN = "PAPCAA",
ISSN = "0003-049X (print), 2326-9243 (electronic)",
ISSN-L = "0003-049X",
bibdate = "Sat Nov 12 16:56:54 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "This paper contains strong criticism of a derivation
of Benford's Law \cite{Logan:1978:FDP}.",
URL = "http://www.jstor.org/stable/986989",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
journal-URL = "http://www.jstor.org/journal/procamerphilsoci",
remark = "This paper contains mathematical derivations of both
Stigler's Law and Benford's Law. Raimi comments on p.
217: ``the Benford law itself as a conclusion to be
derived is by no means as firm as Kepler's planetary
curves. Indeed, it has been pointed out by Diaconis and
Freedman [D-F] [\cite{Diaconis:1979:RP}] that a
statistical analysis of Benford's announced data gives
a high probability to the conjecture that he did a bit
of rounding-off here and there, always in the direction
of his law. The license that a physicist often takes on
the path from his hypotheses to verified, observable,
and repeatable conclusion is not justified here.''.",
}
@Article{Ramnarayan:1985:LMR,
author = "R. Ramnarayan and F. Taylor",
title = "On large moduli residue number system recursive
digital filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "32",
number = "4",
pages = "349--359",
month = apr,
year = "1985",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23567",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "The three moduli set{2^{n} - 1, 2^{n},2^{n} +
1}residue number system, or RNS, has recently been
shown to possess several attractive properties. In
particular, the problem of scaling is much simplified
through the use of an autoscale \ldots{}",
}
@InProceedings{Rao:1985:CCC,
author = "T. R. N. Rao and Kasem Vathanvit",
title = "A Class of {$ A(N + C) $} Codes and Its Properties",
crossref = "Hwang:1985:PSC",
pages = "293--295",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Rao_Vathanvit.pdf",
abstract = "We discuss here a new class of arithmetic codes,
called $ A(N + C) $ codes where $A$ and $C$ are
constant positive integers, $N$ is information to be
coded. $ A(N + C) $ codes are a special case of $ A N +
B $ arithmetic codes which were first studied by Brown.
$ A N $ codes are linear and cannot be used to detect
unidirectional multiple errors. $ A(N + C) $ codes are
non-linear and are useful for detecting and\slash or
correcting symmetric errors, arithmetic errors and
unidirectional errors. Furthermore, $ A(N + C) $ codes
can be constructed to provide constant-weight,
self-complementing and cyclic-code properties. It is
apparent that the codes with these properties have, in
some sense, broader capabilities of error detection and
error correction.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Reed:1985:VRM,
author = "I. S. Reed and T. K. Truong and J. J. Chang and H. M.
Shao and I. S. Hsu",
title = "{VLSI} Residue Multiplier Modulo a {Fermat} Number",
crossref = "Hwang:1985:PSC",
pages = "203--206",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Reed_Truong_Chang_Shao_Hsu.pdf",
abstract = "Multiplication is central in the implementation of
Fermat number transforms (FNT) and other residue number
algorithms. There is need for a good multiplication
algorithm which can be realized easily on a VLSI chip.
In this paper, the Leibowitz multiplier [1] is modified
to realize multiplication in the ring of integers
modulo a Fermat number. The advantage of this new
algorithm over Leibowitz's algorithm is that
Leibowitz's algorithm takes modulo after the product of
multiplication is obtained. Hence time is wasted. In
this new algorithm, modulo is taken in every bit
operation when performing multiplication. Therefore no
time is wasted in this respect. Furthermore, this
algorithm requires only a sequence of cyclic shifts and
additions. The design[s] for this new multiplier are
regular, simple, expandable and therefore, suitable far
VLSI implementation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Rump:1985:HOC,
author = "Siegfried M. Rump",
title = "Higher Order Computer Arithmetic",
crossref = "Hwang:1985:PSC",
pages = "302--308",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Rump.pdf",
abstract = "The floating-point arithmetic on computers is designed
to approximate the corresponding operations over the
real numbers as close as possible. In this paper it is
shown by means of counterexamples that this need not be
true for existing machines. For achieving good
numerical results a floating-point arithmetic
approximating the real operations as close as possible
is probably best. For achieving verifications on
computers, at least a precisely defined computer
arithmetic is indispensable.\par
In this paper we first introduce the Kulisch\slash
Miranker theory, which represents a sound basis for
computer arithmetic. Each operation is precisely
defined and, moreover, is of maximum accuracy. That
means, the computed result is the floating-point number
of the working precision closest to the infinite
precise result. The theory also covers directed
roundings allowing computations with intervals. These
properties hold true for the floating-point numbers of
single and double precision as well as for the vectors,
matrices and complex extensions over those.\par
In the second part of the paper we demonstrate the
theoretical basis for what we call 'Higher Order
Computer Arithmetic'. This is an inclusion theory
allowing the development of algorithms to compute
bounds for the solution of various problems in
numerical analysis. These bounds are automatically
verified to be correct and they are of high accuracy.
Very often they are of maximum accuracy, that means the
left and right bounds of all components of the solution
are adjacent in the floating-point screen. Moreover
existence and uniqueness of a solution within the
computed bounds is automatically verified by the
algorithm. If this verification is not possible, a
respective message is given. We develop the theory and
give algorithms for the solution of systems of linear
and nonlinear equations. As demonstrated by examples
even for extremely ill-conditioned problems existence
and uniqueness of the solution is verified within
bounds of least significant bit accuracy.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Salomon:1985:TGF,
author = "D. Salomon",
title = "Two generalized floating-point representations",
journal = j-BYTE,
volume = "10",
number = "9",
pages = "154--158",
month = sep,
year = "1985",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "BYTE Magazine",
genterm = "ALGORITHMS; DESIGN",
guideno = "03372",
}
@InProceedings{Schaeffer:1985:SPE,
author = "Jonathan Schaeffer and Darrell Makarenko",
title = "Systolic Polynomial Evaluation and Matrix
Multiplication with Multiple Precision",
crossref = "Hwang:1985:PSC",
pages = "110--117",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Schaeffer_Makarenko.pdf",
abstract = "The design and implementation of a systolic VLSI
multi-precision polynomial evaluator and matrix
multiplier is described. The use of bit-serial
arithmetic allows for a very simple cell design (two
registers and an accumulator) enabling a substantial
number of cells to be placed on a chip. A configuration
of $ N^2 $ cells can evaluate $N$ polynomials of $N$
coefficients at $N$ points and perform $N$-width band
matrix multiplication and $ N \times N $ full matrix
multiplication, each in linear time. Using current
technology, 100 polynomials of 100 coefficients can be
evaluated at 100 data points with 32 bit precision in
an estimated one millisecond.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Schoof:1985:ECF,
author = "Ren{\'e} Schoof",
title = "Elliptic Curves Over Finite Fields and the Computation
of Square Roots $ \operatorname {mod} p $",
journal = j-MATH-COMPUT,
volume = "44",
number = "170",
pages = "483--494",
month = apr,
year = "1985",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Y16 (11G20 14G15)",
MRnumber = "86e:11122",
MRreviewer = "Karl Rubin",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "B0250 (Combinatorial mathematics); B0290D (Functional
analysis); C1160 (Combinatorial mathematics); C4120
(Functional analysis); C4240 (Programming and algorithm
theory)",
corpsource = "Amsterdam University, Netherlands",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "computational complexity; deterministic algorithm;
elliptic curve; F/sub q/-points; finite fields;
function evaluation; number theory; square roots mod p;
Weierstrass equation",
treatment = "T Theoretical or Mathematical",
}
@Book{Scott:1985:CNS,
author = "Norman R. Scott",
title = "Computer Number Systems and Arithmetic",
publisher = pub-PH,
address = pub-PH:adr,
pages = "x + 254",
year = "1985",
ISBN = "0-13-164211-1",
ISBN-13 = "978-0-13-164211-9",
LCCN = "QA76.9.C62 S38 1985",
bibdate = "Thu Sep 1 10:14:05 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Shah:1985:PHS,
author = "A. Shah and M. Sid-Ahmed and G. Jullien",
title = "A proposed hardware structure for two-dimensional
recursive digital filters using the residue number
system",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "32",
number = "3",
pages = "285--288",
month = mar,
year = "1985",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23566",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "A hardware structure is proposed for implementing
two-dimensional ($2$-D) recursive digital filters based
on the residue number system (RNS). The parallel
pipelined structure arising from the use of RNS
arithmetic facilitates video bandwidth filtering.
\ldots{}",
}
@Article{Shimada:1985:NAC,
author = "R. Shimada and Y. Ohkura and J. Aoe",
title = "Nonbinary Arithmetic {AN} Codes Using Odd Radix
Expressions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "11",
pages = "1050--1056",
month = nov,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676538",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:33:37 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676538",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Smith:1985:DFI,
author = "S. P. Smith and H. C. Torng",
title = "Design of a Faster Inner Product Processor",
crossref = "Hwang:1985:PSC",
pages = "38--43",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Smith_Torng.pdf",
abstract = "This paper presents the design of a fast inner product
processor, with appreciably reduced latency and cost.
The inner product processor is implemented with a tree
of carry propagate or carry save adders; this tree is
obtained with the incorporation of three innovations in
the conventional multiply/add tree:\par
(1) The leaf-multipliers are expanded into adder
subtrees, thus achieving an $ O(\log N b) $ latency,
where $N$ denotes the number of elements in a vector
and $b$ the number of bits in each element.\par
(2) The partial products, to be summed in producing an
inner product, are reordered according to their
``minimum alignments'' bringing approximately a 20\%
saving in hardware.\par
(3) The reordering also truncates the carry propagation
chain in the final propagation stage by $ 2 \log b - 1
$ positions, significantly reducing the latency
further. A form of the Baugh and Wooley algorithm is
adopted to implement two's complement notation with
changes only in peripheral hardware.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Smith:1985:FIP,
author = "S. P. Smith and H. C. Torng",
title = "A fast inner product processor based on equal
alignments",
journal = j-J-PAR-DIST-COMP,
volume = "2",
number = "4",
pages = "376--390",
month = nov,
year = "1985",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Cornell Univ, Ithaca, NY, USA",
classification = "713; 723; 921; B0290H (Linear algebra); B1265F
(Microprocessors and microcomputers); B2570
(Semiconductor integrated circuits); C4140 (Linear
algebra); C5130 (Microprocessor chips); C5230 (Digital
arithmetic methods)",
corpsource = "Sch. of Electr. Eng., Cornell University, Ithaca, NY,
USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "adder subtrees; Algorithms; alignments; Baugh and
Wooley algorithm; carry-; carry-propagate adder tree;
computer metatheory --- Boolean Algebra; computer
programming; computers --- Multiplying Circuits;
digital arithmetic; equal alignments; fast inner
product processor; free of carry-propagate or
carry-save adders; inner product processor; integrated
circuits, VLSI; leaf-multipliers; matrix algebra;
matrix multiplications; microprocessor chips; minimum;
satellite computers; save adders; special purpose
computers; two's complement notation; VLSI",
treatment = "P Practical",
}
@TechReport{Spafford:1985:RAS,
author = "Eugene Howard Spafford",
title = "A report on the accuracy of some floating point math
functions on selected computers",
institution = "School of Information and Computer Science, Georgia
Institute of Technology",
address = "Atlanta, GA, USA",
pages = "26",
year = "1985",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "GIT-ICS; 85/06",
acknowledgement = ack-nhfb,
keywords = "Operating systems (Computers)",
}
@Article{Sreedharan:1985:ASS,
author = "J. Sreedharan and A. Dhurkadas",
title = "8086 algorithm solves square roots",
journal = j-EDN,
volume = "30",
number = "7",
pages = "272",
month = apr,
year = "1985",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@Article{Stewart:1985:NCD,
author = "G. W. Stewart",
title = "A Note on Complex Division",
journal = j-TOMS,
volume = "11",
number = "3",
pages = "238--241",
month = sep,
year = "1985",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/214408.214414",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Aug 26 23:38:15 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Stewart:1986:CNC}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p238-stewart/",
abstract = "An algorithm for computing the quotient of two complex
numbers is modified to make it more robust in the
presence of underflows.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; complex arithmetic; computer arithmetic;
na",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Numerical algorithms. {\bf G.4}:
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Reliability and robustness.",
}
@Article{Stummel:1985:FEA,
author = "Friedrich Stummel",
title = "Forward error analysis of {Gaussian} elimination. {I}.
Error and residual estimates",
journal = j-NUM-MATH,
volume = "46",
number = "3",
pages = "365--395",
year = "1985",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65G05 (65F10)",
MRnumber = "87d:65054a",
MRreviewer = "Karl-Heinz Bachmann",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "B0290B (Error analysis in numerical methods); C4110
(Error analysis in numerical methods)",
corpsource = "Fachbereich Math., Johann Wolfgang Goethe-University,
Frankfurt, West Germany",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "absolute errors; arithmetic floating-point operations;
associated optimal component-wise error; coefficient
matrices; condition numbers; data perturbations; error
analysis; error estimates; first order approximations;
forward error analysis; Gaussian elimination; general
linear algebraic systems; linearization method; matrix
norms; perturbation theory; residual estimates;
rounding errors; superposition; vector norms",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Swartzlander:1985:AHS,
author = "Earl {Swartzlander, Jr.} and John Eldon",
title = "Arithmetic for High Speed {FFT} Implementation",
crossref = "Hwang:1985:PSC",
pages = "223--230",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Swartzlander_Eldon.pdf",
abstract = "This paper describes recent progress in the
implementation of high speed spectrum analysis systems
with state-of-the-art commercial and semi-custom VLSI
circuits. Initial efforts are producing Fast Fourier
Transform (FFT) and inverse FFT processors that operate
at data rates of up to 40 MHz (complex). The current
implementation computes transforms of up to 16,384
points in length by means of the radix 4 pipeline FFT
algorithm. The interstage reordering is performed by
delay commutators implemented with semi-custom VLSI,
while the arithmetic is performed by commercial single
chip 22 bit floating point adders and multipliers. This
paper explains the pipeline FFT implementation and
focuses attention on the arithmetic used to realize the
design.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Manual{Symbolics:1985:RGS,
title = "Reference Guide to {Symbolics-Lisp}",
organization = "Symbolics, Inc.",
address = "Cambridge, MA, USA",
month = mar,
year = "1985",
bibdate = "Wed Jan 29 17:06:41 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "From \cite{Steele:2004:RHP}: ``The number of digits
printed is the `correct' number\ldots{}''",
}
@Article{Takagi:1985:HSV,
author = "N. Takagi and H. Yasuura and S. Yajima",
title = "High-speed {VLSI} multiplication algorithm with a
redundant binary addition tree",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "9",
pages = "789--796",
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676634",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Sep 16 16:29:25 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Takeda:1985:SCB,
author = "K. Takeda and F. Ishino and Y. Ito and T. Nakashima",
title = "A single-chip 80-bit floating point processor",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "20",
number = "5",
pages = "986--992",
month = oct,
year = "1985",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "A single-chip 80-bit floating point VLSI processor
capable of performing 5.6 million floating point
operations per second has been realized using
1.2-$\mu$m n-well CMOS technology. The processor
handles 80-bit double-extended floating point data
\ldots{}",
}
@InProceedings{Taniguchi:1985:TDI,
author = "Kenji Taniguchi",
title = "Three Dimensional {IC}'s and Application to High Speed
Image Processor",
crossref = "Hwang:1985:PSC",
pages = "216--222",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Taniguchi.pdf",
abstract = "Present state-of-the-art 3-D IC fabrication
technologies are reviewed. Both short interconnection
wiring inherent to 3-D structure and parallel
processing architecture offer high performance for 3-D
integrated circuit. An idea of a high speed image
sensor composed of six layers is proposed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Taylor:1985:HFP,
author = "F. Taylor",
title = "A hybrid floating-point logarithmic number system
processor",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "32",
number = "1",
pages = "92--95",
month = jan,
year = "1985",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "The attributes of the traditional floating-point
processor and the logarithmic number system are
combined. The result is a hybrid system which offers
some advantages over the familiar floating-point
system. The new system, called the(FU)^{2}",
}
@InProceedings{Taylor:1985:MER,
author = "Fred J. Taylor",
title = "A More Efficient Residue Arithmetic Implementation of
the {FFT}",
crossref = "Hwang:1985:PSC",
pages = "243--250",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Taylor1.pdf",
abstract = "After 20 years, the FFT remains restricted in its real
time capabilities. To overcome this throughput
obstacle, fast residue arithmetic units are studied
based on several recent innovations in the field of
complex finite rings. A dedicated machine is designed
which makes use of these new results and is compared to
conventional FFT designs. Using high speed
semiconductor memory to implement the required residue
arithmetic mappings, speed and complexity metrics of a
basic FFT unit are shown to be improved. However, the
derived architecture and arithmetic introduce a new and
challenging set of magnitude scaling problems. They are
resolved with the result being an integrated residue
arithmetic FFT system capable of supporting very high
real time data rates.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Taylor:1985:RFU,
author = "F. J. Taylor and G. Papadourakis and A. Skavantzos and
A. Stouraitis",
title = "A Radix-$4$ {FFT} Using Complex {RNS} Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "6",
pages = "573--576",
month = jun,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.5009414",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:32:52 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009414",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Taylor:1985:RSD,
author = "George S. Taylor",
title = "Radix 16 {SRT} dividers with overlapped quotient
selection stages: a 225 Nanosecond Double Precision
Divider for the {S-1 Mark IIB}",
crossref = "Hwang:1985:PSC",
pages = "64--71",
year = "1985",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Taylor.pdf",
abstract = "This paper compares the three simplest SRT division
methods by using them to design a divider that produces
four quotient bits per cycle (radix 16). The three
methods are distinguished by the number of bits found
per stage of quotient selection logic:\par
(a) one bit per stage (radix 2) with quotient digits
chosen from the set $ \{ - 1, 0, 1 \} $,\par
(b) two bits per stage (radix 4) with quotient digits $
\{ - 2, - 1, 0, 1, 2 \} $, or\par
(c) two bits per stage (radix 4) with quotient digits $
\{ - 3, - 2, - 1, 0, 1, 2, 3 \} $.\par
For each method, we compare several ways to overlap
multiple stages of quotient selection logic and we
consider both irredundant and redundant (carry-save)
representations for the remainder.\par
The cost and performance of each alternative is
evaluated in terms a specific ECL gate array
technology. We find that we can build a 15\% faster
divider with radix four stages than with radix two
stages, for about the same amount of hardware. Between
the two radix 4 alternatives, method (c) offers more
speed than method (b) at the cost of 20\% more
hardware.\par
A radix 16 divider using method (b) has been built for
the S-1 Mark IIB computer under development at Lawrence
Livermore Laboratory. This divider consists of eight
ECL gate arrays and has a 12.5 nanosecond cycle time.
It performs IEEE single and double precision floating
point division in 150 and 225 nanoseconds,
respectively, the shortest times reported for any
general purpose computer.",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "ARITH-7",
}
@MastersThesis{Tesnow:1985:IDS,
author = "Kurt Alan Tesnow",
title = "Implementation of the digital simulation of a
synchronous machine using a floating-point processor",
type = "Thesis ({M.S.})",
school = "Department of Electrical Engineering and Applied
Physics, Case Western Reserve University",
address = "Cleveland, OH 44106, USA",
pages = "vii + 255",
year = "1985",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Thies:1985:NPE,
author = "Klaus-Dieter Thies",
title = "{Die 8087\slash 80287 numerischen Prozessor
Erweiterungen f{\"u}r 8086\slash 80286 Systeme}
\toenglish {The 8087\slash 80287 Numeric Processor
Extension for 8086\slash 80286 Systems} \endtoenglish",
publisher = pub-TEWI,
address = pub-TEWI:adr,
pages = "355",
year = "1985",
ISBN = "3-921803-53-5",
ISBN-13 = "978-3-921803-53-0",
LCCN = "????",
bibdate = "Sat Nov 09 10:08:28 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Tsuji:1985:REF,
author = "Kumiko Tsuji",
title = "Round-off errors in floating-point additions",
journal = j-MEM-FAC-SCI-KYUSHU-UNIV-A,
volume = "39",
number = "2",
pages = "209--225",
year = "1985",
CODEN = "MFKAAF",
ISSN = "0373-6385 (print), 1883-2172 (electronic)",
ISSN-L = "0373-6385",
MRclass = "65G05 (65-04)",
MRnumber = "86j:65056",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Memoirs of the Faculty of Science, Kyushu Imperial
University. Series A, Mathematics = Kyushu Teikoku
Daigaku Rigakubu kiyo",
reviewer = "Aur{\'e}l Gal{\'a}ntai",
}
@InProceedings{vonGudenberg:1985:FPC,
author = "J. W. von Gudenberg",
title = "Floating-point computation in {PASCAL-SC} with
verified results",
crossref = "Buchberger:1985:PEE",
pages = "322--324",
year = "1985",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "G; G.1.0",
CRclass = "G.1.0 General; G.1.0 Computer arithmetic",
descriptor = "Mathematics of Computing, MATHEMATICAL SOFTWARE;
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic",
genterm = "THEORY; VERIFICATION; ALGORITHMS",
guideno = "12475",
subject = "G. Mathematics of Computing; G.4 MATHEMATICAL
SOFTWARE; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS",
}
@Article{Williamson:1985:NAB,
author = "D. Williamson and S. Sridharan and P. McCrea",
title = "A new approach for block floating-point arithmetic in
recursive filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "32",
number = "7",
pages = "719--722",
month = jul,
year = "1985",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "An approach to block floating-point arithmetic in
recursive second-order direct form digital filters is
proposed. Used in conjunction with residue (or error)
feedback, the method gives improved scaling and
roundoff noise properties compared to an \ldots{}",
}
@InProceedings{Yun:1985:BPS,
author = "David Y. Y. Yun and Chang N. Zhang",
title = "Binary Paradigm and Systolic Array Implementation for
Residue Arithmetic",
crossref = "Hwang:1985:PSC",
pages = "189--193",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Yun_Zhang.pdf",
abstract = "The problem of residue, or modular, arithmetic is
fundamental to symbolic and algebraic computation,
coding theory and applications, as well as to
error-free arithmetic computations. This paper
describes novel algorithms that can lead to efficient
hardware for arithmetic operations in residue domains.
One of the main achievements is in allowing the
flexibility of changing moduli. The technology of
systolic array has been used to implement one of the
most representative operations, the modular multiplier.
It is shown that a linear systolic array can compute
$N$ modular products in time $ O(N) $ with constant
number of cells.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Zaccone:1985:INR,
author = "Richar J. Zaccone and Jesse L. Barlow",
title = "Improved Normalization Results for Digit On-Line
Arithmetic",
crossref = "Hwang:1985:PSC",
pages = "20--27",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Zaccone_Barlow.pdf",
abstract = "In digit on-line arithmetic, operands are introduced 1
digit at a time. After the first few operand digits
have been introduced. the result begins to appear a
digit at a time. This feature of digit on-line
arithmetic allows a significant amount of overlapping
of arithmetic operations.\par
Digit on-line arithmetic can sometimes produce
unnormalized results. This can present a problem for
the divide and square root algorithms. If the divisor
and radicand are highly unnormalized, these algorithms
will not produce the correct results. Two advances in
overcoming this problem are presented. First, several
techniques for producing results that are closer to
being normalized are developed. Second, it is shown
that normalized results are not necessary for divide
and square root to work properly. Combining these
results yields algorithms that will always give the
correct results.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Zadrozny:1985:AFP,
author = "W{\l}odzimierz Zadro{\'z}ny",
title = "Axiomatizations of Floating Point Arithmetics",
crossref = "Hwang:1985:PSC",
pages = "74--81",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Zadrozny.pdf",
abstract = "We present a universal scheme for axiomatizing
floating point arithmetic. The schema can be used to
axiomatize any floating point arithmetic. It consists
of a labeled graph with vertices describing some
arithmetical properties and edges containing
appropriate axioms. The language of floating point
arithmetic is developed gradually in this scheme. The
scheme can provide a vehicle for studying and
implementing various versions of floating point
arithmetic.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Zorpette:1985:BBN,
author = "Glenn Zorpette",
title = "The beauty of 32 bits: This near-optimum bit width has
unprecedented potential for the well-informed designer
of microprocessor-based systems",
journal = j-IEEE-SPECTRUM,
volume = "22",
number = "9",
pages = "65--71",
month = sep,
year = "1985",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1985.6370815",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Mon Jan 20 06:41:24 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "32 bit microprocessor chip; Companies; Computers;
dynamic RAM; floating-point arithmetic; mainframes;
memory management; microprocessor chips;
Microprocessors; Pipeline processing; pipelining;
processing rates; Random access memory; Registers; Sun;
very large scale integration; VLSI",
}
@TechReport{Adams:1986:FSSa,
author = "Glenn D. Adams",
title = "Functional specification and simulation of a floating
point co-processor for {SPUR} [1]",
type = "Report",
number = "UCB/CSD 87/311",
institution = "University of California. Computer Science Division",
address = "Berkeley, CA.",
pages = "52",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer architecture.; Floating-point arithmetic.;
Integrated circuits --- Design and construction.",
remark = "Sponsored by DARPA. Monitored by Naval Electronic
Systems Command.",
}
@MastersThesis{Adams:1986:FSSb,
author = "Glenn D. Adams",
title = "Functional specification and simulation of a floating
point co-processor for {SPUR}: research project",
type = "{Master of Science, Plan II}",
school = "University of California, Berkeley. Dept. of
Electrical and Engineering and Computer Sciences",
address = "Berkeley, CA.",
pages = "various",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Agarwal:1986:NSV,
author = "Ramesh C. Agarwal and James W. Cooley and Fred G.
Gustavson and James B. Shearer and Gordon Slishman and
Bryant Tuckerman",
title = "New Scalar and Vector Elementary Functions for the
{IBM System\slash 370}",
journal = j-IBM-JRD,
volume = "30",
number = "2",
pages = "126--144",
month = mar,
year = "1986",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.302.0126",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "76W05",
MRnumber = "840 341",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
note = "See clarification \cite{Agarwal:1987:CNS}.",
abstract = "Algorithms have been developed to compute short-and
long-precision elementary functions: SIN, COS, TAN,
COTAN, LOG, LOG10, EXP, POWER, SQRT, ATAN, ASIN, ACOS,
ATAN2, and CABS, in scalar (28 functions) and vector
(22 functions) mode. They have been implemented as part
of the new VS FORTRAN library recently announced along
with the IBM 3090 Vector Facility. These algorithms are
essentially table-based algorithms. An important
feature of these algorithms is that they produce
bitwise-identical results on scalar and vector
System\slash 370 machines. Of these, for five functions
the computed value result is always the correctly
rounded value of the infinite-precision result. For the
rest of the functions, the value returned is one of the
two floating-point neighbors bordering the
infinite-precision result, which implies exact results
if they are machine-representable. For the five
correctly rounded elementary functions, scalar and
vector algorithms are designed independently to
optimize performance in each case.",
accepted = "2 December 1985",
acknowledgement = ack-nhfb,
ajournal = "IBM J. Res. Develop.",
classcodes = "C6140D (High level languages); C7310 (Mathematics
computing)",
classification = "723",
corpsource = "IBM Res. Div., Yorktown Heights, NY, USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
journalabr = "IBM J Res Dev",
keywords = "ACOS; Algorithms; algorithms; ASIN; ATAN; ATAN2;
bitwise-identical results; CABS; computer metatheory;
computer programming; computer programming languages
--- fortran; COS; COTAN; design; elementary functions;
EXP; FORTRAN; fortran library; functions; IBM
computers; IBM System/370; infinite-precision result;
LOG; LOG10; mainframes; measurement; performance;
POWER; scalar elementary functions; SIN; SQRT;
subroutines; table-based algorithms; TAN; vector
elementary; VS FORTRAN library",
received = "5 November 1985",
remark-1 = "Numerous figures show errors in ulps, in either linear
or logarithmic scales, as dot plots over a range of
arguments, an idea that the authors credit to a
suggestion by Cleve Moler, then consulting with IBM
Palo Alto labs; such plots are used extensively in
\cite{Beebe:2017:MFC}.",
remark-2 = "From pages 128--129: ``A great deal of satisfaction
was obtained from the fact that five of the intrinsic
functions reported here always deliver correctly
rounded results; these are SQRT, DSQRT, CABS, CDABS,
and EXP. One important aspect of this is that correctly
rounded results were obtained with surprisingly little
sacrifice in performance.''",
remark-3 = "From page 132: ``Our CABS and CDABS functions satisfy
$\e/u < 0.5$ (this can also be called a half-ulp
criterion). They have best-possible rounding, except
that unavoidably there are cases when $| e/u | = 0.5$,
in which case it would be equally correct to round
downward or upward; we choose to round upward. This is
consistent with the System/370 definition of
rounding.''",
remark-4 = "From pages 134--135: ``Tuckerman's condition is of
historic significance, as its use allowed us to produce
IBM's first elementary function that delivered
correctly rounded results for all arguments.''",
remark-5 = "From page 137: ``X**2.0 usually produces a correctly
rounded value, while X*X always produces the truncated
value of $X^2$ .''",
remark-6 = "From page 139: ``Generating precise times is
difficult, since seemingly inconsequential changes in
the timing procedure may have a noticeable effect on
the measured times. For example, on the 3081KX the
performance of the STM [store multiple] and LM [load
multiple] instructions is severely degraded near page
boundaries. This means that in the rare event that the
save area of a subroutine is near a page boundary, the
speed of execution of the subroutine will be
substantially decreased.''",
subject = "C.4 Computer Systems Organization, PERFORMANCE OF
SYSTEMS \\ I.1.2 Computing Methodologies, ALGEBRAIC
MANIPULATION, Algorithms \\ F.3.3 Theory of
Computation, LOGICS AND MEANINGS OF PROGRAMS, Studies
of Program Constructs, Functional constructs \\ C.1.2
Computer Systems Organization, PROCESSOR ARCHITECTURES,
Multiple Data Stream Architectures (Multiprocessors),
Array and vector processors",
treatment = "N New Development; P Practical",
}
@Book{Apple:1986:ANM,
author = "{Apple Computer, Inc.} and Don Reed",
title = "{Apple} Numerics Manual",
publisher = pub-AW,
address = pub-AW:adr,
pages = "vii + 295",
year = "1986",
ISBN = "0-201-17741-2",
ISBN-13 = "978-0-201-17741-1",
LCCN = "QA297 .A66; QA76.8.A662 A59 1986",
bibdate = "Thu Nov 29 23:38:40 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
note = "See also \cite{Apple:1988:ANM,Apple:1994:IMP}.",
acknowledgement = ack-nhfb,
keywords = "SANE (Standard Apple Numeric Environment)",
remark = "Standard Apple Numeric Environment for all Macintosh
and Apple II computers.",
subject = "Numerical calculations; Computer programs; Apple
computer",
}
@Article{Ardalan:1986:FPE,
author = "S. Ardalan",
title = "Floating-point error analysis of recursive
least-squares and least-mean-squares adaptive filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "33",
number = "12",
pages = "1192--1208",
month = dec,
year = "1986",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "A floating-point error analysis of the Recursive Least
Squares (RLS) and Least-Mean-Squares (LMS) algorithms
is presented. Both the prewindowed growing memory RLS
algorithm (lambda = 1) for stationary systems and the
exponentially windowed RLS \ldots{}",
}
@Article{Bayoumi:1986:LBV,
author = "Magdy A. Bayoumi",
title = "Lower bounds for {VLSI} implementation of residue
number system architectures",
journal = j-INTEGRATION-VLSI-J,
volume = "4",
number = "3",
pages = "263--269",
month = sep,
year = "1986",
CODEN = "IVJODL",
DOI = "https://doi.org/10.1016/0167-9260(86)90004-0",
ISSN = "0167-9260 (print), 1872-7522 (electronic)",
ISSN-L = "0167-9260",
bibdate = "Thu Nov 18 09:57:37 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Since the number of components that can fit on a
single chip is large and rapidly growing, the
asymptotic analysis and computational complexity have
become applicable to the VLSI systems. We propose a
model of computation devoted to VLSI structures based
on Residue Number System (RNS). The developed model
employs the `cut theorem' which has been used by most
of the abstract VLSI models. It is not as general as
other reported models, but it gives tighter lower
bounds and more accurate measures of performance for
RNS structures. This computational model relates the
area and time complexities with the inherent properties
of RNS, the moduli size and the dynamic range. The
model supports the look-up table implementation
approach and it is technology-independent.",
acknowledgement = ack-nhfb,
fjournal = "Integration, the VLSI journal",
keywords = "area-time complexity; lower bounds; RNS; VLSI",
}
@InProceedings{Beims:1986:FPP,
author = "B. Beims",
title = "The Floating-Point Performance Standard Gets Even
Faster!",
crossref = "Wescon:1986:WCR",
pages = "35/1/1--13",
year = "1986",
bibdate = "Wed Sep 14 19:13:54 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Berger:1986:NNF,
author = "P. A. Berger",
title = "The {National NS32381} Floating Point Slave
Processor",
crossref = "Wescon:1986:WCR",
pages = "35/2/1--6",
year = "1986",
bibdate = "Mon Sep 12 08:32:02 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Bernstein:1986:MIC,
author = "Robert L. Bernstein",
title = "Multiplication by Integer Constants",
journal = j-SPE,
volume = "16",
number = "7",
pages = "641--652",
month = jul,
year = "1986",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.4380160704",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Sat May 31 13:36:16 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Methods are given for finding a sequence of `add',
`subtract' and `shift' instructions to multiply the
contents of a register by an integer constant. Each
method generalizes the previous one and requires only a
few intermediate or scratch registers. A variation of
the last method is used in the PL.8 compiler and uses
an unnoticeable amount of the overall compile time.
Some statistics roughly indicating the effectiveness of
the methods are presented.",
acknowledgement = ack-nhfb,
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}
@Article{Campbell:1986:NSR,
author = "R. A. Campbell",
title = "{NS32000} Square Roots",
journal = j-DDJ,
volume = "11",
number = "3",
pages = "122--123, 106",
month = mar,
year = "1986",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Fri Dec 08 13:05:56 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Campbell:1986:SS,
author = "R. A. Campbell",
title = "In Search of a Sine",
journal = j-DDJ,
volume = "11",
number = "12",
pages = "30--32",
month = dec,
year = "1986",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Thu Sep 1 10:15:57 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@MastersThesis{Cao:1986:BFP,
author = "Hai Cao",
title = "A bit-slice floating point processor",
type = "Project ({M.S., Electrical and Electronic
Engineering})",
school = "California State University",
address = "Sacramento, CA, USA",
pages = "vii + 104",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Karl E. Stoffers, Chairperson.",
acknowledgement = ack-nhfb,
keywords = "Bit slice microprocessors.",
}
@Article{Cathey:1986:LEI,
author = "J. Cathey",
title = "Letter to the editor [Integer Square Root]",
journal = j-DDJ,
volume = "11",
number = "8",
pages = "14, 82--85",
month = aug,
year = "1986",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Thu Sep 08 07:59:25 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@InProceedings{Chadha:1986:IHP,
author = "K. Chadha",
title = "{Intel} 80387: high performance, single chip numerics
coprocessor for the 80386",
crossref = "Wescon:1986:WCR",
pages = "35/4/1--5",
year = "1986",
bibdate = "Wed Sep 7 22:31:45 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Chakraborti:1986:IMR,
author = "N. B. Chakraborti and J. S. Soundararajan and A. L. N.
Reddy",
title = "An Implementation of Mixed-Radix Conversion for
Residue Number Applications",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-35",
number = "8",
pages = "762--764",
month = aug,
year = "1986",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1986.1676829",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 14:09:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676829;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35258",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "A method of residue number system (RNS) conversion to
mixed-radix (MR) representation is presented. This
method is found to be cost-effective and efficient,
particularly for moduli size 4/5 bits. A comparison of
conversion times and hardware \ldots{}",
}
@Article{Chowdary:1986:APR,
author = "N. Chowdary and W. Steenaart",
title = "Accumulation of product roundoff errors in modified
{FFT}'s",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "33",
number = "1",
pages = "103--107",
month = jan,
year = "1986",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "In this paper, expressions are derived for the mean
square error in modified radix-2 FFT algorithms. To
reduce the mean square error at the output of a special
purpose, high-speed low-order(n {leq} 32)FFT processor
implemented in fixed- \ldots{}",
}
@Article{Clenshaw:1986:GEL,
author = "C. W. Clenshaw and Daniel W. Lozier and F. W. J. Olver
and P. R. Turner",
title = "Generalized Exponential and Logarithmic Functions",
journal = j-COMPUT-MATH-APPL,
volume = "12",
number = "5--6",
pages = "1091--1101",
month = sep # "\slash " # dec,
year = "1986",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(86)90233-6",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
MRclass = "33A70 (39B10 65G05)",
MRnumber = "MR0871348 (88a:33027)",
bibdate = "Fri Jul 09 06:27:26 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Generalizations of the exponential and logarithmic
functions are defined and an investigation is made of
two possible versions of these functions. Some
applications are described, including computer
arithmetic, properties of very large and very small
numbers, and the determination of functional roots.",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Clenshaw:1986:UAR,
author = "C. W. Clenshaw and F. W. J. Olver",
title = "Unrestricted algorithms for reciprocals and square
roots",
journal = j-BIT,
volume = "26",
number = "4",
pages = "475--492",
month = dec,
year = "1986",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01935054",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65D20",
MRnumber = "87k:65019",
MRreviewer = "Luciano Biasini",
bibdate = "Wed Jan 4 18:52:19 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=26&issue=4;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=26&issue=4&spage=475",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
xxpages = "476--492??",
}
@PhdThesis{Coonen:1986:CPS,
author = "Jerome Toby Coonen",
title = "Contributions to a proposed standard for binary
floating-point arithmetic",
type = "Thesis ({Ph.D.})",
school = "University of California, Berkeley",
address = "Berkeley, CA, USA",
pages = "various",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Binary system (Mathematics)",
}
@MastersThesis{Crowell:1986:ECU,
author = "Deborah Susan Crowell",
title = "Error-free computation using multiple-modulus residue
arithmetic",
type = "Thesis ({M.S.})",
school = "University of Tennessee, Knoxville",
address = "Knoxville, TN, USA",
pages = "vi + 106",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Algorithms.; Approximation theory --- Data
processing.; Floating-point arithmetic.; Modular
arithmetic.",
}
@Article{Curtis:1986:CPL,
author = "T. W. Curtis and P. Allison",
title = "A {CORDIC} Processor for Laser Trimming",
journal = j-IEEE-MICRO,
volume = "6",
number = "3",
pages = "61--71",
month = may # "\slash " # jun,
year = "1986",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1986.304680",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Sep 08 00:48:52 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@InProceedings{Desrosiers:1986:CFP,
author = "B. Desrosiers and J.-L. Peter and C. Sitbon",
title = "Custom Floating Point Chip Designed with a Cohesive
Structured Method",
crossref = "IEEE:1986:PII",
pages = "402--405",
year = "1986",
bibdate = "Wed Sep 7 22:31:45 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{DuCroz:1986:FFP,
author = "J. Du Croz",
title = "{FPV} -- a Floating-Point Validation Package",
crossref = "Unicom:1986:SQA",
pages = "47--55",
year = "1986",
bibdate = "Thu Sep 01 11:58:18 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Dutka:1986:SRT,
author = "Jacques Dutka",
title = "On square roots and their representations",
journal = j-ARCH-HIST-EXACT-SCI,
volume = "36",
number = "1",
pages = "21--39",
month = mar,
year = "1986",
CODEN = "AHESAN",
DOI = "https://doi.org/10.1007/BF00357439",
ISSN = "0003-9519 (print), 1432-0657 (electronic)",
ISSN-L = "0003-9519",
MRclass = "01A05 (11-03 11A63)",
MRnumber = "863340 (87m:01003)",
MRreviewer = "Donald Cook",
bibdate = "Fri Feb 4 21:50:24 MST 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=36&issue=1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=36&issue=1&spage=21",
acknowledgement = ack-nhfb,
fjournal = "Archive for History of Exact Sciences",
journal-URL = "http://link.springer.com/journal/407",
MRtitle = "On square roots and their representations",
}
@Article{Dutta:1986:IMF,
author = "U. Dutta and D. Bhattacharya and A. D. Sarma",
title = "Implementation of Multibyte Floating Point Arithmetic
in 8-bit Microprocessor",
journal = j-MECH-ENG-BULL,
volume = "17",
number = "3",
pages = "104--113",
month = sep,
year = "1986",
CODEN = "MEGBBQ",
ISSN = "0379-5527",
bibdate = "Thu Sep 1 10:15:06 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Mechanical Engineering Bulletin",
}
@Article{Feldstein:1986:OUS,
author = "Alan Feldstein and Peter Turner",
title = "Overflow, underflow, and severe loss of significance
in floating-point addition and subtraction",
journal = j-IMA-J-NUMER-ANAL,
volume = "6",
number = "2",
pages = "241--251",
month = apr,
year = "1986",
CODEN = "IJNADH",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65G05",
MRnumber = "89h:65065",
bibdate = "Sat Dec 23 14:52:49 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper it is shown that, under the assumption
of the logarithmic distribution of numbers,
floating-point addition and subtraction can result in
overflow or underflow with alarming frequency?--a
frequency that increases rapidly with machine speed
unless the range of the exponent is also increased. If
numbers are assumed to be distributed in accordance
with Sweeney's (1965) experiments, then severe loss of
significance occurs with large probability in floating
point subtraction. These results have implications for
computer design and lead to the suggestion of a long
word format which will reduce the risks to acceptable
levels.",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
keywords = "Benford's Law; Law of Anomalous Numbers; logarithmic
distribution; overflow; underflow; Zipf's Law",
}
@Article{Ferro:1986:DTF,
author = "F. Ferro",
title = "{DSP} tackles floating-point arithmetic",
journal = j-COMP-DESIGN,
volume = "25",
number = "15",
pages = "53--56",
day = "15",
month = aug,
year = "1986",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bibno = "16915",
catcode = "B.7.1",
CRclass = "B.7.1 Types and Design Styles; B.7.1 Advanced
technologies",
descriptor = "Hardware, INTEGRATED CIRCUITS, Types and Design
Styles, Advanced technologies",
fjournal = "Computer Design",
genterm = "DESIGN",
guideno = "1986-04012",
journalabbrev = "Comput. Des.",
subject = "B. Hardware; B.7 INTEGRATED CIRCUITS",
}
@Article{Gavrielov:1986:NFP,
author = "Moshe Gavrielov and Lev Epstein",
title = "The {NS32081} Floating-Point Unit --- Architecture and
Implementation",
journal = j-IEEE-MICRO,
volume = "6",
number = "2",
pages = "6--12",
month = mar # "\slash " # apr,
year = "1986",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1986.304737",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Dec 14 06:08:58 MST 2000",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Science Citation Index database (1980--2000)",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliationaddress = "Digital Equipment Corp, Hudson, MA, USA",
classcodes = "B1265F (Microprocessors and microcomputers); B2570F
(Other MOS integrated circuits); C5130 (Microprocessor
chips); C5220 (Computer architecture); C5230 (Digital
arithmetic methods)",
classification = "713; 714; 721; 722; 723; 902",
corpsource = "Digital Equipment Corp., Hudson, MA, USA",
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
keywords = "binary floating point arithmetic; binary floating-;
brand; carry propagation circuit; chip design; computer
architecture; computers, microcomputer; Construction;
data storage, semiconductor; digital arithmetic;
digital devices; field effect; floating-point
operations; high-speed; IEEE standard; integrated
circuits; internal structure; logic circuit
implementations; microcode; microprocessor chips; NMOS
processor; ns32081 floating-point processor; NS32081
floating-point unit; parallel multiway-; point
arithmetic; processor concept; semiconductor devices,
MOS; slave; slave processor; software package;
standards",
treatment = "P Practical; R Product Review",
xxtitle = "The {NS32081} Floating-point Unit",
}
@Article{Grappel:1986:SRA,
author = "R. D. Grappel",
title = "Square-root algorithm is fast and simple",
journal = j-EDN,
volume = "31",
number = "8",
pages = "248--248",
month = apr,
year = "1986",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@Article{Gustafson:1986:AHV,
author = "John L. Gustafson and Stuart Hawkinson and Ken Scott",
title = "The architecture of a homogeneous vector
supercomputer",
journal = j-J-PAR-DIST-COMP,
volume = "3",
number = "3",
pages = "297--304",
month = sep,
year = "1986",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Floating Point Systems Inc, Beaverton, OR, USA",
classification = "722; 723; C5220 (Computer architecture); C5440
(Multiprocessor systems and techniques); C6110 (Systems
analysis and programming)",
corpsource = "Floating Point Syst. Inc., Beaverton, OR, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "12 MFLOPS; 64-bit floating-point; 96 MFLOPS;
arithmetic; binary n-cube; computer architecture;
computer systems, digital; dual-ported memory design;
Floating Point; homogeneous vector supercomputer;
interconnection scheme; multiprocessing; parallel;
parallel architecture; parallel architectures; parallel
machines; Parallel Processing; pipeline processing;
pipeline vector arithmetic; pipelined vector
arithmetic; programming; software development;
supercomputer; Systems; technology; vector processing;
VLSI",
treatment = "P Practical",
}
@Book{Hamming:1986:NMS,
author = "R. W. (Richard Wesley) Hamming",
title = "Numerical methods for scientists and engineers",
publisher = pub-DOVER,
address = pub-DOVER:adr,
edition = "Second",
pages = "ix + 721",
year = "1986",
ISBN = "0-486-65241-6 (paperback)",
ISBN-13 = "978-0-486-65241-2 (paperback)",
LCCN = "QA297 .H28 1986",
bibdate = "Fri Aug 20 09:12:08 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$14.95",
URL = "http://www.loc.gov/catdir/description/dover032/86016226.html",
acknowledgement = ack-nhfb,
remark = "Reprint of \cite{Hamming:1973:NMS}.",
subject = "numerical analysis; data processing",
}
@Article{Heath:1986:NRD,
author = "J. Heath",
title = "A note on {``Realization of digital filters using
input-scaled floating-point arithmetic''}",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "34",
number = "4",
pages = "995--995",
month = aug,
year = "1986",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Heath:1979:RDF}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "In [1] and [2], a theoretical Bode plot with
experimental data points is shown. The experimental
data points on the Bode plot are not correct \ldots{}",
}
@Article{Henning:1986:KBD,
author = "D. Henning",
title = "{Konvertierung bin{\"a}rer in dezimale
Gleitkommazahlen f{\"u}r me{\ss}technische Anwendungen}
\toenglish {Conversion of Binary [Numbers] to Decimal
Floating-Point Numbers for Measurement Applications}
\endtoenglish",
journal = "Radio Fernsehen Elektronik",
volume = "35",
number = "11",
pages = "731--733",
month = "????",
year = "1986",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
keywords = "decimal floating-point arithmetic",
}
@Article{Higginbotham:1986:AF,
author = "T. F. Higginbotham",
title = "Another factor of $ (10^{31} - 1) / 9 $",
journal = j-SIGNUM,
volume = "21",
number = "3",
pages = "12--12",
month = jul,
year = "1986",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/1057958.1057960",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Aug 07 18:41:01 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A second factor of $ (10^{31} - 1) / 9 $ was found to
be 6943319 with the use of an eight spoke wheel [1].
The spokes D(i) were 1, 7, 11, 13, 17, 19, 23, and 29.
The possible factors 2, 3, and 5 were tested prior to
starting the wheel. The constant multiplier was 30. The
possible divisors were of the form $ 30 \times K +
D(i), K = 0, 1, 2, 3, \ldots {} $. The program was
written in COBOL for the Honeywell DPS 8, running under
CP-6. The picture clauses were selected such that
31-digit decimal arithmetic was used. Execution time
was about forty-five minutes.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "decimal arithmetic",
remark = "Maple 8 reports in 2 sec on a 1400 MHz Itanium IA-64:
ifactor((10^31 - 1)/9) = (57336415063790604359)
(6943319) (2791).",
}
@Article{Hill:1986:DDS,
author = "Mark Hill and Susan Eggers and Jim Larus and George
Taylor and Glenn Adams and B. K. Bose and Garth Gibson
and Paul Hansen and Jon Keller and Shing Kong and
Corinna Lee and Daebum Lee and Joan Pendleton and Scott
Ritchie and David Wood and Ben Zorn and Paul Hilfinger
and Dave Hodges and Randy Katz and John Ousterhout and
Dave Patterson",
key = "C.0.B RISC",
title = "Design decisions in {SPUR}",
journal = j-COMPUTER,
volume = "19",
number = "11",
pages = "8--22",
month = nov,
year = "1986",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "University of California, Berkeley",
bibno = "9486",
catcode = "C.1.2; C.2.4; D.4.3; C.0; D.3.0; B.3.2; D.3.2",
content = "SPUR (Symbolic Processing Using RISCs) is a
multiprocessor workstation under development at the
University of California at Berkeley for parallel
processing research. Its development is part of a
long-term effort to study hardware and software issues
in multiprocessing, in general, and parallel processing
in LISP, in particular. This paper concentrates on the
initial architectural research and development of SPUR.
A SPUR processor is a general-purpose RISC processor
that provides support for Common LISP and IEEE
floating-point. A processor is implemented on a single
board with about 200 standard chips and three custom
two-micron CMOS chips: the cache controller, the CPU,
and the floating-point coprocessor. The chip that
manages the cache handles cache access by the CPU,
performing address translation, accessing shared memory
over the SPUR bus, and maintaining cache consistency.
Operating systems researchers are investigating network
file systems, network page servers, the effects of
large physical memories on virtual memory
implementations, and workload distribution. Programming
languages researchers ar",
CRclass = "C.1.2 Multiple Data Stream Architectures
(Multiprocessors); C.1.2 Parallel processors; C.2.4
Distributed Systems; D.4.3 File Systems Management; C.0
Instruction set design; D.3.0 General; B.3.2 Design
Styles; B.3.2 Cache memories; D.3.2 Language
Classifications; D.3.2 LIS-11",
CRnumber = "8710-0848",
descriptor = "Computer Systems Organization, PROCESSOR
ARCHITECTURES, Multiple Data Stream Architectures
(Multiprocessors), Parallel processors; Computer
Systems Organization, COMPUTER-COMMUNICATION NETWORKS,
Distributed Systems; Software, OPERATING SYSTEMS, File
Systems Management; Computer Systems Organization,
GENERAL, Instruction set design; Software, PROGRAMMING
LANGUAGES, General; Hardware, MEMORY STRUCTURES, Design
Styles, Cache memories; Software, PROGRAMMING
LANGUAGES, Language Classifications, LIS-11",
fjournal = "Computer",
genterm = "DESIGN; HUMAN FACTORS; PERFORMANCE; EXPERIMENTATION",
guideno = "1986-03762",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
journalabbrev = "Computer",
reviewer = "P. C. Patton",
subject = "C. Computer Systems Organization; C.1 PROCESSOR
ARCHITECTURES; C. Computer Systems Organization; C.2
COMPUTER-COMMUNICATION NETWORKS; D. Software; D.4
OPERATING SYSTEMS; C. Computer Systems Organization;
C.0 GENERAL; D. Software; D.3 PROGRAMMING LANGUAGES; B.
Hardware; B.3 MEMORY STRUCTURES; D. Software; D.3
PROGRAMMING LANGUAGES",
}
@Article{Hongyuan:1986:CSL,
author = "Wang Hongyuan and S. C. Lee",
title = "Comments on {``Sign\slash Logarithm Arithmetic for FFT
Implementation''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-35",
number = "5",
pages = "482--484",
month = may,
year = "1986",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1986.1676792",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 14:09:48 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
note = "See \cite{Swartzlander:1983:SLA}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676792",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Hull:1986:VPE,
author = "T. E. Hull and A. Abrham",
title = "Variable Precision Exponential Function",
journal = j-TOMS,
volume = "12",
number = "2",
pages = "79--91",
month = jun,
year = "1986",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/6497.6498",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D15 (65D20)",
MRnumber = "863 786",
bibdate = "Sun Sep 04 21:17:51 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p79-hull/",
abstract = "The exponential function presented here returns a
result which differs from $ e^x $ by less than one unit
in the last place, for any representable value of $x$
which is not too close to values for which $ e^x $
would overflow or underflow. (For values of $x$ which
are not within this range, an error condition is
raised.) It is a ``variable precision'' function in
that it returns a $p$-digit approximation for a
$p$-digit argument, for any $ p > 0 $ ($p$-digit means
$p$-decimal-digit). The program and analysis are valid
for all $ p > 0 $, but current implementations place a
restriction on $p$. The program is presented in a
Pascal-like programming language called Numerical
Turing which has special facilities for scientific
computing, including precision control, directed
roundings, and built-in functions for getting and
setting exponents.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; decimal floating-point arithmetic; theory;
verification",
review = "ACM CR 8702-0091",
subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation. {\bf G.4}: Mathematics of Computing,
MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}:
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Certification and testing. {\bf G.4}: Mathematics of
Computing, MATHEMATICAL SOFTWARE, Verification.",
}
@TechReport{IBM:1986:IHA,
author = "{IBM Corporation}",
title = "{IBM High-Accuracy Arithmetic Subroutine Library
(ACRITH)}",
type = "Technical Report",
number = "GC 33-6163-02, SC 33-6164-02, GX 33-9009-02",
institution = pub-IBM,
address = pub-IBM:adr,
edition = "Third",
year = "1986",
bibdate = "Thu Jan 21 17:27:09 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
tableofcontents = "1. General Information Manual \\
2. Program Description and User's Guide \\
3. Reference Summary",
}
@Book{IBM:1986:IRP,
author = "{IBM}",
title = "{IBM RT} Personal Computer Technology, publication
{SA23-1057}",
publisher = pub-IBM,
address = pub-IBM:adr,
year = "1986",
bibdate = "Sat Oct 28 08:16:44 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Iiguni:1986:REA,
author = "Y. Iiguni and H. Sakai and H. Tokumaru",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP '86}",
title = "Rounding error analysis of the triangular lattice and
escalator algorithms",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2119--2122",
year = "1986",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "In this paper, first, the normalized Triangular
Lattice and Escalator algorithms for recursive least
squares estimation are presented. Next, roundoff errors
of both algorithms in fixed point arithmetic are
analyzed and compared. Expressions are \ldots{}",
}
@Article{Jansen:1986:HAA,
author = "Paul Jansen and Peter Weidner",
title = "High-Accuracy Arithmetic Software --- Some Tests of
the {ACRITH} Problem-Solving Routines",
journal = j-TOMS,
volume = "12",
number = "1",
pages = "62--70",
month = mar,
year = "1986",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/5960.5962",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65Dxx",
MRnumber = "868 096",
bibdate = "Sat Aug 13 17:26:53 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://doi.acm.org/10.1145/5960.5962;
http://www.acm.org/pubs/citations/journals/toms/1986-12-1/p62-jansen/",
abstract = "The program package ACRITH (High-Accuracy Arithmetic
Subroutine Library) provides FORTRAN subroutines for
the solution of several standard mathematical problems.
The routines use floating point operations with
extended precision and interval arithmetic and are
designated especially for the solution of
ill-conditioned problems. Test results for most of the
routines are presented with emphasis on the practical
usability of the package. It turns out that not all
routines are of equal high quality and reliability; in
the documentation, hints to the implemented numerical
algorithms are completely missing, and the error
messages are not always concise. Some possible
alternatives like symbolic algebra systems or multiple
precision packages are mentioned.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; floating-point testing",
review = "ACM CR 8612-1110",
subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
SOFTWARE, ACRITH. {\bf G.1.0}: Mathematics of
Computing, NUMERICAL ANALYSIS, General, Numerical
algorithms. {\bf I.1.3}: Computing Methodologies,
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
Classifications, FORTRAN. {\bf G.4}: Mathematics of
Computing, MATHEMATICAL SOFTWARE, Reliability and
robustness.",
}
@InProceedings{Johnson:1986:TRH,
author = "T. Johnson and G. Clark",
title = "Techniques for realization of high-speed recursive
digital filters using residue number system
arithmetic",
crossref = "IEEE:1986:III",
volume = "11",
pages = "2623--2626",
month = apr,
year = "1986",
CODEN = "ITCOB4",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Residue-number-arithmetic digital filters offer major
cost and speed advantages over binary-arithmetic
digital filters but suffer one major drawback. The
filter coefficients must remain constant because
efficient means of updating by fractional arithmetic in
residue number systems involves time consuming
overhead. To maintain high speed in the system the
choices are to use RNS in the adders and multipliers
with scaling done in ROM, to do RNS multiplies and
additions and scale as part of CRT conversion at the
output, or to apply a new fractional NTT interpretation
of multiplier output and use RNS throughout. These
methods are discussed in this paper.",
}
@InProceedings{Kabal:1986:PFP,
author = "P. Kabal and B. Sayar",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP '86}",
title = "Performance of fixed-point {FFT}'s: Rounding and
scaling considerations",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "221--224",
year = "1986",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The calculation of the discrete Fourier transform
using a fast Fourier transform (FFT) algorithm with
fixed-point arithmetic is considered. The input data is
scaled to prevent overflow and to maintain accuracy.
The implementation uses 16-bit fixed- \ldots{}",
}
@TechReport{Kahan:1986:RAF,
author = "W. Kahan",
title = "Rational Arithmetic in Floating-Point",
type = "Technical Report",
number = "PAM-343",
institution = inst-BERKELEY-CPAM,
address = inst-BERKELEY-CPAM:adr,
pages = "8",
month = sep,
year = "1986",
bibdate = "Sun Dec 18 15:33:08 GMT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Kreithen:1986:FPC,
author = "Daniel E. Kreithen",
title = "Floating point calculation speeds for the image
processing workstation",
institution = "Brown University, Division of Engineering",
address = "Providence, RI, USA",
pages = "23",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Krishnan:1986:CCN,
author = "R. Krishnan and G. Jullien and W. Miller",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '86}",
title = "Computation of complex number theoretic transforms
using quadratic residue number systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "233--236",
year = "1986",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Very recently, the Quadratic Residue Number System
(QRNS) has been introduced [4,5]. The QRNS is obtained
from a mapping of Gaussian integers over a finite ring
to a ring of conjugate elements. The conjugate ring has
the remarkable property that \ldots{}",
}
@Article{Krishnan:1986:CDS,
author = "R. Krishnan and G. Jullien and W. Miller",
title = "Complex digital signal processing using quadratic
residue number systems",
journal = "Acoustics, Speech, and Signal Processing [see also
IEEE Transactions on Signal Processing], IEEE
Transactions on",
volume = "34",
number = "1",
pages = "166--177",
month = feb,
year = "1986",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26196",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Recently, the quadratic residue number system (QRNS)
has been introduced [6], [7] which allows the
multiplication of complex integers with two real
multiplications. The restriction is that the number
system has either all prime moduli of the form 4K
\ldots{}",
}
@Article{Krishnan:1986:ICN,
author = "R. Krishnan and G. Jullien and W. Miller",
title = "Implementation of complex number theoretic transforms
using quadratic residue number systems",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "33",
number = "8",
pages = "759--766",
month = aug,
year = "1986",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1049/el:19850252",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23583",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "Very recently, the Quadratic Residue Number System
(QRNS) has been introduced [6], [7]. The QRNS is
obtained from a mapping of Gaussian integers over a
finite ring to a ring of conjugate elements. The
conjugate ring has the remarkable property that
\ldots{}",
}
@Article{Krishnan:1986:MQR,
author = "R. Krishnan and G. Jullien and W. Miller",
title = "The modified quadratic residue number system ({MQRNS})
for complex high-speed signal processing",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "33",
number = "3",
pages = "325--327",
month = mar,
year = "1986",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1049/el:19850252",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23578",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "Recently, the Quadratic Residue Number System,(QRNS)
has been introduced [5], [6], which allows the
multiplication of complex integers with two real
multiplications. The restriction is that this special
residue number system has all moduli with \ldots{}",
}
@Article{Kulisch:1986:ADC,
author = "Ulrich W. Kulisch and Willard L. Miranker",
title = "The Arithmetic of the Digital Computer: a New
Approach",
journal = j-SIAM-REVIEW,
volume = "28",
number = "1",
pages = "1--40",
month = mar,
year = "1986",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1028001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65G10 (68M15)",
MRnumber = "87e:65030",
MRreviewer = "G. Blanch",
bibdate = "Sat Mar 29 09:54:03 MDT 2014",
bibsource = "Compendex database;
http://epubs.siam.org/toc/siread/28/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
abstract = "A new approach to the arithmetic of the digital
computer is surveyed. The methodology for defining and
implementing floating-point arithmetic is described.
Shortcomings of elementary floating-point arithmetic
are revealed through sample problems. The development
of automatic computation with emphasis on the user
control of errors is reviewed. The limitations of
conventional rule-of-thumb procedures for error control
in scientific computation are demonstrated by means of
examples. Computer arithmetic is extended so that the
arithmetic operations in the linear spaces and their
interval correspondents which are most commonly used in
computation can be performed with maximum accuracy on
digital computers. A new fundamental computer
operation, the scalar product, is introduced to develop
this advanced computer arithmetic.",
acknowledgement = ack-nhfb,
affiliationaddress = "Univ of California, Computer Science Dep, Santa
Barbara, CA, USA",
classification = "723",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
journalabr = "SIAM Rev",
keywords = "accurate floating-point summation; computer
arithmetic; computer metatheory; computer programming
languages; computers, digital; floating-point
arithmetic",
onlinedate = "March 1986",
referred = "[Layn91a].",
}
@Misc{Kulisch:1986:CGS,
author = "Ulrich Kulisch",
title = "Circuitry for generating scalar products and sums of
floating point numbers with maximum accuracy",
howpublished = "US Patent 4622650",
day = "11",
month = nov,
year = "1986",
bibdate = "Mon Dec 29 16:20:01 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/4622650/fulltext.html",
abstract = "Circuitry for generating scalar products and sums of
floating point numbers with maximum accuracy and
circuitry and a method for electronic computers by
which scalar products of floating point numbers of the
type pi, qi, ES(b,l,e1,e2) are summed with full
precision in a fixed point representation by means of a
summing unit (ALU) and one or more accumulator
registers (ARC1, ARC2) with cells (Ai, j) for storing
of codes of a base b having a length (2l + 2 e1 + 2e2)
for fixed point representation and certain overflow
positions. By control means (SHR, E, Contr) the
mantissas of products are delivered depending on the
value of the respective exponents into the summing unit
(ALU). By control means (RD, Contro), rounding
operations demanded by the higher level computer are
performed, and a rounded floating point number and
overflow (OF) and underflow (UF) criteria are
delivered. Parallel, serial and word organized summing
units (ALU) and accumulator registers (ACR) are usable
and in another embodiment, the multiplication of the
factors (pi, qi) is performed using a table of
multiples store.",
acknowledgement = ack-nhfb,
}
@Article{Lorang:1986:SD,
author = "O. Lorang",
title = "{Schnelle Division} \toenglish {Fast Division}
\endtoenglish",
journal = j-ELECTRONIK,
volume = "22",
pages = "167--168",
year = "1986",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronik",
}
@Article{MacIntyre:1986:UOS,
author = "Ferren MacIntyre and Thomas Dowling",
title = "User-oriented suggestions for floating-point and
complex-arithmetic {Forth} standard extensions",
journal = j-J-FORTH-APPL-RES,
volume = "3",
number = "4",
pages = "65--84",
year = "1986",
CODEN = "JFAREL",
ISSN = "0738-2022",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bibno = "11736",
catcode = "D.3.2; D.3.0; H.1.2; G.1.0",
CRclass = "D.3.2 Language Classifications; D.3.2 FORTH; D.3.0
General; D.3.0 Standards; H.1.2 User/Machine Systems;
H.1.2 Human factors; G.1.0 General; G.1.0 Computer
arithmetic",
descriptor = "Software, PROGRAMMING LANGUAGES, Language
Classifications, FORTH; Software, PROGRAMMING
LANGUAGES, General, Standards; Information Systems,
MODELS AND PRINCIPLES, User/Machine Systems, Human
factors; Mathematics of Computing, NUMERICAL ANALYSIS,
General, Computer arithmetic",
fjournal = "Journal of FORTH Application and Research",
genterm = "LANGUAGES; THEORY; HUMAN FACTORS; STANDARDIZATION",
guideno = "1986-08466",
journalabbrev = "J. FORTH Appl. Res.",
subject = "D. Software; D.3 PROGRAMMING LANGUAGES; D. Software;
D.3 PROGRAMMING LANGUAGES; H. Information Systems; H.1
MODELS AND PRINCIPLES; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS",
}
@Article{Marrin:1986:MBF,
author = "K. Marrin",
title = "Microprocessor brings floating-point capability to
32-bit market",
journal = j-COMP-DESIGN,
volume = "25",
number = "9",
pages = "31--38",
day = "1",
month = may,
year = "1986",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bibno = "20530",
catcode = "B.7.1",
CRclass = "B.7.1 Types and Design Styles; B.7.1 Advanced
technologies",
descriptor = "Hardware, INTEGRATED CIRCUITS, Types and Design
Styles, Advanced technologies",
fjournal = "Computer Design",
genterm = "DESIGN",
guideno = "1986-03960",
journalabbrev = "Comput. Des.",
subject = "B. Hardware; B.7 INTEGRATED CIRCUITS",
}
@Article{Marrin:1986:PBT,
author = "K. Marrin",
title = "Plug-in boards transform {PCs} into floating-point
workstations",
journal = j-COMP-DESIGN,
volume = "25",
number = "4",
pages = "31--34",
day = "15",
month = feb,
year = "1986",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bibno = "19192",
catcode = "K.8; C.1.2; C.4",
CRclass = "C.1.2 Multiple Data Stream Architectures
(Multiprocessors); C.1.2 Array and vector processors",
descriptor = "Computing Milieux, PERSONAL COMPUTING; Computer
Systems Organization, PROCESSOR ARCHITECTURES, Multiple
Data Stream Architectures (Multiprocessors), Array and
vector processors; Computer Systems Organization,
PERFORMANCE OF SYSTEMS",
fjournal = "Computer Design",
genterm = "DESIGN; PERFORMANCE; MEASUREMENT",
guideno = "1986-03913",
journalabbrev = "Comput. Des.",
subject = "K. Computing Milieux; K.8 PERSONAL COMPUTING; C.
Computer Systems Organization; C.1 PROCESSOR
ARCHITECTURES; C. Computer Systems Organization; C.4
PERFORMANCE OF SYSTEMS",
}
@InProceedings{Melear:1986:HSM,
author = "C. Melear and D. Tietjen",
title = "High Speed Math Using a Floating Point Coprocessor",
crossref = "Mini-Micro:1986:EMM",
pages = "14/3/1--8",
year = "1986",
bibdate = "Wed Sep 7 22:31:45 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@MastersThesis{Moore:1986:PFS,
author = "Brian A. Moore",
title = "A pipelined floating-point systolic array arithmetic
processor",
type = "Thesis ({M.S.})",
school = "Brigham Young University. Department of Electrical
Engineering",
address = "Provo, UT, USA",
pages = "vi + 58",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer architecture.; Computer arithmetic and logic
units.; Computers, Pipeline.",
}
@Article{Moshier:1986:CA,
author = "S. L. Moshier",
title = "Computer Approximations",
journal = j-BYTE,
volume = "11",
number = "4",
pages = "161--178",
month = apr,
year = "1986",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "BYTE Magazine",
}
@Article{Ngai:1986:RAT,
author = "Tin-Fook Ngai and Mary Jane Irwin and Shishpal Rawat",
title = "Regular, Area-Time Efficient Carry-Lookahead Adders",
journal = j-J-PAR-DIST-COMP,
volume = "3",
number = "1",
pages = "92--105",
month = mar,
year = "1986",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Mon Apr 14 07:47:57 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Stanford Univ, Stanford, CA, USA",
classification = "723; 921; C5230 (Digital arithmetic methods)",
corpsource = "Department of Electr. Eng., Stanford University, CA,
USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "adders; Adders; area-time efficiency; carry chain
computation; carry logic; carry-lookahead adders;
carry-lookahead adders (cla); computers; digital
arithmetic; fast binary addition; integrated circuits,
VLSI --- Electric Wiring; interconnection wire length;
log n; log N stage design; maximum; regularity; stage
design; VLSI",
treatment = "P Practical",
}
@Article{Nowak:1986:HBU,
author = "M. Nowak",
title = "{Hex-BCD-Um\-wand\-lung} \toenglish {Hexadecimal-BCD
Conversion} \endtoenglish",
journal = j-MC,
volume = "10",
pages = "68",
year = "1986",
ISSN = "0720-4442, 0941-777x , 0943-5409",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "MC: Die Mikrocomputer-Zeitschrift",
}
@PhdThesis{Paez-Monzon:1986:ERC,
author = "Gerard Paez-Monzon",
title = "{{\'E}}tude et {R}{\'e}alisation d'un Co-processeur
Arithm{\'e}tique en Virgule Flottante. ({French})
[{Study} and Implementation of a Floating-Point
Coprocessor]",
type = "Doctorat d'{\'E}tat",
school = "Sciences Appliqu{\'e}es, Universit{\'e} Paris 6",
address = "Paris, France",
pages = "229",
year = "1986",
bibdate = "Thu May 09 09:55:31 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Sous la direction de Gerard Noguez.",
abstract = "Le premier chapitre d'introduction d{\'e}crit
l'{\'e}tat de l'art dans le domaine des
algorithmes-cabl{\'e}s {\'e}l{\'e}mentaires
utilis{\'e}s dans l'arithm{\'e}tique flottante. Nous y
pr{\'e}sentons une classification architecturale des
coprocesseurs arithm{\'e}tiques en virgule flottante.
{\`A} partir d'une comparaison de trois standards de
virgule flottante orient{\'e}s vers les syst{\`e}mes
bases sur microprocesseurs: IEEE-P754, VAX-DEC, et
Hewlett--Packard, le deuxi{\`e}me chapitre explique le
choix de l'architecture externe de coprocesseur. Le
troisi{\`e}me chapitre pr{\'e}sente l'architecture
interne microprogramm{\'e}e et l'organisation du
coprocesseur d{\'e}velopp{\'e} dans l'{\'e}tude,
nomm{\'e}e FPU-IP6. Dans le quatri{\`e}me chapitre,
nous proposons une nouvelle m{\'e}thode pour le
d{\'e}veloppement des microprogrammes. La cle de la
m{\'e}thode est la visualisation de la s{\'e}paration
des phases de planification et d'implantation. Le
cinqui{\`e}me chapitre pr{\'e}sente les microprogrammes
d{\'e}velopp{\'e}s pour notre coprocesseur. Nous
analysons les diff{\'e}rents micro-algorithmes selon le
type d'instruction (E/S, arith, etc) et la
pr{\'e}cision (simple, double). L'organisation de
l'espace de la microm{\'e}moire est present{\'e}e. Le
sixi{\`e}me chapitre d{\'e}crit l'{\'e}tude
realis{\'e}e pour l'int{\'e}gration du coprocesseur
dans le compilateur C et le syst{\`e}me UNIX de la
machine SM90.",
acknowledgement = ack-nhfb,
language = "French",
}
@Article{Payne:1986:PTF,
author = "Mary H. Payne",
title = "Proposal for the transfer of floating point data",
journal = j-SIGNUM,
volume = "21",
number = "3",
pages = "25--26",
month = jul,
year = "1986",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Mon Apr 25 11:24:15 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@Article{Petkovic:1986:SIS,
author = "M. S. Petkovi{\'c} and L. V. Stefanovi{\'c}",
title = "On some improvements of square root iteration for
polynomial complex zeros",
journal = j-J-COMPUT-APPL-MATH,
volume = "15",
number = "1",
pages = "13--25",
month = may,
year = "1986",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0377-0427(86)90235-9",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 11:59:55 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042786902359",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "polynomial root finding",
}
@Article{Pfenninger:1986:SQA,
author = "E. Pfenninger",
title = "{Schneller Quadratwurzel-Algorithmus} \toenglish {Fast
Square-Root Algorithms} \endtoenglish",
journal = j-ELECTRONIK,
volume = "22",
pages = "179--180",
year = "1986",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronik",
}
@Article{Porter:1986:FPM,
author = "K. Porter and J. Kath",
title = "Floating-point methods combine to boost performance",
journal = j-COMP-DESIGN,
volume = "25",
number = "3",
pages = "75--80",
month = feb,
year = "1986",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bibno = "18468",
catcode = "G.1.0; K.1",
CRclass = "G.1.0 General; G.1.0 Computer arithmetic; K.1
Standards",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic; Computing Milieux, THE COMPUTER
INDUSTRY, Standards",
fjournal = "Computer Design",
genterm = "DESIGN; THEORY; ALGORITHMS; PERFORMANCE;
STANDARDIZATION",
guideno = "1986-03910",
journalabbrev = "Comput. Des.",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
K. Computing Milieux; K.1 THE COMPUTER INDUSTRY",
}
@Article{Quong:1986:FPI,
author = "D. Quong",
title = "Floating-point $ \mu {P} $ implements high-speed math
functions",
journal = j-EDN,
volume = "31",
number = "3",
pages = "143--150",
month = feb,
year = "1986",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Wed Sep 7 22:31:45 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@Article{Ramnarayan:1986:LCL,
author = "R. Ramnarayan and F. Taylor",
title = "Limit cycles in large moduli residue number system
digital filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "33",
number = "9",
pages = "912--915",
month = sep,
year = "1986",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1049/el:19850252",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23584",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
}
@Article{Rhyne:1986:SBS,
author = "T. Rhyne and N. R. {Strader II}",
title = "A Signed Bit-Sequential Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-35",
number = "10",
pages = "896--901",
month = oct,
year = "1986",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1986.1676680",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 14:09:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
note = "See comments \cite{Smith:1989:CSB}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676680",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Robertson:1986:NQD,
author = "James Evans Robertson",
title = "Normalization and quotient digit selection for a
variable precision arithmetic unit",
type = "Report",
number = "UIUCDCS-R-86-1229",
institution = "Department of Computer Science, University of Illinois
at Urbana-Champaign",
address = "Urbana, IL, USA",
pages = "14",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.",
remark = "``April 1986.''--Cover. ``UILU-ENG-86-1723.''--Cover.
Bibliography: p. 13.",
}
@Article{Rump:1986:SER,
author = "Siegfried M. Rump",
title = "{Sichere Ergebnisse auf Rechenanlagen} \toenglish
{Safe Results from Computers} \endtoenglish",
journal = j-INFORMATIK-SPEKTRUM,
volume = "9",
number = "3",
pages = "174--183",
month = jun,
year = "1986",
CODEN = "INSKDW",
ISSN = "0170-6012 (print), 1432-122X (electronic)",
ISSN-L = "0170-6012",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Informatik Spektrum",
journal-URL = "http://link.springer.com/journal/287",
}
@Article{Schatte:1986:ALD,
author = "Peter Schatte",
title = "On the asymptotic logarithmic distribution of the
floating-point mantissas of sums",
journal = j-MATH-NACHR,
volume = "127",
pages = "7--20",
year = "1986",
CODEN = "MTMNAQ",
ISSN = "0025-584X",
MRclass = "60F05",
MRnumber = "87m:60059",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
reviewer = "A. Fuchs",
}
@TechReport{Schmickley:1986:CCP,
author = "Ronald D. Schmickley and David H. Bailey",
title = "A comparison of the {Cray-2} performance before and
after the installation of memory psudo-banking",
type = "{NASA} contractor report",
number = "NASA CR-177462",
institution = "National Aeronautics and Space Administration, Ames
Research Center; National Technical Information
Service, distributor",
address = "Moffett Field, CA, USA",
pages = "????",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
govtdocnumber = "NAS 1.26:177462 0830-H-14 (MF)",
keywords = "Accounting.; Computer systems performance.; Cray
computers.; Floating point arithmetic.; Memory
(Computers); Response time (Computers)",
remark = "Distributed to depository libraries in microfiche.
Microfiche. [Washington, D.C.: National Aeronautics and
Space Administration, 1988] 1 microfiche.",
}
@Article{Semba:1986:ADL,
author = "I. Semba",
title = "An Algorithm for Division of Large Integers",
journal = j-INFO-PROC,
volume = "9",
number = "3",
pages = "145--147",
month = "????",
year = "1986",
bibdate = "Thu Sep 1 10:15:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@MastersThesis{Shukla:1986:IMN,
author = "Pankaj N. Shukla",
title = "An implementation on a {MC68000\slash NS32081}
microcomputer of binary floating-point arithmetic based
on the {IEEE 754} standard",
type = "Thesis ({M.S.})",
school = "Michigan Technological University",
address = "1400 Townsend Drive, Houghton, MI 49931-1295, USA",
pages = "vii + 166",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Michigan Technological University. --- Theses
({M.S.}).; MTU Electrical Engineering. --- Thesis
({M.S.}).",
}
@InProceedings{Simcoe:1986:MFP,
author = "R. J. Simcoe and A. Fisher and B. M. Leary and W. R.
Bidermann and W. R. Wheeler",
title = "The {MicroVAX} 78132 Floating Point Chip",
crossref = "IEEE:1986:PII",
pages = "420--425",
year = "1986",
bibdate = "Wed Sep 07 23:14:42 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Book{Soderstrand:1986:RNS,
editor = "Michael A. Soderstrand and W. K. Jenkins and G. A.
Graham and F. J. Taylor",
title = "Residue number system arithmetic: modern applications
in digital signal processing",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "vii + 418",
year = "1986",
ISBN = "0-87942-205-X",
ISBN-13 = "978-0-87942-205-9",
LCCN = "QA247.35 .R45 1986",
bibdate = "Wed Nov 14 14:28:02 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "IEEE Press selected reprint series",
acknowledgement = ack-nhfb,
subject = "modular arithmetic; signal processing; digital
techniques; computer programming",
}
@Article{Soderstrand:1986:VIM,
author = "M. Soderstrand and R. Escott",
title = "{VLSI} implementation in multiple-valued logic of an
{FIR} digital filter using residue number system
arithmetic",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "33",
number = "1",
pages = "5--25",
month = jan,
year = "1986",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1049/el:19850252",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23573",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "Computer simulations using SPICE establish the
feasibility of implementing a highly pipelined
high-speed FIR digital filter using Multiple-Valued
Logic (MVL) Read-Only Memories (ROM's) to implement
Residue Number System (RNS) Arithmetic in VLSI
\ldots{}",
}
@TechReport{Spafford:1986:RASa,
author = "E. H. Spafford and J. C. Flaspohler",
title = "A Report on the Accuracy of Some Floating-Point Math
Functions on Selected Computers",
type = "Technical Report",
number = "GIT-SERC-86/02, GIT-ICS-85/06",
institution = "Georgia Institute of Technology",
pages = "??",
year = "1986",
bibdate = "Mon Sep 12 23:54:04 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Spafford:1986:RASb,
author = "Eugene H. Spafford and John C. Flaspohler",
title = "A Report on the Accuracy of Some Floating Point Math
Functions on Selected Computers",
journal = j-LOGIN,
volume = "11",
number = "2",
pages = "31--56",
month = mar # "\slash " # apr,
year = "1986",
CODEN = "LOGNEM",
ISSN = "1044-6397 (print), 2169-9364 (electronic)",
bibdate = "Tue Feb 20 15:42:13 MST 1996",
bibsource = "ftp://ftp.uu.net/library/bibliography;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Georgia Institute of Technology",
fjournal = ";login: the USENIX Association newsletter",
}
@Article{Stewart:1986:CNC,
author = "G. W. Stewart",
title = "Corrigendum: ``{A} Note on Complex Division''",
journal = j-TOMS,
volume = "12",
number = "3",
pages = "285",
month = sep,
year = "1986",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/7921.356182",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sun Sep 04 21:20:12 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Stewart:1985:NCD}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@InProceedings{Strobach:1986:NFL,
author = "P. Strobach",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP '86}",
title = "New forms of least squares lattice algorithms and a
comparison of their round-off error characteristics",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "573--576",
year = "1986",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Two versions of the most recently introduced ``pure
order recursive'' LS lattice algorithm are discussed in
this paper. An analysis of the round-off error
characteristics of the new order recursive lattice
method is performed and a comparison is made \ldots{}",
}
@Article{Stummel:1986:SOP,
author = "F. Stummel",
title = "Strict optimal a posteriori error and residual bounds
for {Gaussian} elimination in floating-point
arithmetic",
journal = j-COMPUTING,
volume = "37",
number = "2",
pages = "103--124",
year = "1986",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65F05 (65G05)",
MRnumber = "88b:65047",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
reviewer = "Alfonso Laratta",
}
@Manual{Sun:1986:FPG,
title = "Floating-point programmer's guide for the {Sun}
workstation",
publisher = "Sun Microsystems, Inc.",
address = "Mountain View, CA, USA",
edition = "Revision {A} of 19 {September} 1986.",
pages = "various",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units.; Floating-point
arithmetic.",
remark = "``Part Number 800-1552-10.''",
}
@Article{Thun:1986:RNS,
author = "R. Thun",
title = "On residue number system decoding",
journal = "Acoustics, Speech, and Signal Processing [see also
IEEE Transactions on Signal Processing], IEEE
Transactions on",
volume = "34",
number = "5",
pages = "1346--1347",
month = oct,
year = "1986",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26200",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The use of a residue number system (RNS) in digital
systems and especially filter designs is facilitated by
efficient algorithms for the conversion from RNS to
binary numbers. The conversion is generally based on
the Chinese remainder theorem or the \ldots{}",
}
@Article{Troutman:1986:DSF,
author = "W. W. Troutman and P. W. Diodato and A. K. Goksel and
Mean-Sea Tsay and R. H. Krambeck",
title = "Design of a Standard Floating-Point Chip",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "21",
number = "3",
pages = "396--399",
month = jun,
year = "1986",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "Some aspects of design of a VLSI floating-point chip,
which provides the WE{\reg}32100 microprocessor with
math acceleration capabilities, are described. The chip
is implemented in 1.75-$\mu$m twin-tub CMOS II
technology [2] and contains \ldots{}",
}
@Article{Truong:1986:TCD,
author = "T. K. Truong and J. J. Chang and I. S. Hsu and D. Y.
Pei and I. S. Reed",
title = "Techniques for Computing the Discrete {Fourier}
Transform Using the Quadratic Residue {Fermat} Number
Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-35",
number = "11",
pages = "1008--1012",
month = nov,
year = "1986",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1986.1676704",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 14:09:53 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676704",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Twaddell:1986:HPM,
author = "W. Twaddell",
title = "Higher performance marks floating-point chips",
journal = j-COMP-DESIGN,
volume = "25",
number = "8",
pages = "24--30",
day = "15",
month = apr,
year = "1986",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bibno = "19171",
catcode = "B.7.1; C.4",
CRclass = "B.7.1 Types and Design Styles; B.7.1 Advanced
technologies",
descriptor = "Hardware, INTEGRATED CIRCUITS, Types and Design
Styles, Advanced technologies; Computer Systems
Organization, PERFORMANCE OF SYSTEMS",
fjournal = "Computer Design",
genterm = "DESIGN; PERFORMANCE",
guideno = "1986-03952",
journalabbrev = "Comput. Des.",
subject = "B. Hardware; B.7 INTEGRATED CIRCUITS; C. Computer
Systems Organization; C.4 PERFORMANCE OF SYSTEMS",
}
@InProceedings{Vaccaro:1986:SDF,
author = "J. Vaccaro and B. Johnson and C. Nowacki",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '86}",
title = "A systolic discrete {Fourier} transform using residue
number systems over the ring of {Gaussian} integers",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1157--1160",
month = aug,
year = "1986",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A VLSI implementation of a bit-serial systolic
architecture for a DFT processor has been developed
which performs residue number system (RNS) processing
over the ring of Gaussian integers. An architecture for
a 128-point DFT using the chirp z-transform algorithm
is described, and its use in an R2FFT architecture to
obtain a 16,384-point transform is illustrated. Based
on three custom-designed chips, the processor is
capable of transforming data at a continuous 2 MHz
rate. The use of RNS techniques and systolic arrays
provides two dimensions of parallelism, resulting in
hardware of low complexity and high speed. The overall
system has great flexibility in dynamic range, and can
be used in many signal processing applications.",
}
@MastersThesis{Verma:1986:DEF,
author = "Deepak Verma",
title = "Design of an efficient floating point vector
coprocessor of an advanced microcomputer system",
type = "Thesis ({M.S.})",
school = "Department of Computer Engineering and Science, Case
Western Reserve University",
address = "Cleveland, OH 44106, USA",
pages = "viii + 121",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Waterhouse:1986:TMW,
author = "William C. Waterhouse",
title = "The Teaching of Mathematics: Why Square Roots are
Irrational",
journal = j-AMER-MATH-MONTHLY,
volume = "93",
number = "3",
pages = "213--214",
month = mar,
year = "1986",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:38:15 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@TechReport{Weitek:1986:WSW,
author = "{Weitek Corporation}",
title = "{WTL} 1164\slash {WTL} 1165 64-bit {IEEE}
Float\-ing-Point Multiplier\slash Divider and {ALU}",
institution = pub-WEITEK,
address = pub-WEITEK:adr,
month = jul,
year = "1986",
bibdate = "Thu Nov 8 14:50:32 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@TechReport{Wichmann:1986:FPI,
author = "Brian A. Wichmann",
title = "Floating point interval arithmetic for validation",
institution = "National Physical Laboratory, Division of Information
Technology and Computing",
address = "Teddington Middlesex",
pages = "i + 12",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "NPL report; DITC 76/86",
acknowledgement = ack-nhfb,
keywords = "Algorithms.; Floating-point arithmetic.",
}
@Article{Wollenberg:1986:SRD,
author = "R. Wollenberg and R. Milnikel",
title = "{Schnelles Radizierverfahren durch Tabellenzugriff}
\toenglish {Fast Square-rooting Method by Means of
Table Lookup} \endtoenglish",
journal = j-ELECTRONIK,
volume = "6",
pages = "79--82",
year = "1986",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronik",
}
@InProceedings{Agrawal:1987:CEF,
author = "J. C. Agrawal and P. S. Sehdev",
title = "Comparison and Evaluation of Floating Point
Representations in {IBM\slash 370} and {VAX-11\slash
780}",
crossref = "Zunde:1987:EFI",
pages = "353--369",
year = "1987",
bibdate = "Wed Sep 14 20:23:44 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Agarwal:1987:CNS,
author = "Ramesh C. Agarwal and James W. Cooley and Fred G.
Gustavson and James B. Shearer and Gordon Slishman and
Bryant Tuckerman",
title = "Clarification: {``New scalar and vector elementary
functions for the IBM System/370''} [{IBM J. Res.
Develop. {\bf 30} (1986), no. 2, 126--144}]",
journal = j-IBM-JRD,
volume = "31",
number = "2",
pages = "274--274",
month = mar,
year = "1987",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.312.0274",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "76W05",
MRnumber = "MR894626",
bibdate = "Mon Feb 12 08:07:08 2001",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
note = "See \cite{Agarwal:1986:NSV}.",
acknowledgement = ack-nhfb,
ajournal = "IBM J. Res. Develop.",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Ahmad:1987:IDA,
author = "M. Ahmad",
title = "Implementable Decimal Arithmetic Algorithms for
Micro\slash Minicomputers",
journal = j-MICROPROC-MICROPROG,
volume = "19",
number = "2",
pages = "119--128",
month = feb,
year = "1987",
CODEN = "MMICDT",
ISSN = "0165-6074 (print), 1878-7061 (electronic)",
ISSN-L = "0165-6074",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Microprocessing and Microprogramming",
keywords = "decimal floating-point arithmetic",
}
@Article{Anonymous:1987:MAU,
author = "Anonymous",
title = "Multiply-Addition --- An Ultra High Performance
Dataflow",
journal = j-IBM-TDB,
volume = "30",
number = "3",
pages = "982--987",
month = aug,
year = "1987",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Oct 17 12:06:22 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
keywords = "FMA; fused multiply-add",
remark = "Author(s) unknown; I cannot find an online copy of
this paper. This may be the first publication on the
fused multiply-add operation, first implemented in
hardware in early 1990 on the IBM POWER CPU, and
standardized in IEEE 754-2008.",
}
@Book{ANSI:1987:AIS,
author = "{ANSI\slash IEEE}",
title = "{ANSI\slash IEEE Std 854-1987: An American National
Standard: IEEE Standard for Radix-Independent
Floating-Point Arithmetic}",
publisher = pub-IEEE-STD,
address = pub-IEEE-STD:adr,
pages = "v + 14",
day = "5",
month = oct,
year = "1987",
ISBN = "0-7381-1167-8",
ISBN-13 = "978-0-7381-1167-4",
bibdate = "Thu Mar 02 09:40:18 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Revised 1994. INSPEC Accession Number: 3095617.",
price = "US\$44.00",
URL = "http://ieeexplore.ieee.org/iel1/2502/1121/00027840.pdf;
http://ieeexplore.ieee.org/xpl/standardstoc.jsp?isnumber=1121&isYear=1987",
acknowledgement = ack-nhfb,
}
@Article{Ardalan:1987:FPR,
author = "S. Ardalan and S. Alexander",
title = "Fixed-point roundoff error analysis of the
exponentially windowed {RLS} algorithm for time-varying
systems",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "35",
number = "6",
pages = "770--783",
month = jun,
year = "1987",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "A fixed-point roundoff error analysis of the
exponentially windowed RLS algorithm is presented. It
is shown that a tradeoff exists in the choice of the
forgetting factor {\lambda}. In order to reduce the
sensitivity of the algorithm to additive noise, {\&}
\ldots{}",
}
@MastersThesis{Azmi:1987:FPS,
author = "Aqil M. Azmi",
title = "A floating point system with variable-length
exponent",
type = "Thesis ({M.S.})",
school = "University of Colorado",
address = "Boulder, CO, USA",
pages = "viii + 73",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic.; Floating-point arithmetic.",
}
@InProceedings{Balsara:1987:SSS,
author = "Paras T. Balsara and Robert M. Owens",
title = "Systolic and Semi-Systolic Digit Serial Multipliers",
crossref = "Irwin:1987:PSC",
pages = "169--173",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158682",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Balsara_Owens.pdf",
abstract = "Digit serial data transmission can be used to an
advantage in the design of special purpose processors
where communication issues dominate and where digit
pipelining can be used to maintain high data rates.
VLSI signal processing is one such problem domain. We
propose designs of systolic and semi-systolic digit
serial multipliers. These multipliers are programmable
i.e., one operand is pre-stored in the multiplier and
the other operand is fed in a digit serial fashion..
The VLSI implementation of the systolic multiplier is
also given. This systolic multiplier is used in our
VLSI signal processing system.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@MastersThesis{Baranyk:1987:EBP,
author = "Michael L. Baranyk",
title = "Extensions beyond the proposed {IEEE} standard number
754 for binary floating point arithmetic",
type = "Thesis ({M.S.})",
school = "Marquette University",
address = "Milwaukee, WI, USA",
pages = "various",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Binary system (Mathematics); Floating-point
arithmetic.; Institute of Electrical and Electronics
Engineers. --- IEEE; standard 754.",
}
@InProceedings{Barrett:1987:FAR,
author = "Geoff Barrett",
title = "A formal approach to rounding",
crossref = "Irwin:1987:PSC",
pages = "247--254",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158683",
bibdate = "Wed Nov 24 12:49:55 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Barrett.pdf",
abstract = "This paper presents a formal description of rounding,
as specified in the IEEE Standard, and an algorithm to
perform the task along with its proof of correctness.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@TechReport{Barrett:1987:FMA,
author = "Geoff Barrett",
title = "Formal methods applied to a floating point number
system",
type = "Technical monograph",
number = "PRG 58",
institution = "Oxford University Computing Laboratory",
address = "Oxford, England",
pages = "47",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Binary system (Mathematics).; Floating-point
arithmetic.; Formal languages.",
}
@Article{Boettner:1987:QA,
author = "H. B{\"o}ttner",
title = "{Quadratwurzel-Algorithmus} \toenglish {Square-Root
Algorithms} \endtoenglish",
journal = j-MC,
volume = "5",
pages = "58",
year = "1987",
ISSN = "0720-4442, 0941-777x , 0943-5409",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "MC: Die Mikrocomputer-Zeitschrift",
}
@InCollection{Bohlender:1987:DFP,
author = "G. Bohlender and T. Teufel",
title = "A Decimal Floating-Point Processor for Optimal
Arithmetic",
crossref = "Kaucher:1987:CAS",
pages = "31--58",
year = "1987",
bibdate = "Fri Nov 28 11:46:56 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Boisvert:1987:AAH,
author = "Ronald F. Boisvert",
title = "{Algorithm 651}: Algorithm {HFFT}\emdash High-Order
Fast-Direct Solution of the {Helmholtz} Equation",
journal = j-TOMS,
volume = "13",
number = "3",
pages = "235--249",
month = sep,
year = "1987",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/29380.214342",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65V05",
MRnumber = "918 578",
bibdate = "Sun Sep 4 21:40:33 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Johnson:1987:CES}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1987-13-3/p235-boisvert/",
abstract = "HFFT is a software package for solving the Helmholtz
equation on bounded two- and three-dimensional
rectangular domains with Dirichlet, Neumann, or
periodic boundary conditions. The software is the
result of combining new fourth-order accurate compact
finite difference (HODIE) discretizations and a
fast-direct solution technique (the Fourier method). In
this paper we briefly describe the user interface to
HFFT and present an example of its usage and several
details of its implementation.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; theory; verification",
subject = "{\bf G.1.8}: Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations, Elliptic
equations. {\bf G.4}: Mathematics of Computing,
MATHEMATICAL SOFTWARE, Algorithm analysis.",
}
@Article{Bose:1987:DAR,
author = "B. Bose",
title = "$2$-dimensional arithmetic residue check codes",
journal = j-COMPUT-MATH-APPL,
volume = "13",
number = "5--6",
pages = "547--554",
month = "????",
year = "1987",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:01:00 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122187900824",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@InProceedings{Bose:1987:FMD,
author = "B. K. Bose and L. Pei and G. S. Taylor and D. A.
Patterson",
title = "Fast Multiply and Divide for a {VLSI} Floating-Point
Unit",
crossref = "Irwin:1987:PSC",
pages = "87--93",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158684",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Bose_Pei_Taylor_Patterson.pdf",
abstract = "This paper presents the design of a fast and
area-efficient multiply-divide unit used in building a
VLSI floating-point processor (FPU), conforming to the
IEEE standard 754. Details of the algorithms,
implementation techniques and design tradeoffs are
presented. The multiplier and divider are implemented
in 2 micron CMOS technology with two layers of metal,
and occupy 23 square mm (23\% of the entire FPU). We
expect to perform extended-precision multiplication and
division in 1.1 and 2.8 microseconds, respectively.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@PhdThesis{Braune:1987:HSF,
author = "K. Braune",
title = "{Hochgenaue Standardfunktionen f{\"u}r reelle und
komplexe Punkte und Intervalle in beliebigen
Gleitpunktrastern} \toenglish {High-Accuracy Elementary
Functions for Real and Complex Points and Intervals in
Arbitrary Floating-Point Systems} \endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "??",
year = "1987",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InCollection{Breuer:1987:NMR,
author = "P. T. Breuer",
title = "A New Method for Real Rational Uniform Approximation",
crossref = "Mason:1987:AAB",
pages = "265--284",
year = "1987",
bibdate = "Thu Sep 01 12:25:00 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Carter:1987:SAT,
author = "Tony M. Carter",
title = "Structured Arithmetic Tiling of Integrated Circuits",
crossref = "Irwin:1987:PSC",
pages = "41--48",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158685",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Carter.pdf",
abstract = "Robertson's Theory of Decomposition and Structured
Tiling (an IC design technique) are combined in a
structured arithmetic circuit design method. This
method, extended by a set of inverse operators and a
set of multiply operators, is used with computer-aided
design tools to automate the design of arithmetic
circuits.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@InProceedings{Cavallaro:1987:CAS,
author = "Joseph R. Cavallaro and Franklin T. Luk",
title = "{CORDIC} Arithmetic for an {SVD} Processor",
crossref = "Irwin:1987:PSC",
pages = "113--120",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158686",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Cavallaro_Luk.pdf",
abstract = "Arithmetic issues in the calculation of the Singular
Value Decomposition (SVD) are discussed. Traditional
algorithms using hardware division and square root are
replaced with the special purpose CORDIC algorithms for
computing vector rotations and inverse tangents. The
CORDIC $ 2 \times 2 $ SVD processor can be twice as
fast as one assembled from traditional hardware units.
A prototype VISI implementation of a CORDIC SVD
processor array is planned for use in real-time signal
processing applications.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Chandra:1987:ACR,
author = "D. V. Chandra",
title = "Accumulation of coefficient roundoff error in fast
{Fourier} transforms implemented with logarithmic
number system",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "35",
number = "11",
pages = "1633--1636",
month = nov,
year = "1987",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "When a fast Fourier transform (FFT) is implemented on
a digital computer or with special-purpose hardware,
quantization errors will arise due to finite word
lengths in the digital system. This correspondence
presents an analysis of error \ldots{}",
}
@Article{Chen:1987:MFP,
author = "Chang-Fuu Chen",
title = "A modified floating-point code for voice coding and
its applications",
journal = j-J-CHINESE-INST-ENG,
volume = "10",
number = "4",
pages = "421--427",
month = jul,
year = "1987",
CODEN = "CKCKDZ",
ISSN = "0253-3839",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Tatung Institute of Technology, Taipei, Taiwan",
bibno = "43559",
catcode = "E.4; I.2.7; I.2.10; I.5.4",
CRclass = "E.4 Data compaction and compression; I.2.7 Natural
Language Processing; I.2.7 Speech recognition and
understanding; I.2.10 Vision and Scene Understanding;
I.2.10 Modeling and recovery of physical attributes;
I.5.4 Applications; I.5.4 Signal processing",
descriptor = "Data, CODING AND INFORMATION THEORY, Data compaction
and compression; Computing Methodologies, ARTIFICIAL
INTELLIGENCE, Natural Language Processing, Speech
recognition and understanding; Computing Methodologies,
ARTIFICIAL INTELLIGENCE, Vision and Scene
Understanding, Modeling and recovery of physical
attributes; Computing Methodologies, PATTERN
RECOGNITION, Applications, Signal processing",
fjournal = "Journal of the Chinese Institute of Engineers =
Chung-kuo kung ch'eng hsueh kan",
genterm = "THEORY; ALGORITHMS; HUMAN FACTORS; DESIGN",
guideno = "1988-11733",
journalabbrev = "J. Chin. Inst. Eng.",
subject = "E. Data; E.4 CODING AND INFORMATION THEORY; I.
Computing Methodologies; I.2 ARTIFICIAL INTELLIGENCE;
I. Computing Methodologies; I.2 ARTIFICIAL
INTELLIGENCE; I. Computing Methodologies; I.5 PATTERN
RECOGNITION",
}
@InProceedings{Ciminiera:1987:PMB,
author = "Luigi Ciminiera",
title = "Parallel Multipliers Based on Horizontal Compressors",
crossref = "Irwin:1987:PSC",
pages = "63--69",
month = may,
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158687",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Ciminiera.pdf",
abstract = "Two new implementations of parallel multipliers, based
on iterative arrays of logic cells are presented in
this paper. Both are able to compute the product of two
$n$ bit numbers with a delay of $n$ cells, rather $ 2 n
- 1 $ as in classical structures. The high speed
operation is obtained by using pure horizontal
compressors, to accelerate the horizontal signal
propagation, and by adopting a suitable array
structure, to shorten the vertical signal propagation.
The cost and performance advantages over similar
structures based on vertical compressors are
discussed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Clenshaw:1987:LIA,
author = "C. W. Clenshaw and Frank W. J. Olver",
title = "Level-Index Arithmetic Operations",
journal = j-SIAM-J-NUMER-ANAL,
volume = "24",
number = "2",
pages = "470--485",
month = apr,
year = "1987",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0724034",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65G05 (65G99)",
MRnumber = "881377",
MRreviewer = "F. Szidarovszky",
bibdate = "Sun Nov 12 06:18:24 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In a recent paper the authors described a system for
the internal representation of numbers in a computer,
based on repeated exponentiations. The main objective
in introducing this system is to eradicate the problems
of overflow and underflow. The present paper supplies
algorithms for performing the four basic arithmetical
operations in the new system. The algorithm are
accompanied by error analyses, which show that the
algorithms can be executed with fixed-point arithmetic.
Illustrative examples are included.",
acknowledgement = ack-nhfb,
author-dates = "Charles William Clenshaw (15 March 1926--23 September
2004); Frank William John Olver (15 December 1924--23
April 2013)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@InProceedings{Colagrossi:1987:NAT,
author = "A. Colagrossi and A. Miola",
title = "A Normalization Algorithm for Truncated $p$-{ADIC}
Arithmetic",
crossref = "Irwin:1987:PSC",
pages = "212--216",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158688",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Colagrossi_Miola.pdf",
abstract = "This paper presents a new algorithmic approach to cope
with the problems related to the generation and the
manipulation of the pseudo-Hensel-codes in the p-adic
arithmetic. After reviewing some classical properties
and the results of the Hensel code arithmetic, a new
algorithm to manipulate pseudo-Hensel-codes is
presented, discussed and compared with two existing
methods. The lower cost of the proposed new algorithm
will result from the comparison.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@InProceedings{Cosnard:1987:FAC,
author = "M. Cosnard and A. Guyot and B. Hochet and Jean-Michel
Muller and H. Ouaouicha and P. Paul and E. Zysman",
title = "The {FELIN} Arithmetic Coprocessor Chip",
crossref = "Irwin:1987:PSC",
pages = "107--112",
month = may,
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158691",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Cosnard_Guyot_Hochet_Muller_Ouaouicha_Paul_Zysman.pdf",
abstract = "We describe a general VLSI architecture for the
computation of arithmetic expressions including
floating-point transcendental functions. This
architecture, is divided in three parts: a
communication machine, the control part of a
computation machine and the operative part of this
computation machine. In order to compute the most usual
transcendental functions, we introduced some general
algorithms, presented briefly here, including as a
particular case the CORDIC scheme. Our major
architecture goals were regularity, parametrization and
automatic design. The final chip is designed in a 2-Alu
CMOS technology, and its name is FELIN (``Fonctions
EL{\'e}mentaires INt{\'e}gr{\'e}es'' is the French for
``integrated elementary functions'').",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@TechReport{Crockett:1987:PFF,
author = "Thomas W. Crockett",
title = "Performance of {Fortran} Floating-Point Operations on
the {Flex/32} Multicomputer",
type = "{ICASE} Interim Report",
number = "4",
institution = "ICASE, NASA Langley Research Center",
address = "Hampton, VA, USA",
pages = "????",
year = "1987",
bibdate = "Wed Sep 14 20:24:43 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran2.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ovr.bib;
Parallel/ovr.bib",
series = "NASA contractor report; 178364 ICASE interim report; 4
NASA contractor report; NASA CR-178364.",
acknowledgement = ack-nj # " and " # ack-nhfb,
govtdocnumber = "NAS 1.26:178364 830-H-14 (MF)",
keywords = "Computer networks; FORTRAN (Computer program
language)",
remark = "Distributed to depository libraries in microfiche.
Microfiche. [Washington, D.C.?: National Aeronautics
and Space Administration], 1987. 1 microfiche.",
}
@InCollection{Crowell:1987:FPA,
author = "Charles Crowell",
title = "Floating-point arithmetic with the {TMS32020}",
crossref = "Lin:1987:DSP",
pages = "245--268",
year = "1987",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$30.67",
acknowledgement = ack-nhfb,
bibno = "42623",
catcode = "J.2; C.5.3; G.1.0",
CRclass = "J.2 Mathematics and statistics; C.5.3 Microcomputers;
C.5.3 TMS 32010; G.1.0 General; G.1.0 Computer
arithmetic",
descriptor = "Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Mathematics and statistics; Computer
Systems Organization, COMPUTER SYSTEM IMPLEMENTATION,
Microcomputers, TMS 32010; Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic",
genterm = "MEASUREMENT; ALGORITHMS",
guideno = "1988-01737",
subject = "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
ENGINEERING; C. Computer Systems Organization; C.5
COMPUTER SYSTEM IMPLEMENTATION; G. Mathematics of
Computing; G.1 NUMERICAL ANALYSIS",
}
@InProceedings{Demmel:1987:EAA,
author = "James W. Demmel",
title = "On error analysis in arithmetic with varying relative
precision",
crossref = "Irwin:1987:PSC",
pages = "148--152",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158694",
bibdate = "Thu Aug 23 06:14:44 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.netlib.org/na-digest/91/v91n39",
abstract = "Recently Clenshaw\slash Olver and Iri\slash Matsui
proposed new floating point arithmetics which seek to
eliminate overflows and underflows from most
computations. Their common approach is to redistribute
the available numbers to spread out the largest and
smallest numbers much more thinly than in standard
floating point, thus achieving a larger range at the
cost of lower precision at the ends of the range. The
goal of these arithmetics is to eliminate much of the
effort needed to write code which is reliable despite
over\slash underflow. In this paper we argue that for
many codes this eliminated effort will reappear in the
error analyses needed to ascertain or guarantee the
accuracy of the computed solution. Thus reliability
with respect to over\slash underflow has been traded
for reliability with respect to roundoff. We also
propose a hardware flag, analogous to the ``sticky
flags'' of the IEEE binary floating point standard, to
do some of this extra error analysis automatically.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
remark = "Comments on SLI arithmetic proposed by Olver, Lozier,
and Turner, and on Kulisch and Miranker's interval
arithmetic and its implementation in IBM's ACRITH
product.",
}
@TechReport{Dion:1987:MFA,
author = "Jeremy Dion and David Reeves Boggs and Norman P.
Jouppi",
title = "{MultiTitan}: four architecture papers",
institution = "Digital, Western Research Laboratory",
address = "Palo Alto, CA, USA",
pages = "various",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "WRL research report. Digital Equipment Corporation.
Western Research Laboratory; 87-8 Digital Equipment
Corporation. Western Research Laboratory. WRL research
report; 87/8.",
acknowledgement = ack-nhfb,
keywords = "Titan (Computer)",
}
@InProceedings{DuCroz:1987:DFP,
author = "J. {Du Croz} and M. Pont",
title = "The Development of a Floating-Point Validation
Package",
crossref = "Irwin:1987:PSC",
pages = "255--255",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158693",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
remark = "Paper not received in time for publication.",
}
@Article{Duff:1987:EAP,
author = "Iain S. Duff and Jacques Laminie and Alain Lichnewsky
and Fran{\c{c}}ois Thomasset",
title = "An experiment with arithmetic precision in linear
algebra computations",
journal = j-INT-J-NUM-METH-FLUIDS,
volume = "7",
number = "????",
pages = "1077--1092",
year = "1987",
bibdate = "Mon Jan 02 17:53:34 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0363",
}
@Manual{Duhamel:1987:ASR,
author = "Bob Duhamel",
title = "{Atari} System Reference Manual",
address = "6915 Casselberry Way, San Diego, CA 92119, USA",
year = "1987",
bibdate = "Sat Mar 04 16:04:10 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See Chapter 11: The Floating Point Arithmetic
Package.",
URL = "http://atrey.karlin.mff.cuni.cz/~pavel/atari/atr11.html;
http://web.archive.org/web/20040606074520/trident.mcs.kent.edu/~clisowsk/8bit/atrpref.html",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "The ROM O/S on the Atari 6502 handles decimal
floating-point values stored in six-byte fields. The
first byte contains the sign and an excess-64 exponent,
followed by five bytes containing ten BCD digits. The
O/S provides for conversion to and from ASCII string
representation, to and from binary integers, add,
subtract, multiple, divide, log(), log10(), exp(),
exp10(), and polynomial evaluation.",
}
@Article{Dunham:1987:PMA,
author = "C. B. Dunham",
title = "Provably Monotone Approximations {II}",
journal = j-SIGNUM,
volume = "22",
number = "3",
pages = "30--31",
month = jul,
year = "1987",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Sep 13 09:01:31 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "theory",
subject = "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation",
}
@Article{Ercegovac:1987:FCR,
author = "M. D. Ercegovac and T. Lang",
title = "On-the-fly conversion of redundant into conventional
representations",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "7",
pages = "895--897",
month = jul,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.1676986",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Ercegovac:1987:LSC,
author = "Milo{\v{s}} D. Ercegovac and Tomas Lang",
title = "On-Line Scheme for Computing Rotation Factors",
crossref = "Irwin:1987:PSC",
pages = "196--203",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158695",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Ercegovac_Lang.pdf",
abstract = "An integrated radix-2 on-line algorithm for computing
rotation factors for matrix transformations is
presented. The inputs and outputs are in parallel form,
conventional 2's complement, floating-point
representation. The exponents are computed using
conventional arithmetic while the significands are
processed using on-line algorithms. The conventional
result is obtained by using an on-the-fly conversion
scheme. The rotation factors are computed in $ 9 + n $
clock cycles for $n$-bit significands. The clock period
is kept small by the use of carry-save adder schemes.
The implementation and performance of the algorithm are
discussed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@InProceedings{Fandrianto:1987:AHS,
author = "Jan Fandrianto",
title = "Algorithms for High Speed Shared Radix 4 Division and
Radix 4 Square-Root",
crossref = "Irwin:1987:PSC",
pages = "73--79",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158696",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Fandrianto.pdf",
abstract = "An algorithm to implement radix four division and
radix four square-root in a shared hardware for IEEE
standard for binary floating point format will be
described. The algorithm is best suited to be
implemented in either off-the-shelf components or being
a portion of a VLSI floating-point chip. Division and
square-root bits are generated by a non-restoring
method while keeping the partial remainder, partial
radicand, quotient and root all in redundant forms. The
core iteration involves a 8-bit carry look-ahead adder,
a multiplexer to convert two's complement to sign
magnitude, a 19-term next quotient\slash root
prediction PLA, a divisor\slash root multiple selector,
and a carry save adder. At the end, two iterations of
carry look-ahead adder across the length of th,e
mantissa are required to generate the quotient\slash
root in a correctly rounded form. Despite its
simplicity in the hardware requirement, the algorithm
takes only about 30 cycles to compute double precision
division or square-root. Finally, extending the
algorithm to radix eight or higher division\slash
square-root will be discussed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8; correct rounding; floating-point arithmetic",
}
@Periodical{FPS:1987:AR,
author = "{Floating Point Systems, Inc.}",
key = "FPS",
title = "Annual report",
publisher = "Floating Point Systems, Inc.",
address = "Portland, OR, USA",
pages = "various",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer industry --- United States --- Periodicals.;
Floating Point Systems, Inc. --- Periodicals.",
remark = "Description based on: 1987.",
}
@Article{Froggatt:1987:FPC,
author = "Terry Froggatt",
title = "Fixed-point conversion, multiplication, and division
in {Ada}",
journal = j-SIGADA-LETTERS,
volume = "7",
number = "1",
pages = "71--81",
month = jan # "\slash " # feb,
year = "1987",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Sat Aug 9 09:05:24 MDT 2003",
bibsource = "ftp://ftp.uu.net/library/bibliography;
http://portal.acm.org/;
http://www.adahome.com/Resources/Bibliography/articles.ref;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "languages; theory",
subject = "D.3.2 Software, PROGRAMMING LANGUAGES, Language
Classifications, Ada \\ G.1.0 Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic",
}
@Article{Grosse:1987:UCB,
author = "Eric Grosse and Cleve Moler",
title = "Underflow can be Harmful",
journal = j-SIAM-NEWS,
volume = "20",
number = "6",
pages = "1",
year = "1987",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Sat Feb 8 10:30:07 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "https://sinews.siam.org/",
}
@Article{Guyot:1987:WBE,
author = "Alain Guyot and Bertrand Hochet and Jean-Michel
Muller",
title = "A Way to Build Efficient Carry-Skip Adders",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "10",
pages = "1144--1152",
month = oct,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.1676855",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676855",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Hamada:1987:NRN,
author = "Hozumi Hamada",
title = "A New Real Number Representation and Its Operation",
crossref = "Irwin:1987:PSC",
pages = "153--157",
month = may,
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158698",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hamada.pdf",
abstract = "A new internal representation is proposed for real
numbers. It has been named URR for universal
representation of real numbers. This approach is based
on a bisection method which is applied to real number
intervals. With this method, the point of division
increases or decreases in a double exponential manner
in the global range. The main characteristics of the
method are as follows. First, overflow\slash underflow
does not, in practice, occur. Second, since the data
format does not depend on the length but on the value
of the data, a transformation operation is virtually
not needed between systems of long and short data.
Finally, only one bit of resolution is lost compared
with the fixed point form. In addition, arithmetic
operations are slightly complicated compared with
conventional representation, but they present no
special difficulties. This new method is thus the most
suitable internal form as an interface not only between
computers but also between computers and digital
systems which deal with real numbers or physical
(scalar) values.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@InProceedings{Han:1987:FAE,
author = "Tackdon Han and David A. Carlson",
title = "Fast Area-Efficient {VLSI} Adders",
crossref = "Irwin:1987:PSC",
pages = "49--56",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158699",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Han_Carlson.pdf",
abstract = "In this paper, we study area-time tradeoffs in VLSI
for prefix computation using graph representations of
this problem. Since the problem is intimately related
to binary addition the results we obtain lead to the
design of area-time efficient VLSI adders. This is a
major goal of our work: to design {\em very low
latency\/} addition circuitry that is also {\em area
efficient}. To this end, we present a new graph
representation for prefix computation that leads to the
design of a fast, area-efficient binary adder. The new
graph is a combination of previously known graph
representations for prefix computation, and its area is
close to known lower bounds on the VLSI area of
parallel prefix graphs. Using it, we are able to design
VLSI adders having area $ A = O(n \log n) $ whose delay
time is the lowest possible value, i.e., the fastest
possible area-efficient VLSI adder.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Book{Herz-Fischler:1987:MHD,
author = "Roger Herz-Fischler",
title = "A mathematical history of division in extreme and mean
ratio",
publisher = "Wilfrid Laurier University Press",
address = "Waterloo, ON, Canada",
pages = "xvi + 191",
year = "1987",
ISBN = "0-88920-152-8",
ISBN-13 = "978-0-88920-152-1",
LCCN = "A481.H47 1987",
bibdate = "Thu Jul 10 08:02:28 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$65.00",
acknowledgement = ack-nhfb,
libnote = "Not yet in my library.",
}
@Book{Hildebrand:1987:INA,
author = "Francis Begnaud Hildebrand",
title = "Introduction to numerical analysis",
publisher = pub-DOVER,
address = pub-DOVER:adr,
edition = "Second",
pages = "xiii + 669",
year = "1987",
ISBN = "0-486-65363-3 (paperback)",
ISBN-13 = "978-0-486-65363-1 (paperback)",
LCCN = "QA297 .H54 1987",
bibdate = "Fri Aug 20 09:19:58 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/description/dover032/87005370.html",
acknowledgement = ack-nhfb,
remark = "Unabridged, slightly corrected republication of
\cite{Hildebrand:1974:INA}.",
subject = "Numerical analysis",
}
@Article{Himmeroeder:1987:CKC,
author = "H.-J. Himmer{\"o}der and R. M. Toschke",
title = "{c't-KAT-Ce. Ein 68000-Einplatinenrechner, Teil 3:
REAL-Arithmetik} \toenglish {c't-KAT-Ce. A 68000
Single-Board Computer} \endtoenglish",
journal = j-CT,
volume = "1",
pages = "152--158",
year = "1987",
ISSN = "0724-8679",
bibdate = "Sat Feb 24 09:05:58 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "C T: Magazin f{\"u}r Computer Technik (Hannover)",
}
@InProceedings{Hochet:1987:SSL,
author = "Bertrand Hochet and Patrice Quinton and Yves Robert",
title = "Systolic Solution of Linear Systems over {$ \mathrm
{GF}(p) $} with Partial Pivoting",
crossref = "Irwin:1987:PSC",
pages = "161--168",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158700",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hochet_Quinton_Robert.pdf",
abstract = "We propose two systolic architectures for the Gaussian
triangularization and the Gauss--Jordan diagonalization
of large dense $ n \times n $ matrices over $ \mathrm
{GF}(p) $, where $p$ is a prime number. The solution of
large dense linear systems over $ \mathrm {GF}(p) $ is
the major computational step in various algorithms
issued from arithmetic number theory and computer
algebra. The two proposed architectures implement the
elimination with partial pivoting, although the
operation of the array remains purely systolic. The
last section is devoted to the design and layout of a
CMOS 8 by 8 Gauss--Jordan diagonalization systolic chip
over $ \mathrm {GF}(2) $.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Homewood:1987:ITT,
author = "Mark Homewood and David May and David Shepherd and
Roger Shepherd",
title = "The {IMS T800} Transputer",
journal = j-IEEE-MICRO,
volume = "7",
number = "5",
pages = "10--26",
month = sep # "\slash " # oct,
year = "1987",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1987.305012",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Dec 14 06:08:58 MST 2000",
bibsource = "Compendex database;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Parallel/transputer.bib; Science Citation Index
database (1980--2000)",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliationaddress = "Inmos Ltd, Bristol, Engl",
classcodes = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips)",
classification = "714; 722; 723; 921",
corpsource = "Inmos Ltd., Bristol, UK",
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
keywords = "architecture; capability; communication links;
computer architecture; computer graphics; computer
programming languages; computers, microcomputer;
Design; floating-point arithmetic; floating-point unit
design; graphics; IMS T800 transputer; integrated
circuits, VLSI; microprocessor chips; performance;
scientific computer; supercomputers; telecommunication
links",
treatment = "P Practical; R Product Review",
}
@InCollection{HP:1987:IPH,
author = "{Hewlett Packard}",
booktitle = "{HP-71} Reference Manual",
title = "The {IEEE} Proposal for Handling Math Exceptions",
publisher = "Hewlett Packard Company",
address = "Palo Alto, CA, USA",
pages = "338--345",
month = oct,
year = "1987",
bibdate = "Fri Nov 28 17:12:16 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Mfg. \#0071-90110, Reorder \#0071-90010. First edition
October 1983. Manual available from {\em The Museum of
HP Calculators}.",
URL = "http://www.hpmuseum.org/",
abstract = "The IEEE Radix Independent Floating-Point Proposal
divides all of the floating-point ``exceptional
events'' encountered in calculations into five classes
of {\em math exceptions\/}: invalid operation, division
by zero, overflow, underflow, and inexact result.
Associated with each math exception is a flag that is
set by the HP-71 whenever an exception is encountered.
These flags remain set until you clear them. Each of
these flags can be accessed by its number or its
name.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@MastersThesis{Hu:1987:CDT,
author = "Timothy Hu",
title = "Circuit design techniques for a floating-point
processor: research project",
type = "{Master of Science, Plan II}",
school = "University of California, Berkeley. Dept. of
Electrical Engineering and Computer Sciences",
address = "Berkeley, CA, USA",
pages = "70",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hull:1987:TIC,
author = "T. E. Hull and M. S. Cohen",
title = "Toward an Ideal Computer Arithmetic",
crossref = "Irwin:1987:PSC",
pages = "131--138",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158701",
bibdate = "Fri Nov 28 11:41:31 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hull_Cohen.pdf",
abstract = "A new computer arithmetic is described. Closely
related built-in functions are included. A user's point
of view is taken, so that the emphasis is on what
language features are available to a user. The main new
feature is flexible precision control of decimal
floating-point arithmetic. It is intended that the
language facilities be sufficient for describing
numerical processes one might want to implement, while
at the same time being simple to use, and implementable
in a reasonably efficient manner. Illustrative examples
are based on experience with an existing software
implementation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8; decimal floating-point arithmetic",
}
@Article{IEEE:1987:ISB,
author = "{IEEE}",
title = "{IEEE} Standard for Binary Floating-Point Arithmetic",
journal = j-SIGPLAN,
volume = "22",
number = "2",
pages = "9--25",
month = feb,
year = "1987",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1109/IEEESTD.1985.82928",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Fri Sep 09 12:55:55 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@Book{IEEE:1987:RIS,
editor = "{IEEE}",
title = "{854-1987 (R1994) IEEE Standard for Radix-Independent
Floating-Point Arithmetic}",
publisher = pub-IEEE-STD,
address = pub-IEEE-STD:adr,
pages = "16",
year = "1987",
DOI = "https://doi.org/10.1109/IEEESTD.1987.81037",
ISBN = "1-55937-859-X",
ISBN-13 = "978-1-55937-859-8",
bibdate = "Mon Apr 24 07:02:34 2000",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Revised 1994.",
price = "US\$44.00",
URL = "http://standards.ieee.org/reading/ieee/std_public/description/busarch/854-1987_desc.html",
acknowledgement = ack-nj # " and " # ack-nhfb,
keywords = "floating point arithmetic; Floating-point arithmetic.;
Standards",
remark = "At head of title: An American National Standard.
``Approved March 12, 1987 IEEE Standards Board;
Approved September 10, 1987 American National Standards
Institute.''",
}
@MastersThesis{Jensen:1987:CIS,
author = "Debby Jensen",
title = "Control implementation for the {SPUR} floating point
coprocessor: research project",
type = "{Master of Science, Plan II}",
school = "University of California, Berkeley. Dept. of
Electrical Engineering and Computer Sciences",
address = "Berkeley, CA, USA",
pages = "76",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Johnson:1987:AES,
author = "Kenneth C. Johnson",
title = "{Algorithm 650}: Efficient Square Root Implementation
on the 68000",
journal = j-TOMS,
volume = "13",
number = "2",
pages = "138--151",
month = jun,
year = "1987",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/328512.328520",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D15",
MRnumber = "898 489",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Johnson:1987:CES}.",
acknowledgement = ack-nj,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Johnson:1987:CES,
author = "Kenneth C. Johnson",
title = "Corrigendum: {``Algorithm 650: efficient square root
implementation on the 68000'' [ACM Trans. Math.
Software {\bf 13} (1987), no. 2, 138--151]}",
journal = j-TOMS,
volume = "13",
number = "3",
pages = "320--320",
month = sep,
year = "1987",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/29380.356210",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "320. 65D15",
MRnumber = "918 582",
bibdate = "Sat Feb 8 10:30:18 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See
\cite{Johnson:1987:AES,Monahan:1987:AGC,Boisvert:1987:AAH}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@InProceedings{Kahan:1987:BCC,
author = "W. Kahan",
title = "Branch Cuts for Complex Elementary Functions or Much
Ado About Nothing's Sign Bit",
crossref = "Iserles:1987:SAN",
volume = "9",
pages = "165--211",
year = "1987",
MRclass = "65E05",
MRnumber = "88k:65027",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Inst. Math. Appl. Conf. Ser. New Ser.",
URL = "http://people.freebsd.org/~das/kahan86branch.pdf;
http://www.cs.berkeley.edu/~dbindel/class/cs279/",
acknowledgement = ack-nhfb # " and " # ack-nj,
}
@Unpublished{Kahan:1987:CWF,
author = "W. Kahan",
title = "Checking whether floating-point division is correctly
rounded",
year = "1987",
bibdate = "Mon Apr 25 05:40:03 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Lecture notes.",
acknowledgement = ack-nhfb,
keywords = "correct rounding; floating-point arithmetic; rounding
errors",
}
@Misc{Kahan:1987:DPI,
author = "W. Kahan",
title = "Doubled-precision {IEEE Standard 754} floating-point
arithmetic",
howpublished = "Manuscript",
month = feb,
year = "1987",
bibdate = "Thu May 09 07:25:40 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
remark = "Cited in \cite{Higham:1993:AFP}.",
}
@TechReport{Kahan:1987:HAE,
author = "W. Kahan",
title = "Handling Arithmetic Exceptions",
type = "Report",
institution = inst-BERKELEY-MATH-EECS,
address = inst-BERKELEY-MATH-EECS:adr,
day = "14",
month = may,
year = "1987",
bibdate = "Mon Aug 26 10:42:10 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.arithmazium.org/classroom/lib//Kahan_Handling_Arithmetic_Exceptions.pdf",
abstract = "An {\em Exception\/} arises when an operation
performed by a computer has to produce a result to
which some people might reasonably take exception.
Examples are {\em Division by Zero}, {\em Overflow\/ }
and Floating-Point {\em Underflow}. Though most (but
not all) exceptions must be rare, too rare to be topics
cf everyday conversation, they are not so rare that
computer programmers and users can ignore them
altogether. This paper presents proposals, many of them
now implemented on a few computers, to handle
arithmetic exceptions in a generally satisfactory way
at a tolerable cost. The proposals are designed to be
fully compatible with concurrent, overlapped, parallel,
pipelined and vectorized computing on new hardware that
will be designed to support them without {\em precise
interrupts}. {\em Flags\/} and {\em Modes\/} are
proposed to help programmers cope with exceptions; {\em
Retrospective Diagnostics\/} are proposed to help most
of the rest of us, who aspire to use computers without
having to program them. The features of IEEE Standards
754 and 854 are supported by but not obligatory for the
proposals.",
acknowledgement = ack-nhfb,
}
@Book{Kane:1987:MRR,
author = "Gerry Kane",
title = "{MIPS R2000 RISC} Architecture",
publisher = pub-PH,
address = pub-PH:adr,
year = "1987",
ISBN = "0-13-584749-4",
ISBN-13 = "978-0-13-584749-7",
LCCN = "QA76.8.M52 K36 1987",
bibdate = "Wed Dec 15 17:51:38 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kao:1987:ISM,
author = "Rom-Shen Kao and Fred J. Taylor",
title = "Implementation of the Single Modulus Complex {ALU}",
crossref = "Irwin:1987:PSC",
pages = "21--27",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158703",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kao_Taylor.pdf",
abstract = "Recently the complex residue number system, or RNS,
has been a subject of intense study. One special
embodiment of this theory is the single modulus complex
RNS processor which suggests both implementation and
performance advantages. In this paper these conjectures
are tested in the context of a CMOS gate array design
and are found to be valid.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@InProceedings{Kirchner:1987:AVP,
author = "R. Kirchner and U. Kulisch",
title = "Arithmetic for Vector Processors",
crossref = "Irwin:1987:PSC",
pages = "256--269",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158704",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kirchner_Kulisch.pdf",
abstract = "In electronic computers the elementary arithmetic
operations are these days generally approximated by
floating-point operations of highest accuracy. Vector
processors and parallel computers often provide
additional operations like ``multiply and add'',
``accumulate'' or ``multiply and accumulate''. Also
these operations shall always deliver the correct
answer whatever the data are. The user should not be
obliged to execute an error analysis for operations
predefined by the manufacturer. In the first part of
this paper we discuss circuits which allow a fast and
correct computation of sums and scalar products making
use of a matrix shaped arrangement of adders and
pipeline technology. In the second part a variant is
discussed which permits a drastic reduction in the
number of adders required. The methods discussed in
this paper can also be used to build a fast arithmetic
unit for micro computers in VLSI-technology.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Kirchner:1987:SVS,
author = "Reinhard Kirchner and Ulrich Kulisch",
title = "{Schaltungsanordnung und Verfahren zur schnellen
Berechnung von Summen und Skalarprodukten von
Gleitkommazahlen mit maximaler Genauigkeit mittels
Pipelinetechnik. (German)} [Circuit diagrams and
methods for fast computation of sums and scalar
products of floating point numbers with maximal
accuracy via pipeline technique]",
journal = "Beitr{\"a}ge zur angewandten Mathematik und
Statistik",
publisher = pub-HANSER,
address = pub-HANSER:adr,
pages = "139--177",
year = "1987",
MRclass = "68Q25 (68Q10)",
MRnumber = "986 782",
bibdate = "Fri Dec 08 12:20:44 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Koopman:1987:TF,
author = "P. Koopman",
title = "Transcendental Functions",
journal = j-FORTH-DIMENSIONS,
volume = "9",
number = "4",
pages = "21--22",
month = dec,
year = "1987",
CODEN = "FODMD5",
ISSN = "0884-0822",
bibdate = "Thu Sep 1 10:15:30 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Forth Dimensions",
}
@InProceedings{Kornerup:1987:BSA,
author = "Peter Kornerup and David W. Matula",
title = "A Bit-Serial Arithmetic Unit for Rational Arithmetic",
crossref = "Irwin:1987:PSC",
pages = "204--211",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158705",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kornerup_Matula.pdf",
abstract = "We describe a binary implementation of an algorithm of
Gosper to compute the sum, difference, product,
quotient and certain rational functions of two rational
operands applicable to integrated approximate and exact
rational computation. The arithmetic unit we propose is
an eight register computation cell with bit, serial
input and output employing the binary lexicographic
continued fraction (LCF) representation of the rational
operands., The operands and results are processed in a
most-significant-bit first on-line fashion with bit
level logic leading to less delay in the computation
cell when compared to operation on the full partial
quotients of the standard continued fraction
representation. Minimization of delay is investigated
with the aim of supporting greater throughput in
cascaded parallel computation with such computation
cells.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@PhdThesis{Kraemer:1987:ISF,
author = "W. Kr{\"a}mer",
title = "Inverse Standardfunktionen f{\"u}r reelle und komplexe
Intervallargumente mit a priori Fehlerabsch{\"a}tzungen
f{\"u}r beliebige Datenformate \toenglish {Inverse
Elementary Functions for Real and Complex Interval
Arguments with A-Priori Error Estimates for Arbitrary
Data Formats} \endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "??",
year = "1987",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
author-dates = "1952--2014",
}
@InProceedings{Kuninobu:1987:DHS,
author = "Shigeo Kuninobu and Tamotsu Nishiyama and Hisakazu
Edamatsu and Takashi Taniguchi and Naofumi Takagi",
key = "KNE87",
title = "Design of High Speed {MOS} Multiplier and Divider
Using Redundant Binary Representation",
crossref = "Irwin:1987:PSC",
pages = "80--86",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158706",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kuninobu_Nishiyama_Edamatsu_Taniguchi_Takagi.pdf",
abstract = "A high speed multiplier and divider for MOS LSI based
on a new algorithm is presented. When we implement the
multiplier and the divider in LSI. the features such as
high speed operation, small number of transistors and
easy layout are the most important factors. A
computational algorithm using a redundant binary
representation has several excellent features such as
high speed addition operations. We improved the
algorithm and the method of implementation. and
designed an advanced multiplier and divider with the
above mentioned features. We expect that our multiplier
and divider are excellent compared with multipliers
using the Booth algorithm and the Wallace tree. and
with divider using the SRT method, respectively.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Lange:1987:ITA,
author = "Eberhard Lange",
title = "Implementation and Test of the {ACRITH} Facility in a
{System}\slash 370",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "9",
pages = "1088--1096",
month = sep,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.5009539",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:55 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009539",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "floating-point testing",
}
@Article{Leavitt:1987:APF,
author = "Randal Leavitt",
title = "Adjustable Precision Floating Point Arithmetic in
{Ada}",
journal = j-SIGADA-LETTERS,
volume = "7",
number = "5",
pages = "63--78",
month = sep # "\slash " # oct,
year = "1987",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Sat Aug 9 09:05:26 MDT 2003",
bibsource = "ftp://ftp.uu.net/library/bibliography;
http://portal.acm.org/;
http://www.adahome.com/Resources/Bibliography/articles.ref;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "design; performance; theory",
subject = "D.3.2 Software, PROGRAMMING LANGUAGES, Language
Classifications, Ada \\ G.1.0 Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic",
}
@Article{Lien:1987:RCI,
author = "B. Lien and G. Tang",
title = "Reversed {Chebyshev} implementation of {McClellan}
transform and its roundoff error",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "35",
number = "10",
pages = "1435--1439",
month = oct,
year = "1987",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "A new structure, called the reversed Chebyshev
structure, for the fixed point implementation of the
FIR filters designed with the McClellan transformation
is presented. It shows the best roundoff noise
performance among the existing ones for both \ldots{}",
}
@InProceedings{Lin:1987:NFP,
author = "Haixiang X. Lin and Henk J. Sips",
title = "A Novel Floating-Point Online Division Algorithm",
crossref = "Irwin:1987:PSC",
pages = "188--195",
month = may,
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158707",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Lin_Sips.pdf",
abstract = "This paper describes a new online division
(reciprocal) algorithm for (maximally) redundant
floating-point numbers of arbitrary radix. The
algorithm works for normalized, quasi-normalized, and
pseudo-normalized numbers and can therefore be applied
in chained online computations. The online delay of the
proposed algorithm is the smallest reported so far. The
algorithm consists of two steps: the first $m$ digits
of the result are generated by a simple table lookup
method; the remaining $ n - m $ digits are generated by
using an adapted Newton--Raphson iteration method. In
the second step, the online digits are created by using
a fast and simple selection mechanism.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@MastersThesis{Liu:1987:BEF,
author = "Zhi-Shun Alex Liu",
title = "{Berkeley} Elementary Function Test Suite: Research
Project",
type = "{Master of Science, Plan II}",
school = "Computer Science Division, Department of Electrical
Engineering and Computer Science, Univerity of
California at Berkeley",
address = "Berkeley, CA, USA",
month = dec,
year = "1987",
bibdate = "Mon Sep 12 23:52:34 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
keywords = "BeEF test suite; floating-point testing",
}
@Article{Lo:1987:HGA,
author = "H.-Y. Lo and J.-L. Chen",
title = "A Hardwired Generalized Algorithm for Generating the
Logarithm Base-$k$ by Iteration",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "11",
pages = "1363--1367",
month = nov,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.5009477",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 08 08:08:51 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Maenner:1987:FIB,
author = "R. Maenner",
title = "A Fast Integer Binary Logarithm of Large Arguments",
journal = j-IEEE-MICRO,
volume = "7",
number = "6",
pages = "41--45",
month = nov # "\slash " # dec,
year = "1987",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1987.304914",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Article{Magenheimer:1987:IMD,
author = "Daniel J. Magenheimer and Liz Peters and Karl Pettis
and Dan Zuras",
title = "Integer multiplication and division on the {HP
Precision Architecture}",
journal = j-SIGPLAN,
volume = "22",
number = "10",
pages = "90--99",
month = oct,
year = "1987",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:15:15 MST 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@Article{Makarenko:1987:VMM,
author = "Darrell Makarenko and Jonathan Schaeffer",
title = "A {VLSI} multiprecision matrix multiplier and
polynomial evaluator",
journal = j-J-PAR-DIST-COMP,
volume = "4",
number = "6",
pages = "619--628",
month = dec,
year = "1987",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Univ of Alberta, Edmonton, Alberta, Can",
classification = "713; 722; C4140 (Linear algebra); C4240 (Programming
and algorithm theory); C5230 (Digital arithmetic
methods)",
corpsource = "Department of Computer Science, Alberta University,
Edmonton, Alta., Canada",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "32 bit; 32-bit multiplication; algebra; band-matrix
multiplication; bit-serial; computational complexity;
computers --- Multiplying Circuits; Design; digital
arithmetic; evaluations; full-matrix multiplication;
integrated circuits, VLSI; linear-space evaluations;
linear-time; mathematical techniques --- Polynomials;
matrix; matrix multiplier; multiply and accumulate
cells; multiprecision matrix multiplier; polynomial
evaluator; polynomials; two dimensional array; two's
complement numbers; VLSI; VLSI multiprecision; VLSI
multiprecision polynomial evaluator",
treatment = "P Practical",
}
@InProceedings{Manzoul:1987:QCN,
author = "Mahmoud A. Manzoul",
title = "A quaternary complex number {CCD} adder (abstract
only)",
crossref = "Davis:1987:PAC",
pages = "434--434",
year = "1987",
DOI = "https://doi.org/10.1145/322917.323095",
bibdate = "Sat Aug 22 09:06:07 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Complex number arithmetic occurs frequently in digital
signal processing and power systems analysis. Normally,
complex numbers are given two binary words, with one
word for each component (real and imaginary).
Therefore, the standard binary implementation of
complex numbers requires several real arithmetic
operations. Besides, the two components of each complex
number must be tracked down at every stage of the
computation. Different digital representations for
complex numbers have been proposed in an effort to
reduce these problems. Knuth [1] has proposed an
unconventional single component representation of
complex numbers whereby the radix is chosen to be (2j)
with the digit set comprised of the first four positive
integers (0, 1, 2, 3). This is in contrast with the
conventional two components representation with binary
radix whether in Cartesian or Polar coordinates.
Knuth's representation leads to simple and interesting
arithmetic in the complex field [2] [3].",
acknowledgement = ack-nhfb,
}
@Article{Mariella:1987:IDF,
author = "Ray Mariella",
title = "Integers Don't Float",
journal = j-DDJ,
volume = "12",
number = "12",
pages = "48--??",
month = dec,
year = "1987",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Mays:1987:IDA,
author = "Michael E. Mays",
title = "Iterating the Division Algorithm",
journal = j-FIB-QUART,
volume = "25",
number = "3",
pages = "204--213",
month = aug,
year = "1987",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:00:58 MDT 2011",
bibsource = "http://www.fq.math.ca/25-3.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/25-3/mays.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Book{McMcusersmanual:1987:MMF,
author = "{Motorola, Inc.}",
title = "{MC68881\slash MC68882} floating-point coprocessor
user's manual",
publisher = pub-PH,
address = pub-PH:adr,
pages = "various",
year = "1987",
ISBN = "0-13-566936-7 (pbk.)",
ISBN-13 = "978-0-13-566936-5 (pbk.)",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Motorola 68881
(Microprocessor); Motorola 68882 (Microprocessor)",
remark = "Spine title: MC68881/MC68882 user's manual.
``MC68881UM/AD REV 1''--Cover.",
}
@Article{Monahan:1987:AGC,
author = "John F. Monahan",
title = "An Algorithm for Generating Chi Random Variables",
journal = j-TOMS,
volume = "13",
number = "2",
pages = "168--172",
month = jun,
year = "1987",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/328512.328522",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65C10",
MRnumber = "88d:65013",
bibdate = "Sat Nov 19 13:08:24 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Johnson:1987:CES,Monahan:1988:CAG}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Montgomery:1987:SPE,
author = "Peter L. Montgomery",
title = "Speeding the {Pollard} and elliptic curve methods of
factorization",
journal = j-MATH-COMPUT,
volume = "48",
number = "177",
pages = "243--264",
month = jan,
year = "1987",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Y05 (11A51 68Q40)",
MRnumber = "88e:11130",
MRreviewer = "Kevin S. McCurley",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
JSTOR database",
note = "See improvement \cite{Kim:2024:MCA}.",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "C1160 (Combinatorial mathematics); C4240 (Programming
and algorithm theory)",
corpsource = "Syst. Dev. Corp., Santa Monica, CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "computational complexity; elliptic curve; elliptic
curve method; elliptic curve methods; factorization;
Lenstra method; Monte Carlo methods; number; number
theory; parametrisation; Pollard methods; polynomial
preconditioning; theory; Williams method",
treatment = "T Theoretical or Mathematical",
}
@Book{Motorola:1987:MMF,
author = "Motorola",
title = "{MC68881\slash MC68882} Floating-Point Coprocessor
User's Manual",
publisher = pub-PH,
address = pub-PH:adr,
pages = "various",
year = "1987",
ISBN = "0-13-566936-7",
ISBN-13 = "978-0-13-566936-5",
LCCN = "QA76.8.M69 M3 1987",
bibdate = "Fri Dec 08 13:03:15 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Mutrie:1987:FEA,
author = "Mark P. W. Mutrie and Richard H. Bartels and Bruce W.
Char",
title = "Floating-point error analysis using symbolic algebraic
computation",
type = "Research report",
number = "CS-87-08",
institution = "University of Waterloo, Faculty of Mathematics",
address = "Waterloo, Ont., Canada",
pages = "13",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Roundoff errors.",
remark = "Supported in part by the Natural Sciences and
Engineering Research Council of Canada.",
}
@Misc{Nakano:1987:MAD,
author = "Hiraku Nakano",
title = "Method and apparatus for division using interpolation
approximation",
howpublished = "United States Patent 4,707,798",
day = "17",
month = nov,
year = "1987",
bibdate = "Tue Jan 08 22:36:28 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.freepatentsonline.com/4707798.html",
abstract = "A divide method and a divide apparatus for use in a
data processing system. The divisor and dividend are
normalized in a normalization circuit. A table unit
stores a plurality of approximate reciprocal divisors
and differences between adjacent approximate reciprocal
divisors and is addressed by the high-order bits of the
normalized divisor. The approximate reciprocal divisor
read out from the table unit is, in an interpolation
approximation circuit, changed into an interpolation
approximated approximate reciprocal divisor in
accordance with a plurality of bits following the
high-order bits and the difference. A multiplication
unit multiplies the interpolation approximated
approximate reciprocal divisor by the normalized
dividend to output a quotient.",
acknowledgement = ack-nhfb,
}
@Article{Nelsen:1987:PSR,
author = "Roger B. Nelsen and James E. Schultz",
title = "The Probability that the {``Sum} of the Rounds''
Equals the {``Round} of the Sum''",
journal = j-COLLEGE-MATH-J,
volume = "18",
number = "5",
pages = "390--396",
month = nov,
year = "1987",
CODEN = "????",
DOI = "https://doi.org/10.1080/07468342.1987.11973061",
ISSN = "0746-8342 (print), 1931-1346 (electronic)",
ISSN-L = "0746-8342",
bibdate = "Thu Feb 14 09:50:35 MST 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/collegemathj.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib",
URL = "http://www.jstor.org/stable/2686963;
http://www.tandfonline.com/doi/abs/10.1080/07468342.1987.11973061",
acknowledgement = ack-nhfb,
fjournal = "College Mathematics Journal",
journal-URL = "https://maa.tandfonline.com/loi/ucmj20;
https://www.jstor.org/journal/collmathj",
keywords = "rounding in fixed-point addition",
onlinedate = "30 Jan 2018",
remark = "See also \cite{Hopkins:2016:WMN} for a later
independent derivation of part of this work.",
}
@Article{Obermaier:1987:SCI,
author = "A. Obermaier",
title = "{Sin und cosin mit Integerarithmetik} \toenglish {Sine
and Cosine with Integer Arithmetic} \endtoenglish",
journal = j-MC,
volume = "6",
pages = "108--112",
year = "1987",
ISSN = "0720-4442, 0941-777x , 0943-5409",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "MC: Die Mikrocomputer-Zeitschrift",
}
@InProceedings{Olver:1987:CCA,
author = "F. W. J. Olver",
title = "A Closed Computer Arithmetic",
crossref = "Irwin:1987:PSC",
pages = "139--143",
month = may,
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158708",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Olver.pdf",
abstract = "Two closely related new systems of computer arithmetic
are proposed. It is shown that both are closed under
arithmetic operations in finite-precision arithmetic,
thereby offering a permanent solution to the problems
of overflow and underflow. Other advantages of the new
systems pertaining to precision are described, and
there is also a brief discussion of possible ways of
hardware implementation.",
acknowledgement = ack-nhfb,
author-dates = "Frank William John Olver (15 December 1924--23 April
2013)",
keywords = "ARITH-8",
remark = "Reprinted in \cite{Olver:1990:CCA}.",
}
@InProceedings{Olver:1987:ILI,
author = "F. W. J. Olver and P. R. Turner",
title = "Implementation of Level-Index Arithmetic Using Partial
Table Look-Up",
crossref = "Irwin:1987:PSC",
pages = "144--147",
month = may,
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158709",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Olver_Turner.pdf",
abstract = "This paper is concerned with finding fast efficient
algorithms for performing level-index arithmetic. The
approach used combines the advantages of parallel
processing with the use of table look-up. The latter is
used only for short words and the result is a potential
implementation with $ \li $ operation times comparable
with floating-point long multiplications.",
acknowledgement = ack-nhfb,
author-dates = "Frank William John Olver (15 December 1924--23 April
2013)",
keywords = "ARITH-8",
}
@Article{Owens:1987:AC,
author = "Robert Michael Owens and Mary Jane Irwin",
title = "The Arithmetic Cube",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "11",
pages = "1342--1348",
month = nov,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.5009473",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009473",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Papachristou:1987:ATL,
author = "Christos A. Papachristou",
title = "Associative Table Lookup Processing for Multioperand
Residue Arithmetic",
journal = j-J-ACM,
volume = "34",
number = "2",
pages = "376--396",
month = apr,
year = "1987",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Sat Oct 22 00:20:03 1994",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Misc/IMMD_IV.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Parhami:1987:CTL,
author = "B. Parhami",
title = "On the Complexity of Table Lookup for Iterative
Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "10",
pages = "1233--1236",
month = oct,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.1676863",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676863",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Parhami:1987:SUC,
author = "Behrooz Parhami",
title = "Systolic Up\slash Down Counters with Zero and Sign
Detection",
crossref = "Irwin:1987:PSC",
pages = "174--178",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158710",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Parhami.pdf",
abstract = "Although a state encoding scheme for systolic counters
has been presented earlier, several important practical
problems such as zero test, sign detection, overflow,
underflow, and modulo-$n$ (cyclic) counting have not
been dealt with adequately. In this paper, design
principles for unary and binary systolic up\slash down
counters are presented. The unary counters, which are
attractive when dealing with relatively small counts,
are based on the systolic stack concept. The binary
counters use conventional binary number representation,
with several tags associated with each bit position.
The binary counter design presented can be generalized
to counters with higher-radix state encodings.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@InProceedings{Peng:1987:ISM,
author = "Victor Peng and Sridhar Samudrala and Moshe
Gavrielov",
title = "On the Implementation of Shifters, Multipliers, and
Dividers in {VLSI} Floating Point Units",
crossref = "Irwin:1987:PSC",
pages = "95--102",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158711",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Peng_Samudrala_Gavrielov.pdf",
abstract = "Several options for the implementation of
combinatorial shifters, multipliers, and dividers for a
VLSI floating point unit are presented and compared.
The comparisons are made in the context of a single
chip implementation in light of the constraints imposed
by currently available MOS technology.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Perlmutter:1987:A,
author = "D. Perlmutter and A. K.-W. Yuen",
title = "The 80387 and its Applications",
journal = j-IEEE-MICRO,
volume = "7",
number = "4",
pages = "42--57",
month = jul # "\slash " # aug,
year = "1987",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1987.304880",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Wed Sep 7 22:32:00 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Article{Pfeiffer:1987:ADP,
author = "F. W. Pfeiffer",
title = "Automatic differentiation in {PROSE}",
journal = j-SIGNUM,
volume = "22",
number = "1",
pages = "2--8",
month = jan,
year = "1987",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:14 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A programming language is presented in which has the
feature that first and second order partial derivatives
of a function can be calculated using differentiation
arithmetic. The language syntax allows the user to
specify which variables each function is required to be
differentiated with respect to. Model examples are
provided.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "differentiation arithmetic; languages; point
algorithm; program transformation; theory",
subject = "D.3.2 Software, PROGRAMMING LANGUAGES, Language
Classifications \\ F.4.3 Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Formal
Languages, Algebraic language theory",
}
@InProceedings{Piuri:1987:FTS,
author = "Vincenzo Piuri",
title = "Fault-Tolerant Systolic Arrays: An Approach Based upon
Residue Arithmetic",
crossref = "Irwin:1987:PSC",
pages = "230--238",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158712",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Piuri.pdf",
abstract = "Much attention has been recently given to VLSI and WSI
processing arrays: systolic arrays are often adopted to
execute a wide class of algorithms, e.g., for matrix
arithmetic or signal and image processing. In this
paper a fault-tolerant architecture is proposed to
allow reliable computation of systolic arrays by using
physical redundancy and residue number coding. Such
architecture supplies also information for fast
reconfiguration.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Prado:1987:FSR,
author = "J. Prado and R. Alcantara",
title = "A fast square-rooting algorithm using a digital signal
processor",
journal = j-PROC-IEEE,
volume = "75",
number = "2",
pages = "262--264",
month = feb,
year = "1987",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "The computation of square roots is required in signal
processing applications, such as adaptive filtering
using transversal filters or lattice filters, spectral
estimation, and many other fields of engineering
sciences. Actually, all the existing \ldots{}",
}
@Article{Purdy:1987:IDL,
author = "C. N. Purdy and G. B. Purdy",
title = "Integer Division in Linear Time with Bounded Fan-In",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "5",
pages = "640--644",
month = may,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.1676952",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:52 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676952",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Rall:1987:ISC,
author = "L. B. Rall",
title = "An introduction to the scientific computing language
{Pascal-SC}",
journal = j-COMPUT-MATH-APPL,
volume = "14",
number = "1",
pages = "53--69",
year = "1987",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(87)90181-7",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Oct 13 22:36:01 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Microcomputers are now widely used for small-scale
scientific, engineering, and statistical computing.
Pascal-SC (Pascal for Scientific Computing) is a
language developed specifically for this purpose. Its
most important features are: (i) accurate
floating-point arithmetic for real, complex, and
interval numbers, vectors, and matrices, with
controlled rounding if desired; (ii) the convenience of
operator notation for numerical data types and the
ability to accept user-defined operators for
nonstandard data types to make programs easier to
write, read, and document; and (iii) compatibility with
ordinary Pascal, so that Pascal programming techniques
and programs already written in Pascal can be used
immediately. In PascalSC, solutions of linear systems
of equations, inverses of matrices, and eigenvalues and
eigenvectors are computed with guaranteed error bounds,
and scalar products of vectors and sums of arbitrary
length of floating-point numbers are computed to the
closest floating-point number, or rounded upward or
downward as desired. These basic features of Pascal-SC
will be described, together with some applications.",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Rauch:1987:MCH,
author = "K. Rauch",
title = "Math chips: How they work: Augmenting microprocessors,
they speed up math operations while giving systems
designers a variety of performance, cost, and
integration options",
journal = j-IEEE-SPECTRUM,
volume = "24",
number = "7",
pages = "25--30",
month = jul,
year = "1987",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1987.6448961",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Mon Jan 20 06:41:24 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "computer architecture; Coprocessors; desktop
computers; digital arithmetic; math chips; mathematics
coprocessors; microprocessor chips; numeric processors;
operation speed; Process control; Program processors;
satellite computers; standard building blocks;
Standards; Workstations; workstations",
}
@MastersThesis{Reddy:1987:STF,
author = "Chakradher Ayyalaper Reddy",
title = "A self-testing and testable floating point divider",
type = "Thesis ({M.S.})",
school = "Mississippi State University. Department of Electrical
Engineering",
address = "Mississippi State, MS 39762, USA",
pages = "viii + 103",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "floating-point testing; Integrated circuits;
Mississippi State University; Testing.; Very large
scale integration",
}
@InProceedings{Redinbo:1987:PCT,
author = "G. Robert Redinbo",
title = "Protecting Convolution-Type Arithmetic Array
Calculations with Generalized Cyclic Codes",
crossref = "Irwin:1987:PSC",
pages = "219--225",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158713",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Redinbo.pdf",
abstract = "Fault-tolerance in dense high-speed arithmetic units
that calculate convolutions between arrays of data is
introduced through cyclic codes which are defined over
the rings and fields commonly employed by such units.
New systematic encoding and data manipulation
techniques make the application of these generalized
cyclic codes to error detection straightforward and
efficient. The necessary overhead parity computations
have complexity proportional to the number of parity
symbols squared, whereas the error-detecting capability
for both random and burst errors is directly related to
this parity number'.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Rehmer:1987:DIM,
author = "Karl Rehmer",
title = "Development and Implementation of the {Magnavox}
Generic {Ada} Basic Mathematics Package",
journal = j-SIGADA-LETTERS,
volume = "7",
number = "3",
pages = "73--83",
month = may # "\slash " # jun,
year = "1987",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Sat Aug 9 09:05:25 MDT 2003",
bibsource = "ftp://ftp.uu.net/library/bibliography;
http://portal.acm.org/;
http://www.adahome.com/Resources/Bibliography/articles.ref;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "design; floating point, real arithmetic; languages;
theory; verification",
subject = "D.2.2 Software, SOFTWARE ENGINEERING, Tools and
Techniques, Software libraries \\ D.3.2 Software,
PROGRAMMING LANGUAGES, Language Classifications, Ada
\\
G.4 Mathematics of Computing, MATHEMATICAL SOFTWARE",
}
@InProceedings{Robertson:1987:EDC,
author = "James E. Robertson",
title = "Error-Detection and Correction for Addition and
Subtraction through Use of Higher Radix Extensions of
{Hamming} Codes",
crossref = "Irwin:1987:PSC",
pages = "226--229",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158714",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Robertson.pdf",
abstract = "The properties of Hamming codes for error detection
and correction can be extended from the binary parity
check to addition, modulo $ 2 r $. Malfunctions in
hardware during addition, modulo $ 2 r $, can be
detected and corrected. Since carry-save and
signed-digit addition, radix $r$, are included in
addition, modulo $ 2 r $, this extension of Hamming
codes makes possible new techniques for detection and
correction of hardware malfunctions during signed-digit
and carry-save addition.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Rolfe:1987:FIS,
author = "Timothy J. Rolfe",
title = "On a Fast Integer Square Root Algorithm",
journal = j-SIGNUM,
volume = "22",
number = "4",
pages = "6--11",
month = oct,
year = "1987",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "algorithms; performance; theory",
subject = "F.2.1 Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Number-theoretic computations",
}
@Article{Rysavy:1987:MSC,
author = "M. Rysav{\'y}",
title = "{MISHA} --- a system for calculations with arbitrary
arithmetic precision",
journal = j-COMP-PHYS-COMM,
volume = "47",
number = "2--3",
pages = "351--359",
month = nov # "\slash " # dec,
year = "1987",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(87)90120-2",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:28:21 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465587901202",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Scheidt:1987:DFP,
author = "J. K. Scheidt and C. W. Schelin",
title = "Distributions of floating point numbers",
journal = j-COMPUTING,
volume = "38",
number = "4",
pages = "315--324",
year = "1987",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G10",
MRnumber = "88g:65046",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
reviewer = "J. A. Grant",
}
@InProceedings{Scherson:1987:VCO,
author = "Isaac D. Scherson and Yiming Ma",
title = "Vector Computations on Orthogonal Memory Access
Multiprocessor System",
crossref = "Irwin:1987:PSC",
pages = "28--36",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158715",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Scherson_Ma.pdf",
abstract = "An Orthogonal Memory Access system allows a
multiplicity of processors to concurrently access
distinct rows or columns of a rectangular array of data
elements. The resulting tightly-coupled
multi-processing system is feasible with current
technology and has even been suggested for VLSI as a
``reduced mesh''. In this paper we introduce the
architecture and concentrate on its application to a
number of basic vector and. numerical computations.
Matrix multiplication, L-U decomposition. polynomial
evaluation and solutions to linear systems and partial
differential equations, all show a speed-up of $ O(n) $
for a $n$-processor system. The flexibility in the
choice of the number of PEs makes the architecture a
strong competitor in the world of special-purpose
parallel systems. Actually, we prove that the machine
exhibits the same performance as any other system with
the same number of processors within a factor of 3.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8; numerical analysis; parallel algorithms;
parallel architecture; performance analysis; time
complexity",
}
@InProceedings{Schumacher:1987:CAI,
author = "G{\"u}nter Schumacher",
title = "Computer Arithmetic and Ill-Conditioned Algebraic
Problems",
crossref = "Irwin:1987:PSC",
pages = "270--276",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158716",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Schumacher.pdf",
abstract = "n/a",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
remark = "Text illegible because of large white streak on each
page.",
}
@InProceedings{Sharma:1987:ATE,
author = "Ramautar Sharma",
title = "Area-Time Efficient Arithmetic Elements for {VLSI}
Systems",
crossref = "Irwin:1987:PSC",
pages = "58--62",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158717",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Sharma.pdf",
abstract = "Algorithms for the high speed binary arithmetic
operations of addition and multiplication in a VLSI
environment are analyzed for area-time efficiency. It
is shown that some schemes for addition and
multiplication, although good for stand-alone designs,
fail to provide both area and time efficiencies
simultaneously. Solutions that yield area-time
efficient practical implementations of these arithmetic
functions are described.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@InProceedings{Shenoy:1987:AST,
author = "A. Shenoy and R. Kumaresan",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '87}",
title = "An accurate scaling technique in improved residue
number system arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1414--1417",
month = "????",
year = "1987",
DOI = "https://doi.org/10.1109/TC.1987.1676868",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
keywords = "residue arithmetic; residue number system",
summary = "A fast and accurate magnitude scaling technique in the
residue number system (RNS) is proposed. This technique
obtains the residues of the scaled integer, when scaled
by a product of a subset of the moduli, in
approximately log n cycles, where n is \ldots{}",
}
@Article{Shyu:1987:CIM,
author = "H. C. Shyu and T. K. Truong and I. S. Reed",
title = "A Complex Integer Multiplier Using the
Quadratic-Polynomial Residue Number System with Numbers
of Form $ 22 n + 1 $",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "10",
pages = "1255--1258",
month = oct,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.1676868",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676868;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35260",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "A quadratic-polynomial Fermat residue number system
(QFNS) can be used to compute the complex
multiplications needed to perform a DFT. The advantage
of such a QFNS is that complex multiplication can be
accomplished with only two integer \ldots{}",
}
@InCollection{Simar:1987:FPA,
author = "R. {Simar, Jr.}",
title = "Floating-point arithmetic with the {TMS32010}",
crossref = "Lin:1987:DSP",
pages = "213--244",
year = "1987",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bibno = "42622",
catcode = "J.2; C.5.3; G.1.0",
CRclass = "J.2 Mathematics and statistics; C.5.3 Microcomputers;
C.5.3 TMS 32010; G.1.0 General; G.1.0 Computer
arithmetic",
descriptor = "Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Mathematics and statistics; Computer
Systems Organization, COMPUTER SYSTEM IMPLEMENTATION,
Microcomputers, TMS 32010; Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic",
genterm = "MEASUREMENT; ALGORITHMS",
guideno = "1988-01736",
pubcite = "Englewood Cliffs, NJ",
pubname = "Prentice-Hall, Inc.",
subject = "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
ENGINEERING; C. Computer Systems Organization; C.5
COMPUTER SYSTEM IMPLEMENTATION; G. Mathematics of
Computing; G.1 NUMERICAL ANALYSIS",
}
@InProceedings{Smith:1987:SAE,
author = "S. G. Smith and P. B. Denyer",
title = "Synthesis of Area-Efficient {VLSI} Architectures for
Vector and Matrix Multiplication",
crossref = "Irwin:1987:PSC",
pages = "13--20",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158718",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Smith_Denyer.pdf",
abstract = "A methodology is presented for synthesis of
area-efficient, high-performance VLSI modules for
vector and matrix multiplication. Three fundamental
computational elements are employed in the composition
of these architectures: memory register, multiplexer
(1-from-2 data selector), and carry-save add-shift
computer. Two's complement serial\slash parallel
carry-save accumulation provides performance, while the
use of symmetric-coded distributed arithmetic
eliminates redundant computation to effect
area-savings.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@InCollection{Spangler:1987:RMM,
author = "R. A. Spangler",
title = "Revealing the mystery---the machine and how it
functions",
crossref = "Anbar:1987:CM",
pages = "9--46",
year = "1987",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "State University of New York at Buffalo, Buffalo",
bibno = "22925",
catcode = "C.0; B.0",
content = "In this paper, the author tries to describe the way a
digital computer works: from gates, through
instructions, data encoding, and interrupts, to
peripherals of more than a dozen types. He tries to do
this in 29 pages plus a nine-page appendix on
semiconductor technology. He tries to do it for an
audience described in the book's foreword as \par
(1) physicians who were educated in the pre-computer
era, (2) medical students and house staff being
educated now, (3) computer professionals interested in
medical applications, and (4) readers outside of the
medical profession and the computer science community
who are interested in the role of automation in health
care.\par
This is a tall order. The paper comes impressively
close to filling it. In clearly-written prose, Spangler
takes the reader through the overall structure of a
computer; its major components; information, binary
numbers (including floating point), and character
codes; word length issues; gates, combinatorial
circuits and flip-flops; instruction sets, including
subroutines and interrupts; and peripheral devices,
with emphasis on mass storage.\par
A necessary byproduct of covering all this material in
such a short space is a condensed, economical writing
style. Statements are made and concept",
CRnumber = "8802-0079",
descriptor = "Computer Systems Organization, GENERAL; Hardware,
GENERAL",
genterm = "DESIGN",
pubcite = "Rockville, MD",
pubname = "Computer Science Press, Inc.",
reviewer = "E. Mallach",
subject = "C. Computer Systems Organization; C.0 GENERAL; B.
Hardware; B.0 GENERAL",
waffil = "State University of New York at Buffalo, Buffalo",
}
@Manual{Sun:1987:SAM,
key = "Sun Microsystems",
title = "The {SPARC} Architecture Manual",
organization = pub-SUN,
address = pub-SUN:adr,
edition = "Part No: 800-1399-07",
month = aug # " 8",
year = "1987",
bibdate = "Wed Sep 14 23:02:18 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Takagi:1987:LED,
author = "Naofumi Takagi and Shuzo Yajima",
title = "On-Line Error-Detectable High-Speed Multiplier Using
Redundant Binary Representation and Three-Rail Logic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "11",
pages = "1310--1317",
month = nov,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.5009470",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009470",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Taylor:1987:RAI,
author = "Fred J. Taylor",
title = "A residue arithmetic implementation of the {FFT}",
journal = j-J-PAR-DIST-COMP,
volume = "4",
number = "2",
pages = "191--208",
month = apr,
year = "1987",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Univ of Florida, Gainesville, FL, USA",
classification = "723; 921; C4190 (Other numerical methods); C4240
(Programming and algorithm theory); C5230 (Digital
arithmetic methods); C5260 (Digital signal processing);
C5470 (Performance evaluation and testing)",
corpsource = "Department of Electr. Eng., Coll. of Eng., Florida
University, Gainesville, FL, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "complex arithmetic; complexity; computational
complexity; computer metatheory; computerised signal
processing; digital arithmetic; discrete Fourier
transform (DFT); evaluation; Fast Fourier Transforms;
fast Fourier transforms; FFT; FFT system; management
system; mathematical techniques; mathematical
transformations; performance; residue arithmetic;
residue arithmetic number system; sign; sign
management; single-modulus complex residue number
system; speed",
treatment = "T Theoretical or Mathematical; X Experimental",
}
@Article{Thompson:1987:FME,
author = "T. Thompson",
title = "Fast Math --- a first look at {Motorola}'s 68882 math
coprocessor",
journal = j-BYTE,
volume = "12",
number = "12",
pages = "120--121",
month = dec,
year = "1987",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Wed Sep 7 22:32:00 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "BYTE Magazine",
}
@Article{Thompson:1987:IEF,
author = "P. Thompson",
title = "Implementing an Elementary Function Library",
journal = j-SIGNUM,
volume = "22",
number = "2",
pages = "2--5",
month = apr,
year = "1987",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Sep 1 10:15:30 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@InProceedings{Tu:1987:RLD,
author = "Paul K. G. Tu and Milo{\v{s}} D. Ercegovac",
title = "A Radix-4 On-Line Division Algorithm",
crossref = "Irwin:1987:PSC",
pages = "181--187",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158719",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Tu_Ercegovac.pdf",
abstract = "We present an on-line algorithm for radix-4 floating
point division. The divisor is first transformed in to
a range such that the quotient digits are computed as a
function of the scaled partial remainder only.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Turner:1987:DDI,
author = "Peter R. Turner",
title = "The Distribution of l.s.d. and Its Implications for
Computer Design",
journal = j-MATH-GAZ,
volume = "71",
number = "455",
pages = "26--31",
month = mar,
year = "1987",
CODEN = "MAGAAS",
DOI = "https://doi.org/10.2307/3616283",
ISSN = "0025-5572 (print), 2056-6328 (electronic)",
bibdate = "Tue Oct 30 23:36:58 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Gazette",
journal-URL = "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
keywords = "Benford's Law; Law of Anomalous Numbers; logarithmic
distribution; overflow; underflow; Zipf's Law",
}
@InProceedings{Umeo:1987:DTO,
author = "Hiroshi Umeo",
title = "A Design of Time-Optimum and Register-Number-Minimum
Systolic Convolver",
crossref = "Irwin:1987:PSC",
pages = "5--12",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158720",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Umeo.pdf",
abstract = "We present an optimum bit-parallel\slash
word-sequential systolic convolver. Our design is the
best one among the previous many convolvers in the
sense that its optimality in time and space
performances is simultaneously attained without
augmenting any global control, broadcasting,
preloading, and\slash or multi sequential or parallel
I/O ports, which were allowed in most of the previous
designs. As an application of our convolver we give a
systolic polynomial divider which can compute the
polynomial division in exactly $ n + O(1) $ steps on $
[\min (n - m, m) / 2] + O(1) $ systolic cells, for the
division of any degree n polynomial by any degree $m$
polynomial ($ n \geq m $).",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Ushio:1987:CRE,
author = "T. Ushio and C. Hsu",
title = "Chaotic rounding error in digital control systems",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "34",
number = "2",
pages = "133--139",
month = feb,
year = "1987",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "Chaotic behavior due to the round-off effect in
digital control systems is called the chaotic rounding
error. First, we model digital control systems with
finite-wordlength digital compensators by mixed
mappings. A mixed mapping system is described
\ldots{}",
}
@Article{Vachss:1987:CMF,
author = "R. Vachss",
title = "The {Cordic} Magnification Function",
journal = j-IEEE-MICRO,
volume = "7",
number = "5",
pages = "83--84",
month = sep # "\slash " # oct,
year = "1987",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1987.305021",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Article{Vitek:1987:EFA,
author = "V. Vitek",
title = "Enumeration in floating-point arithmetic",
journal = "ASR - Bulletin INORGA",
volume = "21",
number = "6",
pages = "301--305",
month = "????",
year = "1987",
ISSN = "0231-8954",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The paper studies the computer representation of
numbers in floating-point arithmetic and algebraic
operations with these numbers with respect to the
validity of basic algebraic laws. Methods for the
handling of emergency situations are given: overflow
and underflow, illustrated using the example of the
computation of a member of the binomial expansion. (6
Refs.)",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
keywords = "Algebraic operations; Computer representation;
Floating-point arithmetic; Overflow; Underflow",
pubcountry = "Czechoslovakia",
thesaurus = "Carry logic; Digital arithmetic; Error handling",
}
@InProceedings{Wang:1987:EEF,
author = "Kai Hwang and H. C. Wang and Z. Xu",
title = "Evaluating Elementary Functions with {Chebyshev}
Polynomials on Pipeline Nets",
crossref = "Irwin:1987:PSC",
pages = "121--128",
year = "1987",
DOI = "https://doi.org/10.1109/ARITH.1987.6158702",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hwang_Wang_Xu.pdf",
abstract = "Fast evaluation of vector-valued elementary functions
plays a vital role in many real-time applications. In
this paper, we present a pipeline networking approach
to designing a Chebyshev polynomial evaluator for the
fast evaluation of elementary functions over a string
of arguments. In particular, pipeline nets are employed
to perform the preprocessing and postprocessing of
various elementary functions to boost the overall
system performance. Design tradeoffs are analyzed among
representational accuracy, processing speed and
hardware complexity.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Manual{WeitekCorporation:1987:WFP,
title = "{WTL} 1167 floating point coprocessor: preliminary
data",
organization = "{Weitek Corporation}",
address = "Sunnyvale, CA, USA",
pages = "54",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Intel 80386
(Microprocessor) --- Programming.",
remark = "August 1988.",
}
@MastersThesis{Williams:1987:FPL,
author = "Robert Leslie Williams",
title = "A floating point loop engine architecture using
pattern generation",
type = "Thesis ({M.S.})",
school = "University of New Mexico",
address = "Albuquerque, NM, USA",
pages = "ix + 92",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer architecture.; Computer engineering.",
}
@InProceedings{Williams:1987:STC,
author = "T. E. Williams and M. Horowitz and R. L. Alverson and
T. S. Yang",
title = "A self-timed chip for division",
crossref = "Losleben:1987:ARV",
pages = "75--96",
year = "1987",
bibdate = "Mon Sep 16 16:35:03 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Wu:1987:FDS,
author = "I-Chen Wu",
title = "A Fast {$1$-D} Serial-Parallel Systolic Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "10",
pages = "1243--1247",
month = oct,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.1676865",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676865",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Wu:1987:TRF,
author = "Chwan-Ghia Wu and Lih-Ren Tzeng and Tien-Shou Wu",
title = "Time-Redundant Fault-Masking in {ALUs}",
crossref = "Irwin:1987:PSC",
pages = "239--243",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Wu_Cheng_Wu.pdf",
abstract = "A new error correction scheme for bit-sliced ALUs is
presented. The method adopted for fault location is an
extension of a concurrent error detection scheme called
RESO (Recomputing with Shifted Operands). The term
bit-slice is used in the generic sense and the length
of the slice may be one or more bits. The proposed
scheme requires two consecutive computation steps for
normal operations and the possible locations of faults,
if any, can be located provided that the failures are
confined to a certain number of adjacent bit-slices.
The fault-free bit-slices of the ALU are thus figured
out. The final and effective computation is then
carried out through those identified fault-free
bit-slices. A circular structure is proposed to realize
this concept.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
remark = "This paper is missing from the IEEE Xplore database,
so its DOI and text are not available there.",
}
@Article{Zaccone:1987:ENP,
author = "Richard J. Zaccone and Jesse L. Barlow",
title = "Eliminating the Normalization Problem in Digit On-Line
Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "1",
pages = "36--46",
month = jan,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.5009447",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:49 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009447",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Zurawski:1987:DHS,
author = "J. H. P. Zurawski and J. B. Gosling",
title = "Design of a High-Speed Square Root Multiply and Divide
Unit",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "1",
pages = "13--23",
month = jan,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.5009445",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:49 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009445",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Aberth:1988:PNA,
author = "Oliver Aberth",
title = "Precise Numerical Analysis",
publisher = pub-WCB,
address = pub-WCB:adr,
pages = "x + 225",
year = "1988",
ISBN = "0-697-06760-2",
ISBN-13 = "978-0-697-06760-9",
LCCN = "QA297 .A28 1988",
bibdate = "Thu Nov 8 14:50:32 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Aberth addresses elementary issues of precise floating
point computations using variable precision range
arithmetic. Numbers are represented as a variable
precision number $ \pm $ a range. Rational arithmetic
is also considered. Chapters are devoted to
\begin{enumerate} \item rootfinding, \item polynomial
rootfinding, \item numerical linear algebra, \item
differentiation and integration, and \item ordinary
differential equations. \end{enumerate} Differentiation
is handled by a codelist approach like [Rall81a], and
applications to Taylor series are given. Interval
techniques for ordinary differential equations are
based on using an {\it a priori\/} bound to capture
remainder terms. Several methods are illustrated,
including Taylor series methods.",
acknowledgement = ack-nj,
comment = "Text for a one semester, junior level course in
numerical analysis. Includes PC disk with software
written in PBASIC. Sound introductory level discussion
of code lists and error capture techniques.",
keywords = "differentiation; differentiation arithmetic; general
numerical analysis; integration; interval techniques;
linear algebra; ordinary differential equations.;
variable precision arithmetic",
}
@Article{Alt:1988:FEP,
author = "Ren{\'e} Alt",
title = "Floating-point error propagation in iterative methods.
Stochastic methods in round-off error analysis",
journal = j-MATH-COMP-SIM,
volume = "30",
number = "6",
pages = "505--517",
year = "1988",
CODEN = "MCSIDR",
ISSN = "0378-4754 (print), 1872-7166 (electronic)",
ISSN-L = "0378-4754",
MRclass = "65G05 (65F10)",
MRnumber = "90f:65067",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics and Computers in Simulation",
journal-URL = "http://www.sciencedirect.com/science/journal/03784754",
reviewer = "D. Bini",
}
@Article{Alt:1988:FPE,
author = "R. Alt",
title = "Floating-point error propagation in iterative
methods",
journal = j-MATH-COMP-SIM,
volume = "30",
number = "6",
pages = "505--517",
month = dec,
year = "1988",
CODEN = "MCSIDR",
ISSN = "0378-4754 (print), 1872-7166 (electronic)",
ISSN-L = "0378-4754",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bibno = "56847",
catcode = "G.1.0",
CRclass = "G.1.0 General; G.1.0 Computer arithmetic",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic",
fjournal = "Mathematics and Computers in Simulation",
genterm = "THEORY; ALGORITHMS",
guideno = "1988-12109",
journal-URL = "http://www.sciencedirect.com/science/journal/03784754",
journalabbrev = "Math. Comput. Simul.",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{AMD:1988:IFP,
author = "{Advanced Micro Devices}",
title = "{IEEE} floating-point format",
journal = j-MICROPROC-MICROSYS,
volume = "12",
number = "1",
pages = "13--23",
month = jan # "\slash " # feb,
year = "1988",
CODEN = "MIMID5",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
bibno = "23",
categories = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
K. Computing Milieux; K.1 THE COMPUTER INDUSTRY; G.1.0
General; G.1.0 Computer arithmetic; K.1 Standards",
content = "DESIGN; STANDARDIZATION; THEORY",
CRnumber = "1988-12470",
fjournal = "Microprocessors and Microsystems",
guideno = "1",
subject = "mathematics of computing, numerical analysis, general,
computer arithmetic; computing milieux, the computer
industry, standards",
wsub = "Jesse L. Barlow",
}
@Article{An:1988:CRE,
author = "S. H. An and K. Yao",
title = "Convergent and roundoff error properties of reflection
coefficients in adaptive spatial recursive least
squares lattice algorithm",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "35",
number = "2",
pages = "241--246",
month = feb,
year = "1988",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "The spatial recursive least-squares lattice (RLSL)
algorithm is considered and the convergent properties
as well as the finite-precision roundoff effects of the
reflection coefficients are studied in detail. It is
shown that when the forgetting \ldots{}",
}
@Article{Anderson:1988:MRE,
author = "Ned Anderson",
title = "Minimum relative error approximations for $ 1 / t $",
journal = j-NUM-MATH,
volume = "54",
number = "2",
pages = "117--124",
month = nov,
year = "1988",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01396969",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65D15",
MRnumber = "90a:65037",
MRreviewer = "Mariano Gasca",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Corp. Res., Digital Equipment Corp., Hudson, MA, USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "approximation theory; functional equation; geometric
convergence rates; iterative methods; minimum relative
error approximations; polynomial approximations;
polynomials",
treatment = "T Theoretical or Mathematical",
}
@Book{Apple:1988:ANM,
author = "{Apple Computer, Inc.}",
title = "{Apple} Numerics Manual",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Second",
pages = "xxvi + 294",
year = "1988",
ISBN = "0-201-17738-2",
ISBN-13 = "978-0-201-17738-1",
LCCN = "QA76.8.A662 A767 1988",
bibdate = "Wed Sep 07 21:06:52 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$29.95",
series = "The Apple technical library",
acknowledgement = ack-nhfb,
keywords = "Apple II (computer) --- programming; computation by
computer systems --- floating point representation;
Macintosh (computer) --- programming; numerical
calculations --- data processing; SANE (Standard Apple
Numeric Environment)",
}
@Article{Bailey:1988:EHS,
author = "David H. Bailey",
title = "Extra high speed matrix multiplication on the
{Cray-2}",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "9",
number = "3",
pages = "603--607",
month = may,
year = "1988",
CODEN = "SIJCD4",
DOI = "https://doi.org/10.1137/0909040",
ISSN = "0196-5204",
ISSN-L = "0196-5204",
MRclass = "65F30 (65G05 65W05)",
MRnumber = "937 496",
bibdate = "Mon Mar 31 10:00:04 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib",
acknowledgement = ack-nhfb,
classification = "C7310 (Mathematics)",
corpsource = "Ames Res. Center, NASA, Moffett Field, CA, USA",
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
keywords = "Cray-2; floating-point operations; library routines;
mathematics computing; matrix algebra; matrix
multiplication; memory bank contention; numerical
stability",
onlinedate = "May 1988",
treatment = "P Practical",
}
@InProceedings{Bandyopadhyay:1988:SAF,
author = "S. Bandyopadhyay and G. A. Jullien and A. Sengupta",
booktitle = "Proceedings of the International Conference on
Systolic Arrays, 1988. 25--27 May 1988",
title = "A systolic array for fault tolerant digital signal
processing using a residue number system approach",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "577--586",
year = "1988",
CODEN = "????",
DOI = "https://doi.org/10.1109/ARRAYS.1988.18094",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Fault detection and correction using the Chinese
remainder theorem for decoding is investigated. It is
shown that this approach is well suited for
implementation by VLSI circuits for digital signal
processing using systolic architectures. A systolic
\ldots{}",
}
@Article{Banning:1988:PRF,
author = "Craig Banning",
title = "Perfectly Rounded Floats",
journal = j-CUJ,
volume = "6",
number = "2",
pages = "14--??",
month = feb,
year = "1988",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@Article{Barany:1988:FEI,
author = "T. E. Barany",
title = "Fast evaluation of integer roots in microcontroller
systems",
journal = j-MICROPROC-MICROSYS,
volume = "12",
number = "6",
pages = "341--344",
month = jul # "--" # aug,
year = "1988",
CODEN = "MIMID5",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Fri Dec 08 13:06:02 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Microprocessors and Microsystems",
}
@TechReport{Barlow:1988:EAU,
author = "Jesse Louis Barlow and Richard J. Zaccone",
title = "Error analysis in unnormalized floating point
arithmetic",
type = "Technical report",
number = "CS-88-33",
institution = "Pennsylvania State University, Department of Computer
Science",
address = "University Park, PA, USA",
pages = "12",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.",
remark = "Supported by the National Science Foundation.
Supported by the Office of Naval Research.",
}
@TechReport{Barlowe:1988:EAU,
author = "Jesse L. Barlowe",
title = "Error analysis in unnormalized floating point
arithmetic",
type = "Technical report",
number = "CS-88-10",
institution = "Pennsylvania State University, Department of Computer
Science",
address = "University Park, PA, USA",
pages = "14",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic.; Errors.",
remark = "Supported by the National Science Foundation.
Supported by the Office of Naval Research.",
}
@InProceedings{BenChorin:1988:NPC,
author = "S. Ben-Chorin",
title = "{NS32532-NS32580} processor cluster delivers high
floating-point performance",
crossref = "Midcon:1988:MCP",
pages = "243--248",
year = "1988",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The NS32580 Floating-Point Controller (FPC) teams with
Weitek's WTL3164 Floating-Point Data Path (FPDP) device
and the NS32532 CPU to achieve a floating-point
performance that complements the NS32532's 15 MIPS
peak-integer performance. Due to a pipelined
coprocessor interface and the floating-point controller
design, this processor cluster achieves a peak
floating-point performance of 15 MFLOPs for both
single-precision (32-bit) and double-precision (64-bit)
floating-point instructions, such as add, subtract and
multiply. This high-performance is accomplished without
sacrificing software compatibility with the previous
Series 32000 processor clusters, including precise
floating-point exceptions.",
acknowledgement = ack-nhfb,
affiliation = "Nat. Semicond. Corp., Santa Clara, CA, USA",
classification = "C5130 (Microprocessor chips); C5220 (Computer
architecture)",
keywords = "Floating-Point Controller; Floating-Point Data Path;
Floating-point performance; NS32532 CPU; NS32580;
Pipelined coprocessor interface; Processor cluster;
WTL3164",
thesaurus = "Computer architecture; Microprocessor chips",
}
@InProceedings{Bewick:1988:ANB,
author = "G. Bewick and P. Song and G. De Micheli and M. Flynn",
title = "Approaching a nanosecond: a 32-bit adder",
crossref = "IEEE:1988:PII",
pages = "221--226",
year = "1988",
DOI = "https://doi.org/10.1109/ICCD.1988.25695",
bibdate = "Mon Dec 24 09:52:15 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Birman:1988:DHS,
author = "M. Birman and G. Chu and L. Hu and J. McLeod and N.
Bedard and F. Ware and L. Torban and C. M. Lim",
title = "Design of a high-speed arithmetic datapath",
crossref = "IEEE:1988:PII",
pages = "214--216",
year = "1988",
bibdate = "Wed Sep 7 22:32:00 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@MastersThesis{Blaker:1988:FPB,
author = "David Mark Blaker",
title = "Floating point bit-sequential arithmetic units",
type = "Thesis ({M.S.})",
school = "Lehigh University",
address = "Bethlehem, PA, USA",
pages = "vi + 73",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic.; Floating-point arithmetic.",
}
@Article{Bohlender:1988:IFA,
author = "Gerd Bohlender",
title = "Is floating-point arithmetic still adequate?",
journal = "Systems analysis and simulation",
volume = "46",
publisher = "Akademie-Verlag",
address = "Berlin, Germany",
pages = "105--108",
year = "1988",
MRclass = "68N15 (65G99)",
MRnumber = "976 389",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
xxjournal = "Math. Res.",
xxx = "I (Berlin, 1988)",
}
@TechReport{Bose:1988:VDT,
author = "Bidyut Kumar Bose",
title = "{VLSI} design techniques for floating-point
computation",
type = "Report",
number = "UCB/CSD 88/469",
institution = "University of California, Berkeley, Computer Science
Division",
address = "Berkeley, CA, USA",
pages = "vi + 173",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Integrated circuits ---
Very large scale integration.",
}
@MastersThesis{Brooks:1988:VIF,
author = "Kelvin R. Brooks",
title = "The {VLSI} implementation of a floating-point
multiplier",
type = "Thesis ({M.S.})",
school = "North Carolina A\&T State University",
address = "Greensboro, NC, USA",
pages = "x + 78",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electric engineering.; Integrated circuits --- Very
large scale integration.",
}
@Article{Brosnan:1988:MED,
author = "T. J. Brosnan and N. R. {Strader II}",
title = "Modular error detection for bit-serial
multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "37",
number = "9",
pages = "1043--1052",
month = sep,
year = "1988",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.2255",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 08:33:28 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2255",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Byington:1988:HGB,
author = "Carl Byington",
title = "How to get better floating-point results",
journal = j-BYTE,
volume = "13",
number = "3",
pages = "229--236",
month = mar,
year = "1988",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bibno = "44973",
catcode = "C.5.3; G.1.0; D.1.m",
CRclass = "C.5.3 Microcomputers; G.1.0 General; G.1.0 Computer
arithmetic; D.1.m Miscellaneous",
descriptor = "Computer Systems Organization, COMPUTER SYSTEM
IMPLEMENTATION, Microcomputers; Mathematics of
Computing, NUMERICAL ANALYSIS, General, Computer
arithmetic; Software, PROGRAMMING TECHNIQUES,
Miscellaneous",
fjournal = "BYTE Magazine",
genterm = "DESIGN; RELIABILITY",
guideno = "1988-05276",
subject = "C. Computer Systems Organization; C.5 COMPUTER SYSTEM
IMPLEMENTATION; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS; D. Software; D.1 PROGRAMMING
TECHNIQUES",
}
@Article{Callahan:1988:EII,
author = "D. Callahan and J. Cocke and K. Kennedy",
title = "Estimating interlock and improving balance for
pipelined architectures",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "4",
pages = "334--358",
month = aug,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 17:13:17 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5220 (Computer architecture); C5230 (Digital
arithmetic methods)",
corpsource = "Department of Computer Science, Rice University,
Houston, TX, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "arithmetic; bandwidth; digital arithmetic; DO loops;
execution order constraints; fine-grain parallelism;
floating-point; memory; parallel architectures;
pipeline; pipeline balance; pipeline interlock;
pipelined architectures; processing",
treatment = "P Practical",
}
@Article{Capocelli:1988:EVN,
author = "R. M. Capocelli and R. Giancarlo",
title = "Efficient {VLSI} networks for converting an integer
from binary system to residue number system and vice
versa",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "35",
number = "11",
pages = "1425--1430",
month = nov,
year = "1988",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1109/31.14466",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=565",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "VLSI networks for converting integers from binary to
residue number systems are presented Both direct and
reverse conversion are treated. The networks are
improvements, with respect to area or time or both, of
previously proposed \ldots{}",
}
@TechReport{Cappello:1988:SSSa,
author = "Peter R. Cappello and Willard L. Miranker",
title = "Systolic super summation with reduced hardware",
type = "Technical report",
number = "TRCS88-27",
institution = "University of California, Santa Barbara, College of
Engineering Department of Computer Science",
address = "Santa Barbara, CA, USA",
pages = "8",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; computer science
--- mathematics; floating-point arithmetic",
remark = "``A principle limitation in accuracy for scientific
computation performed with floating-point arithmetic
may be traced to the computation of repeated sums, such
as those which arise in inner products. A design is
proposed for a systolic super summer, a cellular piece
of hardware for the summation of floating-point
numbers. The apparatus receives floating-point
summands, converting them into a fixed-point form by a
sieve-like cellular array. The emerging fixed-point
numbers then are summed in a pipelined array of long
accumulators. The architectural regularity of the sieve
makes it ideal for implementation in VLSI circuit
technology.'' Supported by the Office of Naval
Research.",
}
@Misc{Cappello:1988:SSSb,
author = "Peter R. Cappello and Willard L. Miranker",
title = "Systolic super summation device",
howpublished = "US Patent 4751665",
day = "14",
month = jun,
year = "1988",
bibdate = "Mon Dec 29 16:20:01 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/4751665/fulltext.html",
abstract = "A cellular architecture for a systolic super summer
for high throughput performance of repeated sums of
floating-point numbers. The summer receives pipelined
inputs of streams of summands, converts the
floating-point summands into a fixed-point form by a
sieve-like pipelined cellular network , and sums the
emerging fixed-point numbers in a corresponding network
of extremely long accumulators. The throughput per unit
area of the hardware approaches that of a tree network,
but without the long wires and signal propagation that
are intrinsic to tree networks.",
acknowledgement = ack-nhfb,
}
@Article{Capps:1988:OAL,
author = "C. David Capps and R. Aaron Falk and Theodore L.
Houk",
title = "Optical Arithmetic\slash Logic Unit Based on Residue
Arithmetic and Symbolic Substitution",
journal = j-APPL-OPTICS,
volume = "27",
number = "9",
pages = "1682--1686",
month = may,
year = "1988",
CODEN = "APOPAI",
ISSN = "0003-6935",
bibdate = "Fri Jun 24 18:13:20 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "There has been difficulty in achieving a fully
parallel, digital optical adder or multiplier. The
primary obstacle is the carry operation inherent in any
fixed-radix number system. The concepts of residue
number representation and symbolic substitution can be
combined to produce a parallel optical arithmetic/logic
unit.",
acknowledgement = ack-nhfb,
fjournal = "Applied Optics",
journal-URL = "http://www.osapublishing.org/ao/browse.cfm",
}
@Article{Cardarilli:1988:SPD,
author = "G. C. Cardarilli and R. Lojacono and G. Martinelli and
M. Salerno",
title = "Structurally passive digital filters in residue number
systems",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "35",
number = "2",
pages = "149--158",
month = feb,
year = "1988",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1109/31.1716",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=107",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "The possibility of realizing structural passive
digital filters in terms of residue number systems
(RNS) is considered. For this purpose, an algorithm is
proposed for realizing the RNS rotator, which
represents the basic element of these filters.
\ldots{}",
}
@Article{Cavallaro:1988:CAS,
author = "Joseph R. Cavallaro and Franklin T. Luk",
title = "{CORDIC} arithmetic for an {SVD} processor",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "3",
pages = "271--290",
month = jun,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Cornell Univ, Ithaca, NY, USA",
classification = "721; 722; 723; 921; C5230 (Digital arithmetic
methods); C5440 (Multiprocessor systems and
techniques)",
corpsource = "Sch. of Electr. Eng., Cornell University, NY, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "Algorithms; computer architecture; computer
programming; computers, digital --- Computational
Methods; CORDIC arithmetic; Decomposition; digital
arithmetic; hardware division; inverse tangents;
mathematical techniques --- Algorithms; parallel
processing; real-time; rotations; signal processing
applications; Singular Value; singular value
decomposition; special-purpose arithmetic techniques;
square root; SVD processor; vector; vector rotations;
VLSI implementation",
treatment = "P Practical",
}
@Article{Chaitin:1988:RA,
author = "Gregory J. Chaitin",
title = "Randomness in Arithmetic",
journal = j-SCI-AMER,
volume = "259",
number = "1",
pages = "80--85 (Intl. ed. 52--57)",
month = jul,
year = "1988",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican0788-80",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Wed May 22 15:04:14 MDT 2013",
bibsource = "Distributed/QLD/1988.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciam1980.bib",
URL = "http://www.nature.com/scientificamerican/journal/v259/n1/pdf/scientificamerican0788-80.pdf",
acknowledgement = ack-nhfb,
country = "USA",
date = "01/07/93",
descriptors = "Randomness; Arithmetic",
enum = "9449",
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
keywords = "algorithmic information theory; computability theory;
halting problem; incompleteness theorem; number theory;
Pascal's triangle; randomness",
remark = "(VBI-001989)",
xxnewdata = "1998.01.30",
}
@Article{Chen:1988:GCM,
author = "M. C. Chen",
title = "The generation of a class of multipliers: synthesizing
highly parallel algorithms in {VLSI}",
journal = j-IEEE-TRANS-COMPUT,
volume = "37",
number = "3",
pages = "329--338",
month = mar,
year = "1988",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.2170",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 08:33:25 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2170",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Cheng:1988:ATM,
author = "Kuo-kuang Cheng and Robert R. Seban",
title = "Algorithm theory and the microarchitecture of an
optimal {VLSI} floating point divider",
institution = "Department of Computer Science, College of Engineering
and Applied Sciences, Arizona State University",
address = "Tempe, AZ, USA",
pages = "17",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "CR-R; 89028 TR; 88-032 Report (Arizona State
University. College of Engineering and Applied
Sciences); 89:28. Technical report (Arizona State
University. Department of Computer Science); 88-032.",
acknowledgement = ack-nhfb,
remark = "``December 22, 1988.''",
}
@Article{Cody:1988:AMS,
author = "W. J. Cody",
title = "{Algorithm 665}: {MACHAR}: a Subroutine to Dynamically
Determine Machine Parameters",
journal = j-TOMS,
volume = "14",
number = "4",
pages = "303--311",
month = dec,
year = "1988",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/50063.51907",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sun Sep 04 22:33:58 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p303-cody/",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms",
subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
SOFTWARE, Portability. {\bf G.1.0}: Mathematics of
Computing, NUMERICAL ANALYSIS, General, Computer
arithmetic.",
}
@InCollection{Cody:1988:FPS,
author = "W. J. Cody",
title = "Floating-point standards --- theory and practice",
crossref = "Moore:1988:RCR",
pages = "99--107",
year = "1988",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Argonne National Laboratory, Argonne, IL",
bibno = "60186",
catcode = "B.7.1; K.1",
CRclass = "B.7.1 Types and Design Styles; K.1 Standards",
descriptor = "Hardware, INTEGRATED CIRCUITS, Types and Design
Styles; Computing Milieux, THE COMPUTER INDUSTRY,
Standards",
genterm = "THEORY; RELIABILITY; STANDARDIZATION; RELIABILITY",
guideno = "1988-01977",
subject = "B. Hardware; B.7 INTEGRATED CIRCUITS; K. Computing
Milieux; K.1 THE COMPUTER INDUSTRY",
waffil = "Ohio State University, Columbus",
}
@Article{Cosentino:1988:FTS,
author = "R. J. Cosentino",
title = "Fault tolerance in a systolic residue arithmetic
processor array",
journal = j-IEEE-TRANS-COMPUT,
volume = "37",
number = "7",
pages = "886--890",
month = jul,
year = "1988",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.2239",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 08:33:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2239",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Davila:1988:FPA,
author = "J. M. Davila and A. J. Phillips and D. Tabak",
title = "Floating Point Arithmetic on a {RISC}",
journal = j-MICROPROC-MICROPROG,
volume = "23",
number = "1--5",
pages = "179--184",
month = mar,
year = "1988",
CODEN = "MMICDT",
ISSN = "0165-6074 (print), 1878-7061 (electronic)",
ISSN-L = "0165-6074",
bibdate = "Thu Sep 1 10:15:06 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Microprocessing and Microprogramming",
}
@MastersThesis{Duerksen:1988:CAP,
author = "Joel L. Duerksen",
title = "A comparative analysis of the performance of floating
point and integer based line drawing algorithms for
raster displays",
type = "Thesis ({M.S.})",
school = "Department of Computer Science, Ball State
University",
address = "Muncie, IN 47306, USA",
pages = "ix + 206",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Algorithms.; Computer graphics.",
}
@Article{Dunham:1988:PMA,
author = "C. B. Dunham",
title = "Provably Monotone Approximations {III}",
journal = j-SIGNUM,
volume = "23",
number = "1",
pages = "10--10",
month = jan,
year = "1988",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Sep 13 09:05:50 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "theory",
subject = "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation",
}
@Article{Duprat:1988:HPE,
author = "Jean Duprat and Jean-Michel Muller",
title = "Hardwired polynomial evaluation",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "3",
pages = "291--309",
month = jun,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "CNRS, Grenoble, Fr",
classification = "721; 722; 723; 921; C4130 (Interpolation and
function approximation); C5230 (Digital arithmetic
methods)",
corpsource = "Inst. Nat. Polytech. de Grenoble, France",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "computer architecture; computers, digital ---
Circuits; digital arithmetic; elementary functions;
hardwired polynomial evaluation; mathematical
functions; mathematical techniques; Polynomials;
polynomials; special-purpose circuits; VLSI
implementation",
treatment = "P Practical",
}
@InProceedings{Ercegovac:1988:LAD,
author = "M. D. Ercegovac and T. Lang",
title = "On-Line Arithmetic: a Design Methodology and
Applications in Digital Signal Processing",
crossref = "Brodersen:1988:VSP",
volume = "3",
pages = "252--263",
year = "1988",
bibdate = "Fri Dec 08 10:42:22 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[66--77]{Swartzlander:1990:CAb}.",
acknowledgement = ack-nhfb,
}
@Article{Ercegovac:1988:LSC,
author = "Milo{\v{s}} D. Ercegovac and Tomas Lang",
title = "On-line scheme for computing rotation factors",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "3",
pages = "209--227",
month = jun,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Univ of California, Los Angeles, CA, USA",
classification = "721; 722; 723; 921; C5230 (Digital arithmetic
methods)",
corpsource = "Department of Computer Science, California University,
Los Angeles, CA, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "algorithm; Algorithms; clock period; computer
programming; computers, digital --- Computational
Methods; computing rotation factors; digital
arithmetic; floating-point; low-precision estimates;
mathematical techniques --- Algorithms; matrix
transformations; on-line algorithm; online scheme;
radix-2 online; representation; rotation factors
computing; systolic arrays",
treatment = "P Practical; T Theoretical or Mathematical",
}
@Article{Fam:1988:ECM,
author = "A. T. Fam",
title = "Efficient complex matrix multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "37",
number = "7",
pages = "877--879",
month = jul,
year = "1988",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.2236",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 08:33:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2236",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Farnum:1988:CSF,
author = "Charles Farnum",
title = "Compiler Support for Floating-Point Computation",
journal = j-SPE,
volume = "18",
number = "7",
pages = "701--709",
month = jul,
year = "1988",
CODEN = "SPEXBL",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Sat May 24 19:46:39 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}
@Article{Fiske:1988:RAP,
author = "S. Fiske and W. J. Dally",
title = "The reconfigurable arithmetic processor",
journal = j-COMP-ARCH-NEWS,
volume = "16",
number = "2",
pages = "30--36",
month = may,
year = "1988",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 12 09:40:45 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{Fitzpatrick:1988:PVF,
author = "S. Fitzpatrick",
title = "Processeur {\`a} virgule flottante {\`a} 33 {Mflops}
\toenglish {33 Mflops Floating-Point Processor}
\endtoenglish",
journal = "Electronique Industrielle",
volume = "148",
pages = "30--32",
day = "15",
month = sep,
year = "1988",
bibdate = "Sat Oct 24 15:01:51 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Fuccio:1988:DAS,
author = "M. L. Fuccio and R. N. Gadenz and C. J. Garen and J.
M. Huser and B. Ng and S. P. Pekarich and K. D. Ulery",
title = "The {DSP32C}: {AT\&T}'s Second-Generation
Floating-Point Digital Signal Processor",
journal = j-IEEE-MICRO,
volume = "8",
number = "6",
pages = "30--48",
month = nov # "\slash " # dec,
year = "1988",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.16779",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
summary = "The WEDSP32C high-performance, programmable digital
signal processor supports 32-bit floating-point
arithmetic and is upwardly compatible with its
predecessor, the WEDSP32. Because it is implemented in
0.75-$\mu$m (effective channel length) CMOS technology
\ldots{}",
}
@Article{Gibson:1988:GBA,
author = "J. K. Gibson",
title = "A generalisation of {Brickell}'s algorithm for fast
modular multiplication",
journal = j-BIT,
volume = "28",
number = "4",
pages = "755--763",
month = dec,
year = "1988",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01954895",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "68Q25 (68P25 68U99)",
MRnumber = "89m:68058",
MRreviewer = "Ricardo Baeza-Yates",
bibdate = "Wed Jan 4 18:52:20 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=28&issue=4;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=28&issue=4&spage=755",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Grehan:1988:BBL,
author = "R. Grehan and T. Thompson",
title = "{Borland} beefs up its languages",
journal = j-BYTE,
volume = "13",
number = "10",
pages = "151--154",
month = oct,
year = "1988",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 12 17:54:09 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C6140D (High level languages); C6150C (Compilers,
interpreters and other processors); C6150G (Diagnostic,
testing, debugging and evaluating systems)",
fjournal = "BYTE Magazine",
keywords = "Borland International; Built-in source-level
debuggers; Command-line interface version; Expanded
memory; Floating-point emulation; High-speed assembler;
In-line assembly language support; Integrated
development environment; Line-oriented environment;
Premier development languages; Stand-alone debugger;
TASM; Turbo Assembler; Turbo C; Turbo Debugger; Turbo
language; Turbo Pascal",
thesaurus = "C language; Pascal; Program assemblers; Program
compilers; Program debugging; Software packages",
}
@Article{Grehan:1988:FPCa,
author = "Rick Grehan",
title = "Floating-Point Without a Coprocessor",
journal = j-BYTE,
volume = "13",
number = "9",
pages = "313--319",
month = sep,
year = "1988",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
bibno = "47602",
catcode = "C.3; G.0",
descriptor = "Computer Systems Organization, SPECIAL-PURPOSE AND
APPLICATION-BASED SYSTEMS; Mathematics of Computing,
GENERAL",
fjournal = "BYTE Magazine",
genterm = "DESIGN; THEORY; MANAGEMENT",
guideno = "1988-05346",
subject = "C. Computer Systems Organization; C.3 SPECIAL-PURPOSE
AND APPLICATION-BASED SYSTEMS; G. Mathematics of
Computing; G.0 GENERAL",
}
@Article{Grehan:1988:FPCb,
author = "R. Grehan",
title = "Floating-Point Without a Coprocessor, Part 2",
journal = j-BYTE,
volume = "13",
number = "10",
pages = "293--297 (or 293--298??)",
month = oct,
year = "1988",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 12 17:54:09 MDT 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
classification = "C1160 (Combinatorial mathematics); C6110 (Systems
analysis and programming); C7310 (Mathematics)",
fjournal = "BYTE Magazine",
keywords = "Addition; Binary floating-point mathematics package;
Division; Floating-point accumulators; Floating-point
number manipulation; Maths chip emulation;
Multiplication; Number input/output; Primary math
operations; Pseudocode routines; Subtraction",
thesaurus = "Input-output programs; Mathematics computing; Number
theory; Programming; Software packages",
}
@MastersThesis{Helminen:1988:AFP,
author = "Brenda K. Helminen",
title = "An analysis of the floating point and communication
performance of the {FPS} {T-Series} hypercube",
type = "Thesis ({M.S.})",
school = "Michigan Technological University",
address = "Houghton, MI, USA",
pages = "viii + 69",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Michigan Technological University. --- Theses
({M.S.}).; MTU Computer Science. --- Thesis ({M.S.}).",
}
@MastersThesis{Ho:1988:ADI,
author = "Naven Chuen Wing Ho",
title = "Analysis and design of an instantaneous floating point
amplifier",
type = "Thesis ({M.S.})",
school = "Department of Electrical Engineering, Cullen College
of Engineering, University of Houston",
address = "Houston, TX, USA",
pages = "xv + 185",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Amplifiers (Electronics); Seismic waves --- Data
processing.",
}
@Book{Holt:1988:BR,
editor = "Wayne E. Holt and Steven M. Cooper and Jason M. Goertz
and Scott E. Levine and Joanna L. Mosher and Stanley R.
{Sieler, Jr.} and Jacques {Van Damme}",
title = "Beyond {RISC}\emdash An Essential Guide to
Hewlett--Packard Precision Architecture",
publisher = pub-SRNI,
address = pub-SRNI:adr,
pages = "xvii + 342",
year = "1988",
ISBN = "0-9618813-7-2",
ISBN-13 = "978-0-9618813-7-5",
LCCN = "QA76.8.H66 B49 1988",
bibdate = "Thu Sep 15 11:34:06 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Hsu:1988:CVA,
author = "I. S. Hsu and T. K. Truong and L. J. Deutsch and I. S.
Reed",
title = "A comparison of {VLSI} architecture of finite field
multipliers using dual, normal, or standard bases",
journal = j-IEEE-TRANS-COMPUT,
volume = "37",
number = "6",
pages = "735--739",
month = jun,
year = "1988",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.2212",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 08:33:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2212",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Iacobovici:1988:HFC,
author = "S. Iacobovici",
title = "High-performance floating-point coprocessor for the
{NS32532 CPU}",
crossref = "Wescon:1988:WCR",
pages = "1.3/1--6",
year = "1988",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The need to match the integer processing performance
of the NS32532 CPU with the floating-point performance
teams the NS32580 floating-point controller with
Weitek's WTL3164 floating-point data path to achieve a
peak performance of 15 MFLOPS for single- or
double-precision. Using a pipelined slave protocol this
solution is software compatible with existing Series
32000 software base and supports precise exception
handling. Together, NS32532-NS32580-WTL3164 provide a
high-performance, well-balanced solution for scientific
applications, as well as number crunching, graphics and
image processing.",
acknowledgement = ack-nhfb,
affiliation = "National Semicond. Corp., Santa Clara, CA, USA",
classification = "C5130 (Microprocessor chips); C5230 (Digital
arithmetic methods)",
keywords = "15 MFLOPS; Double-precision; Exception handling;
Floating-point coprocessor; Graphics; Image processing;
NS32532 CPU; NS32580 floating-point controller;
Pipelined slave protocol; Processing performance;
Scientific applications; Series 32000 software; Single
precision arithmetic; WTL3164 floating-point data
path",
numericalindex = "Computer speed 1.5E+07 FLOPS",
thesaurus = "Digital arithmetic; Microprocessor chips",
}
@Article{Iacobovici:1988:PIH,
author = "S. Iacobovici",
title = "A pipelined interface for high floating-point
performance with precise exceptions",
journal = j-IEEE-MICRO,
volume = "8",
number = "3",
pages = "77--87",
month = may # "\slash " # jun,
year = "1988",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.542",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
summary = "Two options are presented that were considered for a
pipelined interface between a central processing unit
(CPU) and a floating-point coprocessor (FPU), along
with the CPU recovery mechanisms that provide precise
floating-point exceptions for each \ldots{}",
}
@Article{Irwin:1988:SIP,
author = "M. J. Irwin",
title = "Special issue on parallelism in computer arithmetic",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "3",
pages = "205--208",
month = jun,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 17:13:17 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods); C5440
(Multiprocessor systems and techniques)",
corpsource = "Pennsylvania State University, University Park, PA,
USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "computer arithmetic; digital arithmetic; lookahead
adders; parallel processing; parallelism; pipelined
arithmetic processors; VLSI systems",
treatment = "G General Review; P Practical",
}
@Article{Jenkins:1988:SCP,
author = "W. K. Jenkins and E. J. Altman",
title = "Self-checking properties of residue number error
checkers based on mixed radix conversion",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "35",
number = "2",
pages = "159--167",
month = feb,
year = "1988",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1109/31.1717",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=107",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "It has been shown previously that a mixed-radix
converter can be modified to perform all the essential
functions of an error checker for error detection and
correction in residue number system hardware
architectures. Since the computations in a \ldots{}",
}
@PhdThesis{Johnstone:1988:DFP,
author = "Paul Johnstone",
title = "Decimal floating point representation",
type = "Thesis ({Ph.D.})",
school = "Tulane University",
address = "New Orleans, LA 70118, USA",
pages = "vi + 101",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Binary system (Mathematics); decimal floating-point
arithmetic; Floating-point arithmetic.",
}
@TechReport{Jouppi:1988:MFA,
author = "Norman Paul Jouppi and Jeremy Dion and David Reeves
Boggs and Michael J. K. Nielsen",
title = "{MultiTitan}: four architecture papers",
institution = "Digital Western Research Laboratory",
address = "Palo Alto, CA, USA",
edition = "[Revised]",
pages = "various",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "WRL research report; 87/8",
acknowledgement = ack-nhfb,
keywords = "Computer architecture.; MultiTitan (Computer)",
remark = "``April 10, 1988.'' MultiTitan central processor unit
/ Norman P. Jouppi --- MultiTitan floating point unit /
Norman P. Jouppi --- MultiTitan cache control unit /
Jeremy Dion --- MultiTitan intra-processor bus / David
Boggs, Jeremy Dion, Michael J. K. Nielsen.",
}
@TechReport{Jouppi:1988:UVS,
author = "Norman P. Jouppi and Jonathan Bertoni and David W.
Wall",
title = "A unified vector\slash scalar floating-point
architecture",
type = "Report",
number = "WRL TN-3",
institution = "Digital Western Research Laboratory",
address = "Palo Alto, CA, USA",
pages = "19",
year = "1988",
bibdate = "Thu May 09 08:38:06 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Joy:1988:OCT,
author = "Edward Bennett Joy and Paul R. Beaudet and Pankaj K.
Das",
title = "Optical communications techniques\slash floating point
residue number system",
institution = "School of Electrical Engineering, Georgia Institute of
Technology",
address = "Atlanta, GA, USA",
pages = "17",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer network architectures.; Computers --- Optical
equipment.",
remark = "Issued as R and D status reports [nos. 1--7], Contract
funds status reports [nos. 1--8], Final technical
report, and Final report, Project E-21-T01. Final
technical report has author: Paul R. Beaudet. Final
report has author: Pankaj K. Das. Final technical
report has title: Floating point residue number system.
Final report has title: New techniques in optical
communications and signal processing.",
}
@Article{Juffa:1988:SAF,
author = "N. Juffa",
title = "{Schnelle Algorithmen f{\"u}r Sin und Cos} \toenglish
{Fast Algorithms for Sin and Cos} \endtoenglish",
journal = j-MC,
volume = "5",
pages = "105--107",
year = "1988",
ISSN = "0720-4442, 0941-777x , 0943-5409",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "MC: Die Mikrocomputer-Zeitschrift",
}
@Misc{Kahan:1988:AFP,
author = "William Kahan",
title = "Arithmazium: The Floating Point Expos{\'e}",
howpublished = "Web site",
month = may # "\slash " # jul,
year = "1988",
bibdate = "Wed Jun 05 09:50:01 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "This site includes 27 lectures with notes and videos
for CS 279 (Computer System Support for Scientific and
Engineering Computation). The class handouts amount to
more than 2000 pages.",
URL = "https://www.arithmazium.org/classroom/wk88_toc.html",
acknowledgement = ack-nhfb,
}
@TechReport{Kahan:1988:CSS,
author = "W. Kahan and David Goldberg",
title = "Computer System Support for Scientific and Engineering
Computation",
type = "Report",
institution = inst-BERKELEY-CS,
address = inst-BERKELEY-CS:adr,
day = "26",
month = jul,
year = "1988",
bibdate = "Mon Aug 26 10:39:23 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Revised 14 June 1990.",
URL = "http://www.arithmazium.org/classroom/lib//Lecture_25_notes_slides.pdf",
acknowledgement = ack-nhfb,
}
@Article{Kahaner:1988:BRP,
author = "D. K. Kahaner",
title = "Benchmarks for `real' programs",
journal = j-SIAM-NEWS,
pages = "A-61",
month = nov,
year = "1988",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Mon Sep 16 16:15:31 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "https://sinews.siam.org/",
}
@InProceedings{Kanada:1988:VMA,
author = "Yasumasa Kanada",
booktitle = "Proceedings of Supercomputing 88. Vol. {II}: Science
and Applications",
title = "Vectorization of multiple-precision arithmetic program
and 201,326,000 decimal digits of {$ \pi $}
calculation",
crossref = "Martin:1988:SPN",
volume = "2",
pages = "117--128",
year = "1988",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 16:53:44 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/agm.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/pi.bib",
abstract = "More than 200 million decimal places of {$ \pi $} were
calculated using an arithmetic geometric mean formula
independently discovered by E. Salamin and R. P. Brent
in 1976. Correctness of the calculation was verified
through Borwein's quartic convergent formula developed
in 1983. The computation took CPU times of 5 hours 57
minutes for the main calculation and 7 hours 30 minutes
for the verification calculation on the HITAC S-820
model 80 supercomputer with 256 MB of main memory and 3
GB of high speed semiconductor storage, Extended
Storage, to shorten I/O time.\par Computation was
completed in 27th of January 1988. At that day two
programs generated values up to $ 3 \times 2^{26} $,
about 201 million. The two results agreed except for
the last 21 digits. These results also agree with the
133,554,000 places of calculation of $ \pi $ which was
done by the author in January 1987. Compare to the
record in 1987, 50\% more decimal digits were
calculated with about $ 1 / 6 $ of CPU time.\par
Computation was performed with real arithmetic based
vectorized Fast Fourier Transform (FFT) multiplier and
newly vectorized multiple-precision add, subtract and
(single word) constant multiplication programs.
Vectorizations for the later cases were realized
through first order linear recurrence vector
instruction on the S-820. Details of the computation
and statistical tests on the first 200 million digits
of $ \pi - 3 $ are reported.",
acknowledgement = ack-nhfb,
classification = "C4190 (Other numerical methods); C7310
(Mathematics)",
corpsource = "Comput. Centre, Tokyo University, Japan",
keywords = "arithmetic geometric mean formula; Borwein's quartic
convergent formula; fast Fourier transform; fast
Fourier transforms; first order linear recurrence
vector instruction; HITAC S-820 model 80 supercomputer;
mathematics computing; multiple-precision arithmetic
program; multiplier; parallel processing; pi
calculation; S-820; vectorization",
sponsororg = "IEEE; ACM SIGARCH",
treatment = "P Practical",
}
@InProceedings{Kanada:1988:VMP,
author = "Yasumasa Kanada",
booktitle = "Proceedings of Supercomputing 88. Vol. {II}: Science
and Applications",
title = "Vectorization of multiple-precision arithmetic program
and 201,326,000 decimal digits of {$ \pi $}
calculation",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "117--128",
year = "1988",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 16:53:44 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "More than 200 million decimal places of {\pi} were
calculated using an arithmetic geometric mean formula
independently discovered by E. Salamin and R. P. Brent
in 1976. Correctness of the calculation was verified
through Borwein's quartic convergent formula developed
in 1983. The computation took CPU times of 5 hours 57
minutes for the main calculation and 7 hours 30 minutes
for the verification calculation on the HITAC S-820
model 80 supercomputer with 256 MB of main memory and 3
GB of high speed semiconductor storage, Extended
Storage, to shorten I/O time.\par
Computation was completed in 27th of January 1988. At
that day two programs generated values up to $ 3 \times
2^{26} $, about 201 million. The two results agreed
except for the last 21 digits. These results also agree
with the 133,554,000 places of calculation of $ \pi $
which was done by the author in January 1987. Compare
to the record in 1987, 50\% more decimal digits were
calculated with about $ 1 / 6 $ of CPU
time.\par
Computation was performed with real arithmetic based
vectorized Fast Fourier Transform (FFT) multiplier and
newly vectorized multiple-precision add, subtract and
(single word) constant multiplication programs.
Vectorizations for the later cases were realized
through first order linear recurrence vector
instruction on the S-820. Dertails of the computation
and statistical tests on the first 200 million digits
of $ \pi - 3 $ are reported.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kida:1988:FPP,
author = "H. Kida and M. Watabe and T. Nakamikawa and S.
Morinaga and S. Kawasaki and H. Inayoshi",
title = "A floating point processing unit for the {GMICRO}
{CPU}",
crossref = "Sakamura:1988:TPO",
bookpages = "xi + 384",
pages = "301--316",
year = "1988",
DOI = "https://doi.org/10.1007/978-4-431-68081-9_21",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Describes the architecture and implementation of a
newly developed floating point processing unit (FPU).
It was developed as a high performance 32-bit
coprocessor of the 32-bit GMICRO microprocessor, which
satisfies the IEEE 754 Standard for Binary
Floating-Point Arithmetic. High performance was
achieved by the high speed coprocessor's interface with
the GMICRO CPU and the pipeline processing. The
coprocessor's interface was designed to minimize
CPU-FPU communication overhead caused by transferring
commands, operands and coprocessor information.
Furthermore, to improve operation speed, the FPU
performs pipeline processing named command pipeline.
The FPU has three main elements, the bus control unit,
format conversion unit, and execution control unit. In
order to perform high speed calculations, each element
in the chip is designed to operate in parallel. (5
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Hitachi Ltd., Tokyo, Japan",
classification = "C5220 (Computer architecture)",
confdate = "1988",
conflocation = "Japan",
keywords = "32 Bit; Coprocessor; Floating point processing unit;
FPU; GMICRO CPU; GMICRO microprocessor; IEEE 754;
Standard for Binary Floating-Point Arithmetic",
numericalindex = "Word length 3.2E+01 bit",
pubcountry = "Japan",
thesaurus = "Computer architecture; Microprocessor chips",
}
@Article{Kirchner:1988:AAV,
author = "R. Kirchner and U. Kulisch",
title = "Accurate arithmetic for vector processors",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "3",
pages = "250--270",
month = jun,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Univ Kaiserslautern, West Ger",
classification = "721; 722; 723; C5230 (Digital arithmetic methods);
C5440 (Multiprocessor systems and techniques)",
corpsource = "Fachbereich Inf., Kaiserslautern University, West
Germany",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "arithmetic operations; Computational Methods; computer
systems, digital --- Parallel Processing; computers;
computers, digital; computers, microcomputer; digital
arithmetic; dot products; implementation techniques;
local memory; microcomputers; parallel; parallel
processing; pipelined compound operations; sums; vector
processors; VLSI technology",
treatment = "P Practical",
}
@Article{Knuth:1988:FM,
author = "Donald E. Knuth",
title = "{Fibonacci} multiplication",
journal = j-APPL-MATH-LETT,
volume = "1",
number = "1",
pages = "57--60",
year = "1988",
CODEN = "AMLEEL",
ISSN = "0893-9659 (print), 1873-5452 (electronic)",
ISSN-L = "0893-9659",
MRclass = "11B39",
MRnumber = "89f:11031",
MRreviewer = "W. Herget",
bibdate = "Fri Mar 22 18:03:29 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/08939659",
}
@Article{Kornerup:1988:LAU,
author = "Peter Kornerup and David W. Matula",
title = "An on-line arithmetic unit for bit-pipelined rational
arithmetic",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "3",
pages = "310--330",
month = jun,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Odense Univ, Odense, Den",
classification = "722; 723; 921; C5230 (Digital arithmetic methods)",
corpsource = "Odense University, Denmark",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "algorithm of Gosper; Algorithms; binary version;
bit-pipelined rational arithmetic; computer metatheory
--- Binary Sequences; computer programming; computers,
digital --- Computational Methods; difference; digital
arithmetic; functions; mathematical techniques ---
Algorithms; on-line arithmetic unit; online arithmetic
unit; product; quotient; rational; sum",
treatment = "P Practical",
}
@InProceedings{Krishnan:1988:IRN,
author = "R. Krishnan",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, 7--9 June 1988",
title = "Implementation of recursive and nonrecursive digital
filters using the single multiplexed {ROM} in the
quadratic residue number system",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1297--1300",
year = "1988",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1988.15166",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Recursive and nonrecursive digital filters have been
implemented using the proposed single-multiplexed
dual-clock computational module (SDCM) in the bit-slice
architecture. The amount of memory requirements has
been reduced to 50\% required for the \ldots{}",
}
@InProceedings{Krishnan:1988:SCR,
author = "R. Krishnan",
booktitle = "International Conference on Acoustics, Speech, and
Signal Processing, {ICASSP-88, 11--14} April 1988",
title = "A single-channel {ROM}-based complex digital filter
implementation in the quadratic residue number
systems",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1842--1845",
year = "1988",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1988.196981",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The implementation of complex digital filters using
the quadratic residue number system (QRNs) and modified
quadratic residue number system (MQRNS) is considered.
These QRNS/MQRNS-based filter architectures are
memory-intensive because the lookup- \ldots{}",
}
@InProceedings{Lai:1988:FAI,
author = "K. Lai and J. Valerio",
title = "The floating-point architecture of {Intel's 80960}",
crossref = "Wescon:1988:WCR",
pages = "1.5/1--3",
year = "1988",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Intel 80960KB is a microprocessor with hardware
floating-point support integrated on-chip. In a
departure from previous microprocessors, the 80960KB
incorporates full floating-point support within the
processor instead of relying on a coprocessor. As
floating-point speeds increase, the off-chip
coprocessor interface becomes a significant performance
bottleneck. Additionally, component and system cost,
board space, and cleanliness of architecture are other
good reasons to have on-chip floating-point support.
The implementation delivers accurate results with good
performance: 1.1 single-precision Linpack MFLOPS, and
4.1 single-precision mega-Whetstones per second. (0
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Intel Corp., Hillsboro, OR, USA",
classification = "C5130 (Microprocessor chips); C5220 (Computer
architecture); C5230 (Digital arithmetic methods)",
keywords = "1.1 MFLOPS; Board space; Cleanliness; Component costs;
Floating-point architecture; Intel 80960KB; Linpack;
Microprocessor; On-chip floating-point support;
Performance; System cost",
numericalindex = "Computer speed 1.1E+06 FLOPS",
thesaurus = "Computer architecture; Digital arithmetic;
Microprocessor chips",
}
@InProceedings{Lai:1988:IFS,
author = "K. Lai and J. Valerio",
title = "Integrated floating-point solution for the {Intel
80960KB}",
crossref = "Midcon:1988:MCP",
pages = "249--251",
year = "1988",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Intel 80960KB is a microprocessor with hardware
floating-point support integrated on-chip. In a
departure from previous microprocessors, the 80960KB
incorporates full floating-point support within the
processor instead of relying on a coprocessor. As
floating-point speeds increase, the off-chip
coprocessor interface becomes a significant performance
bottleneck. Additionally, component and system cost,
board space, and cleanliness of architecture are other
good reasons to have on-chip floating-point support.
The implementation delivers accurate results with good
performance: 1.1 single precision Linpack MFLOPS, and
4.1 single precision mega Whetstones per second. (0
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Intel Corp., Hillsboro, OR, USA",
classification = "C5130 (Microprocessor chips)",
keywords = "Floating-point support; Integrated floating point;
Intel 80960KB; Microprocessor; Onchip floating point",
thesaurus = "Digital arithmetic; Microprocessor chips",
}
@Article{Lawson:1988:SRR,
author = "Charles L. Lawson",
title = "Series reversion as the reversed chain rule",
journal = j-SIGNUM,
volume = "23",
number = "1",
pages = "7--9",
month = jan,
year = "1988",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:16 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Lawson gives Fortran subroutines for differentiation
arithmetic. A subroutine SWPRO for products corresponds
to Chang's ATS [Chang74a]. The chain rule is
implemented by repeated calls to SWPRO. Series
reversion for implicit functions is implemented by
reversing the chain rule. An application is given to
Keppler's equation, $ M - E + e \sin (E) = 0 $.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "design; differentiation arithmetic; implicit
functions; languages; theory",
subject = "D.3.3 Software, PROGRAMMING LANGUAGES, Language
Constructs, Modules, packages \\ G.4 Mathematics of
Computing, MATHEMATICAL SOFTWARE \\ D.3.3 Software,
PROGRAMMING LANGUAGES, Language Constructs, Procedures,
functions, and subroutines",
}
@TechReport{Liu:1988:BEF,
author = "Zhi-Shun Alex Liu",
title = "{Berkeley} Elementary Function Test Suite",
institution = "Computer Science Division, Department of Electrical
Engineering and Computer Science, Univerity of
California at Berkeley",
address = "Berkeley, CA, USA",
pages = "ii + 59",
day = "30",
month = dec,
year = "1988",
bibdate = "Mon Sep 12 23:52:34 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.netlib.org/fp/ucbtest.tgz;
http://www.ucbtest.org/zaliu-papers/zaliu-beef-doc.pdf",
abstract = "A suite of programs is presented to test how
accurately the elementary transcendental functions exp,
log, sin, cos and atan have been implemented in a
computer's run-time library. The suite is written in
the language C and designed to run on any computer with
binary floating-point arithmetic rounded in a
reasonable way. The suite makes no appeal to
extra-precise arithmetic; the tests use only whatever
arithmetic capabilities are present in the environment
where the transcendental functions are to be used.
Despite this limitation, the tests run fast and deliver
indication of accuracy to within a small fraction of an
ULP (Unit in the Last Place) of the functions under
test. This account includes the proofs of the test
suite's claims to accuracy.",
acknowledgement = ack-nj,
keywords = "BeEF test suite; floating-point testing",
}
@InProceedings{Lu:1988:MCF,
author = "P. Y. Lu and A. Jain and J. Kung and P. H. Ang",
title = "A 30-{MFLOP} 32b {CMOS} Floating-Point Processor",
crossref = "IEEE:1988:IIS",
pages = "28, 29, 285",
year = "1988",
bibdate = "Fri Dec 08 13:04:40 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Luk:1988:AAB,
author = "Franklin T. Luk and Haesun Park",
title = "An analysis of algorithm-based fault tolerance
techniques",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "2",
pages = "172--184",
month = apr,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Cornell Univ, Ithaca, NY, USA",
classification = "722; 723; C4110 (Error analysis in numerical
methods); C4140 (Linear algebra); C5230 (Digital
arithmetic methods); C5470 (Performance evaluation and
testing)",
corpsource = "Sch. of Electr. Eng., Cornell University, Ithaca, NY,
USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "algorithm-based fault tolerance; analysis;
computation; computer programming --- Algorithms;
computer systems, digital; decomposition; error
analysis; Fault Tolerant Capability; fault tolerant
computing; floating point error; Gaussian elimination;
Gaussian elimination with pairwise pivoting; LU; lu
decomposition; matrix algebra; pairwise pivoting; qr
decomposition; QR decomposition; rank-one perturbation;
rounding errors; roundoff errors; systolic array;
transient error; unified checksum scheme",
treatment = "T Theoretical or Mathematical",
}
@MastersThesis{Lyu:1988:PFP,
author = "Chung-nan Lyu",
title = "Pipelined floating point divider with built-in testing
circuits",
type = "Thesis ({M.S.})",
school = "Ohio University",
address = "Athens, OH, USA",
pages = "90",
month = jun,
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "floating-point testing; parallel processing
(electronic computers)",
}
@Article{Magenheimer:1988:IMD,
author = "Daniel J. Magenheimer and Liz Peters and Karl W.
Peters and Dan Zuras",
title = "Integer Multiplication and Division on the {HP
Precision Architecture}",
journal = j-IEEE-TRANS-COMPUT,
volume = "37",
number = "8",
pages = "980--990",
month = aug,
year = "1988",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.2248",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Aug 04 16:38:15 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Marchyulaitis:1988:SRN,
author = "Saulyus Marchyula{\u\i}tis",
title = "Summation of real numbers in arithmetic with a
floating point. {A} probability approach to determining
the variance of absolute round-off error. ({Russian})",
journal = "Statist. Problemy Upravleniya",
volume = "82",
pages = "57--68",
year = "1988",
MRclass = "65G05 (65C20)",
MRnumber = "89k:65056",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
language = "Russian",
}
@Article{Maurer:1988:DVW,
author = "P. M. Maurer",
title = "Design Verification of the {WE} 32106 Math Accelerator
Unit",
journal = j-IEEE-DES-TEST-COMPUT,
volume = "5",
number = "3",
pages = "11--21",
month = jun,
year = "1988",
ISSN = "0740-7475 (print), 1558-1918 (electronic)",
ISSN-L = "0740-7475",
bibdate = "Wed Sep 7 22:32:00 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Design \& Test of Computers",
}
@Article{McLellan:1988:DCF,
author = "E. J. McLellan and G. M. Wolrich and R. A. J.
Yodlowski",
title = "Development of the {CVAX} floating-point chip",
journal = j-DEC-TECH-J,
volume = "??",
number = "7",
pages = "109--120",
month = aug,
year = "1988",
CODEN = "DTJOEL",
ISSN = "0898-901X",
bibdate = "Wed Sep 7 22:32:00 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Digital Technical Journal",
}
@InProceedings{Melear:1988:IFP,
author = "C. Melear",
title = "An integrated floating point unit for a {RISC}
architecture",
crossref = "Wescon:1988:WCR",
pages = "1.2/1--8",
year = "1988",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "RISC architectures require multiple bus structures
that allow for instructions, operands, and results to
all travel about the processor on each clock cycle.
Thus, by putting the floating point unit on these
multiple bus structures, it can receive instructions
and operands on each clock cycle. Some number of cycles
later, as more floating point instructions are issued,
floating point results can also be sent out on the
destination bus, yielding burst execution rates equal
to the clock rate. The present clock rate is 20 MHz and
will be increased eventually to the 40 MHz area. At 20
MHz, sustained execution rates of 7 MFLOPS are typical.
Performance rates of 10.5 MWhetstones have also been
demonstrated (20 MHz clock). The floating point unit is
only one part of the RISC processor. By combining all
the aspects of software, memory system interfacing and
high performance hardware like the 88100 floating point
unit, mainframe performance moves one step closer to
the desktop computer world.",
acknowledgement = ack-nhfb,
affiliation = "Motorola, Austin, TX, USA",
classification = "C5130 (Microprocessor chips); C5220 (Computer
architecture); C5230 (Digital arithmetic methods)",
keywords = "20 MHz; 7 MFLOPS; 88100 Floating point unit; Burst
execution rates; Clock cycle; Clock rate; Desktop
computer; Execution rates; Memory system interfacing;
Multiple bus structures; Performance rates; RISC
architecture",
numericalindex = "Frequency 2.0E+07 Hz; Computer speed 7.0E+06 FLOPS",
thesaurus = "Digital arithmetic; Microprocessor chips; Reduced
instruction set computing",
}
@Article{Milnikel:1988:SRF,
author = "R. Milnikel and R. Wollenberg",
title = "{Schnelles Radizierverfahren f{\"u}r Gleitkommazahlen
im IEEE-Format} \toenglish {Fast Square-rooting method
for Floating-point Numbers in IEEE Format}
\endtoenglish",
journal = j-ELECTRONIK,
volume = "8",
pages = "114--1122",
year = "1988",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronik",
}
@Article{Monahan:1988:CAG,
author = "John F. Monahan",
title = "Corrigendum: ``{An} Algorithm for Generating Chi
Random Variables''",
journal = j-TOMS,
volume = "14",
number = "1",
pages = "111--111",
month = mar,
year = "1988",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/42288.356228",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "111. 65C10",
MRnumber = "89d:65006, 88d:65013",
bibdate = "Fri Mar 28 10:45:16 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Monahan:1987:AGC}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Manual{Motorola:1988:GPF,
title = "96-bit general purpose floating-point digital-signal
processor technical summary",
organization = "Motorola, Inc.",
address = "Phoenix, AZ, USA",
pages = "23",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Motorola semiconductor technical data",
acknowledgement = ack-nhfb,
keywords = "Integrated circuits.; Signal processing --- Digital
techniques.",
remark = "Caption title. ``BR574/D.''",
}
@Book{Motorola:1988:MFP,
author = "{Motorola, Inc.Staff}",
title = "{MC} 68881 and 68882 Floating-Point Coprocessor User's
Manual",
publisher = pub-PH,
address = pub-PH:adr,
month = feb,
year = "1988",
ISBN = "0-13-566936-7",
ISBN-13 = "978-0-13-566936-5",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$22.50",
acknowledgement = ack-nhfb,
language = "eng",
}
@Article{Nakamura:1988:SCP,
author = "S. Nakamura and K.-Y. Chu",
title = "A single chip parallel multiplier by {MOS}
technology",
journal = j-IEEE-TRANS-COMPUT,
volume = "37",
number = "3",
pages = "274--282",
month = mar,
year = "1988",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.2164",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 08:33:25 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2164",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Nikolos:1988:EDT,
author = "D. Nikolos and A. M. Paschalis and G. Philokyprou",
title = "Efficient design of totally self-checking checkers for
all low-cost arithmetic codes",
journal = j-IEEE-TRANS-COMPUT,
volume = "37",
number = "7",
pages = "807--814",
month = jul,
year = "1988",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.2226",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 08:33:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2226",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Normand:1988:PSP,
author = "J. M. Normand",
title = "{Percola}: a special purpose programmable 64-bit
floating-point processor",
crossref = "ACM:1988:ICS",
pages = "55--65",
year = "1988",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$49.00",
URL = "http://doi.acm.org/10.1145/55364.55370",
acknowledgement = ack-nhfb,
affiliation = "Centre d'Etudes Nucl{\'e}aires, Saclay, France",
bibno = "55370",
catcode = "G.3; C.5.1; C.5.3; J.2; G.3; B.6.3",
CRclass = "G.3 Random number generation; C.5.1 Large and Medium
(``Mainframe'') Computers; C.5.1 Super (very large)
computers; C.5.3 Microcomputers; C.5.3 Motorola 68000;
J.2 Physics; G.3 Statistical computing; B.6.3 Design
Aids; B.6.3 Optimization",
descriptor = "Mathematics of Computing, PROBABILITY AND STATISTICS,
Random number generation; Computer Systems
Organization, COMPUTER SYSTEM IMPLEMENTATION, Large and
Medium (``Mainframe'') Computers, Super (very large)
computers; Computer Systems Organization, COMPUTER
SYSTEM IMPLEMENTATION, Microcomputers, Motorola 68000;
Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Physics; Mathematics of Computing,
PROBABILITY AND STATISTICS, Statistical computing;
Hardware, LOGIC DESIGN, Design Aids, Optimization",
genterm = "ALGORITHMS; DESIGN",
guideno = "1988-15563",
subject = "G. Mathematics of Computing; G.3 PROBABILITY AND
STATISTICS; C. Computer Systems Organization; C.5
COMPUTER SYSTEM IMPLEMENTATION; C. Computer Systems
Organization; C.5 COMPUTER SYSTEM IMPLEMENTATION; J.
Computer Applications; J.2 PHYSICAL SCIENCES AND
ENGINEERING; G. Mathematics of Computing; G.3
PROBABILITY AND STATISTICS; B. Hardware; B.6 LOGIC
DESIGN",
waffil = "Rennes",
wauthedit = "Lenfant, J.",
wsub = "Conference Proceedings",
}
@Article{Oklobdzija:1988:IAV,
author = "Vojin G. Oklobdzija and Earl R. Barnes",
title = "On implementing addition in {VLSI} technology",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "6",
pages = "716--728",
month = dec,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Yorktown Heights, NY, USA",
classification = "713; 714; 723; B1265B (Logic circuits); B2570D (CMOS
integrated circuits); C5210 (Logic design methods);
C5230 (Digital arithmetic methods)",
corpsource = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "addition; Arithmetic Algorithms; arithmetic
algorithms; carry-lookahead; CMOS integrated circuits;
CMOS technology; Computer Aided Design; Computer
Programming--Algorithms; digital arithmetic; estimates;
integrated; Integrated Circuits, VLSI; logic circuits;
logic design; Logic Levels; logic levels; quick;
recurrence solver schemes; Semiconductor Devices, MOS;
Single-chip VLSI Processor; VLSI; VLSI Implementation;
VLSI technology; VLSI-; VLSI-cmos Technology",
treatment = "P Practical",
}
@InProceedings{Papadourakis:1988:VDP,
author = "G. M. Papadourakis and J. Condorodis",
booktitle = "1988 International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP-88, 11--14} April 1988",
title = "A {VLSI} design of processing element for
reconfigurable systolic architectures based on {LNS}",
volume = "4",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2080--2083",
year = "1988",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 16:14:38 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The design and development of a processing element
(PE) in an orthogonal systolic architecture, using the
state of the art in VLSI technology, is presented. The
goal was to create a high-speed, high-precision PE
which would be adaptive to a highly \ldots{}",
}
@Article{Papamichalis:1988:TFP,
author = "P. Papamichalis and R. {Simar, Jr.}",
title = "The {TMS320C30} Floating-Point Digital Signal
Processor",
journal = j-IEEE-MICRO,
volume = "8",
number = "6",
pages = "13--29",
month = nov # "\slash " # dec,
year = "1988",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.16778",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
summary = "The 320C30 is a fast processor with a large memory
space and floating-point-arithmetic capabilities. The
authors describe the 320C30 architecture in detail,
discussing both the internal organization of the device
and the external interfaces. They also \ldots{}",
}
@InProceedings{Perlman:1988:AFP,
author = "R. M. Perlman",
title = "The {Am29027} --- a floating-point accelerator for the
{Am29000} streamlined instruction processor",
crossref = "Wescon:1988:WCR",
pages = "1.4/1--7",
year = "1988",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Am29000, a 32-bit RISC processor, sets new
standards of performance for integer processing. A 25
MHz Am29000 with cache can achieve in excess of 35600
Dhrystones. Even with simple video DRAM memory, the
Am29000 has a performance of 24300 Dhrystones. Although
the Am29000 contains no hardware dedicated to
floating-point computation, it can emulate
floating-point operations in software at speeds that
were heretofore achieved only by dedicated
floating-point coprocessors. For numerically-intensive
applications, the Am29000 can be augmented with the
Am29027 arithmetic accelerator. The Am29027 is a
single-chip floating-point unit that performs single-,
double-, and mixed-precision operations, and completely
implements IEEE standard 754 for those operations
supported. The Am29027 offers two operating modes: a
low-latency mode, for scalar operations, and a pipeline
mode, for vector and matrix calculations. When
configured in pipeline mode, the AM29027 can achieve a
peak throughput of 16 MFLOPS.",
acknowledgement = ack-nhfb,
affiliation = "Adv. Micro Devices, Sunnyale, CA, USA",
classification = "C5130 (Microprocessor chips); C5230 (Digital
arithmetic methods)",
keywords = "16 MFLOPS; 32 Bit; Am29000 streamlined instruction
processor; Am29027 arithmetic accelerator; Cache;
Floating-point operations; IEEE standard 754;
Low-latency mode; Matrix calculations; Mixed-precision
operations; Pipeline mode; RISC processor; Scalar
operations; Vector calculations; Video DRAM memory",
numericalindex = "Word length 3.2E+01 bit; Computer speed 1.6E+07
FLOPS",
thesaurus = "Digital arithmetic; Microprocessor chips; Pipeline
processing; Reduced instruction set computing",
}
@Article{Pichat:1988:APC,
author = "M. A. Pichat",
title = "All possible computed results in correct
floating-point summation. Stochastic methods in
round-off error analysis",
journal = j-MATH-COMP-SIM,
volume = "30",
number = "6",
pages = "541--552",
year = "1988",
CODEN = "MCSIDR",
ISSN = "0378-4754 (print), 1872-7166 (electronic)",
ISSN-L = "0378-4754",
MRclass = "65G05",
MRnumber = "90d:65090",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics and Computers in Simulation",
journal-URL = "http://www.sciencedirect.com/science/journal/03784754",
reviewer = "Luciano Biasini",
}
@MastersThesis{Pier:1988:IPA,
author = "Richard Michael Pier",
title = "An {IBM PC\slash AT}-based floating point imaging
workstation architecture",
type = "Thesis ({M.S.E.E.})",
school = "University of Washington",
address = "Seattle, WA, USA",
pages = "vi + 35",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer architecture.; IBM Personal Computer AT.;
Image processing --- Equipment and supplies.;
Microcomputer workstations.",
}
@Article{Pitas:1988:FPE,
author = "I. Pitas and M. G. Strintzis",
title = "Floating point error analysis of two-dimensional, fast
{Fourier} transform algorithms",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "35",
number = "1",
pages = "112--115",
month = jan,
year = "1988",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "Floating-point error is conducted for three algorithms
commonly used for the calculation of two-dimensional
fast Fourier transforms (FFTs), namely, the
conventional row-column FFT, the vector-radix FFT, and
the polynomial-transform FFT. The respective \ldots{}",
}
@Article{Plauger:1988:PFP,
author = "P. J. Plauger",
title = "Properties of floating-point arithmetic",
journal = j-COMP-LANG-MAG,
volume = "5",
number = "3",
pages = "17--22",
month = mar,
year = "1988",
CODEN = "COMLEF",
ISSN = "0749-2839",
bibdate = "Thu Sep 1 10:14:15 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Language Magazine",
}
@InProceedings{Prandolini:1988:VIB,
author = "R. Prandolini and S. Sridharan",
title = "{VLSI} implementation of a block floating point
coprocessor for the {TMS320} fixed point digital signal
processor",
crossref = "IREE:1988:AMC",
pages = "33--40",
year = "1988",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The design of a co-processor which can be interfaced
to the TMS32020 fixed-point digital signal processor is
described. The co-processor enables efficient
implementation of block floating-point arithmetic for
digital filtering using the TMS32020.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Electr. and Electron. Syst. Eng., Queensland
Inst. of Technol., Brisbane, Qld., Australia",
classification = "B1265F (Microprocessors and microcomputers); B1270F
(Digital filters); B2570 (Semiconductor integrated
circuits); C5130 (Microprocessor chips); C5240 (Digital
filters); C5260 (Digital signal processing)",
keywords = "Block floating point coprocessor; Block floating-point
arithmetic; Digital filtering; TMS320 fixed point
digital signal processor; VLSI implementation",
thesaurus = "Digital filters; Digital signal processing chips;
VLSI",
}
@Article{Prather:1988:CET,
author = "R. E. Prather",
title = "Comparison and Extension of Theories of {Zipf} and
{Halstead}",
journal = j-COMP-J,
volume = "31",
number = "3",
pages = "248--252",
month = jun,
year = "1988",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compendex database;
http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/248.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/249.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/250.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/251.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/252.tif",
acknowledgement = ack-nhfb,
affiliation = "Trinity Univ, San Antonio, TX, USA",
affiliationaddress = "Trinity Univ, San Antonio, TX, USA",
classcodes = "C6110B (Software engineering techniques)",
classification = "723",
corpsource = "Comput. and Inf. Sci., Trinity University, San
Antonio, TX, USA",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "behavioural psychology; computer programming; computer
software; empirical law; Halstead metrics; Halstead's
hypothesis; length estimates; Measurements;
probabilistic hypothesis; process; programming;
software engineering; software metrication; software
science; Zipf metrics; Zipf's law",
treatment = "T Theoretical or Mathematical",
}
@Book{Press:1988:NRC,
author = "W. H. Press and B. P. Flannery and S. A. Teukolsky and
W. T. Vetterling",
title = "Numerical Recipes in {C}: The Art of Scientific
Computing",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xxii + 735",
year = "1988",
ISBN = "0-521-43724-5",
ISBN-13 = "978-0-521-43724-0",
LCCN = "QA76.73.C15 N865 1988",
bibdate = "Thu Sep 01 10:34:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@MastersThesis{Rajanala:1988:ISP,
author = "Arunkumar V. Rajanala",
title = "{IEEE 754} single precision standard compatible
floating point processor implemented using silicon
compiler technology",
type = "Thesis ({M.S.})",
school = "Oregon State University",
address = "Corvallis, OR, USA",
pages = "77",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Microprocessors.",
}
@InProceedings{Randal:1988:FPC,
author = "V. T. Randal and J. L. Schmalzel and A. P. Shepherd",
title = "Floating-Point Computation Using a Microcontroller",
crossref = "Harris:1988:PAI",
pages = "1243--1244",
year = "1988",
bibdate = "Wed Sep 07 22:02:38 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Razaz:1988:TPM,
author = "M. Razaz and J. L. Schonfelder",
title = "Test Procedures for Measurement of Floating-Point
Characteristics of Computing Environments",
journal = j-COMP-J,
volume = "31",
number = "1",
pages = "12--16",
month = feb,
year = "1988",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ of Birmingham, Birmingham, Engl",
affiliationaddress = "Univ of Birmingham, Birmingham, Engl",
classcodes = "C5470 (Performance evaluation and testing)",
classification = "723",
corpsource = "Department of Electron. and Electr. Eng., Birmingham
University, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "arithmetic; arithmetic processors; CDC; computer
testing; computers, digital; computing environments;
conversion test; DEC; digital arithmetic;
floating-point arithmetic; floating-point
characteristics; floating-point testing; IBM; ICL;
mantissa; minimum representable number; nominal
decimal; normalisation base; number representation;
operations; parameters; performance evaluation;
precision; precision-dependent; procedures;
representation test; test; Testing",
treatment = "P Practical",
}
@InProceedings{Ries:1988:MFP,
author = "P. S. Ries",
title = "An 8 {MFLOP} Floating-Point Coprocessor for a {RISC}
Microprocessor",
crossref = "Electro:1988:ECR",
pages = "48/1/1--8",
year = "1988",
bibdate = "Wed Sep 7 22:32:00 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Robertazzi:1988:BOF,
author = "T. G. Robertazzi and S. C. Schwartz",
title = "Best {``Ordering''} for Floating-Point Addition",
journal = j-TOMS,
volume = "14",
number = "1",
pages = "101--110",
month = mar,
year = "1988",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/42288.42343",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65G99 (65V05)",
MRnumber = "89b:65117",
bibdate = "Sat Nov 19 13:08:22 1994",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p101-robertazzi/",
acknowledgement = ack-nhfb,
affiliation = "State University of New York at Stony Brook, Stony
Brook; Princeton University, Princeton, NJ",
bibno = "42343",
catcode = "G.1.0",
content = "This paper compares a variety of methods for
accumulating a floating-point sum. Wilkinson pointed
out that if we compute the $\sum^n_{i = 1} x_i$ in
strictly increasing order in magnitude of the $x_i$,
then we obtain a better bound on the rounding error
than if the sum is computed in random order
[1].\par
The authors discuss five different accumulation
strategies. They compare these accumulation strategies
for when the $x_i$ are uniformly distributed and for
when they are exponentially distributed. First they
compare a random order for summing the $x_i$, summing
in decreasing order of magnitude, and summing in
increasing order of magnitude. Not surprisingly,
summing in increasing order of magnitude is the best
and summing in decreasing order of magnitude is the
worst. In fact, it is not difficult to show this for
any class of distributions where the mean and variance
exist.\par
The interesting results in the paper concern two other
accumulation strategies. Both of these are shown to be
better than summing in increasing order of magnitude
for both the uniform and exponential distribution.
Fortunately, one of these strategies is the tree sum
(or fan-in sum) that is often used in parallel
computation. The paper calls this strategy the
``adjacency'' ordering.",
CRclass = "G.1.0 General; G.1.0 Computer arithmetic",
CRnumber = "8810-0794",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
genterm = "ALGORITHMS; PERFORMANCE",
journal-URL = "https://dl.acm.org/loi/toms",
journalabbrev = "ACM Trans. Math. Softw.",
keywords = "accurate floating-point summation; algorithms;
performance",
review = "ACM CR 8810-0794",
reviewer = "Jesse L. Barlow",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS,
General, Computer arithmetic",
}
@Article{Rowen:1988:MRF,
author = "Chris Rowen and Mark Johnson and Paul Ries",
title = "The {MIPS R3010} Floating-Point Coprocessor",
journal = j-IEEE-MICRO,
volume = "8",
number = "3",
pages = "53--62",
month = may # "\slash " # jun,
year = "1988",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.540",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Science Citation Index database (1980--2000)",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliationaddress = "MIPS Computer Systems, Sunnyvale, CA, USA",
classcodes = "B1265F (Microprocessors and microcomputers); B2570
(Semiconductor integrated circuits); C5130
(Microprocessor chips); C5220 (Computer architecture);
C5230 (Digital arithmetic methods)",
classification = "714; 722; 723",
corpsource = "MIPS Comput. Syst., Sunnyvale, CA, USA",
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
keywords = "32-bit R31010 floating-point coprocessor; accelerator
chip; computer architecture; computer systems, digital
--- Parallel Processing; computers, microcomputer;
Design; design techniques; digital arithmetic;
floating-point; instruction set computing; integrated
circuits, VLSI; microprocessor chips; million
instruction per second (MIPS) processor; MIPS R3010
floating-point coprocessor; reduced;
reduced-instruction-set-computer;
reduced-instruction-set-computer (RISC); VLSI",
summary = "A description is given of the R3010 floating-point
accelerator chip, a coprocessor that is based on
advanced reduced-instruction-set-computer (RISC)
architecture and VLSI design techniques and provides
high-speed floating-point operation. The 75000-
\ldots{}",
treatment = "P Practical",
xxauthor = "C. Rowen and P. Ries and M. Johnson",
}
@InProceedings{Roylance:1988:EMS,
author = "G. Roylance",
title = "Expressing Mathematical Subroutines Constructively",
crossref = "ACM:1988:PAC",
pages = "8--13",
year = "1988",
bibdate = "Thu Sep 01 11:52:13 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Santoro:1988:PIA,
author = "M. Santoro and M. Horowitz",
booktitle = "Digest of Technical Papers, {IEEE} International
Solid-State Circuits Conference",
title = "A pipelined $ 64 \times 64 $ b iterative array
multiplier",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "35--36",
month = feb,
year = "1988",
bibdate = "Mon Dec 24 10:19:42 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Schatte:1988:ASC,
author = "Peter Schatte",
title = "On the almost sure convergence of floating-point
mantissas and {Benford}'s law",
journal = j-MATH-NACHR,
volume = "135",
pages = "79--83",
year = "1988",
CODEN = "MTMNAQ",
ISSN = "0025-584X",
MRclass = "60F15 (11K31)",
MRnumber = "89g:60114",
bibdate = "Fri Dec 08 12:49:25 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
reviewer = "S. A. Book",
}
@Article{Schatte:1988:MDC,
author = "P. Schatte",
title = "On Mantissa Distribution in Computing and {Benford}'s
Law",
journal = j-J-INFO-PROC-CYBERNETICS-EIK,
volume = "24",
number = "9",
pages = "443--455",
month = "????",
year = "1988",
CODEN = "JICYE5",
ISSN = "0863-0593",
bibdate = "Thu Sep 1 10:14:16 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Journal of Information Processing and Cybernetics:
EIK",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Scherson:1988:MOA,
author = "Isaac D. Scherson and Smil Ruhman",
title = "Multi-operand arithmetic in a partitioned associative
architecture",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "6",
pages = "655--668",
month = dec,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Princeton, NJ, USA",
classification = "722; 723; 921; C5220 (Computer architecture); C5230
(Digital arithmetic methods)",
corpsource = "Department of Electr. Eng., Princeton University, NJ,
USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "16-bit precision; Analysis; Associative
Multiplication; associative multiplication; common
filter vector; Computer Architecture; Computer
Metatheory; concurrency; Convolution; convolution; Data
Storage, Digital--Associative; digital arithmetic;
Disjoint Data Sets; disjoint data sets; Filter Vectors;
Mathematical Techniques; Multi-operand Arithmetic;
multioperand arithmetic; multiplier bits; parallel
architectures; parallel processing; Partitioned
Associative Architecture; partitioned associative
architecture",
treatment = "P Practical",
}
@InProceedings{Schwarz:1988:CLI,
author = "Jerry Schwarz",
title = "A {C++} Library for Infinite Precision Floating
Point",
crossref = "USENIX:1988:UPC",
bookpages = "362",
pages = "271--281",
year = "1988",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "ftp://ftp.uu.net/library/bibliography;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Real library supports infinite precision floating
point computation in C++. Arbitrary precision rational
arithmetic and transcendental functions are
supported.",
acknowledgement = ack-nhfb,
affiliation = "AT\&T Bell Laboratories, Murray Hill",
classification = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques)",
confdate = "17--21 Oct. 1988",
conflocation = "Denver, CO, USA",
keywords = "C++ library; Infinite precision floating point;
Rational arithmetic; Real library; Transcendental
functions",
thesaurus = "C language; Digital arithmetic; Object-oriented
programming; Subroutines",
}
@Article{Scott:1988:CMM,
author = "Michael Scott",
title = "{CUG247} --- {M.I.R.A.C.L.} --- a Multi-Pre\-ci\-sion
Arithmetic Library",
journal = j-CUJ,
volume = "6",
type = "{CUG} New Release",
number = "5",
pages = "76--??",
month = may,
year = "1988",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@Article{Shepherd:1988:LEC,
author = "Roger Shepherd and Charles Farnum",
title = "Letter to the {Editor}: Compiler support for
floating-point computation",
journal = j-SPE,
volume = "18",
number = "12",
pages = "1193--1194",
month = dec,
year = "1988",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.4380181208",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Wed Sep 10 12:36:39 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/spe.bib",
acknowledgement = ack-nhfb,
fjournal = "Software --- Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
onlinedate = "30 Oct 2006",
}
@Article{Simon:1988:SP,
author = "Barry Simon and Richard M. Wilson",
title = "Supercalculators on the {PC}",
journal = j-NAMS,
volume = "35",
number = "7",
pages = "978--1001",
month = sep,
year = "1988",
CODEN = "AMNOAN",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
bibdate = "Wed Jun 12 16:56:18 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "Notices Amer. Math. Soc.",
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
mynote = "September",
}
@Article{Smith:1988:ASD,
author = "S. G. Smith and P. B. Denyer",
title = "Advanced serial-data computation",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "3",
pages = "228--249",
month = jun,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Univ of Edinburgh, Edinburgh, Scotl",
classification = "716; 718; 721; 722; 723; C5230 (Digital arithmetic
methods)",
corpsource = "Department of Electr. Eng., Edinburgh University, UK",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "arithmetic operations; bit-parallel architectures;
Computational Methods; computational modules; computer
architecture; computers, digital; digital arithmetic;
dynamic range; high-; multiwire; multiwire techniques;
performance computer arithmetic; serial data
architectures; serial data computation; serial-data
architectures; signal processing --- Digital
Techniques; symmetric-coded distributed arithmetic;
techniques",
treatment = "P Practical",
}
@Article{Sohie:1988:DSP,
author = "G. R. L. Sohie and K. L. Kloker",
title = "A Digital Signal Processor with {IEEE} Floating-Point
Arithmetic",
journal = j-IEEE-MICRO,
volume = "8",
number = "6",
pages = "49--67",
month = nov # "\slash " # dec,
year = "1988",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.16780",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
summary = "A overview is given of Motorola's DSP96002, a digital
signal processor that implements IEEE-standard
floating-point arithmetic. It is designed for graphics,
image processing, spectral analysis and scientific
computing applications. Performance peaks \ldots{}",
}
@Article{Sridharan:1988:BFP,
author = "S. Sridharan and G. Dickman",
title = "Block floating-point implementation of digital filters
using the {DSP56000}",
journal = j-MICROPROC-MICROSYS,
volume = "12",
number = "6",
pages = "299--308",
month = aug,
year = "1988",
CODEN = "MIMID5",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Queensland Institute of Technology, Queensland,
Australia; Queensland Institute of Technology,
Queensland, Australia",
bibno = "49397",
catcode = "G.m; I.5.4; C.3; C.5.3",
CRclass = "I.5.4 Applications; I.5.4 Signal processing; C.3
Signal processing systems; C.5.3 Microcomputers; C.5.3
Microprocessors",
descriptor = "Mathematics of Computing, MISCELLANEOUS; Computing
Methodologies, PATTERN RECOGNITION, Applications,
Signal processing; Computer Systems Organization,
SPECIAL-PURPOSE AND APPLICATION-BASED SYSTEMS, Signal
processing systems; Computer Systems Organization,
COMPUTER SYSTEM IMPLEMENTATION, Microcomputers,
Microprocessors",
fjournal = "Microprocessors and Microsystems",
genterm = "ALGORITHMS; DESIGN",
guideno = "1988-12500",
journalabbrev = "Microprocess. Microsyst.",
subject = "G. Mathematics of Computing; G.m MISCELLANEOUS; I.
Computing Methodologies; I.5 PATTERN RECOGNITION; C.
Computer Systems Organization; C.3 SPECIAL-PURPOSE AND
APPLICATION-BASED SYSTEMS; C. Computer Systems
Organization; C.5 COMPUTER SYSTEM IMPLEMENTATION",
}
@Book{Startz:1988:IPC,
author = "Richard Startz",
title = "8087\slash 80287\slash 80387 for the {IBM PC} and
Compatibles: Applications and Programming with
{Intel}'s Math Coprocessors",
publisher = pub-BRADY,
address = pub-BRADY:adr,
edition = "Third",
pages = "xviii + 296",
year = "1988",
ISBN = "0-13-246604-X",
ISBN-13 = "978-0-13-246604-2",
LCCN = "QA76.8.I2923 S79 1988",
bibdate = "Wed Sep 14 20:23:49 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Stasinski:1988:MRE,
author = "R. Stasinski and E. Lukasik",
booktitle = "Acoustics, Speech, and Signal Processing, 1988.
{ICASSP-88., 1988} International Conference on. 11--14
April 1988",
title = "Minimization of rounding errors in {WFTA} programs",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1423--1426",
year = "1988",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Two ideas linked with high-precision computation of
WFTAs (Winograd-Fourier transform algorithm) using
fixed-point arithmetic are analyzed. Use of the best,
optimized small-N DFT (discrete Fourier transform)
modules is considered. The sizes \ldots{}",
}
@Article{Stouraitis:1988:FPL,
author = "Thanos Stouraitis and Fred J. Taylor",
title = "Floating-point to logarithmic encoder error analysis",
journal = j-IEEE-TRANS-COMPUT,
volume = "37",
number = "7",
pages = "858--863",
month = jul,
year = "1988",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.2232",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Ohio State University of University, Columbus;
University of Florida, Gainesville",
ajournal = "IEEE Trans. Comput.",
bibno = "48698",
catcode = "F.2.1; G.m; C.1.m",
CRclass = "F.2.1 Numerical Algorithms and Problems; F.2.1
Number-theoretic computations; C.1.m Miscellaneous",
descriptor = "Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Number-theoretic computations; Mathematics of
Computing, MISCELLANEOUS; Computer Systems
Organization, PROCESSOR ARCHITECTURES, Miscellaneous",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
genterm = "DESIGN; THEORY; VERIFICATION",
guideno = "1988-08687",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
journalabbrev = "IEEE Trans. Comput.",
subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.m MISCELLANEOUS; C. Computer Systems Organization;
C.1 PROCESSOR ARCHITECTURES",
summary = "The logarithmic number (LNS), which supports
high-speed, high-precision arithmetic, is envisioned as
a possible arithmetic coprocessor attachment to a
floating-point (FLP) processor. An error analysis of an
FLP-to-LNS encoder is presented. Analytic \ldots{}",
}
@Manual{Sun:1988:PG,
title = "Programmer's guides",
publisher = "Sun Microsystems",
address = "Mountain View, CA, USA",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "12 volumes in 1 case.",
acknowledgement = ack-nhfb,
keywords = "Operating systems (Computers); Sun computers ---
Programming.; SunOS (Computer operating system)",
remark = "Title from container. Contents sheet has title: 4.0
programmer's guides minibox. ``Revision A, of 9 May
1988.''--Contents. ``825-1050-10.''--Contents. C
programmer's guide --- Assembly language reference for
the Sun-2 and Sun-3 --- Programming utilities and
libraries --- Debugging tools --- Network programming
--- Writing device drivers --- Floating point
programmer's guide --- SunView 1 programmer's guide ---
SunView 1 system programmer's guide --- Pixrect
reference manual --- SunCGI reference manual ---
SunCore reference manual.",
}
@Article{Taylor:1988:BLN,
author = "F. J. Taylor and R. Gill and J. Joseph and J. Radke",
title = "A 20 Bit Logarithmic Number System Processor",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-37",
number = "2",
pages = "190--199",
year = "1988",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.2148",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jun 24 19:49:19 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The architecture and performance of a 20-bit
arithmetic processor based on the logarithmic number
system (LNS) is described. The processor performed LNS
multiplication and division rapidly and with a low
hardware complexity. Addition and subtraction in the
LNS require the support of a table lookup unit. A
scheme is proposed to minimize this complexity using a
partitioned memory (ROM) and a PLA (programmable logic
array). For performance evaluation, the target
technology is integrated Schottky logic. The processor
is shown to compare well with, if not to outperform,
existing floating point (FLP) processors of equivalent
range and precision. The speed-power-product ratio of
an equivalent FLP processor, compared with that of the
LNS processor, is reported to be 20 to 1 in the case of
the square and square-root operation and 1 to 1 in the
case of addition and subtraction. For multiplication
and division, this ratio is about 5 to 1.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Misc{Taylor:1988:HFP,
author = "Fred J. Taylor",
title = "Hybrid floating point\slash logarithmic number system
arithmetic processor",
howpublished = "United States Patent 4,720,809",
day = "19",
month = jan,
year = "1988",
bibdate = "Tue Jan 08 21:48:35 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.freepatentsonline.com/4720809.html",
abstract = "A hybrid arithmetic processor which combines
attributes of conventional floating point (F.P.)
arithmetic with logarithmic number system (LNS)
arithmetic. The arithmetic processor includes an input
section (forward code converter) for converting input
operands in F.P. format to intermediate operands in LNS
format, an LNS arithmetic section for performing an
arithmetic operation on the LNS intermediate operands
and providing an intermediate output in LNS format, and
an output section (inverse code converter) for
converting the LNS intermediate output to an output in
F.P. format. Significantly, output is provided in
normalized floating point format but without the need
for a time-consuming exponent alignment operation.
Arithmetic operations, including addition and
multiplication, are accomplished at a high speed, which
speed moreover is constant and independent of the data.
An efficient accumulator structure and the structure of
an ultra-fast numeric processor are disclosed.",
acknowledgement = ack-nhfb,
}
@InProceedings{Thistle:1988:PAH,
author = "M. R. Thistle and B. J. Smith",
title = "A processor architecture for {Horizon}",
crossref = "IEEE:1988:PSN",
volume = "1",
pages = "35--41",
year = "1988",
bibdate = "Thu Apr 16 07:55:03 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5220 (Computer architecture); C5440 (Multiprocessor
systems and techniques)",
corpsource = "Supercomput. Res. Center, Lanham, MD, USA",
keywords = "floating-point operations; Horizon; horizontal
instruction set; parallel architectures; parallel
machines; processor architecture; scalable
shared-memory MIMD computer; scalable shared-memory
multiple-instruction-stream-multiple-data-stream
computer; scalar processors; three-dimensional
nearest-neighbor network",
sponsororg = "IEEE; ACM",
treatment = "P Practical",
}
@TechReport{Tsao:1988:AST,
author = "Nai-kuan Tsao",
title = "On the accuracy of solving triangular systems in
parallel",
institution = "National Aeronautics and Space Administration; For
sale by the National Technical Information Service",
address = "Washington, DC, USA",
pages = "????",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "NASA technical memorandum; 101384 ICOMP; 88-19",
acknowledgement = ack-nhfb,
govtdocnumber = "NAS 1.15:101384 0830-D (MF)",
keywords = "Algorithms.; Error analysis.; Errors.; Floating point
arithmetic.",
remark = "Distributed to depository libraries in microfiche.
Microfiche. [Washington, D.C.: National Aeronautics and
Space Administration, 1989] 1 microfiche.",
}
@Article{Venkaiah:1988:CMS,
author = "V. Ch Venkaiah and S. K. Sen",
title = "Computing a matrix symmetrizer exactly using modified
multiple modulus residue arithmetic",
journal = j-J-COMPUT-APPL-MATH,
volume = "21",
number = "1",
pages = "27--40",
month = jan,
year = "1988",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:20:37 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042788903858",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Voelzke:1988:FSAa,
author = "H. V{\"o}lzke",
title = "{Flie{\ss}komma-Arithmetik und
IEEE-Spez\-i\-fi\-ka\-tion\-en. Teil 1: Standards und
Strukturen} \toenglish {Floating-point Arithmetic and
its IEEE Specification. Part 1: Standards and
Structures} \endtoenglish",
journal = j-MC,
volume = "10",
pages = "123--129",
year = "1988",
ISSN = "0720-4442, 0941-777x , 0943-5409",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "MC: Die Mikrocomputer-Zeitschrift",
}
@Article{Voelzke:1988:FSAb,
author = "H. V{\"o}lzke",
title = "{Flie{\ss}komma-Arithmetik und
IEEE-Spez\-i\-fi\-ka\-tion\-en. Teil 2: Entwurf eines
Flie{\ss}kommapakets} \toenglish {Floating-point
Arithmetic and its IEEE Specification. Part 2: Design
of a Floating-Point Package} \endtoenglish",
journal = j-MC,
volume = "11",
pages = "78--95",
year = "1988",
ISSN = "0720-4442, 0941-777x , 0943-5409",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "MC: Die Mikrocomputer-Zeitschrift",
}
@Article{Voelzke:1988:FSAc,
author = "H. V{\"o}lzke",
title = "{Flie{\ss}komma-Arithmetik und
IEEE-Spez\-i\-fi\-ka\-tion\-en. Teil 3: Die verwendeten
Algorithmen} \toenglish {Floating-point Arithmetic and
its IEEE Specification. Part 3: The Algorithms Used}
\endtoenglish",
journal = j-MC,
volume = "12",
pages = "95--108",
year = "1988",
ISSN = "0720-4442, 0941-777x , 0943-5409",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "MC: Die Mikrocomputer-Zeitschrift",
}
@Article{Weyland:1988:LCS,
author = "Nicholas J. Weyland and Edward A. Puckett",
title = "Lossless coding for sources of floating-point and
fixed-precision numbers",
journal = j-IEEE-TRANS-INF-THEORY,
volume = "34",
number = "4",
pages = "882--888",
month = jul,
year = "1988",
CODEN = "IETTAW",
DOI = "https://doi.org/10.1109/18.9791",
ISSN = "0018-9448 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
MRclass = "94A29",
MRnumber = "89i:94023",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Information Theory",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
summary = "A procedure for constructing binary models for sources
of floating-point and fixed-precision numbers is given
and used together with the minimum description length
principle to find optimal models. These models are used
to design noiseless source code \ldots{}",
}
@Article{Wilson:1988:FPS,
author = "Pete Wilson",
title = "Floating-Point Survival Kit",
journal = j-BYTE,
volume = "13",
number = "3",
pages = "217--217",
month = mar,
year = "1988",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Oct 31 18:51:38 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "BYTE Magazine",
}
@Article{Wilson:1988:NDP,
author = "Fred Wilson",
title = "A Note on Division of Positive Integers",
journal = j-SIGMICRO,
volume = "19",
number = "1--2",
pages = "4--4",
month = jun,
year = "1988",
CODEN = "SIGMDJ",
DOI = "https://doi.org/10.1145/62197.1096672",
ISSN = "0163-5751, 1050-916X",
ISSN-L = "0163-5751",
bibdate = "Fri Apr 16 10:27:39 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
URL = "https://dl.acm.org/doi/10.1145/62197.1096672",
abstract = "At the risk of flaunting a marginal grasp of the
obvious I would like to make a few observations on the
division of fixed point numbers.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMICRO Newsletter",
journal-URL = "https://dl.acm.org/loi/sigmicro",
}
@Article{Wilson:1988:NFP,
author = "R. Wilson",
title = "Newest floating-point processors blur architectural
distinctions",
journal = j-COMP-DESIGN,
volume = "27",
number = "8",
pages = "32--43",
day = "15",
month = apr,
year = "1988",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bibno = "44373",
catcode = "B.7.1; C.1.1; C.1.1",
CRclass = "B.7.1 Types and Design Styles; B.7.1 Memory
technologies; C.1.1 Single Data Stream Architectures;
C.1.1 RISC; C.1.1 Single Data Stream Architectures;
C.1.1 CISC",
descriptor = "Hardware, INTEGRATED CIRCUITS, Types and Design
Styles, Memory technologies; Computer Systems
Organization, PROCESSOR ARCHITECTURES, Single Data
Stream Architectures, RISC; Computer Systems
Organization, PROCESSOR ARCHITECTURES, Single Data
Stream Architectures, CISC",
fjournal = "Computer Design",
genterm = "PERFORMANCE; DESIGN",
guideno = "1988-05955",
journalabbrev = "Comput. Des.",
subject = "B. Hardware; B.7 INTEGRATED CIRCUITS; C. Computer
Systems Organization; C.1 PROCESSOR ARCHITECTURES; C.
Computer Systems Organization; C.1 PROCESSOR
ARCHITECTURES",
}
@Article{Wollard:1988:TSS,
author = "K. Wollard",
title = "Technology '88: Solid state",
journal = j-IEEE-SPECTRUM,
volume = "25",
number = "1",
pages = "44--46",
month = jan,
year = "1988",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/6.4483",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Mon Jan 20 06:41:24 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "16 Mbit; 4 Mbit; application-specific ICs; Consumer
electronics; digital integrated circuits; Electronics
industry; EPROM; floating-point digital signal
processors; GaAs-Si; Government; high-density
packaging; integrated circuit technology; Japan;
Manufacturing industries; Microprocessors; Production;
Semiconductor device manufacture; solid state; Solid
state circuits; Trade agreements; US",
}
@Book{Young:1988:SNMa,
author = "David M. Young and Robert Todd Gregory",
title = "A Survey of Numerical Mathematics",
volume = "I",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "x + 492 + A22 + B16 + I18",
year = "1988",
ISBN = "0-486-65691-8",
ISBN-13 = "978-0-486-65691-5",
LCCN = "QA297.Y63 1972",
MRclass = "65-02",
MRnumber = "92b:65005b",
bibdate = "Wed Jan 17 10:30:33 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Corrected reprint of the 1973 original.",
URL = "http://www.zentralblatt-math.org/zmath/en/search/?an=0732.65002",
ZMnumber = "0732.65002",
acknowledgement = ack-nhfb,
tableofcontents = "1: Numerical Analysis as a Subject Area \\
1.1 Introduction \\
1.2 Some pitfalls in computation \\
1.3 Mathematical and computer aspects of an algorithm
\\
1.4 Numerical instability of algorithms and
ill-conditioned problems \\
1.5 Typical problems of interest to the numerical
analyst \\
1.6 Iterative methods \\
2: Elementary Operations with Automatic Digital
Computers \\
2.1 Introduction \\
2.2 Binary arithmetic \\
2.3 Conversion from base $D$ to base $B$ representation
\\
2.4 Representation of integers on a binary computer \\
2.5 Floating-point representations \\
2.6 Computer-representable numbers \\
2.7 Floating-point arithmetic operations \\
2.8 Fortran analysis of a floating-point number \\
2.9 Calculation of elementary functions \\
3: Surveillance of Number Ranges \\
3.1 Introduction \\
3.2 Allowable number ranges \\
3.3 Basic real arithmetic operations \\
3.4 The quadratic equation \\
3.5 Complex arithmetic operations \\
4: Solution of Equations \\
4.1 Introduction \\
4.2 Attainable accuracy \\
4.3 Graphical methods \\
4.4 The method of bisection \\
4.5 The method of false position \\
4.6 The secant method \\
4.7 General properties of iterative methods \\
4.8 Generation of iterative methods \\
4.9 The Newton method \\
4.10 Muller's method \\
4.11 Orders of convergence of iterative methods \\
4.12 Acceleration of the convergence \\
4.13 Systems of nonlinear equations \\
5: Roots of Polynomial Equations \\
5.1 Introduction \\
5.2 General properties of polynomials \\
5.3 The Newton method and related methods \\
5.4 Muller's method and Cauchy's method \\
5.5 Location of the roots \\
5.6 Root acceptance and refinement \\
5.7 Matrix related methods: the modified Bernoulli
method \\
5.8 Matrix related methods: the IP method \\
5.9 Polyalgorithms \\
5.10 Other methods \\
6: Interpolation and Approximation \\
6.1 Introduction \\
6.2 Linear interpolation \\
6.3 Convergence and accuracy of linear interpolation
\\
6.4 Lagrangian interpolation \\
6.5 Convergence and accuracy of Lagrangian
interpolation \\
6.6 Interpolation with equal intervals \\
6.7 Hermite interpolation \\
6.8 Limitations on polynomial interpolation: smooth
interpolation \\
6.9 Inverse interpolation \\
6.10 Approximation by polynomials \\
6.11 Least squares approximation by polynomials \\
6.12 Rational approximation \\
6.13 Trigonometric interpolation and approximation \\
6.14 Interpolation in two variables \\
7: Numerical Differentiation and Quadrature \\
7.1 Introduction \\
7.2 The method of undetermined weights \\
7.3 Numerical differentiation \\
7.4 Numerical quadrature --- equal intervals \\
7.5 The Euler--MacLaurin formula \\
7.6 Romberg integration \\
7.7 Error determination \\
7.8 Numerical quadrature --- unequal intervals \\
8: Ordinary Differential Equations \\
8.1 Introduction \\
8.2 Existence and uniqueness \\
8.3 Analytic methods \\
8.4 Integral equation formulation --- the Picard method
of successive approximations \\
8.5 The Euler method \\
8.6 Methods based on numerical quadrature \\
8.7 Error estimation for predictor-corrector methods
\\
8.8 A numerical example \\
8.9 Runge--Kutta methods \\
8.10 Methods based on numerical differentiation \\
8.11 Higher-order equations and systems of first-order
equations \\
8.12 The use of high-speed computers \\
Appendix A \\
Appendix B \\
Appendix C \\
Bibliography \\
Index",
}
@InProceedings{Yuen:1988:IFP,
author = "A. K. Yuen",
title = "{Intel}'s floating-point processors",
crossref = "Electro:1988:ECR",
pages = "48/5/1--7",
year = "1988",
bibdate = "Wed Sep 7 22:32:00 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Zhou:1988:NBS,
author = "B. B. Zhou",
title = "A new bit-serial systolic multiplier over {$ \mathrm
{GF}(2^m) $}",
journal = j-IEEE-TRANS-COMPUT,
volume = "37",
number = "6",
pages = "749--751",
month = jun,
year = "1988",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.2216",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 08:33:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2216",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Zoicas:1988:PBG,
author = "A. Zoicas and K. Grohe and C. Kellerhoff",
title = "{PC} based general-purpose floating-point {DSP $ \mu
$PD77230} board with various analog front end options
and application software packages",
crossref = "Lacoume:1988:SPI",
pages = "1233--1236 vol.3",
year = "1988",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "3 vol.",
abstract = "The EBIBM-77230 FFT is a software and hardware DSP
engineering environment incorporated in a PC in the
form of a plug-in board. It offers no downgrade from
the ideal in terms of its processing power, which
amounts of 27 MFLOPs, its open architecture, standard
cross-software support and interfaces to popular
commercial DSP packages. A variety of analog front-end
options and supervisor modules (for stand-alone
operation) can be hooked onto the board itself thereby
opening its application to most DSP areas. A math
library, which features interfaces to most high level
languages (C, Fortran, Pascal, Basic), brings
workstation computational power to the PC. The
EBIBM-77230 FFT bridges the gap between fast high
precision number crunching and an accessible
user-friendly environment. The turn-around time from an
idea to its real-time execution is thus minimised and
cost-wise it is an economic solution in relation to
most DSP working environments.",
acknowledgement = ack-nhfb,
affiliation = "NEC Electron. GmbH, Dusseldorf, West Germany",
classification = "B1265F (Microprocessors and microcomputers); B6140
(Signal processing and detection); C5130
(Microprocessor chips); C5150 (Other circuits for
digital computers); C7410F (Communications)",
keywords = "27 MFLOPS; Analog front end; Application software
packages; Basic; C; DSP engineering environment;
EBIBM-77230 FFT; Fortran; General purpose floating
point DSP; High level languages; Interfaces; Math
library; Microprocessor D77230 board; Open
architecture; Pascal; PC; Personal computer; Plug-in
board; Supervisor modules",
numericalindex = "Computer speed 2.7E+07 FLOPS",
thesaurus = "Add-on boards; Computerised signal processing;
Microcomputer applications; Microprocessor chips;
Software packages",
}
@InProceedings{Ahmed:1989:EEF,
author = "H. M. Ahmed",
title = "Efficient Elementary Function Generation with
Multipliers",
crossref = "Ercegovac:1989:PSC",
pages = "52--59",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Ahmed.pdf",
acknowledgement = ack-nhfb # " and " # ack-nj,
keywords = "ARITH-9",
}
@Article{Amit:1989:MRE,
author = "G. Amit and U. Shaked",
title = "Minimization of roundoff errors in digital
realizations of {Kalman} filters",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "37",
number = "12",
pages = "1980--1982",
month = dec,
year = "1989",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "A comparison between D. Williamson's method (IEEE
Trans. Autom. Contr., vol.AC-30, p.930-9, 1985) and the
0-1 method for the design of the digital Kalman filter
is made. The 0-1 method is shown to be much better than
Williamson's method and the \ldots{}",
}
@InProceedings{Arison:1989:SAN,
author = "D. Arison and A. Genusov and L. Gerzberg",
title = "System applications of a new 32-bit floating-point
{DSP} processor",
crossref = "Chen:1989:TSA",
pages = "890--897 vol.2",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors present the ZR34325, a novel
floating-point vector signal processor in the context
of system applications. The ZR34325 represents the
first full IEEE floating-point integrated array
processor on silicon, supplemented with the pertinent
scalar and control flow capabilities. The ZR34325
directly executes embedded DSP (digital signal
processing) and array processing primitives on
multidimensional arrays. Furthermore, an integrated
development environment which includes a system
software simulation, vectorized and parametric DSP,
arithmetic and matrix library, C-based
assembler/linker, and hardware development tools
facilities top-down complete application development.
The ZR34325 enables very efficient multiprocessor
multitasking schemes for tasks where execution time is
either data independent or data dependent. The authors
show the top-down integrated design methodology via
sample signal/image processing application examples
such as Kalman filtering, spectral analysis, and
constant false alarm rate processing for radar
applications as well as two-dimensional image
filtering.",
acknowledgement = ack-nhfb,
affiliation = "Zoran Corp., Santa Clara, CA, USA",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5260 (Digital signal
processing)",
keywords = "32 Bit; Arithmetic library; C-based assembler/linker;
Digital signal processing; False alarm rate processing;
Floating-point DSP processor; Image filtering; Kalman
filtering; Matrix library; Multidimensional arrays;
Radar; Spectral analysis; Vector signal processor;
ZR34325",
numericalindex = "Word length 3.2E+01 bit",
thesaurus = "Computerised signal processing; Digital signal
processing chips; Parallel processing",
}
@InProceedings{Arnold:1989:RLN,
author = "M. G. Arnold and T. A. Bailey and J. R. Cowles and J.
J. Cupal",
title = "Redundant logarithmic number systems",
crossref = "Ercegovac:1989:PSC",
pages = "144--151",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Arnold.pdf",
abstract = "A new number system that offers advantages over
conventional floating-point and sign/logarithm number
systems is described. Called redundant logarithmic
arithmetic, it relies, like conventional logarithmic
arithmetic, on table lookups to make the arithmetic
unit simpler than an equivalent floating-point unit.
The cost of 32-b subtraction in a redundant logarithmic
number system is lower than that of previously
published logarithmic subtraction methods. Another
advantage of a redundant logarithmic number system is
that a single arithmetic unit can use the same hardware
to add, subtract, or multiply in similar times. (25
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Wyoming University, Laramie, WY, USA",
classification = "C5230 (Digital arithmetic methods)",
keywords = "Add; ARITH-9; Floating-point; Multiply; Number system;
Redundant logarithmic arithmetic; Sign/logarithm number
systems; Subtract; Table lookups",
thesaurus = "Digital arithmetic; Table lookup",
}
@Article{Ashton:1989:AFP,
author = "C. Ashton",
title = "The {Am29C327} floating point processor",
journal = "Electronic Product Design",
volume = "10",
number = "3",
pages = "51--59",
month = mar,
year = "1989",
bibdate = "Wed Sep 7 22:32:01 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Azmi:1989:TFP,
author = "A. M. Azmi and F. Lombardi",
title = "On a tapered floating point system",
crossref = "Ercegovac:1989:PSC",
pages = "2--9",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Azmi.pdf",
abstract = "R. Morris (see IEEE Trans. Comput., vol. TC-20, p.
1578--1579, 1971), suggested adding an extra field to
the fixed floating point system, so that exponents can
be stored more efficiently. The exponents are stored in
the smallest possible space, passing the extra bits to
the mantissa. The extra field is used to monitor the
current length of the exponent. The gain in precision
and/or exponent range outweighs the overhead of the
extra field and the processing speed. The authors
provide implementation details, error analysis, and
some future research ideas. Simulation results are
provided for comparison purposes.",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. and Comput. Eng., Colorado
University, Boulder, CO, USA",
classification = "C5230 (Digital arithmetic methods)",
keywords = "ARITH-9; Error analysis; Exponents; Tapered floating
point system",
thesaurus = "Digital arithmetic",
}
@Article{Bailey:1989:FPA,
author = "D. H. Bailey and H. D. Simon and J. T. Barton",
title = "Floating Point Arithmetic in Future Supercomputers",
journal = j-IJSA,
volume = "3",
number = "3",
pages = "86--90",
month = "Fall",
year = "1989",
CODEN = "IJSAE9",
ISSN = "0890-2720",
bibdate = "Thu Aug 22 17:56:36 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
UnCover library database",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Supercomputer Applications",
journal-URL = "http://hpc.sagepub.com/content/by/year",
}
@Article{Baran:1989:MST,
author = "N. Baran",
title = "The {Mac SE} takes off",
journal = j-BYTE,
volume = "14",
number = "2",
pages = "113--116",
month = feb,
year = "1989",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 12 17:54:09 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5430 (Microcomputers)",
fjournal = "BYTE Magazine",
keywords = "16 MHz; 2 MBytes; 4 MBytes; 68030 CPU; 68882
Floating-point unit; Apple Macintosh SE/30; Built-in
memory management unit; FPU; Logic board; Mac SE/30;
MMU; Motorola 68030 processor; SIMM-mounted ROMs;
Single in-line memory module RAM chips",
numericalindex = "Frequency 1.6E+07 Hz; Memory size 2.1E+06 Byte;
Memory size 4.2E+06 Byte",
thesaurus = "Apple computers; Microcomputers",
}
@Article{Bardin:1989:IUI,
author = "B. Bardin and C. Colket and D. Smith",
title = "Implementation of unsigned integers in {Ada}",
journal = j-SIGADA-LETTERS,
volume = "9",
number = "1",
pages = "47--70",
month = jan # "\slash " # feb,
year = "1989",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Thu Mar 20 07:41:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
acknowledgement = ack-nhfb,
classcodes = "C6140D (High level languages); C6130 (Data handling
techniques)",
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "Ada; address arithmetic; digital arithmetic; full
range; logical operations; modular arithmetic; numeric
literals; symbol manipulation; unsigned integers",
treatment = "P Practical",
}
@Article{Barrett:1989:FMA,
author = "Geoff Barrett",
title = "Formal methods applied to a floating-point number
system",
journal = j-IEEE-TRANS-SOFTW-ENG,
volume = "15",
number = "5",
pages = "611--621",
month = may,
year = "1989",
CODEN = "IESEDJ",
DOI = "https://doi.org/10.1109/32.24710",
ISSN = "0098-5589 (print), 1939-3520 (electronic)",
ISSN-L = "0098-5589",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A formalization of the IEEE standard for binary
floating-point arithmetic (ANSI/IEEE Std. 754-1985) is
presented in the set-theoretic specification language
Z. The formal specification is refined into four
sequential components, which unpack the operands,
perform the arithmetic, and pack and round the result.
This refinement follows proven rules and so
demonstrates a mathematically rigorous method of
program development. In the course of the proofs,
useful internal representations of floating-point
numbers are specified. The procedures presented form
the basis for the floating-point unit of the Inmos IMS
T800 transputer.",
acknowledgement = ack-nhfb,
affiliation = "Oxford University, Oxford, UK",
bibno = "65476",
catcode = "F.3.1; C.5.3; D.2.1; D.2.0; B.2.0; B.5.1",
content = "It is paradoxical that no programming language can be
completely defined unless it has a formally defined
syntax, yet at the same time, languages have informal
semantic descriptions. This is most evident in
arithmetic, in which the closest thing to a formal
description lies in the IEEE standard for binary
floating point arithmetic adopted by ANSI in 1985. The
standard is written in natural language, with the
attendant possibility of ambiguity and inconsistency.
The author of this paper has given a formal version of
the standard in the Z specification language, which can
be thought of as a structured version of predicate
logic. After giving a cogent argument for the use of
formal methods in standardization, the author presents
a stage-by-stage development of the formal description
of the standard; while doing this, he stresses the
modularity of the description, as exemplified by the
separation of normal and exceptional conditions.\par
As he introduces the concepts of Z, the author gives
brief explanations of the notation, but for a beginner
in the field, the paper is best read in conjunction
with the original standard and a description of
Z.\par
A very powerful argument for the formal approach lies
in the specification's use. The INMOS T800 floating
point unit was developed by means of a series of
refinements of the formal specification; the",
CRclass = "F.3.1 Specifying and Verifying and Reasoning about
Programs; F.3.1 Specification techniques; C.5.3
Microcomputers; C.5.3 INMOS Transputer; D.2.1
Requirements/Specifications; D.2.1 Z; D.2.0 General;
D.2.0 Standards; B.2.0 General; B.5.1 Design; B.5.1
Arithmetic and logic units",
CRnumber = "9004-0316",
descriptor = "Theory of Computation, LOGICS AND MEANINGS OF
PROGRAMS, Specifying and Verifying and Reasoning about
Programs, Specification techniques; Computer Systems
Organization, COMPUTER SYSTEM IMPLEMENTATION,
Microcomputers, INMOS Transputer; Software, SOFTWARE
ENGINEERING, Requirements/Specifications, Z; Software,
SOFTWARE ENGINEERING, General, Standards; Hardware,
ARITHMETIC AND LOGIC STRUCTURES, General; Hardware,
REGISTER-TRANSFER-LEVEL IMPLEMENTATION, Design,
Arithmetic and logic units",
fjournal = "IEEE Transactions on Software Engineering",
genterm = "ALGORITHMS; DOCUMENTATION; LANGUAGES; STANDARDIZATION;
THEORY",
guideno = "1989-06803",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=32",
journalabbrev = "IEEE Trans. Softw. Eng.",
reviewer = "Simon Thompson",
subject = "F. Theory of Computation; F.3 LOGICS AND MEANINGS OF
PROGRAMS; C. Computer Systems Organization; C.5
COMPUTER SYSTEM IMPLEMENTATION; D. Software; D.2
SOFTWARE ENGINEERING; D. Software; D.2 SOFTWARE
ENGINEERING; B. Hardware; B.2 ARITHMETIC AND LOGIC
STRUCTURES; B. Hardware; B.5 REGISTER-TRANSFER-LEVEL
IMPLEMENTATION",
}
@InProceedings{Bedard:1989:WFD,
author = "N. Bedard and M. Birman and G. Chu and L. Hu and C. M.
Lim and J. McLeod and L. Torban and F. Ware",
title = "The {Weitek} 64-bit floating-point datapath unit",
crossref = "Chen:1989:TSA",
pages = "898--902 (vol. 2)",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors describe the WTL 3165 and WTL 3364,
jointly referred to as the WTL 3X64, which are each
64-bit floating-point data path units designed for
high-speed operation in pipelined environment while
making possible full compliance with the IEEE standard
for binary floating-point arithmetic. It also provides
full interruptibility, even in a pipelined environment.
The architecture and performance of the 3X64 are
described, and a detailed block diagram is presented.",
acknowledgement = ack-nhfb,
affiliation = "Weitek Corp., Sunnyvale, CA, USA",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5220 (Computer architecture); C5230 (Digital
arithmetic methods); C5260 (Digital signal
processing)",
keywords = "64 Bit; Architecture; Binary floating-point
arithmetic; Computerised signal processing; DSP chip;
Floating-point data path units; Interruptibility;
Pipelined environment; Weitek; WTL 3165; WTL 3364; WTL
3X64",
numericalindex = "Word length 6.4E+01 bit",
thesaurus = "CMOS integrated circuits; Computerised signal
processing; Digital arithmetic; Digital signal
processing chips; Parallel architectures; Pipeline
processing",
}
@Book{Beliankov:1989:NPO,
author = "A. Ia Beliankov",
title = "Nekotorye primeneniia otsenochnoi (``gruboi'')
arifmetiki",
publisher = "VTS AN SSSR",
address = "Moskva, Russia",
pages = "35",
year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Soobshcheniia po vychislitelnoi matematike",
acknowledgement = ack-nhfb,
keywords = "Algebras, Linear.; Computer arithmetic.;
Floating-point arithmetic.",
remark = "At head of title: Akademiia nauk SSSR. Vychislitelnyi
tsentr.",
}
@InProceedings{Benschneider:1989:MUP,
author = "B. J. Benschneider and W. J. Bowhill and E. M. Cooper
and M. N. Gavrielov and P. E. Gronowski and V. K.
Maheshwari and V. Peng and J. D. Pickholtz and S.
Samudrala",
title = "A 50 {MHz} Uniformly Pipelined 64b Floating-Point
Arithmetic Processor",
crossref = "Wuorinen:1989:DTP",
pages = "50--51, 288",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A description is given of a uniformly pipelined,
50-MHz, 64-b floating-point arithmetic processor
implemented in a 1.5- mu m (drawn) CMOS technology
which performs single- and double-precision
floating-point operations and integer multiplication as
defined by a superminicomputer architecture standard.
The chip is composed of an interface section and a
five-segment execution core. The core insists of a
divider, bypassed in all instruction except division,
and four fully pipelined stages that are uniformly
utilized in the execution of all instructions. The
performance is summarized. First pass silicon has been
functionally verified at 50 MHz with a set of over one
million vectors.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Digital Equipment Corp., Hudson, MA, USA",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5220 (Computer architecture); C5230 (Digital
arithmetic methods)",
confdate = "15-17 Feb. 1989",
conflocation = "New York, NY, USA",
confsponsor = "IEEE; University of Pennsylvania",
keywords = "1.5 Micron; 50 MHz; 64 Bit; CMOS technology; Divider;
Double-precision floating-point operations;
Five-segment execution core; Floating-point arithmetic
processor; Fully pipelined stages; Integer
multiplication; Interface section; Single-precision
floating point; Superminicomputer architecture
standard",
numericalindex = "Frequency 5.0E+07 Hz; Word length 6.4E+01 bit; Size
1.5E-06 m",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Microprocessor chips; Pipeline processing",
}
@Article{Benschneider:1989:PMC,
author = "Bradley J. Benschneider and William J. Bowhill and
Elizabeth M. Cooper and Moshe N. Gavrielov and Paul E.
Gronowski and Vijay K. Maheshwari and Victor Peng and
Jeffrey D. Pickholtz and Sridhar Samudrala",
title = "A pipelined {50-MHz} {CMOS} 64-bit floating-point
arithmetic processor",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "24",
number = "5",
pages = "1317--1323",
month = oct,
year = "1989",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A 135K transistor, uniformly pipelined 50-MHz CMOS
64-bit floating-point arithmetic processor chip is
described. The execution unit is capable of sustaining
pipelined performance of one 32-bit or 64-bit result
every 20 ns for all operations except double-precision
multiply (40 ns) and divide. The chip employs an
exponent difference prediction scheme and a unified
leading-one and sticky-bit computation logic for the
addition and subtraction operations. A hardware
multiplier using a radix-8 modified Booth algorithm and
a divider using a radix-2 SRT algorithm are employed.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Digital Equipment Corp., Hudson, MA, USA",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5230 (Digital arithmetic methods)",
fjournal = "IEEE Journal of Solid-State Circuits",
keywords = "20 Ns; 40 Ns; 50 MHz; 64 Bit; Addition; CMOS; Divider;
Execution unit; Exponent difference prediction scheme;
Floating-point arithmetic processor; Hardware
multiplier; Microprocessor; Processor chip; Radix-2 SRT
algorithm; Radix-8 modified Booth algorithm; Sticky-bit
computation logic; Subtraction; Unified leading-one;
Uniformly pipelined",
numericalindex = "Word length 6.4E+01 bit; Frequency 5.0E+07 Hz; Time
2.0E-08 s; Time 4.0E-08 s",
summary = "A 135K transistor, uniformly pipelined 50-MHz CMOS
64-bit floating-point arithmetic processor chip is
described. The execution unit is capable of sustaining
pipelined performance of one 32-bit or 64-bit result
every 20 ns for all operations except \ldots{}",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Microprocessor chips; Pipeline processing",
}
@Misc{Bleher:1989:MCA,
author = "J. Hartmut Bleher and Axel T. Gerlicher and Siegfried
M. Rump and Dieter K. Unkauf",
title = "Method and circuit arrangement for adding floating
point numbers",
howpublished = "US Patent 4866651",
day = "12",
month = sep,
year = "1989",
bibdate = "Mon Dec 29 16:18:28 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/4866651/fulltext.html",
abstract = "For successively adding a series of floating point
numbers, a floating point adder stage (FIG. 2) is used
which, in addition to the sum of two floating point
operands, emits the remainder, truncated from the
smaller operand, as a floating point number. For
obtaining an exact sum of the operands, these
remainders are summed in the form of intermediate sums.
A circuit arrangement for parallel operation comprises
series-connected floating point adder stages (FIG. 6),
the intermediate sum occurring at the output of each
stage and the intermediate remainder being buffered.
Remainders are in each case passed on to the next
stage, their value decreasing until they are zero. A
serially operating arrangement (FIG. 8) comprises a
single adder stage (30) and a register stack (34) for
buffering the intermediate sums and the final result. A
remainder occurring is stored in a remainder register
(32) at the output of the adder stage and added to the
intermediate sums until the remainder is zero.
Subsequently, a fresh operand is applied to the input
of the adder stage.",
acknowledgement = ack-nhfb,
}
@InProceedings{Boddie:1989:FDC,
author = "J. R. Boddie and R. N. Gadenz and C. J. Garen and J.
M. Huser and B. Ng and S. P. Pekarich",
title = "A 32-bit floating-point {DSP} with {C} compiler",
crossref = "Chen:1989:TSA",
pages = "880--884 vol.2",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A novel digital signal processor (the DSP32C) has been
developed which performs 32-bit floating point
operations at a rate of 25 MFLOPS (million
floating-point operations per second) and can be
programmed using a standard C compiler. The authors
present an overview of the architecture and instruction
set with emphasis on the enhancements over its
predecessor, the DSP32. The performance is expressed
with common signal processor benchmarks. The
application development environment is described which
highlights the C compiler and hardware development
system. Finally, an application example illustrates the
power and ease of this DSP.",
acknowledgement = ack-nhfb,
affiliation = "AT\&T Bell Lab., Holmdel, NJ, USA",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5260 (Digital signal processing); C6150C
(Compilers, interpreters and other processors)",
keywords = "25 MFLOPS; 32 Bit; Architecture; C compiler;
Computerised signal processing; DSP32C; Floating point
digital signal processor; Instruction set",
numericalindex = "Word length 3.2E+01 bit; Computer speed 2.5E+07
FLOPS",
thesaurus = "CMOS integrated circuits; Computerised signal
processing; Digital signal processing chips; Program
compilers",
}
@TechReport{Bohlender:1989:FST,
author = "Gerd Bohlender and Gudenberg, J. Wolff von (Jurgen
Wolff) and Willard L. Miranker",
title = "Floating-point systems for theorem proving",
type = "Research report",
number = "RC 15101 (\#67356)",
institution = "IBM T.J. Watson Research Center",
address = "Yorktown Heights, NY, USA",
pages = "14",
day = "2",
month = nov,
year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "There are a number of existing floating-point systems
(programming languages and libraries) which allow the
computer user to produce computation with guarantees.
These systems may be conveniently used as a component
in theorem proving. Following a brief description of
the methodology which underlies these systems, we
tabulate them, indicating some properties and noting
where they may be obtained for use. A brief appendix
supplies an introduction to the formalism of the
methodology.",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.",
}
@InProceedings{Brackert:1989:DLM,
author = "R. H. {Brackert, Jr.} and M. D. Ercegovac and A. N.
{Willson, Jr.}",
title = "Design of an on-line multiply-add module for recursive
digital filters",
crossref = "Ercegovac:1989:PSC",
pages = "34--41",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Brackert.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@Article{Brightman:1989:ASF,
author = "T. Brightman",
title = "Advancing the Standard in Floating-Point Performance",
journal = j-HIGH-PERFORM-SYST,
volume = "10",
number = "11",
pages = "59, 62--64",
month = nov,
year = "1989",
CODEN = "HPSYEA",
ISSN = "0279-2834",
bibdate = "Wed Dec 13 18:25:43 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Cyrix FasMath 83D87 is a floating-point
coprocessor chip that combines Intel 80387 socket and
software compatibility with the high performance of
Weitek's industry-leading coprocessor. The chip is a
VLSI CMOS integrated circuit built initially using
1.2-micron double-layer-metal, single-layer-polysilicon
process technology. It was designed to minimize
complications in the design of high-performance desktop
and laptop computer systems.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Cyrix Corp., Richardson, TX, USA",
chemicalindex = "Si/int Si/el",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips)",
fjournal = "High performance systems",
keywords = "Cyrix FasMath 83D87; Desktop computer systems;
Double-layer-metal; Floating-point coprocessor chip;
Intel 80387; Laptop computer systems; Math coprocessor;
Si; Single-layer-polysilicon process technology; Socket
compatibility; Software compatibility; VLSI CMOS
integrated circuit",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Microprocessor chips; Satellite computers; VLSI",
}
@Article{Buell:1989:MIA,
author = "D. Buell and R. Ward",
title = "A Multiprecise Integer Arithmetic Package",
journal = j-J-SUPERCOMPUTING,
volume = "3",
number = "??",
pages = "89--107",
month = "????",
year = "1989",
CODEN = "JOSUED",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Sun Sep 11 21:56:51 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
}
@InProceedings{Carter:1989:CHH,
author = "T. M. Carter",
title = "{Cascade}: hardware for high\slash variable precision
arithmetic",
crossref = "Ercegovac:1989:PSC",
pages = "184--191",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Carter.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@InProceedings{Chan:1989:ADC,
author = "P. K. Chan and M. D. F. Schlag",
title = "Analysis and design of {CMOS Manchester} adders with
variable carry-skip",
crossref = "Ercegovac:1989:PSC",
pages = "86--95",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Chan.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@InProceedings{Chen:1989:DRN,
author = "J. T. Chen and W. K. Jenkins",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, 8--11 May 1989",
title = "Design of a residue number system digital correlator
for real-time processing in ultrasonic blood flow
measurements",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "208--211",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1989.100328",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The design of a high-speed digital correlator for
implementing the real-time correlation function
required in an ultrasonic blood flowmeter is presented.
In order to achieve the necessary real-time processing
rates, a residue number system (RNS) \ldots{}",
}
@Article{Chen:1989:FCN,
author = "S. G. Chen and P. Y. Hsieh",
title = "Fast Computation of the {$N$ th} Root",
journal = j-COMPUT-MATH-APPL,
volume = "17",
number = "10",
pages = "1423--1427",
year = "1989",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Thu Sep 15 18:41:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
xxmonth = "(none)",
}
@Article{Chen:1989:FCTa,
author = "S.-G. Chen and P. Y. Hsieh",
title = "Fast computation of the {$N$}-th root",
journal = j-COMPUT-MATH-APPL,
volume = "17",
number = "10",
pages = "1423--1427",
month = "????",
year = "1989",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(89)90024-2",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:01:11 MST 2017",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122189900242",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
remark = "From the abstract: ``A new class of iterative methods
for computing a differentiable function is proposed,
which is based on Pad{\'e} approximation to Taylor's
series of the function. It leads to a faster algorithm
than Newton's method for $ x^{1 / N} $ and a different
interpretation of Newton's method.''",
}
@MastersThesis{Chinn:1989:DIA,
author = "Patty Chinn",
title = "The design, implementation, and applications of an
{ACT8837} floating point processor in an image
processing hardware subsystem",
type = "Thesis ({M.S.E.E.})",
school = "University of Washingto",
address = "Seattle, WA, USA",
pages = "vi + 45 + 1",
year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Image processing --- Digital techniques.",
}
@Book{Chow:1989:MXR,
editor = "Paul Chow",
title = "The {MIPS-X RISC} Microprocessor",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "xxiv + 231",
year = "1989",
ISBN = "0-7923-9045-8",
ISBN-13 = "978-0-7923-9045-9",
LCCN = "QA76.8.M524 M57 1989",
bibdate = "Tue Dec 14 23:27:43 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/microchip.bib",
series = "The Kluwer international series in engineering and
computer science",
ZMnumber = "0706.68010",
acknowledgement = ack-nhfb,
keywords = "MIPS-X (microprocessor); VLSI, computer architecture,
and digital signal processing SECS 81",
}
@InProceedings{Clenshaw:1989:LIA,
author = "C. W. Clenshaw and F. W. J. Olver and Peter R.
Turner",
title = "Level-index arithmetic: an introductory survey",
crossref = "Turner:1989:NAP",
pages = "95--168",
year = "1989",
DOI = "https://doi.org/10.1007/BFb0085718",
MRclass = "65Q05",
MRnumber = "1022263",
bibdate = "Tue Oct 09 09:58:20 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
author-dates = "Charles William Clenshaw (15 March 1926--23 September
2004); Frank William John Olver (15 December 1924--23
April 2013)",
}
@Article{Clenshaw:1989:RSU,
author = "C. W. Clenshaw and Peter R. Turner",
title = "Root squaring using level-index arithmetic",
journal = j-COMPUTING,
volume = "43",
number = "2",
pages = "171--185",
month = jun,
year = "1989",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/BF02241860",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G99 (65H05)",
MRnumber = "1 034 362",
bibdate = "Sun Nov 12 06:18:24 2023",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
author-dates = "Charles William Clenshaw (15 March 1926--23 September
2004)",
fjournal = "Computing. Archives for Scientific Computing",
journal-URL = "http://link.springer.com/journal/607",
subject-dates = "Frank William John Olver (15 December 1924--23 April
2013)",
xxtitle = "{Das Graeffe-Verfahren mit H{\"o}henindexarithmetik}",
}
@TechReport{Cody:1989:AXF,
author = "W. J. Cody",
title = "Algorithm {XXX}: Functions to Support the {IEEE}
Standard for Binary Floating-Point Arithmetic",
number = "MCS-P90-0789",
institution = "Mathematics and Computer Science Division, Argonne
National Laboratory",
address = "Argonne, IL, USA",
pages = "??",
month = jul,
year = "1989",
bibdate = "Thu Sep 01 10:38:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Dadda:1989:PC,
author = "Luigi Dadda",
title = "Polyphase convolvers",
crossref = "Ercegovac:1989:PSC",
pages = "78--85",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Dadda.pdf",
acknowledgement = ack-nhfb,
author-dates = "29 April 1923--26 October 2012",
keywords = "ARITH-9",
}
@Article{Dadda:1989:SIM,
author = "Luigi Dadda",
title = "On serial-input multipliers for two's complement
numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "38",
number = "9",
pages = "1341--1345",
month = sep,
year = "1989",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.29478",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 8 19:00:41 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=29478",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
author-dates = "29 April 1923--26 October 2012",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Dally:1989:MOF,
author = "W. J. Dally",
title = "Micro-optimization of floating-point operations",
journal = j-COMP-ARCH-NEWS,
volume = "17",
number = "2",
pages = "283--289",
month = apr,
year = "1989",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 12 09:40:39 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{DAngelo:1989:DEA,
author = "S. D'Angelo and G. R. Sechi",
title = "Definition of elementary arithmetic operations by
using {ACM}",
journal = j-SIGMICRO,
volume = "20",
number = "3",
pages = "160--162",
month = aug,
year = "1989",
CODEN = "SIGMDJ",
DOI = "https://doi.org/10.1145/75395.75414",
ISSN = "0163-5751, 1050-916X",
ISSN-L = "0163-5751",
bibdate = "Fri Apr 16 10:27:41 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
URL = "https://dl.acm.org/doi/10.1145/75395.75414",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMICRO Newsletter",
journal-URL = "https://dl.acm.org/loi/sigmicro",
}
@Misc{Darley:1989:FPI,
author = "Henry M. Darley and Michael C. Gill and Dale C. Earl
and Dinh T. Ngo and Paul C. Wang and Maria B. L. Hipona
and Jim Dodrill",
title = "Floating Point\slash Integer Processor with Divide and
Square Root Functions",
day = "31",
month = oct,
year = "1989",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "U.S. Patent No. 4,878,190 held by Texas Instruments.
Expired 2008-01-29.",
URL = "https://patentimages.storage.googleapis.com/bb/ca/c5/ed5ce0fc874200/US4878190.pdf",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@InProceedings{deLange:1989:DMA,
author = "A. A. J. de Lange and A. J. van der Hoeven and E. F.
Deprettere and P. Dewilde and J. Bu",
title = "The design of a 50 Mflop arithmetic chip for massively
parallel pipelined {DSP} algorithms: the floating point
pipeline {CORDIC} processor",
crossref = "IEE:1989:EEC",
pages = "410--414",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The paper describes a high performance VLSI CORDIC
arithmetic chip. It performs 15 10/sup 6/ rotations/sec
(50 Mflops) and can be applied as a processing element
in parallel/pipelined processor structures (systolic
and wavefront arrays) for real time/high speed signal
processing algorithms and matrix computation
applications. The authors present a novel optimized
(floating point) CORDIC algorithm, and architecture,
its performance and layout. Algorithm, architecture,
performance and layout are parametrized which allows
automatic generation of the chip layout for any
required chip performance, accuracy and dynamic range
of arithmetic operations.",
acknowledgement = ack-nhfb,
affiliation = "Delft University of Technol., Netherlands",
classification = "B1265F (Microprocessors and microcomputers); B2570
(Semiconductor integrated circuits); C5220 (Computer
architecture); C5230 (Digital arithmetic methods);
C5260 (Digital signal processing)",
keywords = "50 MFLOPS; Chip layout automatic generation; Dynamic
range; Floating point pipeline CORDIC processor; High
speed signal processing algorithm; Matrix computation
applications; Parallel structure; Pipelined processor
structure; Real time signal processing; Systolic
arrays; VLSI CORDIC arithmetic chip; Wavefront arrays",
numericalindex = "Computer speed 5.0E+07 FLOPS",
thesaurus = "Digital arithmetic; Digital signal processing chips;
Parallel architectures; Pipeline processing; VLSI",
}
@TechReport{Demmel:1989:FPE,
author = "J. Demmel",
title = "On Floating Point Errors in {Cholesky}",
type = "{LAPACK} Working Note",
number = "14",
institution = inst-UT-CS,
address = inst-UT-CS:adr,
month = oct,
year = "1989",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "UT-CS-89-87, October 1989.",
URL = "http://www.netlib.org/lapack/lawns/lawn14.ps;
http://www.netlib.org/lapack/lawnspdf/lawn14.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Dennis:1989:AAD,
author = "A. M. Dennis and C. B. Marshall and I. A. Burgess",
booktitle = "{IEE} Colloquium on Signal Processing Applications of
Finite Field Mathematics, 1 June 1989",
title = "Algorithm and architecture design for the
implementation of high order {FIR} filters using the
residue number system",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1/1--1/5",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1989.266615",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The computational speed requirements of future signal
processing algorithms necessitate the use of special
purpose multiprocessor systems implemented using VLSI
technology. Finite field arithmetic and algorithms
offer an extra degree of freedom in \ldots{}",
}
@InProceedings{Dowling:1989:MVF,
author = "E. Dowling and M. Griffin and M. Lynch and F. Taylor",
title = "A multi-purpose {VLSI} floating-point array
processor",
crossref = "Chen:1989:TSA",
pages = "730--734 vol.2",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A 3*3 single-instruction multiple-data (SIMD) array
processor for the IBM PC/AT is described. This array
processor is a modified bus-connected architecture
(MBCA) using TI's SN74ACT8847 64-bit VLSI
floating-point units for processing elements. The array
processor can operate four different modes of
operation: scalar, vector processor, full utilization,
and simulated systolic. In full utilization mode, this
array processor can sustain a 90-MFLOP computational
rate. System software is also discussed, and attention
is given to how it will be used with the SIGLAB
programming environment.",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. Eng., Florida University,
Gainesville, FL, USA",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5220 (Computer architecture); C5430
(Microcomputers); C5440 (Multiprocessor systems and
techniques)",
keywords = "64 Bit; 90 MFLOPS; Full utilization mode; IBM PC/AT;
Modes of operation; Modified bus-connected
architecture; SIGLAB programming environment; SIMD;
Single-instruction multiple-data; SN74ACT8847; VLSI
floating-point array processor",
numericalindex = "Word length 6.4E+01 bit; Computer speed 9.0E+07
FLOPS",
thesaurus = "CMOS integrated circuits; IBM computers;
Microcomputers; Microprocessor chips; Parallel
architectures; Parallel processing; VLSI",
}
@TechReport{Dritz:1989:RPS,
author = "K. W. Dritz",
title = "Rationale for the Proposed Standard for a Generic
Package of Elementary Functions for {Ada}",
type = "Report",
number = "ANL-89/2 Rev. 1",
institution = "Argonne National Laboratory, Mathematics and Computer
Science Division",
address = "Argonne, IL, USA",
pages = "??",
month = oct,
year = "1989",
bibdate = "Thu Sep 01 12:08:24 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Dunham:1989:ICA,
author = "C. B. Dunham",
title = "Improvement of complex arithmetic by use of double
elements",
journal = j-SIGNUM,
volume = "24",
number = "4",
pages = "3--7",
month = oct,
year = "1989",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:18 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "algorithms; theory",
subject = "G.1.3 Mathematics of Computing, NUMERICAL ANALYSIS,
Numerical Linear Algebra, Matrix inversion \\ G.1.0
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic",
}
@Article{Dunham:1989:PAH,
author = "C. B. Dunham",
title = "Perturbation Analysis of {Horner}'s Method for Nice
Cases",
journal = j-SIGNUM,
volume = "24",
number = "2 and 3",
pages = "8--9",
month = apr # "/" # jul,
year = "1989",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@Article{Dunham:1989:S,
author = "C. B. Dunham",
title = "Summation",
journal = j-SIGNUM,
volume = "24",
number = "1",
pages = "14--15",
month = jan,
year = "1989",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Sep 13 08:58:48 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "accurate floating-point summation",
}
@InProceedings{Duprat:1989:SRA,
author = "Jean Duprat and Yves Herreros and Jean-Michel Muller",
title = "Some results about on-line computation of functions",
crossref = "Ercegovac:1989:PSC",
pages = "112--118",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Duprat.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@InProceedings{Elleithy:1989:ARA,
author = "K. M. Elleithy and M. A. Bayoumi and K. P. Lee",
title = "{$ \theta (\log N) $} architectures for {RNS}
arithmetic decoding",
crossref = "Ercegovac:1989:PSC",
pages = "202--209",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Elleithy.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@InProceedings{Ercegovac:1989:FRD,
author = "M. D. Ercegovac and T. Lang",
title = "On-the-fly rounding for division and square root",
crossref = "Ercegovac:1989:PSC",
pages = "169--173",
year = "1989",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Ercegovac_rounding.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
summary = "In division and square root implementation based on
digit-recurrence algorithms, the result is obtained in
digit-serial form, from most significant digit to least
significant. To reduce the complexity of the
result-digit selection and to allow the \ldots{}",
}
@InProceedings{Ercegovac:1989:FSC,
author = "Milo{\v{s}} D. Ercegovac and Algirdas Avi{\v{z}}ienis
and Earl Swartzlander",
title = "Foreword: {9th Symposium on Computer Arithmetic
(ARITH9)}",
crossref = "Ercegovac:1989:PSC",
pages = "v--v",
year = "1989",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_contents.pdf;
http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_foreword.pdf;
http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_preface.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@InProceedings{Ercegovac:1989:IMC,
author = "M. D. Ercegovac and T. Lang",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, 8--11 May 1989",
title = "Implementation of module combining multiplication,
division, and square root",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "150--153",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The implementation of a module that performs radix-$2$
multiplication, division, and square root is presented.
The module is compact because most of the components
are shared by all three operations, the complexity
being similar to that of a radix-$2$ \ldots{}",
}
@InProceedings{Ercegovac:1989:RSR,
author = "Milo{\v{s}} D. Ercegovac and Tomas Lang",
title = "Radix-4 square root without initial {PLA}",
crossref = "Ercegovac:1989:PSC",
pages = "162--168",
year = "1989",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Ercegovac_radix4.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
summary = "A systematic derivation of a radix-$4$ square root
algorithm using redundance in the partial residuals and
the result is presented. Unlike other similar schemes,
the algorithm does not use a table-lookup or
programmable logic array (PLA) for the \ldots{}",
}
@InProceedings{Fandrianto:1989:AHS,
author = "Jan Fandrianto",
title = "Algorithms for high-speed shared radix 8 division and
radix 8 square root",
crossref = "Ercegovac:1989:PSC",
pages = "68--75",
year = "1989",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Fandrianto.pdf",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "ARITH-9",
summary = "An algorithm for performing radix-$8$ division and
square root in a shared hardware is described. To
achieve short iteration cycle time, it utilizes an
optimized `next quotient/root prediction PLA' generally
used in a radix-$4$ SRT division with minimal
\ldots{}",
}
@InBook{Feldstein:1989:NAP,
author = "Alan Feldstein and Richard H. Goodman",
title = "Some aspects of floating point computation",
crossref = "Turner:1989:NAP",
pages = "169--181",
year = "1989",
DOI = "https://doi.org/10.1007/BFb0085718",
MRclass = "65G05",
MRnumber = "022 264",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The floating point format is widely used in computing
because it allows for the representation of numbers
with greatly varying magnitude. This paper introduces
some general aspects of floating point representation
and includes a discussion of the implications of
balanced and unbalanced exponent ranges. A statistical
approach is presented in order to analyze the error in
floating point computations. The shortening of computer
words is discussed and is applied to study aspects of
the fraction error and the relative error.",
acknowledgement = ack-nhfb,
}
@InProceedings{Fowler:1989:AHS,
author = "D. L. Fowler and J. E. Smith",
title = "An accurate, high speed implementation of division by
reciprocal approximation",
crossref = "Ercegovac:1989:PSC",
bookpages = "xv + 247",
pages = "60--67",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Fowler.pdf",
abstract = "While unlimited accuracy is theoretically possible, it
is very important to minimize the number of iteration
steps to improve performance and/or to reduce hardware
requirements. Consequently, there is an important
accuracy/speed/cost tradeoff in reciprocal
approximation implementations. A reciprocal
approximation implementation is discussed, with special
attention given to these tradeoffs. An interpolation
method is used to ensure that an initial approximation,
held in a ROM table, is as accurate as possible. A
method for implementing the iteration steps is given.
Special instructions are used so that maximum accuracy
can be carried between iteration operations. For 64-b
floating-point operands (53-b mantissa), a table lookup
and only two iterations are required, and high accuracy
is maintained. The rounded reciprocal rarely differs
from a true round-to-nearest value based on an infinite
precision result. When the results do differ (less than
once every 1000 calculations), the difference in
accuracy is shown to be less than 0.025 of a least
significant bit (LSB).",
acknowledgement = ack-nhfb,
affiliation = "Astronaut. Corp. of America, Madison, WI, USA",
classification = "C4130 (Interpolation and function approximation);
C5230 (Digital arithmetic methods); C6130 (Data
handling techniques)",
confdate = "6-8 Sept. 1989",
conflocation = "Santa Monica, CA, USA",
confsponsor = "IEEE; IFIP; University of California",
keywords = "ARITH-9; Division; Hardware requirements; High speed
implementation; Interpolation; Reciprocal
approximation; ROM table; Rounded reciprocal; Table
lookup",
thesaurus = "Digital arithmetic; Interpolation; Table lookup",
}
@Article{Fried:1989:ONC,
author = "S. Fried",
title = "Optimizing numeric coprocessing",
journal = j-BYTE,
volume = "14",
number = "11",
pages = "221--224",
month = "????",
year = "1989",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 12 17:47:21 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods); C5470
(Performance evaluation and testing)",
fjournal = "BYTE Magazine",
keywords = "Addition; Compiler optimizations; CPU code;
Floating-point operations; Multiplication; Numeric
coprocessing; Optimisation; Weitek 3167",
thesaurus = "Computer testing; Digital arithmetic; Performance
evaluation; Satellite computers",
}
@InProceedings{Fu:1989:PMI,
author = "B. Fu and A. Saini and P. P. Gelsinger",
title = "Performance and Microarchitecture of the i486{\TM}
Processor",
crossref = "IEEE:1989:PII",
pages = "182--187",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The i486 microprocessor includes a carefully tuned,
five-stage pipeline with an integrated 8-kB cache. A
variety of techniques previously associated only with
RISC (reduced-instruction-set computer) processors are
used to execute the average instruction in 1.8 clocks.
This represents a 2.5* reduction from its predecessor,
the 386 microprocessor. The pipeline and clock count
comparisons are described in detail. In addition, an
onchip floating-point unit is included which yields a
4* clock count reduction from the 387 numeric
coprocessor. The microarchitecture enhancements and
optimizations used to achieve this goal, most of which
are non-silicon-intensive, are discussed. All
instructions of the 386 microprocessor and the 387
numeric coprocessor are implemented in a completely
compatible fashion.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Intel Corp., Santa Clara, CA, USA",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips)",
confdate = "2-4 Oct. 1989",
conflocation = "Cambridge, MA, USA",
confsponsor = "IEEE",
keywords = "386 Microprocessor; 387 Numeric coprocessor; Clock
count; Five-stage pipeline; I486 processor; Intel;
Microarchitecture; Onchip floating-point unit;
Performance",
thesaurus = "Microprocessor chips",
}
@Article{Fujiyama:1989:FD,
author = "T. Fujiyama and Y. Shimazu and T. Tokuda and S.
Tsujimichi",
title = "A 24-bit floating-point {DSP}",
journal = "Mitsubishi Denki Giho",
volume = "63",
number = "12",
pages = "59--62",
month = "????",
year = "1989",
ISSN = "0369-2302",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors report on a new high-speed 24-bit floating
point DSP (digital signal processor) and its
development tools. The DSP features a short 75 ns
instruction cycle and low 750 mW power dissipation.
Other features include a large memory space, internal
RAM that can be configured as a cache, and speed
control via an internal clock prescaler that is
accessed by a special instruction. The DSP is suitable
for application in audio and image processing,
communications and numerical control.",
acknowledgement = ack-nhfb,
affiliation = "Mitsubishi Electr. Corp., Tokyo, Japan",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5260 (Digital signal
processing)",
keywords = "24 Bit; 24-Bit floating-point DSP; 75 Ns; 750 MW;
Audio processing; Communications; Development; Digital
signal processor; DSP chips; Image processing;
Instruction cycle; Internal clock prescaler; Memory;
Numerical control; Power dissipation; RAM; Speed
control",
language = "Japanese",
numericalindex = "Power 7.5E-01 W; Time 7.5E-08 s; Word length 2.4E+01
bit",
pubcountry = "Japan",
thesaurus = "Computerised signal processing; Digital signal
processing chips",
}
@InProceedings{Gamberger:1989:ISN,
author = "D. Gamberger",
title = "Incompletely specified numbers in the residue number
system-definition and applications",
crossref = "Ercegovac:1989:PSC",
pages = "210--215",
year = "1989",
DOI = "https://doi.org/10.1109/ARITH.1989.72828",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Gamberger.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9; residue arithmetic; residue number system",
summary = "Incompletely specified numbers in the residue number
system (RNS) are defined in order to make
multiplicative inverse computation of a number
regardless of its magnitude possible. Incompletely
specified RNS is the general RNS model in which
\ldots{}",
}
@InProceedings{Games:1989:AIQ,
author = "R. A. Games and D. Moulin and S. D. O'Neil and J. J.
Rushanan",
booktitle = "International Conference on Acoustics, Speech, and
Signal Processing, {ICASSP-89, 23--26} May 1989",
title = "Algebraic-integer quantization an residue number
system processing",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "948--951",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1989.266586",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The algebraic-integer number representation, in which
the signal sample is represented by a set of (typically
four to eight) small integers, combines with residue
number system (RNS) processing to produce processors
composed of simple parallel \ldots{}",
}
@InProceedings{Goel:1989:RTA,
author = "B. D. Goel and M. M. Jamali and S. C. Kwatra",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, 8--11 May 1989",
title = "Real time architecture for vector quantization in
residue number system",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "204--207",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1989.100327",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A fast and simplified systolic array architecture for
real-time implementation of vector quantization is
proposed. The proposed architecture uses the residue
number system (RNS) for arithmetic operations. The
arithmetic operations can be precomputed \ldots{}",
}
@TechReport{Goldberg:1989:FCS,
author = "David Goldberg",
title = "Floating-point and computer systems",
type = "Technical report",
number = "CSL-89-9",
institution = "Xerox Corp., Palo Alto Research Center",
address = "Palo Alto, CA, USA",
pages = "58",
year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.",
remark = "``August 1989.'' ``A version of this paper will appear
in Computing Surveys.''",
}
@InProceedings{Gonnella:1989:ACF,
author = "J. Gonnella and J. Periard",
booktitle = "{IEEE} Military Communications Conference, 1989.
{MILCOM '89}. Conference Record. Bridging the Gap.
Interoperability, Survivability, Security, 1989",
title = "The application of core functions to residue number
system signal processing",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "604--608",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/MILCOM.1989.103996",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The authors briefly outline core-based residue number
system (RNS) processing. An RNS adaptive array
processor using Choleski decomposition and forward
elimination/back substitution is described as an
example. The RNS adaptive processor was \ldots{}",
}
@MastersThesis{Gordon:1989:RDF,
author = "Stephen E. Gordon",
title = "Recursive digital filtering with digital differential
analyzers and floating point incremental coders",
type = "Thesis ({M.S.E.C.E.})",
school = "University of Massachusetts at Amherst",
address = "Amherst, MA, USA",
pages = "xi + 123",
year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Digital filters (Mathematics)",
}
@Article{Grassmann:1989:PAR,
author = "Winfried K. Grassmann",
title = "A probabilistic analysis of rounding errors of
floating point numbers. {Eighteenth Manitoba Conference
on Numerical Mathematics and Computing (Winnipeg, MB,
1988)}",
journal = j-CONG-NUM,
volume = "68",
pages = "171--182",
year = "1989",
ISSN = "0384-9864",
MRclass = "65G05",
MRnumber = "90d:65089",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Congressus Numerantium",
}
@Article{Grehan:1989:FPR,
author = "R. Grehan",
title = "Floating-Point Revisited",
journal = j-BYTE,
volume = "14",
number = "4",
pages = "311--318",
month = apr,
year = "1989",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 1 10:15:05 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "BYTE Magazine",
}
@InProceedings{Griffin:1989:ESR,
author = "M. Griffin and M. Sousa and F. Taylor",
booktitle = "International Conference on Acoustics, Speech, and
Signal Processing, {ICASSP-89, 23--26} May 1989",
title = "Efficient scaling in the residue number system",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1075--1078",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1989.266618",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A unified residue number system scaling technique that
allows the designer a great deal of flexibility in
choosing the scale factor is presented. The technique
is based on the L({\&}epsi;+{\delta})-CRT (Chinese
remainder theorem). By embedding \ldots{}",
}
@InProceedings{Griffin:1989:RNS,
author = "M. F. Griffin and F. J. Taylor",
booktitle = "International Conference on Acoustics, Speech, and
Signal Processing, {ICASSP-89, 23--26} May 1989",
title = "A residue number system reduced instruction set
computer ({RISC}) concept",
volume = "4",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2581--2584",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1989.266995",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A reduced-instruction-set RNS (residue number system)
processor is proposed for digital signal processing
algorithms. Issues leading toward a RNS RISC are
examined, namely suitable RNS algorithms. It is argued
that this is a reasonable next step in \ldots{}",
}
@Article{Groeger:1989:DRG,
author = "Detlef Gr{\"o}ger",
title = "{Zur Division mit Rest auf Gleitkommarechnern.
(German)} [On division with remainder on floating point
computers]",
journal = j-MATH-SEMESTERBER,
volume = "36",
number = "1",
pages = "106--111",
year = "1989",
ISSN = "0720-728x (print), 1432-1815 (electronic)",
ISSN-L = "0720-728X",
MRclass = "65G99 (11Y16)",
MRnumber = "90g:65070",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Semesterberichte",
language = "German",
}
@InProceedings{Guyot:1989:JLM,
author = "Alain Guyot and Bertrand Hochet and Jean-Michel
Muller",
title = "{JANUS}, an on-line multiplier\slash divider for
manipulating large numbers",
crossref = "Ercegovac:1989:PSC",
pages = "106--111",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Guyot.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@Article{Hoffmann:1989:PAR,
author = "C. M. Hoffmann",
title = "The Problems of Accuracy and Robustness in Geometric
Computation",
journal = j-COMPUTER,
volume = "22",
number = "3",
institution = "Purdue U",
pages = "31--39, 41",
month = mar,
year = "1989",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Sat Sep 14 07:29:35 MDT 1996",
bibsource = "Graphics/rosenfeld/1989.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Misc/IMMD_IV.bib",
acknowledgement = ack-nhfb,
affiliation = "Computer Science Dept., Purdue University, West
Lafayette, IN, USA",
classification = "C1160 (Combinatorial mathematics); C4190 (Other
numerical methods); C4290 (Other computer theory)",
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
keywords = "Accuracy; Degeneracies avoidance; Degenerate
positions; Floating-point computation; Geometric
computation; Geometric operations; Interacting numeric
data; Interacting symbolic data; Limited-precision
rational arithmetic; Linear elements; Model, IMAGE PART
MEASUREMENT; Numerical precision; Perturbation-free
methods; Purely symbolic representations;
Representation; Robustness; Symbolic data alteration",
thesaurus = "Computational geometry",
}
@InProceedings{Hohne:1989:PHP,
author = "R. A. Hohne and R. Siferd",
booktitle = "Proceedings of the {IEEE 1989} National Aerospace and
Electronics Conference, {NAECON 1989}, 22--26 May
1989",
title = "A programmable high performance processor using the
residue number system and {CMOS} {VLSI} technology",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "41--43",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/NAECON.1989.40188",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The authors describe the general architecture of RNS
(residue number system) processors, the VLSI
implementation of the associated hardware, and finally,
an RNS processor designed by the authors. The 2-{\mu}m
CMOS implementation of the processor \ldots{}",
}
@Article{Hollingsworth:1989:CPI,
author = "Walter Hollingsworth and Howard Sachs and Alan Jay
Smith",
title = "The {Clipper\TM} Processor: Instruction Set
Architecture and Implementation",
journal = j-CACM,
volume = "32",
number = "2",
pages = "200--219",
month = feb,
year = "1989",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Sep 26 13:49:15 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "design; measurement; performance",
review = "ACM CR 9002-0119",
subject = "C.5.3 Computer Systems Organization, COMPUTER SYSTEM
IMPLEMENTATION, Microcomputers, CLIPPER \\ C.1.1
Computer Systems Organization, PROCESSOR ARCHITECTURES,
Single Data Stream Architectures,
Single-instruction-stream, single-data-stream
processors (SISD) \\ C.4 Computer Systems Organization,
PERFORMANCE OF SYSTEMS \\ C.0 Computer Systems
Organization, GENERAL, Instruction set design",
}
@Article{Hoshi:1989:RPV,
author = "T. Hoshi and K. Koya and A. Kuwata and T. Uno and M.
Kashimura and T. Kuwata and T. Nishigouri and K. Obuchi
and N. Morikawa",
title = "{RISC} processor {V}/sub {R}/3000",
journal = j-NEC-TECH-J,
volume = "42",
number = "11",
pages = "34--38",
month = dec,
year = "1989",
CODEN = "NECGEZ",
ISSN = "0285-4139",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Outlines NEC's first RISC type microprocessor, the
V/sub R/3000 and its developmental environment. V/sub
R/3000 is fully compatible with the R3000 developed by
MIPS Computer Systems, USA. It offers one of the
fastest microprocessor systems in the world, together
with a floating point processor V/sub R/3010 that is
fully compatible with the R3010.",
acknowledgement = ack-nhfb,
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5220 (Computer architecture)",
fjournal = "NEC Technical Journal = NEC giho",
keywords = "Floating point processor; NEC; RISC type
microprocessor; V/sub R/3000; V/sub R/3010",
language = "Japanese",
pubcountry = "Japan",
thesaurus = "Microprocessor chips; Reduced instruction set
computing",
}
@InProceedings{Hu:1989:ARM,
author = "Y. H. Hu and S. Naganathan",
title = "Angle Recoding Method for Efficient Implementation of
the {CORDIC} Algorithm",
crossref = "IEEE:1989:IISa",
pages = "175--178 (Vol. 1)",
year = "1989",
bibdate = "Thu Sep 01 11:41:20 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Book{Huck:1989:ACA,
author = "Jerome C. Huck and Michael J. Flynn",
title = "Analyzing Computer Architectures",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiii + 188",
year = "1989",
ISBN = "0-8186-8857-2, 0-8186-4857-0 (microfiche),
0-8186-8857-2 (casebound)",
ISBN-13 = "978-0-8186-8857-7, 978-0-8186-4857-1 (microfiche),
978-0-8186-8857-7 (casebound)",
LCCN = "QA76.9.A73 H83 1989",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Computer Society order number 857. IEEE catalog
number EH0285-7. SAN 264-620X.",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@Article{Husby:1989:FPE,
author = "D. Husby and R. Atac and A. Cook and J. Deppe and M.
Fischler and I. Gaines and T. Nash and T. Pham and T.
Zmuda and E. Eichten and G. M. Hockney and P. B.
Mackenzie and H. B. Thacker and D. Toussaint",
title = "A floating point engine for lattice gauge
calculations",
journal = j-IEEE-TRANS-NUCL-SCI,
volume = "36",
number = "1",
pages = "734--737",
month = feb,
year = "1989",
CODEN = "IRNSAM",
ISSN = "0018-9499 (print), 1558-1578 (electronic)",
ISSN-L = "0018-9499",
LCCN = "TK6540 .I573 Jan-June 1988",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0105825",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Nuclear Science",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23",
summary = "The Fermilab Advanced Computer Program Multiple Array
Processor System, which dedicated to solving problems
in the field of quantum chromodynamics, is discussed. A
typical system with 256 processors, 2.5 Gb of memory,
and 64 Gb of online tape storage \ldots{}",
}
@InProceedings{Hwang:1989:OAU,
author = "Kai Hwang and D. K. Panda",
title = "Optical arithmetic using high-radix symbolic
substitution rules",
crossref = "Ercegovac:1989:PSC",
pages = "226--232",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Hwang.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@Book{IEC:1989:IBF,
author = "{IEC}",
title = "{IEC 60559 (1989-01)}: Binary floating-point
arithmetic for microprocessor systems",
publisher = pub-IEC,
address = pub-IEC:adr,
pages = "45",
year = "1989",
bibdate = "Mon Apr 24 06:17:57 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "This Standard was formerly known as IEEE 754.",
price = "US\$86.00",
URL = "http://www.iec.ch/cgi-bin/procgi.pl/www/iecwww.p?wwwlang=E&wwwprog=cat-det.p&wartnum=019113",
acknowledgement = ack-nhfb,
remark = "Working Draft, 1997-11-21, WG14/N794 J11/97-158 of the
ISO C9X Standard references ``Binary floating-point
arithmetic for microprocessor systems, second edition
(IEC 559:1993)''. However, I cannot locate that edition
at the IEC Web site. The 1997 renumbering of IEC
Standards by the addition of 60000 indicates that this
document should now be IED 60559:1993, but only the
1989 version is listed in the IEC catalog.",
}
@MastersThesis{Intwala:1989:BFP,
author = "Jaiprakash D. Intwala",
title = "{8085A} based floating point arithmetic system",
type = "Thesis ({M.S.})",
school = "California State University, Northridge",
address = "Northridge, CA, USA",
pages = "viii + 81",
year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Jain:1989:SLU,
author = "V. K. Jain and D. L. Landia and C. E. Alvarez",
title = "Systolic {L-U} Decomposition Array With a New
Reciprocal Cell",
crossref = "IEEE:1989:PII",
pages = "460--465",
year = "1989",
bibdate = "Sun Sep 11 20:59:19 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Jamieson:1989:SNR,
author = "M. J. Jamieson",
title = "Short Notes: Rapidly Converging Iterative Formulae for
Finding Square Roots and their Computational
Efficiencies",
journal = j-COMP-J,
volume = "32",
number = "1",
pages = "93--94",
month = feb,
year = "1989",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/32.1.93",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65H05",
MRnumber = "89k:65063",
bibdate = "Tue Dec 4 14:48:26 MST 2012",
bibsource = "Compendex database;
http://comjnl.oxfordjournals.org/content/32/1.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/;
https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "This work generalizes the Pythagorean sums in
\cite{Dubrulle:1983:CNM,Moler:1983:RSR}.",
URL = "http://comjnl.oxfordjournals.org/content/32/1/93.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/tiff/93.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/tiff/94.tif",
abstract = "A derivation is given of rapidly converging iterative
formulae for finding square roots which include, as
special cases, some recently published examples. Their
computational efficiencies are investigated for
sequential and parallel implementation. It is concluded
that the most efficient method is equivalent to
sequential application of the Newton Raphson formula; a
simple modification is suggested which brings the
advantage of root bracketing at little extra
computational cost.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Glasgow University,
UK",
affiliationaddress = "Glasgow, Scotl",
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
classification = "723; 921; B0290F (Interpolation and function
approximation); C4130 (Interpolation and function
approximation)",
corpsource = "Department of Computer Science, Glasgow University,
UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "computational; Computational efficiencies;
Computational Efficiency; Computer Metatheory;
Convergence; convergence of numerical methods;
Converging iterative formulae; converging iterative
formulae; efficiencies; formula; function
approximation; Iterative Methods; iterative methods;
Newton Raphson; Newton Raphson formula, Mathematical
Techniques; Parallel implementation; parallel
implementation; Square Roots; Square roots; square
roots",
thesaurus = "Convergence of numerical methods; Function
approximation; Iterative methods",
treatment = "P Practical",
}
@InProceedings{Jenkins:1989:AFP,
author = "W. K. Jenkins and J. K. Yun",
booktitle = "European Conference on Circuit Theory and Design, 5--8
Sep 1989",
title = "Analysis of fixed point roundoff effects in transform
domain {LMS} adaptive filters",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "228--232",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "One of the disadvantages of the well known LMS FIR
adaptive digital filter is that, for a colored noise
input signals, the filter tends to converge slowly. One
way to improve the convergence rate is to prefilter the
input signal with an \ldots{}",
}
@Article{Johnson:1989:IMA,
author = "K. R. Johnson",
title = "An Iterative Method for Approximating Square Roots",
journal = j-MATH-MAG,
volume = "62",
number = "4",
pages = "253--259",
month = oct,
year = "1989",
CODEN = "MAMGA8",
ISSN = "0025-570X",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Mathematics Magazine",
journal-URL = "http://www.maa.org/pubs/mathmag.html",
}
@InProceedings{Johnstone:1989:HRF,
author = "Paul Johnstone and Frederick E. Petry",
title = "Higher Radix Floating Point Representations",
crossref = "Ercegovac:1989:PSC",
pages = "128--135",
year = "1989",
DOI = "https://doi.org/10.1109/ARITH.1989.72818",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Johnstone.pdf",
abstract = "An examination is made of the feasibility of
higher-radix floating-point representations and, in
particular, decimal-based representations. Traditional
analyses of such representations have assumed the
format of a floating-point datum to be roughly
identical to that of traditional binary floating-point
encodings such as the IEEE P754 task group standard
representations. The authors relax this restriction and
propose a method of encoding higher-radix
floating-point data with range, precision, and storage
requirements comparable to those exhibited by
traditional binary representations. The results of
other authors are extended to accommodate the proposed
representation. A decimal alternative to traditional
binary representations is proposed, and the behavior of
such a system is contrasted with that of a comparable
binary system.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Telerate Syst. Inc., New Orleans, LA, USA",
classification = "C5230 (Digital arithmetic methods)",
confdate = "6-8 Sept. 1989",
conflocation = "Santa Monica, CA, USA",
confsponsor = "IEEE; IFIP; University of California",
keywords = "ARITH-9; Binary representations; decimal
floating-point arithmetic; Decimal-based
representations; encodings; higher radix floating point
representation; IEEE P754 task group standard
representations",
thesaurus = "Digital arithmetic",
}
@Article{Jones:1989:EDC,
author = "Tom Jones",
key = "C.5.1 Convex C2",
title = "Engineering design of the {Convex C2}",
journal = j-COMPUTER,
volume = "22",
number = "1",
pages = "36--44",
month = jan,
year = "1989",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Convex Computer Corp., Richardson, TX",
bibno = "58556",
catcode = "C.5.1; C.5.1; B.4.3; B.7.1; C.1.2",
content = "The Convex C220 and C240 supercomputers are 64-bit
multiprocessors that are tightly coupled through a
shared main memory. Each processor contains an
integrated vector processor. A microcoded instruction
set controls all processor features, including the
vector processor. The system is implemented in 100K
emitter-coupled logic with a cycle time of 40
nanoseconds. The C220 contains two processors, an I/O
system, and memory. The C240 contains four processors,
a larger I/O system, and memory. This paper describes
the design process of this computer family and tries to
illuminate the methods and rationale behind
project-related decisions.\par
The original C1 system was designed in early 1983 using
transistor-transistor logic and complementary
metal-oxide semiconductor (CMOS) technologies. The bulk
of the machine consisted of medium- and
small-scale-integration logic, and the vector
functional units were built with 8,000-gate CMOS
arrays. The original C1 (later dubbed the C1-XL) had no
scalar floating-point hardware but sent the operands to
the vector processor. In 1984, floating-point
add-and-multiply functional units were designed in
20,000-gate CMOS arrays, and the C1 was upgraded to the
C1-XP. That machine, with minor changes, became the
C120 when the C2 was announced.\par
This paper is unusually frank for a retrospective
design trade-off study. The author describes",
CRclass = "C.5.1 Large and Medium (``Mainframe'') Computers;
C.5.1 Super (very large) computers; C.5.1 Large and
Medium (``Mainframe'') Computers; C.5.1 Convex C2;
B.4.3 Interconnections (subsystems); B.7.1 Types and
Design Styles; B.7.1 Gate arrays; C.1.2 Multiple Data
Stream Architectures (Multiprocessors); C.1.2
Interconnection architectures",
CRnumber = "8909-0654",
descriptor = "Computer Systems Organization, COMPUTER SYSTEM
IMPLEMENTATION, Large and Medium (``Mainframe'')
Computers, Super (very large) computers; Computer
Systems Organization, COMPUTER SYSTEM IMPLEMENTATION,
Large and Medium (``Mainframe'') Computers, Convex C2;
Hardware, INPUT/OUTPUT AND DATA COMMUNICATIONS,
Interconnections (subsystems); Hardware, INTEGRATED
CIRCUITS, Types and Design Styles, Gate arrays;
Computer Systems Organization, PROCESSOR ARCHITECTURES,
Multiple Data Stream Architectures (Multiprocessors),
Interconnection architectures",
fjournal = "Computer",
genterm = "DESIGN; MANAGEMENT; PERFORMANCE; ECONOMICS",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
journalabbrev = "Computer",
reviewer = "P. C. Patton",
subject = "C. Computer Systems Organization; C.5 COMPUTER SYSTEM
IMPLEMENTATION; C. Computer Systems Organization; C.5
COMPUTER SYSTEM IMPLEMENTATION; B. Hardware; B.4
INPUT/OUTPUT AND DATA COMMUNICATIONS; B. Hardware; B.7
INTEGRATED CIRCUITS; C. Computer Systems Organization;
C.1 PROCESSOR ARCHITECTURES",
}
@Book{Jorke:1989:AAM,
author = "G{\"u}nter Jorke and Bernhard Lampe and Norbert
Wengel",
title = "{Arithmetische Algorithmen der Mikrorechentechnik}
\toenglish {Arithmetic Algorithms of Microcomputing}
\endtoenglish",
publisher = pub-VEB-VERLAG-TECHNIK,
address = pub-VEB-VERLAG-TECHNIK:adr,
pages = "323",
year = "1989",
ISBN = "3-341-00515-3",
ISBN-13 = "978-3-341-00515-6",
LCCN = "????",
bibdate = "Fri Sep 16 16:30:36 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
xxnote = "fpbiblio.txt 1.8 has order Lampe, Jorke, Wengel, but
RLIN catalog has Jorke, Lampe, Wengel.",
}
@Article{Joslin:1989:EPN,
author = "David A. Joslin",
title = "Extended {Pascal} --- numerical features",
journal = j-SIGPLAN,
volume = "24",
number = "6",
pages = "77--80",
month = jun,
year = "1989",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:15:40 MST 2003",
bibsource = "Compendex database; http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Extended Pascal standard, drafted by the Joint
X3J9\slash IEEE-770 Pascal Standards Committee (JPC) in
conjunction with the ISO Pascal working group
(ISO\slash IEC JTC1\slash SC22\slash WG2), completed
its second public comment period at the end of 1988.
The comments received have been considered by JPC and
the ISO group, and the standard is now almost certainly
in its final form. Earlier papers by this author
described the main features of the standard by means of
illustrative examples. This is now the first in an
occasional series of articles, by this author and other
JPC \& WG2 members, describing in more detail various
extensions which have been made to the Pascal language;
rationale is given where appropriate. This paper
describes the predefined type COMPLEX, the range and
precision of type REAL, and the EXPONENTIATION
operators.",
acknowledgement = ack-nhfb,
affiliationaddress = "Middlesbrough, Engl",
classification = "723; 902",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
journalabr = "SIGPLAN Not",
keywords = "Complex Arithmetic; Computer Operating
Systems--Program Compilers; Computer Programming
Languages; design; Extended Pascal; languages; pascal;
standardization; Standards",
subject = "D.2.1 Software, SOFTWARE ENGINEERING,
Requirements/Specifications \\ D.3.2 Software,
PROGRAMMING LANGUAGES, Language Classifications,
Pascal",
}
@TechReport{Jouppi:1989:UVSa,
author = "Norman Paul Jouppi and Jonathan Bertoni and David
Wayne Wall",
title = "A unified vector\slash scalar floating-point
architecture",
institution = "Digital Western Research Laboratory",
address = "Palo Alto, CA, USA",
pages = "v + 23",
month = jul,
year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "WRL research report; 89/8",
acknowledgement = ack-nhfb,
keywords = "Computer architecture.; Floating-point arithmetic.;
MultiTitan (Computer); Scalar field theory.;
Supercomputers.; Vector processing (Computer science)",
}
@Article{Jouppi:1989:UVSb,
author = "N. P. Jouppi and J. Bertoni and D. W. Wall",
title = "A unified vector\slash scalar floating-point
architecture",
journal = j-COMP-ARCH-NEWS,
volume = "17",
number = "2",
pages = "134--143",
month = apr,
year = "1989",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 12 09:40:39 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Misc{Kahan:1989:PCA,
author = "W. Kahan",
title = "Paradoxes in Concepts of Accuracy",
howpublished = "Lecture notes from Joint Seminar on Issues and
Directions in Scientific Computation, Berkeley",
year = "1989",
bibdate = "Sat Sep 17 18:40:08 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kak:1989:BAS,
author = "S. C. Kak and A. O. Barbir",
booktitle = "Proceedings of the Twenty-First Southeastern Symposium
on System Theory, 26--28 March 1989",
title = "The {Brahmagupta} algorithm for square rooting",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "456--459",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "An algorithm for square root evaluation is introduced.
Novel features of the algorithm include suitability for
parallel processing and multi-initial guesses of the
root. An extension of the algorithm to the nth rooting
is provided. A VLSI \ldots{}",
}
@Article{Kaneko:1989:VRM,
author = "K. Kaneko and T. Okamoto and M. Nakajima and Y.
Nakakura and S. Gokita and J. Nishikawa and Y. Tanikawa
and H. Kadota",
title = "A {VLSI RISC} with {20-MFLOPS} peak, 64-bit
floating-point unit",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "24",
number = "5",
pages = "1331--1340",
month = oct,
year = "1989",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "A microprocessor designed as a processing element of a
scientific parallel computer system is described. This
chip consists of a simple integer processor core and
dedicated floating-point hardware and executes 64-bit
floating-point addition, subtraction \ldots{}",
}
@Article{Kaneko:1989:VRP,
author = "K. Kaneko and T. Okamoto and M. Nakajima and Y.
Nakakura and S. Gokita and J. Nishikawa and Y. Tanikawa
and H. Kadota",
title = "A {VLSI RISC} with 20-{MFLOPS} peak, 64-bit
floating-point unit",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "24",
number = "5",
pages = "1331--1340",
month = oct,
year = "1989",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A microprocessor designed as a processing element of a
scientific parallel computer system is described. This
chip consists of a simple integer processor core and
dedicated floating-point hardware and executes 64-bit
floating-point addition, subtraction, and
multiplication at a rate of every 50 ns and division
every 350 ns. The processor, which employs RISC
architecture and Harvard-style bus organization,
executes most of the 47 instructions in one 50-ns
cycle. The chip is fabricated in 1.2- mu m n-well CMOS
technology, containing 440K transistors in a
14.4*13.5-mm/sup 2/ die. The authors provide an
overview of the processor, especially focusing on the
functions for a parallel system, floating-point
hardware, and the new divide algorithm.",
acknowledgement = ack-nhfb,
affiliation = "Semicond. Research Center, Matsushita Electr. Ind.
Co., Ltd., Osaka, Japan",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5230 (Digital arithmetic methods)",
fjournal = "IEEE Journal of Solid-State Circuits",
keywords = "1.2 Micron; 20 MFLOPS; 350 Ns; 50 Ns; 64 Bit;
Addition; Dedicated floating-point hardware; Division;
Floating-point unit; Harvard-style bus organization;
Integer processor core; Microprocessor; Multiplication;
N-well CMOS technology; RISC architecture; Scientific
parallel computer system; Subtraction; VLSI",
numericalindex = "Computer speed 2.0E+07 FLOPS; Word length 6.4E+01
bit; Time 5.0E-08 s; Time 3.5E-07 s; Size 1.2E-06 m",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Microprocessor chips; Parallel processing; Reduced
instruction set computing; VLSI",
}
@InProceedings{Kawarai:1989:OPM,
author = "S. Kawarai and T. Murakami",
booktitle = "Acoustics, Speech, and Signal Processing, 1989.
{ICASSP-89., 1989} International Conference on. 23--26
May 1989",
title = "An optimization procedure to minimize the roundoff
noise in cascade floating-point digital filters",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "884--887",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The authors study the roundoff errors in
floating-point arithmetic and present an optimization
procedure for cascade floating-point digital filters.
Applying the isosceles trapezoidal distribution to the
error analysis of cascade floating-point \ldots{}",
}
@Article{Kawasaki:1989:FPV,
author = "S. Kawasaki and M. Watabe and S. Morinaga",
title = "A floating-point {VLSI} chip for the {TRON}
architecture: an architecture for reliable numerical
programming",
journal = j-IEEE-MICRO,
volume = "9",
number = "3",
pages = "26--44",
month = may # "\slash " # jun,
year = "1989",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.31476",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
summary = "A description is given of the Gmicro/FPU
(floating-point unit), a chip that provides
floating-point instructions for both the Gmicro/200 and
the Gmicro/300 microprocessors. The VLSI
central-processing-unit architecture, for which it is
designed, \ldots{}",
}
@InProceedings{Koc:1989:SAI,
author = "{\c{C}}. K. Ko{\c{c}} and P. R. Cappello",
title = "Systolic arrays for integer {Chinese} remaindering",
crossref = "Ercegovac:1989:PSC",
pages = "216--223",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Koc.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@InProceedings{Kohn:1989:ISM,
author = "L. Kohn and N. Margulis",
title = "The {i860} 64-bit supercomputing microprocessor",
crossref = "ACM:1989:PSN",
pages = "450--456",
year = "1989",
bibdate = "Wed Apr 15 19:32:44 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5220 (Computer architecture)",
corpsource = "Intel Corp., Santa Clara, CA, USA",
keywords = "64 bit; caches; floating point unit; i860 64-bit
supercomputing microprocessor; Intel; memory
management; microprocessor chips; multiplier units;
parallel architectures; parallelism; pipelined adder;
pipelining; reduced instruction set computing; RISC
based microprocessor; three-dimensional graphics",
sponsororg = "ACM; IEEE",
treatment = "P Practical",
}
@InProceedings{Kohn:1989:TM,
author = "L. Kohn and S.-W. Fu",
title = "A 1,000,000 Transistor Microprocessor",
crossref = "Wuorinen:1989:DTP",
pages = "54--55, 290",
year = "1989",
bibdate = "Wed Sep 7 22:32:01 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Komori:1989:FPE,
author = "S. Komori and H. Takata and T. Tamura and F. Asai and
T. Ohno and O. Tomisawa and T. Yamasaki and K. Shima
and H. Nishikawa and H. Terada",
title = "A 40-{MFLOPS} 32-bit floating-point processor with
elastic pipeline scheme",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "24",
number = "5",
pages = "1341--1347",
month = oct,
year = "1989",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors present a 40-MFLOPS 32-bit floating-point
processor (FP) which is a component chip for a
data-driven single-board processor. The FP is the first
practical LSI chip which has introduced the elastic
pipeline scheme. All parts in the FP are autonomously
controlled by self-timed circuits, and no system clock
is needed for processing. The elastic pipeline scheme
provides data buffering capability and stabilization of
circuit operation at the same time. Pipelining has been
extensively utilized so that high throughput over
40-MFLOPS can be achieved. An automatic power
conservation technique, called `latch mode control', is
also described.",
acknowledgement = ack-nhfb,
affiliation = "LSI Res. and Dev. Lab., Misubishi Electr. Corp.,
Hyogo, Japan",
classification = "B1265F (Microprocessors and microcomputers); B2570
(Semiconductor integrated circuits); C5130
(Microprocessor chips)",
fjournal = "IEEE Journal of Solid-State Circuits",
keywords = "32 Bit; 40 MFLOPS; Automatic power conservation;
Component chip; Data buffering capability; Data-driven
single-board processor; Elastic pipeline scheme;
Floating-point processor; Latch mode control; LSI chip;
Microprocessor; Self-timed circuits; Stabilization",
numericalindex = "Computer speed 4.0E+07 FLOPS; Word length 3.2E+01
bit",
thesaurus = "Large scale integration; Microprocessor chips;
Pipeline processing",
}
@InProceedings{Komori:1989:MBFa,
author = "S. Komori and H. Takata and T. Tamura and F. Asai and
T. Ohno and O. Tomisawa and T. Yamasaki and K. Shima
and H. Nishikawa and H. Terada",
title = "A 40 {MFLOPS} 32-bit Floating-Point Processor",
crossref = "Wuorinen:1989:DTP",
pages = "46--47, 286",
year = "1989",
bibdate = "Wed Sep 7 22:32:01 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Komori:1989:MBFb,
author = "S. Komori and H. Takata and T. Tamura and F. Asai and
T. Ohno and O. Tomisawa and T. Yamasaki and K. Shima
and H. Nishikawa and H. Terada",
title = "A {40-MFLOPS} 32-bit floating-point processor with
elastic pipeline scheme",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "24",
number = "5",
pages = "1341--1347",
month = oct,
year = "1989",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "The authors present a 40-MFLOPS 32-bit floating-point
processor (FP) which is a component chip for a
data-driven single-board processor. The FP is the first
practical LSI chip which has introduced the elastic
pipeline scheme. All parts in the FP are \ldots{}",
}
@InProceedings{Komori:1989:MFP,
author = "S. Komori and H. Takata and T. Tamura and F. Asai and
T. Ohno and O. Tomisawa and T. Yamasaki and K. Shima
and H. Nishikawa and H. Terada",
title = "A 40 {MFLOPS} 32-bit floating-point processor",
crossref = "Wuorinen:1989:DTP",
pages = "46--47, 286",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A 40 MFLOPS (million floating-point operations per
second), 32-bit floating-point processor (FP) for a
single-board data-driven processor is developed using a
pipeline configuration called the elastic pipeline
structure. Because there is no need to add controls for
pipeline flushing by virtue of the data-driven
processing principle, it is possible to employ
extensively subdivided pipeline stages. The elastic
mode of data transfer between pipeline stages and
distributed execution controls along the pipeline
result in minimum deterioration of the inherent logic
switching speed. The structure of the FP is shown
together with details of the ALU (arithmetic logic
unit) block. The fabrication process and chip
specifications are summarized.",
acknowledgement = ack-nhfb,
affiliation = "Mitsubishi Electr. Corp., Hyogo, Japan",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5220 (Computer architecture); C5230 (Digital
arithmetic methods)",
keywords = "32 Bit; 40 MFLOPS; ALU; Chip specifications; CMOS
chip; Data transfer; Distributed execution controls;
Elastic pipeline structure; Fabrication process;
Floating-point processor; Logic switching speed;
Pipeline configuration; Single-board data-driven
processor; Subdivided pipeline stages",
numericalindex = "Computer speed 4.0E+07 FLOPS; Word length 3.2E+01
bit",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Microprocessor chips; Pipeline processing",
}
@InProceedings{Kornerup:1989:ERB,
author = "Peter Kornerup and David W. Matula",
title = "Exploiting Redundancy in Bit-Pipelined Rational
Arithmetic",
crossref = "Ercegovac:1989:PSC",
pages = "119--126",
year = "1989",
DOI = "https://doi.org/10.1109/ARITH.1989.72817",
bibdate = "Wed Nov 14 18:29:43 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Kornerup.pdf",
abstract = "The authors develop and analyze a redundant
continued-fraction representation of the rationals in
the implementation of an arithmetic unit for computing
the sum, difference, product, quotient, and other
useful functions of two rational operands. Their
representation of operands and results allows the
computations of the unit to be performed in a signed
bit-serial, online fashion. Several such units can then
be interconnected for the computation of more
complicated expressions in a pipelined manner.
Redundancy is used to help achieve a small bounded
online delay and uniform throughput",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@InProceedings{Krishna:1989:NAC,
author = "H. Krishna and Kuo Yu Lin",
booktitle = "Twenty-Third Asilomar Conference on Signals, Systems
and Computers, 1989",
title = "New algorithms for correcting errors in redundant
residue number systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "653--657",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1989.266586",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
}
@InProceedings{Krishnan:1989:CBN,
author = "R. Krishnan",
booktitle = "Twenty-Third Asilomar Conference on Signals, Systems
and Computers, 1989",
title = "Conventional binary number system ({BNS}) versus
residue number system ({RNS}) digital signal processing
architecture suitable for complex digital filtering",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "873--877",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1989.266586",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
}
@InProceedings{Krishnan:1989:ESA,
author = "R. Krishnan",
booktitle = "International Conference on Acoustics, Speech, and
Signal Processing, {ICASSP-89, 23--26} May 1989",
title = "An efficient systolic array {VLSI} cell architecture
for the implementation of transversal filter based on
the quadratic residue number systems",
volume = "4",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2585--2588",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1989.266996",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The author presents efficient direct and indirect
implementations of transversal filter architectures
using the quadratic residue number system (QRNS). In
the case of the direct transversal filter, a systolic
array architecture has been developed \ldots{}",
}
@Misc{Kulisch:1989:CGS,
author = "Ulrich Kulisch and Reinhard Kirchner",
title = "Circuitry for generating sums, especially scalar
products",
howpublished = "US Patent 4866653",
day = "12",
month = sep,
year = "1989",
bibdate = "Mon Dec 29 16:20:01 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/4866653/fulltext.html",
abstract = "Circuitry for the summation, especially for
generation, of scalar products, to which one summand in
floating-point representation is conveyed per machine
cycle (ZT), in which, after conversion into fixed point
representation, it is received in a summing unit with
an accumulator (AS1,-AS4) comprising the whole exponent
range. The accumulator is subdivided into row sections,
which are longer than the mantissa of the summands.
Partial exponents (EPK1,-EPK4) generated in an exponent
analyzer (EXA) control the mantissa positioner (PM) or
are allocated to the mantissas and delivered
continuously and cycle-wise to transfer registers
(RE1,-RE4; RVS1,-RVS4; RNS1, RNS4), controlling
summation row-wise. The carriers are allocated to the
accumulator sections and intermediately stored in carry
memory sections (CS1,-CS4) and are not added digit
positionwise to the contents of each adjacent memory
section until the sum is output, further carries being
continuously processed. Afterwards the rounded result
mantissa (ME) is generated in transfer registers (RA1,
RA2, RPR) arranged downstream and the result exponent
(EE) is generated in an exponent generator (EXG).",
acknowledgement = ack-nhfb,
}
@InProceedings{Lai:1989:HNS,
author = "F. S. Lai and C. E. Wu",
title = "A hybrid number system multiplier for graphics and
complex arithmetic applications",
crossref = "IEEE:1989:ISV",
pages = "352--356",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A hybrid multiplier design which supports 32-bit
floating-point, 24-bit fixed-point and 32-bit
logarithmic number systems is described. Except for
additions and subtractions, floating-point operations
such as multiplication, division, and square root are
all performed in the logarithmic number system domain.
A modified squaring approach is adopted for fixed-point
multiplications with little extra hardware. The
performance of this multiplier is shown to be superior
to that of conventional binary multipliers for most
graphics and digital signal processing applications,
and the size of the multiplier is comparable to that of
conventional multipliers in terms of silicon area.",
acknowledgement = ack-nhfb,
affiliation = "IBM Thomas J. Watson Res Center, Yorktown-Heights, NY,
USA",
classification = "B1265B (Logic circuits); C5230 (Digital arithmetic
methods); C5260 (Digital signal processing); C5540
(Terminals and graphic displays)",
keywords = "Complex arithmetic; Digital signal processing;
Division; Fixed-point multiplications; Floating-point
operations; Graphics; Hybrid number system multiplier;
Logarithmic number; Modified squaring approach;
Multiplication; Square root",
thesaurus = "Computer graphic equipment; Computerised signal
processing; Digital arithmetic; Multiplying circuits",
}
@InProceedings{Langston:1989:DBT,
author = "J. L. Langston and K. Hinman",
booktitle = "{IEEE} Military Communications Conference, 1989.
{MILCOM '89}. Conference Record. Bridging the Gap.
Interoperability, Survivability, Security, 1989",
title = "Digital beamforming techniques and processors based on
quadratic residue number system techniques",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "609--614",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/MILCOM.1989.103997",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A very-high-performance digital beamforming processor
has been implemented using ASICs (application-specific
integrated circuits) fabricated in readily available
commercial CMOS process technology by using QRNS
(quadratic residue number system) \ldots{}",
}
@TechReport{Lee:1989:FIR,
author = "Jeong-A Lee and Tomas Lang",
title = "Floating-point implementation of redundant {CORDIC}
for {QR} decomposition",
type = "Technical report",
number = "CSD-890044",
institution = "Computer Science Dept., University of California",
address = "Los Angeles, CA, USA",
pages = "15 + 8",
year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Decomposition method.; Matrices.",
remark = "``July 1989.'' Supported by the National Science
Foundation.",
}
@Article{Lee:1989:MGR,
author = "Corinna Lee",
title = "Multistep Gradual Rounding",
journal = j-IEEE-TRANS-COMPUT,
volume = "38",
number = "4",
pages = "595--600",
month = apr,
year = "1989",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.21152",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 8 19:00:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://dlib.computer.org/tc/books/tc1989/pdf/t0593.pdf;
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=21152;
http://www.computer.org/tc/tc1989/t0595abs.htm",
abstract = "A value $V$ is to be rounded to an arbitrary precision
resulting in the value $ V' $. Conventional rounding
technique uses one step to accomplish this.
Alternatively, {\em multistep rounding\/} uses several
steps to round the value $V$ to successively shorter
precisions with the final rounding step producing the
desired value $ V' $. This alternate rounding method is
one way to implement, with the minimum of hardware, the
denormalization process that the IEEE Floating-Point
Standard 754 requires when underflow occurs. There are
certain cases for which multistep rounding produces a
different result than single-step rounding. To prevent
such a {\em step error}, the author introduces a
rounding procedure called {\em gradual rounding} that
is very similar to conventional rounding with the
addition of two tag bits associated with each
floating-point register.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "double rounding",
}
@Article{Lee:1989:QCC,
author = "Jon Lee",
title = "A quirk of the {CRAY CFT77} compiler: {IF} (logical)
in lieu of {IF} (arithmetic)",
journal = j-J-SUPERCOMPUTING,
volume = "3",
number = "4",
pages = "351--355",
month = dec,
year = "1989",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1007/BF00128170",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Wed Jul 6 11:13:01 MDT 2005",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=3&issue=4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0920-8542&volume=3&issue=4&spage=351",
acknowledgement = ack-nhfb,
affiliation = "Flight Dynamics Lab., Wright-Patterson AFB, OH, USA",
classification = "C5440 (Multiprocessor systems and techniques); C6110
(Systems analysis and programming); C6150C (Compilers,
interpreters and other processors); C7440 (Civil and
mechanical engineering)",
corpsource = "Flight Dynamics Lab., Wright-Patterson AFB, OH, USA",
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
keywords = "CFT77 compiler; CIVIC; computational fluid dynamics
code; conditional IF exit; DO-loops; homogeneous
turbulence; optimised code; parallel programming;
program compilers; vectorization",
treatment = "X Experimental",
}
@Book{Levy:1989:CPA,
author = "Henry M. Levy and Richard H. {Eckhouse, Jr.}",
title = "Computer programming and architecture: the {VAX}",
publisher = pub-DP,
address = pub-DP:adr,
edition = "Second",
pages = "xix + 444",
year = "1989",
ISBN = "1-55558-015-7",
ISBN-13 = "978-1-55558-015-5",
LCCN = "QA76.8.V32 L48 1989",
bibdate = "Wed Sep 14 22:51:31 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Lewis:1989:ADB,
author = "D. M. Lewis and L. K. Yu",
title = "Algorithm design for a 30-bit integrated logarithmic
processor",
crossref = "Ercegovac:1989:PSC",
pages = "192--199",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Lewis.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@InProceedings{Lin:1989:LCA,
author = "H. Lin and H. J. Sips",
title = "On-line {CORDIC} algorithms",
crossref = "Ercegovac:1989:PSC",
pages = "26--33",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Lin.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@InProceedings{Lo:1989:CED,
author = "J.-C. Lo and S. Thanawastien and T. R. N. Rao",
title = "Concurrent error detection in arithmetic and logical
operations using {Berger} codes",
crossref = "Ercegovac:1989:PSC",
pages = "233--240",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Lo.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@InProceedings{Lu:1989:VMI,
author = "P. Y. Lu and K. Dawallu",
title = "A {VLSI} Module for {IEEE} Floating-Point
Multiplication\slash Division\slash Square Root",
crossref = "IEEE:1989:PII",
bookpages = "xvii + 587",
pages = "366--368",
year = "1989",
bibdate = "Wed Nov 06 12:08:38 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The major objective of this VLSI module design is to
determine how to modify a fast floating-point
multiplier so that it can perform division and square
root in accordance with IEEE standards. This has been
achieved by applying the Newton-Ralphson iteration only
on the mantissa and adjusting the iterated result by a
rounding algorithm. Using 1.0- mu m CMOS standard cell
technology, the total area of this module is
approximately 7.0 mm*6.5 mm, which is just 25\% larger
than the floating-point multiplier. The module can
compute multiplication, division, and square root in 3,
31, and 43 cycles, respectively. The cycle time, under
nominal conditions, is expected to be 20 ns. (2
Refs.)",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "LSI Logic Corp., Menlo Park, CA, USA",
classification = "B1265B (Logic circuits); B2570D (CMOS integrated
circuits); C4130 (Interpolation and function
approximation); C5230 (Digital arithmetic methods)",
keywords = "1 Micron; 20 Ns; 7 To 6.5 mm; CMOS standard cell
technology; Cycle time; Fast floating-point multiplier;
Floating point division; Floating point square root;
IEEE standards; Iterated result; Mantissa; Multiplier
modification; Newton-Ralphson iteration; Rounding
algorithm; VLSI module design",
numericalindex = "Time 2.0E-08 s; Size 1.0E-06 m; Size 6.5E-03 to
7.0E-03 m",
thesaurus = "Cellular arrays; CMOS integrated circuits; Digital
arithmetic; Dividing circuits; Iterative methods;
Modules; Multiplying circuits; VLSI",
}
@InProceedings{Malarkey:1989:RNS,
author = "E. C. Malarkey and G. E. Marx and J. D. Fogarty and D.
Mergerian and H. K. Hahn and J. C. Bradley and P. R.
Beaudet and R. Fenton",
booktitle = "{IEEE} Military Communications Conference, 1989.
{MILCOM '89}. Conference Record. Bridging the Gap.
Interoperability, Survivability, Security, 1989",
title = "Residue-number-system-based optical adaptive
processor",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "620--623",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/MILCOM.1989.103999",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "An optical adaptive processor with 4 degrees of
freedom is under development. This processor is based
upon the use of optical lookup tables and operates
within the residue number system to provide adaptive
tap weights for nulling applications. The \ldots{}",
}
@InProceedings{Mansour:1989:CAS,
author = "Y. Mansour and B. Schieber and P. Tiwari",
booktitle = "30th Annual Symposium on Foundations of Computer
Science, 1989",
title = "The complexity of approximating the square root",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "325--330",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The authors prove upper and lower bounds for
approximately computing the square root using a given
set of operations. The bounds are extended to hold for
approximating the kth root, for any fixed k. Several
tools from approximation \ldots{}",
}
@Article{Marshall:1989:TUT,
author = "Mark Marshall",
title = "Techniques for user testing of the 68882",
journal = j-MICROPROC-MICROSYS,
volume = "13",
number = "6",
pages = "382--386",
month = jul # "\slash " # aug,
year = "1989",
CODEN = "MIMID5",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "NCR Corp., Wichita, KS",
bibno = "72545",
catcode = "B.5.3; C.5.3; B.5.1",
content = "This short, clearly written paper describes how NCR
Corporation developed a series of programs to test the
Motorola 68882 floating-point coprocessor for
Motorola's 68020 and 68030 microprocessors. Integrated
circuits are tested for two reasons: to ensure that a
properly working unit meets its specifications, and to
ensure that a particular unit works properly. As
Marshall points out, manufacturers cannot always be
relied upon to perform either of these tests perfectly.
The programs described in this paper have been used
both to monitor the quality of incoming parts and to
verify that device mask or specification changes do not
effect the part's usability for NCR's
purposes.\par
This paper describes the methods by which NCR's
2700-instruction, 550,000-clock cycle test program was
developed and how it works. Since the internal workings
of the 68882 are not visible to the user, NCR adopted
the functional testing approach. Of particular interest
is NCR's sequential approach to the testing proper,
which assumes that ``no element is functional unless
previously tested.'' While the specifics of each step
vary from one microprocessor to another, the principles
still apply.\par
This is not a research paper. It does not disclose
startling new results or advance the frontiers of human
knowledge. It does show how state-of-the-art
engineering practice can achieve desirable \ldots{}",
CRclass = "B.5.3 Reliability and Testing; B.5.3 Test generation;
C.5.3 Microcomputers; B.5.1 Design",
CRnumber = "9006-0473",
descriptor = "Hardware, REGISTER-TRANSFER-LEVEL IMPLEMENTATION,
Reliability and Testing, Test generation; Computer
Systems Organization, COMPUTER SYSTEM IMPLEMENTATION,
Microcomputers; Hardware, REGISTER-TRANSFER-LEVEL
IMPLEMENTATION, Design",
fjournal = "Microprocessors and Microsystems",
genterm = "ALGORITHMS; DESIGN; VERIFICATION",
guideno = "1989-09211",
journalabbrev = "Microprocess. Microsyst.",
keywords = "floating-point testing",
reviewer = "E. Mallach",
subject = "B. Hardware; B.5 REGISTER-TRANSFER-LEVEL
IMPLEMENTATION; C. Computer Systems Organization; C.5
COMPUTER SYSTEM IMPLEMENTATION; B. Hardware; B.5
REGISTER-TRANSFER-LEVEL IMPLEMENTATION",
}
@Article{Mastrovito:1989:VDM,
author = "E. D. Mastrovito",
title = "{VLSI} designs for multiplication over finite fields
{$ \mathrm {GF}(2^m) $}",
journal = j-LECT-NOTES-COMP-SCI,
volume = "357",
pages = "397--309",
year = "1989",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Fri Jun 24 21:09:00 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Maytal:1989:DCG,
author = "B. Maytal and S. Iacobovici and D. B. Alpert and D.
Biran and J. Levy and S. Y. Tov",
title = "Design considerations for a general-purpose
microprocessor",
journal = j-COMPUTER,
volume = "22",
number = "1",
pages = "66--76",
month = jan,
year = "1989",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Sat Sep 14 07:29:35 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Misc/IMMD_IV.bib",
acknowledgement = ack-nhfb,
affiliation = "Nat. Semicond., Santa Clara, CA, USA",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5220 (Computer architecture)",
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
keywords = "32 Bit; Clock frequency; Data-flow monitoring
mechanisms; Floating-point operations; General-purpose
microprocessor; Instruction-flow; Market requirements;
Memory hierarchy; Memory reference transactions;
Microarchitecture; Multiprocessing support; NS 32532;
On-chip caches; Packaging technologies; Pipeline;
System interface; Target applications; VLSI",
numericalindex = "Word length 3.2E+01 bit",
thesaurus = "Computer architecture; Microcomputers; Microprocessor
chips",
}
@InProceedings{Milenkovic:1989:DPG,
author = "V. Milenkovic",
booktitle = "30th Annual Symposium on Foundations of Computer
Science, 1989",
title = "Double precision geometry: a general technique for
calculating line and segment intersections using
rounded arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "500--505",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "For the first time it is shown how to reduce the cost
of performing specific geometric constructions by using
rounded arithmetic instead of exact arithmetic. By
exploiting a property of floating-point arithmetic
called monotonicity, a technique \ldots{}",
}
@Article{Milutinovic:1989:MSD,
author = "V. Milutinovic and M. Bettinger and W. Helbig",
title = "Multiplier\slash shifter design tradeoffs in a 32-bit
microprocessor",
journal = j-IEEE-TRANS-COMPUT,
volume = "38",
number = "6",
pages = "874--880",
month = jun,
year = "1989",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.24298",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 8 19:00:40 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=24298",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Molnar:1989:MBF,
author = "K. Molnar and C.-Y. Ho and D. Staver and B. Davis and
R. Jerdonek",
title = "A 40 {MHz} 64-Bit Floating-Point Co-Processor",
crossref = "Wuorinen:1989:DTP",
pages = "48--49, 287",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An arithmetic coprocessor capable of executing 64-bit
double-precision floating-point, 32-bit
single-precision floating-point, and 32-bit integer
instructions has been integrated onto a 1.0-cm*1.1-cm
chip in a 1.2- mu m, single-poly, double-metal bulk
CMOS process. The chip contains 17000 transistors and
includes a register file, two accumulators, and
separate interface, multiplication, and addition
subprocessors. The coprocessor which is the arithmetic
unit for a multichip microprocessor system, is packaged
in a 132-pin leadless ceramic chip carrier. The
coprocessor can be issued a new instruction each 25-ns
clock cycle, and 64-bit double-precision arithmetic
with full IEEE rounding is executed at a peak rate of
26.7 MFLOPs (million floating-point operations per
second). The waveforms of a store instruction operating
at 40 MHz are shown.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Gen. Electr. Corp. Res. and Dev. Center, Schenectady,
NY, USA",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5230 (Digital arithmetic methods)",
keywords = "1.2 Micron; 26.7 MFLOPS; 32-Bit integer instructions;
40 MHz; 64 Bit; Accumulators; Addition subprocessors;
Arithmetic coprocessor; Double-metal bulk CMOS process;
Double-precision floating-point; Floating point
coprocessor; Interface subprocessor; Leadless ceramic
chip carrier; Multichip microprocessor system;
Multiplication subprocessor; Peak rate; Register file;
Single-precision floating-point; Store instruction;
Waveforms",
numericalindex = "Frequency 4.0E+07 Hz; Word length 6.4E+01 bit; Size
1.2E-06 m; Computer speed 2.67E+07 FLOPS",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Microprocessor chips",
}
@InProceedings{Montuschi:1989:EIH,
author = "Paolo Montuschi and Luigi Cinimera",
title = "On the efficient implementation of higher radix square
root algorithms",
crossref = "Ercegovac:1989:PSC",
pages = "154--161",
year = "1989",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Montuschi.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
summary = "Square root nonrestoring algorithms operating with a
radix higher than two (but power of 2) are discussed.
Formulas are derived delimiting the feasibility space
of the class of algorithms considered as a function of
the different parameters. This \ldots{}",
}
@Book{Moshier:1989:MPM,
author = "Stephen L. B. Moshier",
title = "Methods and Programs for Mathematical Functions",
publisher = pub-ELLIS-HORWOOD,
address = pub-ELLIS-HORWOOD:adr,
pages = "vii + 415",
year = "1989",
ISBN = "0-7458-0289-3",
ISBN-13 = "978-0-7458-0289-3",
LCCN = "QA331 .M84 1989",
MRclass = "*65D20, 26-04, 33-04, 65-02, 65C99",
bibdate = "Thu Sep 01 10:33:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\pounds 48.00",
URL = "http://www.moshier.net/;
http://www.netlib.org/cephes",
ZMnumber = "0701.65011",
acknowledgement = ack-nj,
shorttableofcontents = "Preface / vii \\
1: Floating Point Arithmetic / 1 \\
2: Approximation Methods / 75 \\
3: Software Notes / 129 \\
4: Elementary Functions / 143 \\
5: Probability Distributions and Related Functions /
201 6: Bessel Functions / 263 \\
7: Other Special Functions / 333 \\
Bibliography / 411 \\
Index / 413",
tableofcontents = "Preface / vii \\
1: Floating Point Arithmetic / 1 \\
1.1 Numeric Data Structures / 1 \\
1.2 Rounding / 5 \\
1.3 Addition and Subtraction / 6 \\
1.4 Multiplication / 7 \\
1.4.1 Long Multiplication in Binary Radix / 8 \\
1.4.2 Multiplication in Word Integer Radix / 8 \\
1.4.3 Fast Multiplication / 9 \\
1.5 Division / 10 \\
1.5.1 Long Division / 10 \\
1.5.2 Division by Taylor Series / 11 \\
1.5.3 Newton--Raphson Division / 11 \\
1.6 C Language / 12 \\
1.7 An Extended Double Arithmetic: ieee.c / 13 \\
1.8 Binary - Decimal Conversion / 46 \\
1.8.1 etoasc.c / 47 \\
1.8.2 asctoe.c / 54 \\
1.9 Analysis of Error / 58 \\
1.9.1 Roundoff and Cancellation / 58 \\
1.9.2 Error Propagation / 60 \\
1.9.3 Error as a Random Variable / 61 \\
1.9.4 Order of Summation / 62 \\
1.10 Complex Arithmetic / 62 \\
1.10.1 cmplx.c / 64 \\
1.10.2 Absolute Value: cabs.c / 67 \\
1.11 Rational Arithmetic / 69 \\
1.11.1 euclid.c / 70 \\
2: Approximation Methods / 75 \\
2.1 Power Series / 75 \\
2.2 Chebyshev Expansions / 76 \\
2.2.1 chbevl.c / 79 \\
2.3 Pad{\'e} Approximations / 80 \\
2.4 Least Maximum Approximations / 82 \\
2.4.1 Best Polynomial Approximations / 82 \\
2.4.2 Best Rational Approximations / 85 \\
2.4.3 Special Rational Forms / 87 \\
2.5 A Program to Find Best Approximations: remes.c / 88
\\
2.6 Forms of Approximation / 111 \\
2.7 Asymptotic Expansions / 113 \\
2.8 Continued Fractions / 114 \\
2.8.1 Continued Fractions from Recurrences / 115 \\
2.8.2 Recurrences from Differential Equations / 116 \\
2.8.3 Computing Continued Fractions / 117 \\
2.9 Polynomials / 117 \\
2.9.1 polevl.c / 118 \\
2.10 Newton--Raphson Iterations / 119 \\
2.10.1 Division / 120 \\
2.10.2 Exponent Separation / 121 \\
2.10.3 Square Root / 122 \\
2.10.4 sqrt.c / 123 \\
2.10.5 Longhand Square Root / 124 \\
2.10.6 esqrt.c / 124 \\
2.10.7 Cube Root / 126 \\
2.10.8 cbrt.c / 127 \\
3: Software Notes / 129 \\
3.1 Design Strategy / 129 \\
3.2 Testing / 131 \\
3.3 System Utilities / 132 \\
3.3.1 mconf.h / 132 \\
3.3.2 mtherr.c / 134 \\
3.3.3 const.c / 136 \\
3.4 Arithmetic Utilities / 137 \\
3.4.1 efloor.c / 138 \\
3.4.2 efrexp.c / 140 \\
3.4.3 eldexp.c / 140 \\
4: Elementary Functions / 143 \\
4.1 $e^x$ / 143 \\
4.1.1 exp.c / 145 \\
4.2 $\ln x$ / 147 \\
4.2.1 log.c / 149 \\
4.3 Argument Transformation for Circular Functions /
152 \\
4.4 Sine and cosine / 153 \\
4.4.1 sin.c / 154 \\
4.4.2 cos.c / 156 \\
4.5 Tangent and Cotangent / 157 \\
4.5.1 tan.c / 158 \\
4.6 Complex Circular Functions / 161 \\
4.7 $\sin^{-1} x $ / 162 \\
4.7.1 asin.c / 163 \\
4.8 $\cos^{-1} x $ / 165 \\
4.8.1 acos.c / 165 \\
4.9 $\tan^{-1} x$ / 166 \\
4.9.1 atan.c / 168 \\
4.9.2 atan2.c / 169 \\
4.10 Complex Inverse Circular Functions / 170 \\
4.11 $\sinh x$ / 170 \\
4.11.1 sinh.c / 171 \\
4.12 $\cosh x$ / 172 \\
4.12.1 cosh.c / 173 \\
4.13 $\tanh x$ / 173 \\
4.13.1 tanh.c / 174 \\
4.14 $\sinh^{-1} x $ / 175 \\
4.14.1 asinh.c / 176 \\
4.15 $\cosh^{-1} x $ / 177 \\
4.15.1 acosh.c / 178 \\
4.16 $\tanh^{-1} x$ / 179 \\
4.16.1 atanh.c / 180 \\
4.17 Power Function / 181 \\
4.17.1 Real Exponent / 182 \\
4.17.2 pow.c / 182 \\
4.17.3 Integer Exponent / 189 \\
4.17.4 powi.c / 190 \\
4.18 Testing / 192 \\
4.19 Single Precision Polynomial Approximations / 193
\\
4.19.1 $\cos x$ / 193 \\
4.19.2 $\cosh^{-1} x $ / 193 \\
4.19.3 $\exp x$ / 196 \\
4.19.4 $\ln x$ / 196 \\
4.19.5 $\sin x$ / 197 \\
4.19.6 $\sin^{-1} x $ / 197 \\
4.19.7 Square Root / 197 \\
4.19.8 $\tan x$ / 198 \\
4.19.9 $\tan^{-1} x$ / 198 \\
4.19.10 $\tanh x$ / 199 \\
4.19.11 $tanh^{-1} x$ / 199 \\
5: Probability Distributions and Related Functions /
201 \\
5.1 $n!$ / 202 \\
5.1.1 fac.c / 204 \\
5.2 $\Gamma(x)$ / 206 \\
5.2.1 gamma.c / 210 \\
5.2.2 lgam.c / 214 \\
5.3 Incomplete Gamma Integral / 217 \\
5.3.1 igamc.c / 218 \\
5.3.2 igam.c / 220 \\
5.3.3 Functional Inverse of Incomplete Gamma Integral /
221 \\
5.3.4 igami.c / 221 \\
5.4 Gamma Distribution / 222 \\
5.4.1 gdtr c / 222 \\
5.4.2 gdtrc.c / 223 \\
5.5 $\chi^2$ Distribution / 223 \\
5.5.1 chdtrc.c / 224 \\
5.5.2 chdtr.c / 224 \\
5.5.3 chdtrl.c / 224 \\
5.6 Poisson Distribution / 225 \\
5.6.1 pdtrc.c / 225 \\
5.6.2 pdtr.c / 226 \\
5.6.3 pdtri.c / 226 \\
5.7 Beta Function / 227 \\
5.7.1 beta.c / 227 \\
5.8 Incomplete Beta Integral / 229 \\
5.8.1 ibet.c / 231 \\
5.8.2 Functional Inverse of Incomplete Beta Integral /
238 \\
5.9 Beta Distribution / 241 \\
5.9.1 btdtr.c / 241 \\
5.10 Binomial Distribution / 241 \\
5.10.1 bdtrc.c / 242 \\
5.10.2 bdtr.c / 243 \\
5.10.3 bdtri.c / 244 \\
5.11 Negative Binomial Distribution / 244 \\
5.11.1 nbdtr.c / 245 \\
5.11.2 nbdtrc.c / 245 \\
5.12 F Distribution / 246 \\
5.12.1 fdtrc.c / 247 \\
5.12.2 fdtr.c / 247 \\
5.12.3 fdtrci.c / 248 \\
5.13 Student's $t$ distribution / 249 \\
5.13.1 stdtr.c / 250 \\
5.14 Gaussian Distribution / 252 \\
5.14.1 ndtr.c / 254 \\
5.14.2 erfc.c / 256 \\
5.14.3 erf.c / 257 \\
5.14.4 Functional Inverse of Gaussian Distribution /
258 \\
5.14.5 ndtri.c / 259 \\
6: Bessel Functions / 263 \\
6.1 $J_0(x)$ / 263 \\
6.1.1 jO.c / 265 \\
6.2 $Y_0(x)$ / 268 \\
6.2.1 yO.c / 269 \\
6.3 Modulus and Phase / 270 \\
6.4 $J_1(x)$ / 271 \\
6.4.1 jl.c / 272 \\
6.5 $Y_1(x)$ / 275 \\
6.5.1 yl.c / 275 \\
6.6 $J_n(x)$ / 276 \\
6.1 $I_0(x)$ / 277 \\
6.7.1 i0.c / 278 \\
6.8 $I_1(x)$ / 281 \\
6.8.1 i1.c / 283 \\
6.9 $I_\nu(x)$ / 285 \\
6.9.1 iv.c / 286 \\
6.10 $K_0(x)$ / 287 \\
6.10.1 kO.c / 287 \\
6.11 $K_1(x)$ / 291 \\
6.11.1 kl.c / 291 \\
6.12 $K_n(x)$ / 294 \\
6.12.1 kn.c / 295 \\
6.13 $J_\nu(x)$ / 299 \\
6.13.1 jv.c / 301 \\
6.14 Airy Functions / 315 \\
6.14.1 airy.c / 322 \\
6.15 $Y_n(x)$ / 328 \\
6.15.1 yn.c / 329 \\
6.16 Testing / 330 \\
7: Other Special Functions / 333 \\
7.1 Hypergeometric Functions / 333 \\
7.1.1 $_2F_1$ / 334 \\
7.1.2 hyp2fi.c / 335 \\
7.1.3 $_1F_1$ / 341 \\
7.1.4 hyplfi.c / 342 \\
7.1.5 $_2F_0$ / 346 \\
7.1.6 hyp2ffi.c / 346 \\
7.2 Struve Functions / 348 \\
7.2.1 hypl1f2.c / 348 \\
7.2.2 hyp3f0.c / 349 \\
7.2.3 yv.c / 351 \\
7.2.4 struve.c / 351 \\
7.3 $\psi(x)$ / 352 \\
7.3.1 psi.c / 354 \\
7.4 Exponential Integral / 355 \\
7.4.1 en.c / 356 \\
7.5 Sine and Cosine Integrals / 360 \\
7.5.1 sici.c / 362 \\
7.5.2 Hyperbolic Sine and Cosine Integrals / 367 \\
7.5.3 shichi.c / 370 \\
7.6 Dilogarithm / 374 \\
7.6.1 spence.c / 375 \\
7.7 Dawson's Integral / 377 \\
7.7.1 dawsn.c / 378 \\
7.8 Fresnel Integrals / 381 \\
7.8.1 fresnl.c / 383 \\
7.9 Elliptic Functions / 387 \\
7.9.1 $K(m)$ / 387 \\
7.9.2 ellpk.c / 388 \\
7.9.3 $F(\phi|m)$ / 389 \\
7.9.4 ellik.c / 390 \\
7.9.5 $E(m)$ / 392 \\
7.9.6 ellpe.c / 392 \\
7.9.7 $E(\phi|m)$ / 393 \\
7.9.8 ellie.c / 394 \\
7.9.9 Jacobian Elliptic Functions / 396 \\
7.9.10 ellpj.c / 398 \\
7.10 Zeta Functions / 400 \\
7.10.1 hurwiz.c / 400 \\
7.10.2 Riemann Zeta Function / 402 \\
7.10.3 zetac.c / 405 \\
Bibliography / 411 \\
Index / 413",
}
@Manual{Motorola:1989:DIF,
title = "{DSP96002}: {IEEE} floating-point dual-port processor:
user's manual",
organization = "{Motorola, Inc.}",
address = "Phoeniz, AZ, USA",
pages = "various",
year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Signal processing.",
remark = "Cover title. Spine title: DSP96002 user's manual.
``DSP96002UM/AD''--Cover.",
}
@Book{Motorola:1989:FPC,
author = "{Motorola, Inc.}",
title = "{MC68881}\slash {MC68882} Floating-Point Coprocessor
User's Manual",
publisher = pub-PH,
address = pub-PH:adr,
edition = "Second",
pages = "various",
year = "1989",
ISBN = "0-13-567009-8",
ISBN-13 = "978-0-13-567009-5",
LCCN = "????",
bibdate = "Fri Dec 08 13:02:55 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Book{Motorola:1989:MFP,
author = "{Motorola, Inc.Staff}",
title = "{MC} 68881 and 68882 Floating-Point Coprocessor User's
Manual",
publisher = pub-PH,
address = pub-PH:adr,
edition = "0002",
month = aug,
year = "1989",
ISBN = "0-13-567009-8",
ISBN-13 = "978-0-13-567009-5",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$27.00",
acknowledgement = ack-nhfb,
keywords = "MICROPROCESSORS; TECHNOLOGY --- COMPUTERS AND COMPUTER
TECHNOLOGY",
language = "eng",
}
@Book{Motorola:1989:MMF,
author = "{Motorola, Inc.}",
title = "{MC68881\slash MC68882} floating-point coprocessor
user's manual",
publisher = pub-PH,
address = pub-PH:adr,
edition = "Second",
pages = "various",
year = "1989",
ISBN = "0-13-567009-8 (pbk.)",
ISBN-13 = "978-0-13-567009-5 (pbk.)",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Microprocessors ---
Handbooks, manuals, etc.; Motorola 68881
(Microprocessor); Motorola 68882 (Microprocessor)",
remark = "Spine title: MC68881/882 user's manual. ``MC68881UM/AD
REV 2''--Cover.",
}
@Book{Motorola:1989:MRM,
author = "Motorola",
title = "{MC88100} {RISC} Microprocessor User's Manual",
publisher = pub-MOTOROLA,
address = pub-MOTOROLA:adr,
edition = "Second",
year = "1989",
ISBN = "0-13-567090-X",
ISBN-13 = "978-0-13-567090-3",
LCCN = "QA76.8.M75 M3 1990",
bibdate = "Wed Jul 6 14:23:15 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/microchip.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Overview \\
Features \\
Introduction \\
Execution Units and Register File \\
Execution Model \\
Programming Model \\
Processor States \\
Reset State \\
Flow-Control Instructions \\
Register with 9-Bit Vector Table Index \\
Instruction Categories \\
Programming Tips \\
Instruction Set \\
Opcode Summary \\
Signal Description \\
Data Processor Bus Signals \\
Exceptions \\
Exception Overview \\
Exception Vectors and Vector Base Register (VBR) \\
Exception Priority \\
Exception Processing \\
Instruction Unit Exceptions \\
Integer Overflow Exception (Vector Offset \$48) \\
Memory Access Exceptions \\
FPU Exception Processing \\
FPU Exception Processing Registers \\
Timing Factors \\
Execution Example \\
Instruction Set Timing Summary \\
Applications Information \\
Cache Memory Management Units \\
Power and Ground Considerations \\
Master/Checker Operations \\
Synchronization Operations \\
Electrical Characteristics",
}
@Article{Mulcahy:1989:FPR,
author = "L. P. Mulcahy",
title = "On fixed-point roundoff error analysis",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "37",
number = "10",
pages = "1623",
month = oct,
year = "1989",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "The author points out the existence of work published
by the author (US Department of Commerce, Tech. Rep.
AD-A086826, 57 pp., Apr. 1980) prior to the appearance
of the paper by Barnes et al. (ibid., vol.ASSP-33,
p.595-606, June 1985) covering the same \ldots{}",
}
@InProceedings{Nakayama:1989:BMF,
author = "T. Nakayama and S. Kojima and H. Harigai and H.
Igarashi and K. Tamada and T. Toba",
title = "An 80 b, 6.7 {MFLOPS} floating-point processor with
vector\slash matrix instructions",
crossref = "Wuorinen:1989:DTP",
pages = "52--53, 289",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A description is given of an 80-b CMOS VLSI
floating-point processor (FPP) in 1.2- mu m
double-metal layer CMOS which contains 433000
transistors on an 11.6-mm*14.9-mm die. It operates at
20 MHz, dissipates 1.5 W, and is assembled in a 68-lead
pin-grid-array package. The FPP is designed as a
coprocessor for 32-b microprocessors. It implements
data formats, arithmetic rounding modes, and exception
types which are defined by the IEEE 754 standard. The
chip can handle single (32 b), double (64 b), and
double-extended (80 b) floating-point data formats. The
complex-instruction-set-computer- (CISC-) like
78-instruction set includes 22 mathematical functions
such as sin, cos, arctan, exp, and log, and 24
vector/matrix operations such as add, multiply, and
inner product. The features and performance of the
device are summarized.",
acknowledgement = ack-nhfb,
affiliation = "NEC, Kawasaki, Japan",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5230 (Digital arithmetic methods)",
keywords = "1.2 Micron; 1.5 W; 20 MHz; 6.7 MFLOPS; 80 Bit;
Arithmetic rounding modes; CMOS VLSI floating-point
processor; Complex instruction set computer; Data
formats; Double-metal layer CMOS; Exception types;
Mathematical functions; Pin-grid-array package; Power
dissipation; Vector/matrix instructions",
numericalindex = "Word length 8.0E+01 bit; Computer speed 6.7E+06
FLOPS; Size 1.2E-06 m; Frequency 2.0E+07 Hz; Power
1.5E+00 W",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Microprocessor chips; VLSI",
}
@Article{Nakayama:1989:FCV,
author = "T. Nakayama and H. Harigai and S. Kojima and H. Kaneko
and H. Igarashi and T. Toba and Y. Yamagami and Y.
Yano",
title = "A 6.7-{MFLOPS} floating-point coprocessor with
vector\slash matrix instructions",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "24",
number = "5",
pages = "1324--1330",
month = oct,
year = "1989",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An 80-bit floating-point coprocessor which implements
24 vector/matrix instructions and 22 mathematical
functions is described. This processor can execute
floating-point addition/rounding and pipelined
multiplication concurrently, under the control of
horizontal-type microinstructions. The SRT division
method and CORDIC trigonometrical algorithm are used
for a favorable cost/performance implementation. The
performance of 6.7 MFLOPS in the vector-matrix
multiplication at 20 MHz has been attained by the use
of parallel operations. The vector/matrix instruction
is about three times faster than conventional add and
multiply instructions. The chip has been fabricated in
1.2- mu m double-metal layer CMOS process containing
433000 transistors on a 11.6*14.9-mm/sup 2/ die size.",
acknowledgement = ack-nhfb,
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5230 (Digital arithmetic methods)",
fjournal = "IEEE Journal of Solid-State Circuits",
keywords = "1.2 Micron; 20 MHz; 6.7 MFLOPS; 80 Bit; CMOS process;
CORDIC trigonometrical algorithm; Double-metal layer;
Floating-point coprocessor; Horizontal-type
microinstructions; Mathematical functions; Parallel
operations; Pipelined multiplication; SRT division
method; Vector/matrix instructions; VLSI
microprocessor",
numericalindex = "Word length 8.0E+01 bit; Size 1.2E-06 m; Computer
speed 6.7E+06 FLOPS; Frequency 2.0E+07 Hz",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Instruction sets; Microprocessor chips; Parallel
architectures; Pipeline processing; Satellite
computers; VLSI",
}
@InProceedings{Nakayama:1989:MFPa,
author = "T. Nakayama and S. Kojima and H. Harigai and H.
Igarashi and K. Tamada and T. Toba",
title = "An 80b, 6.7 {MFLOPS} Floating-Point Processor with
{Vector/Matrix} Instructions",
crossref = "Wuorinen:1989:DTP",
pages = "52--53, 289",
year = "1989",
bibdate = "Fri Dec 08 13:04:53 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Nakayama:1989:MFPb,
author = "T. Nakayama and H. Harigai and S. Kojima and H. Kaneko
and H. Igarashi and T. Toba and Y. Yamagami and Y.
Yano",
title = "A 6.7-{MFLOPS} Floating-Point Coprocessor with
Vector\slash Matrix Instructions",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "24",
number = "5",
pages = "1324--1330",
month = oct,
year = "1989",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "An 80-bit floating-point coprocessor which implements
24 vector/matrix instructions and 22 mathematical
functions is described. This processor can execute
floating-point addition/rounding and pipelined
multiplication concurrently, under the control
\ldots{}",
}
@InProceedings{Nowacki:1989:ABQ,
author = "C. L. Nowacki and J. D. Harris and M. N. Richard",
booktitle = "{IEEE} Military Communications Conference, 1989.
{MILCOM '89}. Conference Record. Bridging the Gap.
Interoperability, Survivability, Security, 1989",
title = "Adaptive beamforming in quadratic residue number
systems on a cluster array processor",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "624--628",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/MILCOM.1989.104000",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The authors describe a quadratic residue number system
(QRNS) implementation of the Leverrier algorithm for
computing the adjoint and determinant of a matrix on a
prototype parallel signal processor, called the cluster
array processor (CAP). Some \ldots{}",
}
@Article{Ochs:1989:TPF,
author = "T. Ochs",
title = "Theory and practice (floating point arithmetic)",
journal = j-COMP-LANG-MAG,
volume = "6",
number = "3",
pages = "67--70, 72, 74, 77--78, 80--81",
month = mar,
year = "1989",
CODEN = "COMLEF",
ISSN = "0749-2839",
bibdate = "Tue Dec 12 09:20:14 MST 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The IEEE-754 standard for floating point arithmetic
has inherent limits. The author presents a guide to
NaNs, unnormals, underflows and signal infinite
quantities.",
acknowledgement = ack-nhfb # " and " # ack-nj,
classification = "C5230 (Digital arithmetic methods); C6150C
(Compilers, interpreters and other processors)",
fjournal = "Computer Language Magazine",
keywords = "Compilers; Floating point arithmetic; IEEE-754
standard; NaNs; Signal infinite quantities; Underflows;
Unnormals",
thesaurus = "Digital arithmetic; Program compilers",
}
@InProceedings{Petkovsek:1989:CDS,
author = "M. Petkovsek",
title = "Contiguous digit sets and local roundings",
crossref = "Ercegovac:1989:PSC",
pages = "136--143",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Petkovsek.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@Article{Pincin:1989:NAM,
author = "A. Pincin",
title = "A new algorithm for multiplication in finite fields",
journal = j-IEEE-TRANS-COMPUT,
volume = "38",
number = "7",
pages = "1045--1049",
month = jul,
year = "1989",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.30855",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 8 19:00:40 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=30855",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Prince:1989:FTF,
author = "Timothy Prince",
title = "Float Trig Functions For The {C} Preprocessor",
journal = j-CUJ,
volume = "7",
number = "8",
pages = "103--??",
month = aug,
year = "1989",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@InProceedings{Ramamoorthy:1989:HSA,
author = "P. A. Ramamoorthy and B. Potu",
booktitle = "International Conference on Acoustics, Speech, and
Signal Processing, {ICASSP-89, 23--26} May 1989",
title = "High-speed {ADC} using residue number system",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1063--1066",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1989.266615",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "An ADC (analog/digital converter) architecture based
on a residue number system (RNS) and multiple folding
of the input signal is described. The number of
comparators used is equal to the sum of moduli for
obtaining the dynamic range desired. An \ldots{}",
}
@InProceedings{Rao:1989:RNF,
author = "B. D. Rao",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, 8--11 May 1989",
title = "Roundoff noise in floating point state space digital
filters",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "724--727",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The roundoff noise properties of floating-point
state-space digital filters are examined. It is shown
that the roundoff noise behavior of these filters is
related to their coefficient sensitivity. Expressions
for the variance of the output roundoff \ldots{}",
}
@InProceedings{Ray:1989:MCA,
author = "G. A. Ray",
booktitle = "Proceedings of the 32nd Midwest Symposium on Circuits
and Systems, 1989",
title = "Multiple core algorithms for residue number systems",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "833--836",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/MWSCAS.1989.101984",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The core function provides an easily implemented and
efficient means for performing the traditionally
difficult residue operations. However, two problems
with core algorithms are the difficulty in choosing
core coefficients and the many iterations \ldots{}",
}
@InProceedings{Rishe:1989:LEN,
author = "Naphtali Rishe",
title = "Lexicographic Encoding of Numeric Data Fields",
crossref = "Ercegovac:1989:PSC",
pages = "241--246",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Rishe.pdf",
abstract = "This paper proposes a method of variable-radix
representation of numeric data. The method allows
compact representation of arbitrary numbers. Among its
properties is that bitwise lexicographic comparison
($<$, $>$) is consistent with correct numeric
comparison of numbers.",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@Book{Robbins:1989:CXM,
author = "Kay A. Robbins and Steven Robbins",
title = "The {Cray X-MP}\slash {Model} 24",
publisher = pub-SV,
address = pub-SV:adr,
pages = "vi + 165",
year = "1989",
ISBN = "0-387-97089-4, 3-540-97089-4",
ISBN-13 = "978-0-387-97089-9, 978-3-540-97089-7",
LCCN = "QA76.8 C72 R63 1989",
bibdate = "Sat Jan 29 18:17:38 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Saffari:1989:PDW,
author = "B. Saffari",
title = "Putting {DSPs} to work",
journal = j-BYTE,
volume = "14",
number = "13",
pages = "259--272",
month = dec,
year = "1989",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 12 17:47:21 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "B1265F (Microprocessors and microcomputers); B2570
(Semiconductor integrated circuits); B6140 (Signal
processing and detection); C5130 (Microprocessor
chips); C5260 (Digital signal processing)",
fjournal = "BYTE Magazine",
keywords = "Digital filters; Feature extraction; Floating-point
application-specific-IC DSPs; Image processing;
Moments; Pattern recognition architecture; Sound; Space
correction; Time",
thesaurus = "Application specific integrated circuits; Computerised
signal processing; Digital signal processing chips",
}
@InProceedings{Santoro:1989:RAI,
author = "M. R. Santoro and G. Bewick and M. A. Horowitz",
title = "Rounding Algorithms for {IEEE} Multipliers",
crossref = "Ercegovac:1989:PSC",
pages = "176--183",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Santoro.pdf",
acknowledgement = ack-nhfb # " and " # ack-nj,
keywords = "ARITH-9",
summary = "Several technology independent rounding algorithms for
multiplying normalized numbers are presented. The first
is a simple rounding algorithm suitable for software
simulation or moderate performance hardware
multipliers. The next two algorithms are \ldots{}",
}
@Article{Sasaki:1989:AAD,
author = "Tateaki Sasaki and Mutsuko Sasaki",
title = "Analysis of accuracy decreasing in polynomial
remainder sequence with floating-point number
coefficients",
journal = "J. Inform. Process.",
volume = "12",
number = "4",
pages = "394--403",
year = "1989",
MRclass = "65G05 (65Y20)",
MRnumber = "91h:65069",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Schwarz:1989:IIP,
author = "Jerry Schwarz",
title = "Implementing infinite precision arithmetic",
crossref = "Ercegovac:1989:PSC",
pages = "10--17",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Schwarz.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@Article{Scott:1989:FRM,
author = "M. Scott",
title = "Fast rounding in multiprecision floating-slash
arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "38",
number = "7",
pages = "1049--1052",
month = jul,
year = "1989",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.30856",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "A computational algorithm is described which quickly
rounds large fractions into a fixed-length
multiprecision floating-slash representation, using
single-precision operations where possible. An easily
calculated criterion for terminating the \ldots{}",
}
@Article{Shenoy:1989:FBE,
author = "A. P. Shenoy and R. Kumaresan",
title = "Fast base extension using a redundant modulus in
{RNS}",
journal = j-IEEE-TRANS-COMPUT,
volume = "38",
number = "2",
pages = "292--297",
month = feb,
year = "1989",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.16508",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 8 19:00:38 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=16508",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Shimazu:1989:MFP,
author = "Y. Shimazu and T. Kengaku and T. Fujiyama and E.
Teraoka and T. Ohno and T. Tokuda and O. Tomisawa and
S. Tsujimichi",
title = "A 50 {MHz} 24b Floating-Point {DSP}",
crossref = "Wuorinen:1989:DTP",
pages = "44--45, 285",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A 24-bit floating-point digital signal processor (DSP)
has been developed primarily for speech processing and
communication applications. The chip uses 1.0- mu m
double-metal CMOS with tungsten silicide technology.
The instruction set is upward compatible with an 18-bit
DSP. Novel circuit design techniques allowing 40-ns
machine cycle time at 50-MHz clock and less than 600-mW
power dissipation are described. A built-in self-test
is prepared using on-chip IROM and the two 24-bit
linear feedback shift registers which are included in
I/O registers such as the data register, the serial
input registers, and the serial output registers. The
DSP design features are summarized.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
affiliation = "Mitsubishi, Hyogo, Japan",
chemicalindex = "WSi2/int Si2/int Si/int W/int WSi2/bin Si2/bin Si/bin
W/bin",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); B6130 (Speech analysis and
processing techniques); C5130 (Microprocessor chips);
C5230 (Digital arithmetic methods); C5260 (Digital
signal processing)",
keywords = "1 Micron; 24 Bit; 40 Ns; 50 MHz; 600 MW; Built-in
self-test; Circuit design techniques; Clock frequency;
Communication applications; Data register; Double-metal
CMOS; Floating-point digital signal processor; I/O
registers; Instruction set; Linear feedback shift
registers; Machine cycle time; On-chip IROM; Power
dissipation; Serial input registers; Serial output
registers; Speech processing; WSi/sub 2/ technology",
numericalindex = "Frequency 5.0E+07 Hz; Word length 2.4E+01 bit; Time
4.0E-08 s; Power 6.0E-01 W; Size 1.0E-06 m",
thesaurus = "CMOS integrated circuits; Digital arithmetic; Digital
signal processing chips; Speech analysis and
processing",
}
@Article{Sinha:1989:FPA,
author = "B. P. Sinha and P. K. Srimani",
title = "Fast parallel algorithms for binary multiplication and
their implementation on systolic architectures",
journal = j-IEEE-TRANS-COMPUT,
volume = "38",
number = "3",
pages = "424--431",
month = mar,
year = "1989",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.21128",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 8 19:00:38 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=21128",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Sit:1989:MFP,
author = "H. P. Sit and M. R. Nofal and S. Kimn",
title = "An 80 {MFLOPS} Floating-point Engine in the {Intel}
i860{\TM} Processor",
crossref = "IEEE:1989:PII",
pages = "374--379",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The i860 processor is a 64-b microprocessor with 1.02
million transistors. It has a 64-b external data bus
and a 32-b external address bus. It is fabricated with
Intel's CHMOS IV technology (a 1- mu m double-metal
process). The die size is approximately 10 mm*15 mm.
First silicon is functional over commercial temperature
and voltage ranges with an execution speed of 40 MHz.
The floating-point engine consists of a pipelined adder
and a pipelined multiplier, incorporates a special
hardware to support the dual operation instructions,
and operates synchronously with the RISC
(reduced-instruction-set computer) core to execute up
to three operations per clock. Its high performance
lends itself well to a numeric-intensive computation
environment, including vector processing.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
affiliation = "Intel Corp., Santa Clara, CA, USA",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips)",
keywords = "1 Micron; 10 Mm; 15 Mm; 32 Bit; 40 MHz; 64 Bit; 80
MFLOPS; 80 MFLOPS floating-point engine; CHMOS IV
technology; CMOS; Commercial temperature; Die size;
Double-metal process; Dual operation instructions;
Execution speed; Floating-point engine; Intel i860
processor; Numeric-intensive computation environment;
Pipelined adder; Pipelined multiplier;
Reduced-instruction-set computer; RISC core; Three
operations per clock; Vector processing",
numericalindex = "Word length 6.4E+01 bit; Frequency 4.0E+07 Hz; Word
length 3.2E+01 bit; Computer speed 8.0E+07 FLOPS; Size
1.0E-06 m; Size 1.0E-02 m; Size 1.5E-02 m",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Microprocessor chips; Reduced instruction set
computing",
}
@InProceedings{Skavantzos:1989:DFC,
author = "A. Skavantzos",
booktitle = "Twenty-Third Asilomar Conference on Signals, Systems
and Computers, 1989",
title = "Designing fast convolvers for residue number systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "497--501",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1989.266586",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
}
@Article{Smith:1989:CSB,
author = "S. G. Smith",
title = "Comments on {``A signed bit-sequential multiplier''}
by {T. Rhyne} and {N. R. Strader II}",
journal = j-IEEE-TRANS-COMPUT,
volume = "38",
number = "9",
pages = "1328--1330",
month = sep,
year = "1989",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.29473",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 8 19:00:41 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
note = "See \cite{Rhyne:1986:SBS}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=29473",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Spaderna:1989:IFP,
author = "D. Spaderna and P. Green and K. Tam and T. Datta and
M. Kumar",
title = "An integrated floating point vector processor for
{DSP} and scientific computing",
crossref = "IEEE:1989:PII",
pages = "8--13",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The architecture of a high-performance floating-point
microprocessor intended for computation-intensive
applications is presented. Utilizing a massively
parallel execution unit, very high bandwidth onchip
memory, and extensive parallel address calculation
hardware, the processor is expected to achieve peak
execution rates of 400 MFLOPS for single-precision
floating-point numbers. This type of performance is
competitive with that of popular mainframe vector
processors.",
acknowledgement = ack-nhfb,
affiliation = "Sharp Microelectron. Technol. Inc., Vancouver, WA,
USA",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5220 (Computer architecture);
C5260 (Digital signal processing)",
keywords = "400 MFLOPS; Computation-intensive applications; DSP;
Floating-point microprocessor; Integrated floating
point vector processor; Mainframe vector processors;
Massively parallel execution unit; Onchip memory;
Parallel address calculation hardware; Peak execution
rates; Scientific computing; Single-precision
floating-point numbers",
numericalindex = "Computer speed 4.0E+08 FLOPS",
thesaurus = "Digital signal processing chips; Parallel
architectures",
}
@InProceedings{Stearns:1989:SFD,
author = "C. C. Stearns",
title = "Subtractive floating-point division and square root
for {VLSI DSP}",
crossref = "IEE:1989:EEC",
pages = "405--409",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper describes recent architectural developments
in VLSI design for real-time digital signal processing.
In particular, floating point division and floating
point square root architectures applicable to both
adaptive filtering, standard deviation computations,
and general purpose processing are discussed. Emphasis
here is on the internal architectures of the arithmetic
units not on their applications. The research presented
in this paper has been proven feasible and reliable
from extensive gate-level simulation and fabrication in
silicon.",
acknowledgement = ack-nhfb,
classification = "B1265F (Microprocessors and microcomputers); B1270F
(Digital filters); B2570D (CMOS integrated circuits);
C5230 (Digital arithmetic methods); C5240 (Digital
filters); C5260 (Digital signal processing)",
keywords = "Adaptive filtering; Arithmetic units; CMOS technology;
Floating point division; Floating point square root
architectures; Gate-level simulation; General purpose
processing; Real-time digital signal processing;
Semiconductor; Standard deviation computations; VLSI
DSP",
thesaurus = "Adaptive filters; CMOS integrated circuits; Digital
arithmetic; Digital signal processing chips; VLSI",
}
@InProceedings{Stearns:1989:SFP,
author = "C. C. Stearns",
booktitle = "European Conference on Circuit Theory and Design, 5--8
Sep 1989",
title = "Subtractive floating-point division and square root
for {VLSI} {DSP}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "405--409",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "This paper describes recent architectural developments
in VLSI design for real-time digital signal processing.
In particular, floating point division and floating
point square root architectures applicable to both
adaptive filtering, standard \ldots{}",
}
@TechReport{Tang:1989:TCA,
author = "P. T. P. Tang",
title = "Testing Computer Arithmetic by Elementary Number
Theory",
institution = "Mathematics and Computer Science Division, Argonne
National Laboratory",
pages = "??",
month = aug,
year = "1989",
bibdate = "Thu Sep 01 11:57:30 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
keywords = "floating-point testing",
}
@Article{Tang:1989:TDI,
author = "Ping Tak Peter Tang",
title = "Table-Driven Implementation of the Exponential
Function in {IEEE} Floating-Point Arithmetic",
journal = j-TOMS,
volume = "15",
number = "2",
pages = "144--157",
month = jun,
year = "1989",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/63522.214389",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sun Sep 04 22:47:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p144-tang/",
abstract = "Algorithms and implementation details for the
exponential function in both single- and
double-precision of IEEE 754 arithmetic are presented
here. With a table of moderate size, the
implementations need only working-precision arithmetic
and are provably accurate to within 0.54 ulp as long as
the final result does not underflow. When the final
result suffers gradual underflow, the error is still no
worse than 0.77 ulp.",
acknowledgement = ack-nj,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis. {\bf G.1.0}: Mathematics of Computing,
NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
Algorithm analysis.",
}
@Book{Thies:1989:PXA,
author = "Klaus-Dieter Thies",
title = "{PC\slash {XT}\slash {AT} Numerik Buch} \toenglish
{PC\slash XT\slash AT Numeric Book} \endtoenglish",
publisher = pub-TEWI,
address = pub-TEWI:adr,
pages = "xiii + 707",
year = "1989",
ISBN = "3-89362-033-8",
ISBN-13 = "978-3-89362-033-3",
LCCN = "????",
bibdate = "Sat Nov 09 10:09:41 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Tu:1989:DLD,
author = "Paul K. Tu and M. D. Ercegovac",
title = "Design of on-line division unit",
crossref = "Ercegovac:1989:PSC",
pages = "42--49",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Tu.pdf",
abstract = "A gate array implementation of a radix-2
floating-point online division algorithm is presented.
The design requires 111 equivalent gates per bit and
has a cycle time of 24 ns. For 8-b exponent and 24-b
mantissa, the design requires 2497 equivalent gates and
can fit on an LSI Logic LL9320P chip with a utilization
factor 78\%.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, California University,
Los Angeles, CA, USA",
classification = "B1265B (Logic circuits); B2570 (Semiconductor
integrated circuits); C5120 (Logic and switching
circuits); C5230 (Digital arithmetic methods)",
keywords = "24 Ns Cycle time; ARITH-9; Gate array implementation;
LSI Logic LL9320P chip; Online division unit design;
Radix-2 floating-point online division algorithm;
Utilization factor",
numericalindex = "Time 2.4E-08 s",
thesaurus = "Digital arithmetic; Large scale integration; Logic
arrays",
}
@InProceedings{Turner:1989:SIS,
author = "Peter R. Turner",
title = "A software implementation of {SLI} arithmetic",
crossref = "Ercegovac:1989:PSC",
pages = "18--24",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Turner.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@InProceedings{Turrini:1989:OGD,
author = "Silvio Turrini",
title = "Optimal group distribution in carry-skip adders",
crossref = "Ercegovac:1989:PSC",
pages = "96--103",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Turrini.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@Article{Unguru:1989:BRB,
author = "Sabetai Unguru",
title = "Book Review: {{\booktitle{A Mathematical History of
Division in Extreme and Mean Ratio}} by Roger
Herz-Fischler}",
journal = j-ISIS,
volume = "80",
number = "2",
pages = "298--299",
month = jun,
year = "1989",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:23:50 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i211193;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1980.bib",
URL = "http://www.jstor.org/stable/234607",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Article{VanVeen:1989:MBC,
author = "B. D. {Van Veen} and R. Baraniuk",
title = "Matrix based computation of floating-point roundoff
noise",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "37",
number = "12",
pages = "1995--1998",
month = dec,
year = "1989",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "A matrix-based procedure is presented for computing
the output roundoff power for filters implemented with
floating-point arithmetic. The filter's computational
structure is represented in terms of a product of
matrices, known as a factored state \ldots{}",
}
@Article{Vassiliadis:1989:GPO,
author = "S. Vassiliadis and E. M. Schwarz and D. J. Hanrahan",
title = "A General Proof for Overlapped Multiple-Bit Scanning
Multiplications",
journal = j-IEEE-TRANS-COMPUT,
volume = "38",
number = "2",
pages = "172--183",
month = feb,
year = "1989",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.16494",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 8 19:00:37 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=16494",
acknowledgement = ack-mfc # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Vassiliadis:1989:SMF,
author = "S. Vassiliadis and D. S. Lemon and M. Putrino",
title = "{S/370} sign-magnitude floating-point adder",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "24",
number = "4",
pages = "1062--1070",
month = aug,
year = "1989",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A 56-bit S/370 sign-magnitude adder for floating-point
operations implemented in a four-level metal (4LM)
bipolar master-slice technology is described. The
design of the two-to-one adder is based on a carry
lookahead scheme with implicit calculation of the
end-around carry. The implementation of the
floating-point adder and the error-detecting logic
requires one chip of 7500 automatically placed and
wired NAND gates. The chip die size is 7.39 x 7.39 mm
super(2) and it is mounted on a metalized ceramic (MC)
substrate. The floating-point sign-magnitude adder chip
is used in the IBM 9370 model 60 (9375) Engineering
Scientific Accelerator (ESA) card.",
acknowledgement = ack-nhfb,
affiliation = "IBM Corp., Endicott, NY, USA",
classification = "B1265B (Logic circuits); B2570B (Bipolar integrated
circuits); C5120 (Logic and switching circuits)",
fjournal = "IEEE Journal of Solid-State Circuits",
keywords = "algorithms; arithmetic circuits; Carry lookahead
scheme; Chip die size; design; End-around carry;
Engineering scientific accelerator card;
Error-detecting logic; floating point arithmetic;
Four-level metal bipolar master-slice technology; IBM
9370 Model 60; logic circuits; Metallized ceramic
substrate; NAND gates; S/370; Sign-magnitude
floating-point adder",
summary = "A 56 bit S/370 sign-magnitude adder for floating-point
operations implemented in a four-level metal bipolar
master-slice technology is described. The design of the
two-to-one adder is based on a carry lookahead scheme
with implicit calculation of the \ldots{}",
thesaurus = "Adders; Bipolar integrated circuits; Carry logic;
Integrated logic circuits; NAND circuits",
}
@Article{Voelzke:1989:FSAa,
author = "H. V{\"o}lzke",
title = "{Flie{\ss}komma-Arithmetik und
IEEE-Spez\-i\-fi\-ka\-tion\-en. Teil 4: Die
Konvertierungsroutinen} \toenglish {Floating-point
Arithmetic and its IEEE Specification. Part 4:
Conversion Routines} \endtoenglish",
journal = j-MC,
volume = "1",
pages = "66--73",
year = "1989",
ISSN = "0720-4442, 0941-777x , 0943-5409",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "MC: Die Mikrocomputer-Zeitschrift",
}
@Article{Voelzke:1989:FSAb,
author = "H. V{\"o}lzke",
title = "{Flie{\ss}komma-Arithmetik und
IEEE-Spez\-i\-fi\-ka\-tion\-en. Teil 5: Ein- und
Ausgabefunktionen} \toenglish {Floating-point
Arithmetic and its IEEE Specification. Part 5: Input
and Output Functions} \endtoenglish",
journal = j-MC,
volume = "2",
pages = "65--71",
year = "1989",
ISSN = "0720-4442, 0941-777x , 0943-5409",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "MC: Die Mikrocomputer-Zeitschrift",
}
@Article{Vulchanov:1989:SCR,
author = "N. L. Vulchanov and M. M. Konstantinov",
title = "Safe calculation of the relative machine precision in
floating-point computing environments",
journal = j-C-R-ACAD-BULGARE-SCI,
volume = "42",
number = "2",
pages = "45--48",
year = "1989",
CODEN = "DBANAD",
ISSN = "0366-8681",
MRclass = "65G99",
MRnumber = "991 451",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Comptes rendus de l'Acad{\'e}mie bulgare des
sciences",
}
@Article{Wagner:1989:EDD,
author = "Neal R. Wagner and Paul Putter",
title = "Error detecting decimal digits",
journal = j-CACM,
volume = "32",
number = "1",
pages = "106--110",
month = jan,
year = "1989",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/63238.63246",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu May 30 09:41:10 MDT 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Misc/IMMD_IV.bib;
http://www.acm.org/pubs/toc/;
https://www.math.utah.edu/pub/tex/bib/cacm1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/toc/Abstracts/0001-0782/63246.html",
abstract = "We were recently engaged by a large mail-order house
to act as consultants on their use of check digits for
detecting errors in account numbers. Since we were not
experts in coding theory, we looked in reference books
such as Error Correcting Codes [7] and asked colleagues
who were familiar with coding theory. Uniformly, the
answer was: There is no field of order 10; the theory
only works over a field. This article relates our
experiences and presents several of the simple
decimal-oriented error detection schemes that are
available, but not widely known.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "decimal floating-point arithmetic; reliability",
review = "ACM CR 9002-0109",
subject = "{\bf B.4.5}: Hardware, INPUT/OUTPUT AND DATA
COMMUNICATIONS, Reliability, Testing, and
Fault-Tolerance, Error-checking. {\bf E.4}: Data,
CODING AND INFORMATION THEORY, Nonsecret encoding
schemes.",
}
@Article{Wang:1989:ADF,
author = "C. C. Wang",
title = "An algorithm to design finite field multipliers using
a self-dual normal basis",
journal = j-IEEE-TRANS-COMPUT,
volume = "38",
number = "10",
pages = "1457--1460",
month = oct,
year = "1989",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.35840",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 8 19:00:42 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=35840",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Wang:1989:MBC,
author = "Song-Tine Wang and Chi-Suan Wang and Morries Wang and
Shyh-Rurong Wang and Jhy-Kun Wang and Ching-Lu Hon and
Row-Ming Yang and Wei-Hsiung Chuang and Te-Tsoung Tsai
and Ming-Yuan Jang and Gwo-Jeng Pun",
title = "A 34-{MFLOP} 32-bit {CMOS} floating point processor",
crossref = "IEEE:1989:ISV",
pages = "361--364",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A 34-MFLOP 32-bit floating-point processor in 2- mu m
CMOS technology is presented. In order to achieve the
high speed of floating-point operation, the authors use
such techniques as hierarchical design parallel
circuits, and a three-stage pipeline that has been
optimized with equal delay in each stage. It is shown
that the CIC81232Y (multiplier) and CIC81233Y
(arithmetic and logic circuit) are fully compatible
with WTL1232 and WTL1233 in function, but the speeds
are 1.7 times faster.",
acknowledgement = ack-nhfb,
affiliation = "Electron. Res and Service Organ., Hsing-Chu, Taiwan",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5220 (Computer architecture); C5230 (Digital
arithmetic methods)",
keywords = "32 Bit; 32-Bit floating-point processor; 34 MFLOPS;
Arithmetic circuit; CIC81232Y; CIC81233Y; CMOS
technology; Hierarchical design parallel circuits;
Logic circuit; Multiplier; Three-stage pipeline",
numericalindex = "Word length 3.2E+01 bit; Computer speed 3.4E+07
FLOPS",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Microprocessor chips; Pipeline processing",
}
@MastersThesis{Ward:1989:BFP,
author = "Kenneth L. Ward",
title = "A block floating point distributed arithmetic finite
impulse response filter",
type = "Thesis ({M.S.})",
school = "University of Florida",
address = "Gainesville, FL, USA",
year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Digital filters (Mathematics); Filters (Mathematics);
Floating-point arithmetic.",
}
@Article{Wichmann:1989:SPI,
author = "B. A. Wichmann",
title = "Scientific processing in {ISO-Pascal}: a proposal to
get the benefits of mixed precision floating-point",
journal = j-SIGPLAN,
volume = "24",
number = "6",
pages = "20--22",
month = jun,
year = "1989",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:15:40 MST 2003",
bibsource = "Compendex database; http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Although Pascal is a very popular language for
teaching and for use on microprocessors, it has not
been very successful for scientific calculations. Apart
from the pre-eminence of FORTRAN in this application
area, several technical defects in Pascal have
inhibited its use. One defect has been the problem in
Pascal as defined by Jensen and Wirth of the inability
to handle arrays of varying size as parameters to
procedures. The level 1 option in ISO-Pascal addressed
this defect by means of conformant arrays, albeit in a
somewhat inelegant fashion. Array handling in
ISO-Pascal can now be regarded as adequate since level
1 validated compilers are available for the majority of
widely available machines. This note addresses another
defect of Pascal, that no facility is provided to
handle floating point types of more than one
precision.",
acknowledgement = ack-nhfb,
affiliationaddress = "Teddington, Engl",
classification = "723; 902",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
journalabr = "SIGPLAN Not",
keywords = "algorithms; Computer Programming Languages; design;
Floating Point Computation; iso-pascal; languages;
pascal; Scientific Computing; standardization;
Standards",
subject = "D.2.1 Software, SOFTWARE ENGINEERING,
Requirements/Specifications \\ D.3.2 Software,
PROGRAMMING LANGUAGES, Language Classifications, Pascal
\\ E.1 Data, DATA STRUCTURES, Arrays",
}
@Article{Wichmann:1989:TFS,
author = "B. A. Wichmann",
title = "Towards a formal specification of floating point",
journal = j-COMP-J,
volume = "32",
number = "5",
pages = "432--436",
month = oct,
year = "1989",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65G99 (65Y10)",
MRnumber = "91b:65055",
bibdate = "Wed Dec 13 18:44:32 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Although the concept of floating point is well
understood, a formal mathematical treatment appears to
be new. The paper presents a formal definition of
floating point using the Vienna Development Method
(VDM). The relationship between this definition and the
informal definition in the Ada Standard and the work of
W. S. Brown (1981) is discussed.",
acknowledgement = ack-nhfb,
affiliation = "Department of Trade and Ind., NPL, Teddington, UK",
classification = "C5230 (Digital arithmetic methods); C6110B (Software
engineering techniques)",
corpsource = "Department of Trade and Ind., NPL, Teddington, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "digital arithmetic; Floating point; floating point;
Formal specification; formal specification; Method;
Vienna Development; Vienna Development Method",
pubcountry = "UK",
thesaurus = "Digital arithmetic; Formal specification",
treatment = "P Practical",
}
@MastersThesis{Wittman:1989:SCU,
author = "Susan Jean Wittman",
title = "Servo compensation using a floating point digital
signal processor",
type = "Thesis ({M.S.})",
school = "Massachusetts Institute of Technology, Dept. of
Aeronautics and Astronautics",
address = "Cambridge, MA, USA",
pages = "60",
year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supervised by James K. Roberge",
acknowledgement = ack-nhfb,
}
@InProceedings{Zeng:1989:RNP,
author = "B. Zeng and Y. Neuvo",
booktitle = "European Conference on Circuit Theory and Design, 5--8
Sep 1989",
title = "Roundoff noise properties of lattice filters employing
floating-point arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "233--237",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The roundoff noise properties of general lattice
filters are studied for floating-point implementations
using the concept of dummy multipliers. The main
efforts are devoted to the Gray-Markel recursive
structures. It is shown that the roundoff noise
\ldots{}",
}
@Article{Zorpette:1989:PGD,
author = "Glenn Zorpette",
title = "{Parkinson}'s gun director",
journal = j-IEEE-SPECTRUM,
volume = "26",
number = "4",
pages = "43--43",
month = apr,
year = "1989",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/6.24154",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Mon Jan 20 06:41:24 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "antiaircraft guns; Arithmetic; Automatic control;
Cities and towns; controllers; Crystallization;
electromechanical system; gun director; Guns;
Laboratories; M-9; magnetic clutches; operational
amplifiers; Operational amplifiers; position control;
potentiometer; Psychology; Springs; Telephony;
weapons",
}
@Article{Alsup:1990:MFA,
author = "M. Alsup",
title = "{Motorola}'s 88000 Family Architecture",
journal = j-IEEE-MICRO,
volume = "10",
number = "3",
pages = "48--66",
month = may # "\slash " # jun,
year = "1990",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.56325",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Article{Anonymous:1990:MUF,
author = "Anonymous",
title = "{Motorola} unveils 96002 floating point processor",
journal = "Integrated circuits international",
pages = "3--??",
month = jul,
year = "1990",
ISSN = "0263-6522",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Ansari:1990:MBF,
author = "Ahmad Ansari",
title = "A $ 3 \times 3 $ multipurpose bus-connected
floating-point array processor",
type = "Thesis ({M.S.})",
school = "University of Florida",
address = "Gainesville, FL, USA",
pages = "vi + 127",
year = "1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Arnold:1990:RLA,
author = "M. G. Arnold and T. A. Bailey and J. R. Cowles and J.
J. Cupal",
title = "Redundant logarithmic arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "8",
pages = "1077--1086",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57046",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:03 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57046",
abstract = "A number system that offers advantages in some
situations over conventional floating point and
sign/logarithmic number systems is described. Redundant
logarithmic arithmetic, like conventional logarithmic
arithmetic, relies on table lookups to make the
arithmetic unit simpler than an equivalent floating
point unit. The cost of 32 bit subtraction in a
redundant logarithmic number system is lower than
previously published logarithmic subtraction methods.
The total memory requirement for a 29-bit redundant
logarithmic unit is 16 K words compared to 22 K words
by the best previously published conventional sign
logarithm unit, assuming similar addition techniques
are employed. A redundant logarithmic number system can
be implemented with online arithmetic, which would be
impractical for a conventional sign logarithm number
system. The disadvantages of redundant arithmetic are
typical of redundant number systems. First, the
redundancy doubles the storage requirements for data
values. Second, the representation can become
ill-conditioned, especially as a result of iterated
multiplications. Third, division and square root
operations are more difficult to implement in redundant
logarithmic arithmetic.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Wyoming University,
Laramie, WY, USA",
ajournal = "IEEE Trans. Comput.",
classification = "C1160 (Combinatorial mathematics); C1210B
(Reliability theory); C5230 (Digital arithmetic
methods)",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "29-Bit redundant logarithmic unit; 32 Bit subtraction;
Arithmetic unit; Data values; Division;
Ill-conditioned; Iterated multiplications; Memory
requirement; Online arithmetic; Redundant logarithmic
arithmetic; Redundant logarithmic number system; Square
root; Storage requirements; Table lookups",
thesaurus = "Digital arithmetic; Number theory; Redundancy; Table
lookup",
}
@Article{Aspray:1990:BBS,
author = "William Aspray",
title = "Back to Basics: The Stored Program Concept",
journal = j-IEEE-SPECTRUM,
volume = "27",
number = "9",
pages = "51--51",
month = sep,
year = "1990",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/6.58457",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Wed Jan 15 12:40:28 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1990.bib",
abstract = "The history and early development of the stored
program concept are briefly described. This refers to
the ability of a calculating machine to store its
instructions in its internal memory and process them in
its arithmetic unit, so that in the course of a
computation they may be not just executed but also
modified at electronic speeds. John von Neumann, a
faculty member of the Institute for Advanced Study in
Princeton, NJ, participated in the discussions in which
the idea was elaborated, wrote the first report of the
concept, placed it in a theoretical context, and built
his own computer, which was the early model for a
number of others, including the important commercially
manufactured IBM 701. J. Presper Eckert and John
Mauchly perhaps first conceived of the stored program
concept and developed most of the plans for
implementing it in the Edvac, and later incorporated it
in the Univac and other computers produced by their
company. Several British computer scientists, notably
Maurice Wilkes, were the first to implement the idea in
machines initially designed to embody this feature.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "arithmetic unit; calculating machine; Computer aided
instruction; Computer aided manufacturing; Computer
architecture; Context modeling; Digital arithmetic;
file organisation; history; History; internal memory;
Laboratories; Military computing; Prototypes; storage
allocation; stored program concept; Virtual
manufacturing",
}
@InProceedings{Bajwa:1990:FFP,
author = "A. Bajwa and R. Steck",
title = "A fast floating point unit in the i960 general-purpose
embedded processor family",
crossref = "Wescon:1990:WCR",
pages = "218--222",
year = "1990",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Fast, cheap floating point arithmetic is required in
many embedded processor applications. This paper
describes a next-generation floating point unit
designed as an integrated functional unit on Intel's
i960 family of 32-bit embedded RISC processors. High
performance is achieved by utilizing two separate,
concurrent floating point execution units with wide
datapaths, both internally and to general-purpose
registers. Hardware system cost is reduced by
integrating the FPU on the main processor while
software development cost is minimized by using the
i960 Numerics Architecture supported by standard i960
family development tools.",
acknowledgement = ack-nhfb,
affiliation = "Intel Corp., Hillsboro, OR, USA",
availability = "Western Periodicals Co., 13000 Rayner Street, North
Hollywood, CA 91605, USA",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5220 (Computer architecture);
C5230 (Digital arithmetic methods)",
keywords = "32 Bit; 32-Bit embedded RISC processors; Concurrent
floating point execution units; Embedded processor
applications; Fast floating point unit; Floating point
arithmetic; FPU; General-purpose embedded processor
family; General-purpose registers; I960; I960 family;
I960 Numerics Architecture; Integrated functional unit;
Intel; Wide datapaths",
numericalindex = "Word length 3.2E+01 bit",
thesaurus = "Computer architecture; Digital arithmetic;
Microprocessor chips; Reduced instruction set
computing",
}
@TechReport{Barlow:1990:EAU,
author = "Jesse Louis Barlow and Richard J. Zaccone",
title = "Error analysis in unnormalized floating point
arithmetic",
type = "Technical report",
number = "CS-90-23",
institution = "Pennsylvania State University, Department of Computer
Science",
address = "University Park, PA, USA",
pages = "9",
month = apr,
year = "1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supported by the Air Force Office of Scientific
Research. Supported by the National Science Foundation.
Supported by the Office of Naval Research.",
abstract = "The need to construct architectures in VLSI has
focused attention on unnormalized floating point
arithmetic. Certain unnormalized arithmetics allow one
to `pipe on digits,' thus producing significant speed
up in computation and making the input problems of
special purpose devices such as systolic arrays easier
to solve. We consider the error analysis implications
of using unnormalized arithmetic in numerical
algorithms. We also give specifications for its
implementation. Our discussion centers on the example
of Gaussian elimination. We show that the use of
unnormalized arithmetic requires changes in the
analysis of this algorithm. We will show that only for
certain classes of matrices that include diagonally
dominant matrices (either row or column), Gaussian
elimination is as stable in unnormalized arithmetic as
in normalized arithmetic. However, if the diagonal
elements of the upper triangular matrix are post
normalized, then Gaussian elimination is as stable in
unnormalized arithmetic as in normalized arithmetic for
all matrices.",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic.; Floating-point arithmetic.",
}
@MastersThesis{Bhargava:1990:DFP,
author = "Ish Kumar Bhargava",
title = "Design of a floating point data acquisition system and
a development system for the {NC} 4016",
type = "Electrical Engineering Thesis ({M.S.})",
school = "University of Missouri--Rolla",
address = "Rolla, MO, USA",
pages = "ix + 107",
year = "1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Birman:1990:DWS,
author = "Mark Birman and Allen Samuels and George Chu and Chuk
Ting and Larry Hu and John McLeod and John Barnes",
title = "Developing the {WTL3170\slash 3171 Sparc}
Floating-Point Coprocessors",
journal = j-IEEE-MICRO,
volume = "10",
number = "1",
pages = "55--64",
month = jan # "\slash " # feb,
year = "1990",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.46769",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Contending with dual floating-point interfaces at both
25 and 40 MHz posed an extraordinary challenge in
coprocessor development.",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
summary = "The development of the first two members in a family
of scalable-processor-architecture (Sparc)-compatible
parts is described. With varying frequency and latency
performance, the chips work with the first two integer
unit (IU) implementations from \ldots{}",
}
@Article{Blevins:1990:BHI,
author = "D. W. Blevins and E. W. Davis and R. A. Heaton and J.
H. Feif",
title = "{BLITZEN}: a Highly Integrated Massively Parallel
Machine",
journal = j-J-PAR-DIST-COMP,
volume = "8",
number = "2",
pages = "150--160",
month = feb,
year = "1990",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 17:13:17 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5220 (Computer architecture); C5440
(Multiprocessor systems and techniques)",
corpsource = "Microelectron. Center of North Carolina, Research
Triangle Park, NC, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "1.25 micron; 20 MHz; architecture; BLITZEN; CMOS
design rules; CMOS integrated circuits; computer
architecture; global; highly integrated massively
parallel machine; IEEE standard 32-bit floating point;
local control features; memory address; microprocessor
chips; multiplication; parallel processing; static RAM;
VLSI",
treatment = "P Practical",
}
@InBook{Branham:1990:PFP,
author = "Richard L. Branham",
booktitle = "Scientific Data Analysis: An Introduction to
Overdetermined Systems",
title = "Properties of Floating-Point Numbers",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "x + 237 + 36",
pages = "1--19",
year = "1990",
DOI = "https://doi.org/10.1007/978-1-4612-3362-6_1",
ISBN = "1-4612-3362-3 (e-book), 1-4612-7981-X",
ISBN-13 = "978-1-4612-3362-6 (e-book), 978-1-4612-7981-5",
LCCN = "QA76.9.D35",
bibdate = "Sat Dec 31 11:59:38 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
remark = "This introductory chapter discusses floating-point
arithmetic in VAX binary, IBM System\slash 360
hexadecimal, and Sharp pocket calculator decimal
formats, but has no mention of IEEE 754 arithmetic. It
discusses the failure in floating-point arithmetic of
the associative, cancellation, and distributive laws of
exact arithmetic. In the context of accurate
floating-point summation, it describes Kahan's
compensated summation algorithm, Linz'
binary-subdivision summation algorithm, and Wolfe's
cascaded accumulator algorithm, all implemented in
Fortran code given in the chapter figures. It also
treats the error in summation in rounded and truncated
arithmetic, and mentions the importance of guard
digits.",
tableofcontents = "Properties of Floating-Point Numbers \\
Matrices, Norms, and Condition Numbers \\
Sparse Matrices \\
Introduction to Overdetermined Systems \\
Linear Least Squares \\
The L1 Method \\
Nonlinear Methods \\
The Singular Value Decomposition \\
Index",
}
@InProceedings{Buck:1990:PAN,
author = "P. D. Buck and S. L. Day and D. Gonzalez",
title = "Problems with {Ada} numeric routines",
crossref = "Anonymous:1990:PAN",
pages = "195--204",
year = "1990",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Computer programmers believe that their systems will
always perform as expected. Standardization of computer
languages has been a major advance towards this goal.
The Ada language was intended to further advance this
goal by rigorously defining the language. In addition
the language was intended to improve the portability of
programs. The authors' experience shows that the
definition of the Ada language does not ensure
mathematical algorithms will function consistently
across multiple hardware environments. The method used
by the language designers to specify the floating point
data types appears to be the cause of the problem.",
acknowledgement = ack-nhfb,
affiliation = "Nat. University, San Diego, CA, USA",
classification = "C6120 (File organisation); C6130 (Data handling
techniques); C6140D (High level languages)",
keywords = "Ada; Floating point data types; Mathematical
algorithms; Multiple hardware environments; Numeric
routines; Portability",
thesaurus = "Ada; Data structures; Digital arithmetic; Software
portability; Symbol manipulation",
}
@Article{Bursky:1990:FMC,
author = "D. Bursky",
title = "Floating-point math chip delivers 200 mflops peak",
journal = j-ELECTRONIC-DESIGN,
volume = "38",
number = "4",
pages = "51--52, 54, 55",
month = feb,
year = "1990",
CODEN = "ELODAW",
ISSN = "0013-4872 (print), 1944-9550 (electronic)",
ISSN-L = "0013-4872",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "By exploiting its latest process improvements and a
three-layer metal interconnection capability, Bipolar
Integrated Technology has managed to boost
floating-point throughput three- to five-fold over its
previous-generation circuits. The new B3130, a
single-chip double-precision floating-point processor
with 64-bit data buses, can deliver up to 200 MFLOPS of
peak throughput. With more than 55000 equivalent gates
and multiple 64-bit data buses (plus eight parity bits
on each bus), the chip is the highest-complexity ECL
chip to be sold commercially. By employing a high
degree of integration, the single chip packs a 64-bit
ALU, a 54-bit parallel multiplier (for the mantissa),
and a 64-bit divide/square root unit. The chip's
architecture is optimized for vector processing, but it
can also perform scalar calculations. In addition, the
wide data buses and pipelining support eliminate the
loading and unloading bottlenecks that frequently
degrade chip performance.",
acknowledgement = ack-nhfb,
classification = "B1265F (Microprocessors and microcomputers); B2570B
(Bipolar integrated circuits); C5130 (Microprocessor
chips); C5230 (Digital arithmetic methods)",
fjournal = "Electronic Design",
keywords = "200 MFLOPS; 64 Bit; ALU; B3130; Bipolar Integrated
Technology; Bipolar microprocessor; Divide/square root
unit; Double-precision; ECL chip; Floating-point
processor; Multiple data buses; Parallel multiplier;
Pipelining support; Scalar calculations; Three-layer
metal interconnection; Vector processing",
numericalindex = "Computer speed 2.0E+08 FLOPS; Word length 6.4E+01
bit",
thesaurus = "Bipolar integrated circuits; Digital arithmetic;
Emitter-coupled logic; Microprocessor chips; Parallel
architectures; Parallel machines; Pipeline processing;
VLSI",
}
@Article{Carter:1990:RSD,
author = "T. M. Carter and J. E. Robertson",
title = "Radix-$ 16 $ signed-digit division",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "12",
pages = "1424--1433",
month = dec,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.61063",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:05 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=61063",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Carter:1990:STA,
author = "T. M. Carter and J. E. Robertson",
title = "The set theory of arithmetic decomposition",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "8",
pages = "993--1005",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57037",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:03 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57037",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Chen:1990:DIH,
author = "J. T. Chen and W. K. Jenkins and I. A. Hein and W. D.
{O'Brien, Jr.}",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, 1--3 May 1990",
title = "Design and implementation of a high speed residue
number system correlator for ultrasonic time domain
blood flow measurement",
volume = "4",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2893--2896",
year = "1990",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1990.112615",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The design and operation of a high-speed residue
number system (RNS) digital correlator is presented for
implementing the correlation function in a real-time
ultrasonic blood flow measurement system. This
architecture allows for both high-speed \ldots{}",
}
@Article{Chren:1990:NRN,
author = "W. A. {Chren, Jr.}",
title = "A new residue number system division algorithm",
journal = j-COMPUT-MATH-APPL,
volume = "19",
number = "7",
pages = "13--29",
month = "????",
year = "1990",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:01:19 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/089812219090190U",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Ciminiera:1990:HRS,
author = "L. Ciminiera and P. Montuschi",
title = "Higher radix square rooting",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "10",
pages = "1220--1231",
month = oct,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.59853",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=59853",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "A general discussion on nonrestoring square root
algorithms is presented, showing bounds and constraints
delimiting the space of feasible algorithms, for all
the choices of radix, digit set and representation of
the partial remainder. Two classes of \ldots{}",
}
@Article{Clinger:1990:HRF,
author = "William D. Clinger",
title = "How to Read Floating Point Numbers Accurately",
journal = j-SIGPLAN,
volume = "25",
number = "6",
pages = "92--101",
month = jun,
year = "1990",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/93548.93557",
ISBN = "0-89791-364-7",
ISBN-13 = "978-0-89791-364-5",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:15:53 MST 2003",
bibsource = "Compendex database;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
http://www.acm.org/pubs/contents/proceedings/pldi/93542/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigplan1990.bib",
note = "See also output algorithms in
\cite{Knuth:1990:SPW,Steele:1990:HPF,Burger:1996:PFP,Abbott:1999:ASS,Steele:2004:RHP}.",
URL = "http://www.acm.org:80/pubs/citations/proceedings/pldi/93542/p92-clinger/",
abstract = "Consider the problem of converting decimal scientific
notation for a number into the best binary floating
point approximation to that number, for some fixed
precision. This problem cannot be solved using
arithmetic of any fixed precision. Hence the IEEE
Standard for Binary Floating-Point Arithmetic does not
require the result of such a conversion to be the best
approximation. This paper presents an efficient
algorithm that always finds the best approximation. The
algorithm uses a few extra bits of precision to compute
an IEEE-conforming approximation while testing an
intermediate result to determine whether the
approximation could be other than the best. If the
approximation might not be the best, then the best
approximation is determined by a few simple operations
on multiple-precision integers, where the precision is
determined by the input. When using 64 bits of
precision to compute IEEE double precision results, the
algorithm avoids higher-precision arithmetic over 99\%
of the time.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Oregon University, Eugene, OR, USA",
annote = "Published as part of the Proceedings of PLDI'90.",
classification = "722; 723; C1160 (Combinatorial mathematics); C5230
(Digital arithmetic methods); C7310 (Mathematics)",
confdate = "20-22 June 1990",
conference = "Proceedings of the ACM SIGPLAN '90 Conference on
Programming Language Design and Implementation",
conferenceyear = "1990",
conflocation = "White Plains, NY, USA",
confsponsor = "ACM",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
journalabr = "SIGPLAN Not",
keywords = "algorithms; Best binary floating point approximation;
Computer Programming Languages; Computers, Digital ---
Computational Methods; Decimal scientific notation;
Design; Efficient algorithm; experimentation; Fixed
precision; Floating point numbers; Floating Point
Numbers; Higher-precision arithmetic; IEEE double
precision results; IEEE Standard; IEEE-conforming
approximation; Intermediate result; Multiple-precision
integers",
meetingaddress = "White Plains, NY, USA",
meetingdate = "Jun 20--22 1990",
meetingdate2 = "06/20--22/90",
sponsor = "Assoc for Computing Machinery, Special Interest Group
on Programming Languages",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf
G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation.",
thesaurus = "Digital arithmetic; Mathematics computing; Number
theory; Standards",
}
@Article{Codenotti:1990:ATT,
author = "B. Codenotti and G. Lotti and F. Romani",
title = "Area-time trade-offs for matrix-vector
multiplication",
journal = j-J-PAR-DIST-COMP,
volume = "8",
number = "1",
pages = "52--59",
month = jan,
year = "1990",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Inst di Elaborazione dell'Informazione-CNR",
affiliationaddress = "Pisa, Italy",
classification = "722; 723; 921; B0290H (Linear algebra); B1265B
(Logic circuits); C4140 (Linear algebra); C4240
(Programming and algorithm theory)",
corpsource = "Istituto di Elaborazione dell'Inf., CNR, Pisa, Italy",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "algebra; area-time complexity; Area-Time Trade-Offs;
arithmetic; computation; computational complexity;
Computer Systems, Digital; Computers,
Digital--Computational Methods; I/O conventions;
information flow; integrated logic circuits;
Mathematical Techniques--Matrix Algebra; matrix;
Matrix-Vector Multiplication; matrix-vector
multiplication; operations; Parallel Processing; sparse
matrix; VLSI",
treatment = "T Theoretical or Mathematical",
}
@Article{Cosnard:1990:STF,
author = "Michel Cosnard and Jean Duprat and Yves Robert",
title = "Systolic triangularization over finite fields",
journal = j-J-PAR-DIST-COMP,
volume = "9",
number = "3",
pages = "252--260",
month = jul,
year = "1990",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Ecole Normale Superieure de Lyon Lab LIP-IMAG",
affiliationaddress = "Lyon, Fr",
classification = "722; 723; 921; C4140 (Linear algebra); C5220
(Computer architecture); C5230 (Digital arithmetic
methods)",
corpsource = "IMAG, Ecole Normale Superieure de Lyon, France",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "architecture; arithmetic number; computer algebra;
Computer Programming--Algorithms; Computer Systems,
Digital--Parallel Processing; Computers, Digital;
digital arithmetic; finite fields; Gaussian
Elimination; Gaussian elimination; large dense linear
systems; linear algebra; Mathematical
Techniques--Linear Algebra; Modular Multiplication
Algorithm; parallel architectures; partial; pivoting;
Special Purpose Application; systolic; Systolic Arrays;
Systolic Triangularization; systolic triangularization;
theory",
treatment = "P Practical; T Theoretical or Mathematical",
}
@Manual{Cyrix:1990:FCU,
title = "{FasMath} {CX-83S87} user's manual",
publisher = "Cyrix Corp.",
address = "Richardson, TX, USA",
pages = "115 + 5 + 3",
year = "1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Cyrix CX-83X87 (Microprocessor); Floating-point
arithmetic.; Integrated circuits --- Very large scale
integration.; Metal oxide semiconductors,
Complementary.",
remark = "Running title: FasMath 83S87 user manual.",
}
@Article{Darley:1990:TFC,
author = "Merrick Darley and Bill Kronlage and David Bural and
Bob Churchill and David Pulling and Paul Wang and Rick
Iwamoto and Larry Yang",
title = "The {TMS390C602A} Floating-Point Coprocessor for
{Sparc} Systems",
journal = j-IEEE-MICRO,
volume = "10",
number = "3",
pages = "36--47",
month = may # "\slash " # jun,
year = "1990",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.56324",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/microchip.bib",
abstract = "A recent Sparc (scalable processor architecture)
processor consists of a two-chip configuration,
containing the TMS390C601 integer unit (IU) and the
TMS390C602A floating-point unit (FPU). The second
device, an innovative coprocessor that lets the
processor execute single- or double-precision
floating-point instructions concurrently with IU
operations is described. Dedicated floating-point
hardware in the FPU increases the performance of the
system. Running at clock periods as small as 20 ns, the
chip should deliver 5.5 million double-precision
floating-point operations per second under the Linpack
benchmark (50-MHz clock rate). The FPU provides single-
and double-precision arithmetic functions: addition,
subtraction, multiplication, division, square root,
compare, and convert. To minimize its math unit's
latency, the FPU uses a highly parallel architecture
requiring separate math units to optimize additions and
multiplications. Traps stop the execution of a program
to jump to software routine for handling data-dependent
errors or to execute instructions not implemented in
the hardware. Benchmark results are presented. (4
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Texas Instrum. Inc., Dallas, TX, USA",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5230 (Digital arithmetic
methods)",
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
keywords = "Addition; Compare; Convert; Division; Linpack
benchmark; Multiplication; Sparc systems; Square root;
Subtraction; TMS390C601 integer unit; TMS390C602A
floating-point coprocessor; TMS390C602A floating-point
unit; Two-chip configuration",
language = "English",
pubcountry = "USA",
thesaurus = "Digital arithmetic; Microprocessor chips",
}
@Article{Darley:1990:TFP,
author = "Merrick Darley and Bill Kronlage and David Bural and
Bob Churchill and David Pulling and Paul Wang and Rick
Iwamoto and Larry Yang",
title = "The {TMS390C602A} Floating-Point Coprocessor for
{Sparc} Systems",
journal = j-IEEE-MICRO,
volume = "10",
number = "3",
pages = "36--47",
month = may # "\slash " # jun,
year = "1990",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.56324",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A recent Sparc (scalable processor architecture)
processor consists of a two-chip configuration,
containing the TMS390C601 integer unit (IU) and the
TMS390C602A floating-point unit (FPU). The second
device, an innovative coprocessor that lets the
processor execute single- or double-precision
floating-point instructions concurrently with IU
operations is described. Dedicated floating-point
hardware in the FPU increases the performance of the
system. Running at clock periods as small as 20 ns, the
chip should deliver 5.5 million double-precision
floating-point operations per second under the Linpack
benchmark (50-MHz clock rate). The FPU provides single-
and double-precision arithmetic functions: addition,
subtraction, multiplication, division, square root,
compare, and convert. To minimize its math unit's
latency, the FPU uses a highly parallel architecture
requiring separate math units to optimize additions and
multiplications. Traps stop the execution of a program
to jump to software routine for handling data-dependent
errors or to execute instructions not implemented in
the hardware. Benchmark results are presented. (4
Refs.)",
acknowledgement = ack-mfc # " and " # ack-nhfb,
affiliation = "Texas Instrum. Inc., Dallas, TX, USA",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5230 (Digital arithmetic
methods)",
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
keywords = "Addition; Compare; Convert; Division; Linpack
benchmark; Multiplication; Sparc systems; Square root;
Subtraction; TMS390C601 integer unit; TMS390C602A
floating-point coprocessor; TMS390C602A floating-point
unit; Two-chip configuration",
summary = "A recent Sparc (scalable processor architecture)
processor consists of a two-chip configuration,
containing the TMS390C601 integer unit (IU) and the
TMS390C602A floating-point unit (FPU). The second
device, an innovative coprocessor that lets the
\ldots{}",
thesaurus = "Digital arithmetic; Microprocessor chips",
}
@Book{Dewar:1990:MPV,
author = "Robert B. K. Dewar and Matthew Smosna",
title = "Microprocessors: a programmer's view",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xvii + 462",
year = "1990",
ISBN = "0-07-016638-2, 0-07-016639-0 (soft)",
ISBN-13 = "978-0-07-016638-7, 978-0-07-016639-4 (soft)",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Microprocessors --- Programming.",
remark = "Microprocessors --- Introduction to the 80386 ---
Addressing and memory on the 80386 --- Tasking, virtual
memory, and exceptions to the 80386 --- Microprocessors
and floating-point arithmetic --- 68030 user
programming model --- 68030 supervisor state ---
Introduction to RISC architectures --- MIPS processors
--- SPARC architecture --- Intel i860 --- IBM RISC
chips --- INMOS transputer - - Future of microprocessor
design.",
}
@InProceedings{Dixon:1990:HPB,
author = "G. Dixon",
title = "A high performance block floating point {DSP}
chip-set",
crossref = "IEE:1990:ICV",
pages = "9/1--7",
year = "1990",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper describes the design and development of two
ASICs which form the processing kernel of a high
performance sonar signal processor; namely a 24-bit
Block Floating Point Arithmetic Unit (BFPAU), and a
Table Memory And Address Modifier (TMAAM). The system
is based upon a 24-bit block floating point data format
which is a compromise between fixed and floating point
data; possessing the advantage of reducing the data
storage requirement compared to true floating point
while allowing arithmetic to be performed in the faster
fixed-point format whilst retaining the extended
dynamic range provided by floating point. The BFPAU and
TMAAM perform the arithmetic processing; the BFPAU is
the central arithmetic processor aimed at sonar signal
processing in general and beamforming in particular,
while the TMAAM provides a range of essential support
functions such as look-up tables for trigonometric
functions, address generation, exponent control and
normalisation and program sequencing. Two blocks of
dual-port RAM provide storage for system I/O data
transfers, together with two blocks of RAM providing
working data storage for the BFPAU. A block of video
RAM is used to store address and control sequences for
the processing element.",
acknowledgement = ack-nhfb,
affiliation = "Plessey Res. Caswell, Towcester, UK",
classification = "B1265F (Microprocessors and microcomputers); B6320E
(Sonar and acoustic radar)",
keywords = "Address generation; Arithmetic processing; ASICs;
Beamforming; Block floating point DSP chip-set; Data
format; Data storage requirement; Dual-port RAM;
Dynamic range; Exponent control; Fixed-point format;
Look-up tables; Normalisation; Program sequencing;
Sonar signal processor; System I/O data transfers;
Video RAM; Working data storage",
thesaurus = "Application specific integrated circuits; Digital
signal processing chips; Random-access storage; Sonar",
}
@Article{Dotzel:1990:DMG,
author = "G{\"u}nter Dotzel",
title = "Does {Modula-2} generate racehorses? Comparison of
compiler generated code quality for floating point
arithmetic",
journal = j-SIGPLAN,
volume = "25",
number = "12",
pages = "85--88",
month = dec,
year = "1990",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:16:00 MST 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A simple example serves to demonstrate the code
quality generated by two different Modula-2 compilers.
The two compilers are called the Zurich/Hamburger and
the Erlanger. The author lists the Modula-2 source
program, shows an excerpt of the machine code listing
generated by the Erlanger and presents that of the
Zurich/Hamburger. The differences in code quality
concerning instruction count, code size and execution
speed are discussed and summarized. The author also
presents the main program module used for the
benchmarks and a short description of the development
history of Modula-2 and Modula/R.",
acknowledgement = ack-nhfb,
affiliation = "ModulaWare GmbH, Erlangen, West Germany",
classification = "C6140D (High level languages); C6150C (Compilers,
interpreters and other processors); C6150G (Diagnostic,
testing, debugging and evaluating systems)",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "Benchmarks; Code size; Compiler generated code
quality; Development history; Erlanger; Execution
speed; Floating point arithmetic; Instruction count;
Machine code listing; Main program module; Modula-2
compilers; Modula-2 source program; Modula/R;
Zurich/Hamburger",
thesaurus = "Modula; Modula listings; Program compilers; Program
testing",
}
@Article{Dunham:1990:FFE,
author = "C. B. Dunham",
title = "Feasibility of `Perfect' Function Evaluation",
journal = j-SIGNUM,
volume = "25",
number = "4",
pages = "25--26",
month = oct,
year = "1990",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Sep 1 10:15:30 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@Article{Edenfield:1990:PPD,
author = "R. W. Edenfield and M. G. Gallup and W. B. {Ledbetter,
Jr.} and R. C. McGarity and E. E. Quintana and R. A.
Reininger",
title = "The 68040 Processor. {Part} 1, Design and
Implementation",
journal = j-IEEE-MICRO,
volume = "10",
number = "1",
pages = "66--78",
month = jan # "\slash " # feb,
year = "1990",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.46770",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Article{Ercegovac:1990:FMC,
author = "M. D. Ercegovac and T. Lang",
title = "Fast multiplication without carry-propagate addition",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "11",
pages = "1385--1390",
month = nov,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.61047",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:05 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=61047",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Ercegovac:1990:RSR,
author = "M. D. Ercegovac and T. Lang",
title = "Radix-$4$ square root without initial {PLA}",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "8",
pages = "1016--1024",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57040",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:03 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57040",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Ercegovac:1990:SRD,
author = "M. D. Ercegovac and T. Lang",
title = "Simple radix-$4$ division with operands scaling",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "9",
pages = "1204--1208",
month = sep,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57060",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57060",
acknowledgement = ack-sfo # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Fussichen:1990:GAM,
author = "Kenneth Fussichen",
title = "Getting {Ada} into the mainstream in the 1990's",
crossref = "ACM:1990:PDB",
pages = "428--428",
year = "1990",
DOI = "https://doi.org/10.1145/255471.255572",
bibdate = "Thu Aug 07 18:17:35 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Ada offers a great deal to the MIS community. There
are a number of language features that provide
attractive tools to the programmer. Ada's support for
Object Orientation is far superior to that currently
afforded by IBM mainframe languages such as COBOL and
PL/1. This translates into more maintainable code,
which is the key to MIS Ada
acceptance.\par
Unfortunately, Ada introduces problems that do not
currently exist in MIS. Decimal arithmetic and string
manipulation adequate to support reporting are
inherently non-existent. I/O support is inadequate as
are DBMS bindings. Conversions are forced on non-ASCII
hosts. The compiler has the option of reordering fields
within records, rendering non-Ada utilities useless.
There is an inexcusable lack of understanding of the
targeted market.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Gallant:1990:MCI,
author = "John Gallant and Bill Travis",
title = "Math coprocessor {ICs}: Floating-point chips boost
{muP} performance",
journal = j-EDN,
volume = "35",
number = "12",
pages = "63--??",
month = jun,
year = "1990",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Floating-point arithmetic exacts huge penalties in CPU
computation time. Dedicated coprocessor ICs execute
this onerous task automatically and efficiently.",
acknowledgement = ack-nhfb,
fjournal = "EDN",
}
@TechReport{Gay:1990:CRB,
author = "David M. Gay",
title = "Correctly Rounded Binary-Decimal and Decimal-Binary
Conversions",
type = "Numerical Analysis Manuscript",
number = "90-10",
institution = "AT\&T Bell Laboratories",
pages = "16",
month = nov # " 30",
year = "1990",
bibdate = "Sat Apr 28 18:42:55 2001",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://cm.bell-labs.com/cm/cs/doc/90/4-10.ps.gz;
http://www.ampl.com/ampl/REFS/rounding.ps.gz;
http://www.netlib.org/fp/dtoa.c;
http://www.netlib.org/fp/g_fmt.c;
http://www.netlib.org/fp/gdtoa.tgz;
http://www.netlib.org/fp/rnd_prod.s",
acknowledgement = ack-nj,
keywords = "correct rounding; decimal floating-point arithmetic",
}
@InProceedings{Gibson:1990:CII,
author = "D. H. Gibson",
title = "Considerations for including {IEEE} floating point in
large systems",
crossref = "SHARE:1990:PSE",
pages = "47--62",
year = "1990",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "International standards such as ANSI/IEEE Std 754-1985
floating-point arithmetic provide the potential for
application portability. The paper, beginning with a
1984 SHARE requirements statement, sets forth certain
considerations for including IEEE Std 754 floating
point in large systems. A tutorial is presented on IEEE
Std 754 floating-point arithmetic. The considerations
for integrating IEEE into a large system along with an
existing floating point representation are discussed in
three categories: architectural; implementation; usage.
Related topics are identified and discussed. The paper
concludes with a summary of the considerations. (11
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "IBM Corp., Poughkeepsie, NY, USA",
classification = "C5230 (Digital arithmetic methods)",
keywords = "Application portability; Floating-point arithmetic;
IEEE Std 754 floating point; SHARE",
thesaurus = "Digital arithmetic; Standards",
}
@Article{Glass:1990:MC,
author = "L. B. Glass",
title = "Math coprocessors",
journal = j-BYTE,
volume = "15",
number = "1",
pages = "337--348",
month = jan,
year = "1990",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 12 17:47:21 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "B1265B (Logic circuits); B1265F (Microprocessors and
microcomputers); C5130 (Microprocessor chips); C5230
(Digital arithmetic methods)",
fjournal = "BYTE Magazine",
keywords = "Cyrix 83D87; Floating-point maths; IEEE 754
floating-point standard; Integrated Information
Technology; Intel 80287; Intel 80387; Intel 8087; Maths
coprocessors; Motorola 68881; Motorola 68882; NP-3C87;
Weitek Abacus 3167",
thesaurus = "Digital arithmetic; Microprocessor chips; Satellite
computers",
}
@InCollection{Goldberg:1990:CA,
author = "D. Goldberg",
title = "Computer Arithmetic",
crossref = "Hennessy:1990:CAQ",
chapter = "A",
pages = "A-1--A-66",
year = "1990",
bibdate = "Fri Dec 08 13:04:21 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Goodman:1990:SMR,
author = "R. H. Goodman",
title = "Some Models of Relative Error in Products",
journal = j-APPL-NUM-MATH,
volume = "6",
number = "3",
pages = "209--220",
month = mar,
year = "1990",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
bibdate = "Thu Sep 1 10:14:16 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274",
}
@MastersThesis{Goodreau:1990:DIF,
author = "Michael S. Goodreau",
title = "The design and implementation of a floating-point
format conversion integrated circuit",
type = "Thesis ({M.S.E.E.})",
school = "University of Washington",
address = "Seattle, WA, USA",
pages = "ix + 113",
year = "1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.; Integrated circuits ---
Design and construction.",
}
@InCollection{Gries:1990:BDO,
author = "David Gries",
title = "Binary to Decimal, One More Time",
crossref = "Feijen:1990:BOB",
chapter = "16",
pages = "141--148",
year = "1990",
DOI = "https://doi.org/10.1007/978-1-4612-4476-9_17",
bibdate = "Sat Sep 03 09:41:32 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/texbook3.bib",
note = "This paper presents an alternate proof of Knuth's
algorithm \cite{Knuth:1990:SPW} for conversion between
decimal and fixed-point binary numbers.",
URL = "https://link.springer.com/chapter/10.1007/978-1-4612-4476-9_17",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Gu:1990:TIT,
author = "Li Zhen Gu and Xing Yuan Chen",
title = "Table-driven implementation of the trigonometric
functions using {IEEE} floating point operations.
({Chinese})",
journal = "Journal of Tsinghua University",
volume = "30",
number = "3",
pages = "31--38",
year = "1990",
MRclass = "65D20 (65-04)",
MRnumber = "92a:65070",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Tsinghua Univ.",
}
@Book{Hamacher:1990:CO,
author = "V. Carl Hamacher and Zvonko G. Vranesic and Safwat G.
Zaky",
title = "Computer organization",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
edition = "Third",
pages = "xx + 617",
year = "1990",
ISBN = "0-07-025685-3",
ISBN-13 = "978-0-07-025685-9",
LCCN = "QA76.9.A73 H351 1990",
bibdate = "Sat May 18 14:24:11 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "McGraw-Hill series in computer organization and
architecture",
acknowledgement = ack-nhfb,
}
@Article{Hashemian:1990:SRA,
author = "R. Hashemian",
title = "Square Rooting Algorithms for Integer and
Floating-Point Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "8",
pages = "1025--1029",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57041",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:03 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57041",
abstract = "An algorithm for evaluating the square root of
integers and real numbers is developed. The procedure
consists of two parts: one to obtain a close estimate
of the square root and the other to modify the initial
value, iteratively, until a precise root is evaluated.
The major effort in this development has been
concentrated on two objectives: high speed and no
division operation other than division by 2. The first
objective is achieved through a simple two-step
procedure for getting the first estimate, and then
modifying it by employing a fast converging iteration
technique. The second objective is also fulfilled
through applying bit-shift operation rather than
division operation. The algorithm is simulated for both
integer and real numbers, and the results are compared
to two methods being widely used. The results
(tabulated) show considerable improvement in speed
compared to these other two methods.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Department of Electr. Eng., Northern Illinois
University, Dekalb, IL, USA",
ajournal = "IEEE Trans. Comput.",
classification = "C1160 (Combinatorial mathematics); C4130
(Interpolation and function approximation); C5230
(Digital arithmetic methods)",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Bit-shift operation; Close estimate; Division by 2;
Fast converging iteration; Floating-point numbers;
Initial value modification; Integer numbers; Precise
root; Real numbers; Square rooting algorithms",
summary = "An algorithm for evaluating the square root of
integers and real numbers is developed. The procedure
consists of two parts: one to obtain a close estimate
of the square root and the other to modify the initial
value, iteratively, until a precise \ldots{}",
thesaurus = "Digital arithmetic; Iterative methods; Number theory",
}
@Article{Hokenek:1990:LZA,
author = "E. Hokenek and R. K. Montoye",
title = "Leading-zero anticipator ({LZA}) in the {IBM RISC
System\slash 6000} floating-point execution unit",
journal = j-IBM-JRD,
volume = "34",
number = "1",
pages = "71--77",
month = jan,
year = "1990",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Presents a novel technique used in the
multiply-add-fused (MAF) unit of the IBM RISC
System/6000 (RS/6000) processor for normalizing the
floating-point results. Unlike the conventional
procedures applied thus far, the so-called leading-zero
anticipator (LZA) of the RS/6000 carries out processing
of the leading zeros and ones in parallel with
floating-point addition. Therefore, the new circuitry
reduces the total latency of the MAF unit by enabling
the normalization and addition to take place in a
single cycle.",
acknowledgement = ack-nhfb,
affiliation = "IBM Res. Div., Thomas J. Watson Res. Center, Yorktown
Heights, NY, USA",
classification = "B1265B (Logic circuits); C5230 (Digital arithmetic
methods)",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "Circuitry; Floating-point addition; IBM RISC
System/6000 floating-point execution unit; Latency;
Leading-zero anticipator; Multiply-add-fused;
Normalization; Parallel",
thesaurus = "Digital arithmetic; IBM computers; Reduced instruction
set computing",
}
@Article{Hokenek:1990:SGR,
author = "E. Hokenek and R. K. Montoye and P. W. Cook",
title = "Second-Generation {RISC} Floating Point with
Multiply-Add Fused",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "25",
number = "5",
pages = "1207--1213",
month = oct,
year = "1990",
CODEN = "IJSCBC",
DOI = "https://doi.org/10.1109/4.62143",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A 440000-transistor second-generation RISC (reduced
instruction set computer) floating-point chip is
described. The pipeline latency is only two cycles, and
a double-precision result is produced every cycle.
System throughput and accuracy are increased by using a
floating-point multiply-add-fused unit, which carries
out a double-precision accumulate as a two-cycle
pipelined execution with only one rounding error. While
the cycle time (40 ns) is competitive with other CMOS
RISC systems, the floating-point performance stretches
to the range of bipolar RISC systems (7.4-13 MFLOPS
LINPACK). Leading zero anticipation makes the two-cycle
pipeline possible by nearly eliminating the additional
postnormalization time, and it allows for reduced
overall system latency. Partial decode shifters allow
complete time sharing for the multiply and data
alignment. Improved design techniques for logarithmic
addition and higher order counters for multiplication
complete this second-generation RISC floating-point
unit design.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips)",
fjournal = "IEEE Journal of Solid-State Circuits",
keywords = "40 Ns; 7.4 To 13 MFLOPS; Double-precision accumulate;
Double-precision result; Floating-point chip; Higher
order counters; Logarithmic addition; Multiplication;
Multiply-add-fused unit; Partial decode shifters;
Pipeline latency; Reduced instruction set computer;
RISC; Two-cycle pipelined execution",
numericalindex = "Time 4.0E-08 s; Computer speed 7.4E+06 to 1.3E+07
FLOPS",
summary = "A 440000-transistor second-generation RISC (reduced
instruction set computer) floating-point chip is
described. The pipeline latency is only two cycles, and
a double-precision result is produced every cycle.
System throughput and accuracy are increased \ldots{}",
thesaurus = "CMOS integrated circuits; Microprocessor chips;
Pipeline processing; Reduced instruction set
computing",
}
@Article{Hong:1990:DTP,
author = "S. J. Hong",
title = "The design of a testable parallel multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "3",
pages = "411--416",
month = mar,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.48874",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=48874",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Horiguchi:1990:FNR,
author = "Hiroshi Horiguchi",
title = "Floating-Point Numbers and Real Numbers",
journal = j-ADV-SOFT-SCI-TECH,
volume = "1",
number = "??",
pages = "157--??",
year = "1990",
ISSN = "1044-7997",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Advances in software science and technology",
}
@TechReport{IBM:1990:AXI,
author = "{IBM Corporation}",
title = "{ACRITH-XSC}: {IBM} High Accuracy Arithmetic ---
Extended Scientific Computation",
type = "Technical Report",
number = "GC33-6461-01, SC33-6462-00, SC33-6463-00,
SC33-6464-00, SC33-6466-00.",
institution = pub-IBM,
address = pub-IBM:adr,
year = "1990",
bibdate = "Thu Jan 21 17:27:09 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
tableofcontents = "1. General Information \\
2. Reference \\
3. Sample Programs \\
4. How To Use \\
5. Syntax Diagrams",
}
@Book{IBM:1990:IRS,
editor = "Mamata Misra",
title = "{IBM RISC System\slash 6000 Technology, publication
SA23-2619-00}",
publisher = pub-IBM,
address = pub-IBM:adr,
year = "1990",
bibdate = "Wed Sep 14 23:02:26 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Jarvis:1990:ICA,
author = "P. Jarvis",
title = "Implementing {Cordic} Algorithms",
journal = j-DDJ,
volume = "15",
number = "10",
pages = "152--158",
month = oct,
year = "1990",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@InProceedings{Kahan:1990:HCA,
author = "W. Kahan",
title = "How {Cray}'s arithmetic hurts scientific computation
(and what might be done about it)",
crossref = "CUG:1990:PSC",
pages = "42",
day = "14",
month = jun,
year = "1990",
bibdate = "Tue Jan 03 18:17:16 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Manuscript prepared for the Cray User Group meeting in
Toronto, Canada, April 10, 1990.",
URL = "http://754r.ucbtest.org/issues/cray-hurts-uk.pdf;
http://754r.ucbtest.org/issues/cray-hurts-ut.pdf;
http://754r.ucbtest.org/issues/cray-hurts.pdf",
acknowledgement = ack-nhfb,
}
@Misc{Kahan:1990:PCA,
author = "William Kahan",
title = "Paradoxes in concepts of accuracy",
publisher = "Carnegie Mellon University",
address = "Pittsburgh, PA, USA",
year = "1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "1 videocassette (60 min.)",
series = "Distinguished lecture series",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic.; Floating-point arithmetic ---
Data processing.",
remark = "Lecture given February 15, 1990. VHS format. Lecturer,
William Kahan. Paradoxes expose errors in conventional
wisdom about floating-point arithmetic.",
}
@Article{Kalbasi:1990:CYT,
author = "K. Kalbasi",
title = "Can you trust your computer?",
journal = j-IEEE-POT,
volume = "9",
number = "2",
pages = "15--18",
month = apr,
year = "1990",
CODEN = "IEPTDF",
ISSN = "0278-6648 (print), 1558-1772 (electronic)",
ISSN-L = "0278-6648",
bibdate = "Wed Sep 14 19:14:21 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Potentials",
}
@Article{Katsuno:1990:BFP,
author = "A. Katsuno and H. Takahashi and H. Kubosawa and T.
Sato and A. Suga and G. Goto",
title = "A 64-bit Floating-Point Processing Unit with a
Horizontal Instruction Code for Parallel Operations",
crossref = "IEEE:1990:PII",
pages = "347--350",
year = "1990",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Khan:1990:FPA,
author = "A. Khan",
title = "Floating point architecture and implementation",
crossref = "Wescon:1990:WCR",
pages = "205--213",
year = "1990",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Analyzes various requirements of efficient floating
point architecture and implementation. The basic
elements of architecture such as latency, repeat rate
and issue rate are defined. Handling various exceptions
in a precise manner is described. Finally, a
description of one example (MIPS R3010) is provided. (0
Refs.)",
acknowledgement = ack-nhfb,
availability = "Western Periodicals Co., 13000 Rayner Street, North
Hollywood, CA 91605, USA",
classification = "C5130 (Microprocessor chips); C5220 (Computer
architecture); C5230 (Digital arithmetic methods)",
keywords = "Elements of architecture; Floating point architecture;
Issue rate; Latency; MIPS R3010; Repeat rate;
Requirements",
thesaurus = "Computer architecture; Digital arithmetic",
}
@InProceedings{Kiernan:1990:FAE,
author = "J. M. Kiernan and T. B. Blachowiak",
title = "Fast, Accurate Elementary Functions For the {Cray
Y-MP} Computer",
crossref = "CUG:1990:PSC",
pages = "243--252",
year = "1990",
bibdate = "Thu Sep 1 10:15:30 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InCollection{Knuth:1990:SPW,
author = "Donald E. Knuth",
title = "A Simple Program Whose Proof Isn't",
crossref = "Feijen:1990:BOB",
chapter = "27",
pages = "233--242",
year = "1990",
bibdate = "Mon Feb 03 07:07:55 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[Chapter 11]{Knuth:2010:SPD}. This
paper discusses the algorithm used in {\TeX} for
converting between decimal and scaled fixed-point
binary values, and for guaranteeing a minimum number of
digits in the decimal representation. See also
\cite{Clinger:1990:HRF,Clinger:2004:RHR} for decimal to
binary conversion,
\cite{Steele:1990:HPF,Steele:2004:RHP} for binary to
decimal conversion, and \cite{Gries:1990:BDO} for an
alternate proof of Knuth's algorithm.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Koren:1990:EEF,
author = "I. Koren and O. Zinaty",
title = "Evaluating Elementary Functions in a Numerical
Coprocessor Based on Rational Approximations",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-39",
number = "8",
pages = "1030--1037",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57042",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:15:30 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kornerup:1990:ARB,
author = "Peter Kornerup and David W. Matula",
title = "An algorithm for redundant binary bit-pipelined
rational arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "8",
pages = "1106--1115",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57048",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57048",
abstract = "The authors introduce a redundant binary
representation of the rationals and an associated
algorithm for computing the sum, difference, product,
quotient, and other useful functions of two rational
operands, using this representation. The algorithm
extends R.W. Gosper's (1972) partial quotient
arithmetic algorithm and allows the design of an online
arithmetic unit with computations granularized at the
signed bit level. Each input or output port can be
independently set to receive/produce operands/result in
either binary radix or the binary rational
representation. The authors investigate by simulation
the interconnection of several such units for the
parallel computation of more complicated expressions in
a tree-pipelined manner, with particular regard to
measuring individual and compounded online delays",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Laakso:1990:RFP,
author = "T. Laakso and B. Zeng and I. Hartimo and Y. Neuvo",
booktitle = "{IEEE} International Conference on Systems
Engineering, 1990",
title = "Reduction of floating-point roundoff noise in
recursive digital filters with error feedback",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "244--247",
year = "1990",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The reduction of roundoff noise in floating-point
recursive digital filters by means of error feedback is
discussed. Optimal (minimum-noise) error feedback is
formulated, and it is shown to be different from the
optimal solution in the fixed-point \ldots{}",
}
@Article{Lee:1990:OPC,
author = "Vernon A. {Lee, Jr.} and Hans-J. Boehm",
title = "Optimizing programs over the constructive reals",
journal = j-SIGPLAN,
volume = "25",
number = "6",
pages = "102--111",
month = jun,
year = "1990",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/93542.93558",
ISBN = "0-89791-364-7",
ISBN-13 = "978-0-89791-364-5",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:15:53 MST 2003",
bibsource = "Compendex database; http://portal.acm.org/;
http://www.acm.org/pubs/contents/proceedings/pldi/93542/index.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/pldi/93542/p102-lee/",
abstract = "The constructive reals provide programmers with a
useful mechanism for prototyping numerical programs,
and for experimenting with numerical algorithms.
Unfortunately, the performance of current
implementations is inadequate for some potential
applications. In particular, these implementations tend
to be space inefficient, in that they essentially
require a complete computation history to be
maintained. Some numerical analysts propose that the
programmer instead be provided with variable precision
interval arithmetic, and then be required to write code
to restart a computation when the intervals become too
inaccurate. Though this model is no doubt appropriate
at times, it is not an adequate replacement for exact
arithmetic. The correct transformation from a program
operating on the constructive reals to a reasonable
program using iterated interval arithmetic can be
nontrivial and error prone. Here we present a technique
based on program slicing to both automate this process
and reduce the amount of reexecution. Thus the
programmer is still free to use the simpler abstraction
of exact real arithmetic, but we can provide a more
efficient interval arithmetic based implementation.
Some preliminary empirical results are presented.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Rice University",
affiliationaddress = "Houston, TX, USA",
annote = "Published as part of the Proceedings of PLDI'90.",
classification = "722; 723; C6110 (Systems analysis and programming);
C6120 (File organisation); C7310 (Mathematics)",
confdate = "20-22 June 1990",
conference = "Proceedings of the ACM SIGPLAN '90 Conference on
Programming Language Design and Implementation",
conferenceyear = "1990",
conflocation = "White Plains, NY, USA",
confsponsor = "ACM",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
journalabr = "SIGPLAN Not",
keywords = "algorithms; Computer Operating Systems; Computer
Programming Languages --- Design; Constructive reals;
Efficient interval arithmetic based implementation;
Empirical results; Exact real arithmetic; Numerical
algorithms; Numerical analysts; Numerical programs;
Optimizing Compilers; performance; Performance; Program
Compilers; Program slicing; Reexecution; Variable
precision interval arithmetic",
meetingaddress = "White Plains, NY, USA",
meetingdate = "Jun 20--22 1990",
meetingdate2 = "06/20--22/90",
sponsor = "Assoc for Computing Machinery, Special Interest Group
on Programming Languages",
subject = "{\bf D.3.4} Software, PROGRAMMING LANGUAGES,
Processors, Optimization. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems. {\bf
G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
General, Computer arithmetic. {\bf F.2.2} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Computations on discrete structures.",
thesaurus = "Data structures; Mathematics computing; Programming",
}
@Article{Ling:1990:AIM,
author = "H. Ling",
title = "An approach to implementing multiplication with small
tables",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "5",
pages = "717--718",
month = may,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.53588",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=53588",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Lozier:1990:CPL,
author = "D. W. Lozier and F. W. J. Olver",
title = "Closure and Precision in Level-Index Arithmetic",
journal = j-SIAM-J-NUMER-ANAL,
volume = "27",
number = "5",
pages = "1295--1304",
month = oct,
year = "1990",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65-04 (65G05)",
MRnumber = "91f:65002",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{MacDonald:1990:IFP,
author = "Tom MacDonald",
title = "{IEEE} Floating-Point Arithmetic and {C}",
journal = j-JCLT,
volume = "2",
number = "2",
pages = "102--112",
month = sep,
year = "1990",
ISSN = "1042-5721",
bibdate = "Thu Nov 8 14:50:33 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "The Journal of {C} Language Translation",
}
@Article{Mandelbaum:1990:SMD,
author = "D. M. Mandelbaum",
title = "A systematic method for division with high average bit
skipping",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "1",
pages = "127--130",
month = jan,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.46287",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:19:59 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=46287",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@PhdThesis{MangaEbongue:1990:PBV,
author = "Charles {Manga Ebongue}",
title = "Processeur 32 Bits en Virgule Flottante: Techniques de
Validation Fonctionnelle, {{\'E}}lectrique et Test
{\`a} la Conception. ({French}) [32-bit Floating-Point
Processor: Techniques of Functional and Electrical
Validation and Test in the Design]",
type = "Th{\`e}se Doctoral",
school = "Sciences Appliqu{\'e}es, Universit{\'e} Paris 6",
address = "Paris, France",
year = "1990",
bibdate = "Thu May 09 10:03:41 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Sous la direction de Alain Greiner.",
abstract = "Cette th{\`e}se d{\'e}veloppe deux aspects de la
conception des circuits integr{\'e}s: (1) le premier
aspect correspond {\`a} la m{\'e}thodologie
d'implantation du processeur de calcul en virgule
flottante d{\'e}velopp{\'e} au laboratoire MASI par
l'{\'e}quipe de Cao \& VLSI de l'Universit{\'e} Pierre
et Marie Curie, (2) le deuxi{\'e}me aspect pr{\'e}sente
les travaux concernant une m{\'e}thodologie de test
{\`a} la conception conduisant aussi bien {\`a} la
validation fonctionnelle et {\'e}lectrique au cours de
la conception qu'{\`a} la testabilit{\'e} apr{\`e}s
fabrication. Le premier aspect a des implications {\`a}
diff{\'e}rents niveaux: (1) au niveau assemblage par
l'introduction d'une m{\'e}thodologie de conception
sp{\'e}cifique au circuit, (2) au niveau {\'e}lectrique
pour le choix et la conception d'une biblioth{\`e}que
de cellules standards qui tient compte des
caract{\'e}ristiques dynamiques des signaux sur chaque
nud du circuit. Le deuxi{\`e}me aspect a pour
r{\'e}sultat l'introduction d'une technique originale
de recherche de vecteurs de test. De m{\^e}me, la
validation fonctionnelle de ce circuit sera
invoqu{\^e}e en r{\^e}solvant les principaux
probl{\`e}mes de coh{\'e}rence entre les masques
d{\'e}ssin{\'e}s et la liste des interconnexions.",
acknowledgement = ack-nhfb,
language = "French",
}
@Book{Mar:1990:DSP,
editor = "Amy Mar",
title = "Digital signal processing applications using the
{ADSP-2100} family",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xvi + 611",
year = "1990",
ISBN = "0-13-212978-7",
ISBN-13 = "978-0-13-212978-7",
LCCN = "TK5102.5 .D44824 1990",
bibdate = "Sat Jan 15 05:58:58 MST 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "System requirements for computer disks: IBM PC; PC-DOS
3.0.",
subject = "Signal processing; Digital techniques;
Microprocessors",
}
@Article{Margulis:1990:IMI,
author = "N. Margulis",
title = "i860 microprocessor internal architecture",
journal = j-MICROPROC-MICROSYS,
volume = "14",
number = "2",
pages = "89--96",
month = mar,
year = "1990",
CODEN = "MIMID5",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Microprocessors and Microsystems",
}
@Article{Markstein:1990:CEF,
author = "P. W. Markstein",
title = "Computation of elementary functions on the {IBM RISC
System\slash 6000} processor",
journal = j-IBM-JRD,
volume = "34",
number = "1",
pages = "111--119",
month = jan,
year = "1990",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "65-04 (65D20)",
MRnumber = "1 057 659",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The additional speed and precision of the IBM RISC
System\slash 6000 floating-point unit have motivated
reexamination of algorithms to perform division, square
root, and the elementary functions. New results are
obtained which avoid the necessity of doing special
testing to get the last bit rounded correctly in
accordance with all of the IEEE rounding modes in the
case of division and square root. For the elementary
function library, a technique is described for always
getting the last bit rounded correctly in the selected
IEEE rounding mode.",
acknowledgement = ack-nhfb,
affiliation = "IBM Res. Div., Austin, TX, USA",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "correct rounding; Division; Elementary functions;
Floating-point unit; IBM RISC System\slash 6000
processor; IEEE rounding modes; IEEE rounding modes,
IBM RISC System/6000 processor; Square root",
thesaurus = "Digital arithmetic; IBM computers; Reduced instruction
set computing",
}
@InProceedings{Matula:1990:HPD,
author = "D. Matula",
title = "Highly parallel divide and square root algorithms for
a new generation floating point processor",
crossref = "Ullrich:1990:CCA",
pages = "??--??",
year = "1990",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@InProceedings{McCloud:1990:FPU,
author = "S. McCloud and D. Anderson and C. DeWitt and C. Hinds
and Y. W. Ho and D. Marquette and E. Quintana",
title = "A Floating Point Unit for the 68040",
crossref = "IEEE:1990:PII",
pages = "187--190",
year = "1990",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@MastersThesis{Mills:1990:DIH,
author = "Karl Scott Mills",
title = "The design and implementation of a high performance
floating-point image processing and graphics subsystem
for the {NeXT} computer",
type = "Thesis ({M.S.E.E.})",
school = "University of Washington",
address = "Seattle, WA, USA",
pages = "v + 60 + 3",
year = "1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer graphics.; Image processing --- Digital
techniques.",
}
@Article{Montoye:1990:DIR,
author = "R. K. Montoye and E. Hokenek and S. L. Runyon",
title = "Design of the {IBM RISC System\slash 6000}
floating-point execution unit",
journal = j-IBM-JRD,
volume = "34",
number = "1",
pages = "59--70",
month = jan,
year = "1990",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.341.0059",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Mar 25 14:26:59 MST 1997",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
URL = "http://www.research.ibm.com/journal/rd/341/ibmrd3401G.pdf",
abstract = "The IBM RISC System\slash 6000 (RS\slash 6000)
floating-point unit (FPU) exemplifies a
second-generation RISC CPU architecture and an
implementation which greatly increases floating-point
performance and accuracy. The key feature of the FPU is
a unified floating-point multiply-add-fused unit (MAF)
which performs the accumulate operation (A*B)+C as an
indivisible operation. The paper first discusses the
motivation for MAF, explaining in some detail why it is
an appropriate addition to the floating-point
architecture in VLSI. A summary of floating-point
operations is then given, with a discussion to
demonstrate the parallelism that is possible when the
multiply and add are fused. This is followed by a
description of the two-stage pipeline used for the
version of IEEE double-precision floating-point
arithmetic used in the RS\slash 6000 processor, with
delays consistent with its over-all superscalar
second-generation RISC architecture. Then the paper
describes the interaction of logical and physical
design required to incorporate several advances in VLSI
arithmetic while accommodating required delay and
technological (physical) constraints. The results are
then summarized.",
acknowledgement = ack-nhfb,
affiliation = "IBM Res. Div., Thomas J. Watson Res. Center, Yorktown
Heights, NY, USA",
classcodes = "B1265B (Logic circuits); B1130B (Computer-aided
circuit analysis and design); B1265F (Microprocessors
and microcomputers); C5230 (Digital arithmetic
methods); C5220 (Computer architecture); C5210B
(Computer-aided logic design)C7410D (Electronic
engineering)",
classification = "B1130B (Computer-aided circuit analysis and design);
B1265B (Logic circuits); B1265F (Microprocessors and
microcomputers); C5210B (Computer-aided logic design);
C5220 (Computer architecture); C5230 (Digital
arithmetic methods); C7410D (Electronic engineering)",
corpsource = "IBM Res. Div., Thomas J. Watson Res. Center, Yorktown
Heights, NY, USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "Accumulate operation; accumulate operation;
arithmetic; CAD; circuit layout CAD; digital
arithmetic; floating-point architecture; Floating-point
architecture; generation RISC CPU architecture; IBM
computers; IBM RISC System/6000 floating-point
execution unit; IBM RISC System\slash 6000
floating-point execution unit; IEEE double-precision
floating-point; IEEE double-precision floating-point
arithmetic; indivisible; Indivisible operation; logic;
multiply-add-fused unit; operation; Parallelism;
parallelism; reduced instruction set computing;
second-; Second-generation RISC CPU architecture; stage
pipeline; Superscalar second-generation RISC
architecture; superscalar second-generation RISC
architecture; two-; Two-stage pipeline; unified
floating-point; Unified floating-point
multiply-add-fused unit; VLSI arithmetic; VLSI
arithmetic, IBM RISC System/6000 floating-point
execution unit",
thesaurus = "Circuit layout CAD; Digital arithmetic; IBM computers;
Logic CAD; Reduced instruction set computing",
treatment = "P Practical",
}
@Article{Montuschi:1990:SSR,
author = "P. Montuschi and P. M. Mezzalama",
title = "Survey of square rooting algorithms",
journal = j-IEE-PROC-COMPUT-DIGIT-TECH,
volume = "137",
number = "1",
pages = "31--40",
month = jan,
year = "1990",
CODEN = "ICDTEA",
ISSN = "1350-2387 (print), 1359-7027 (electronic)",
ISSN-L = "1350-2387",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEE Proceedings. Computers and Digital Techniques",
summary = "The paper reviews the algorithms for the computation
of square roots for binary machines. After an initial
classification, the algorithms are analysed in detail
by considering their specific peculiarities and
properties. Finally, some comments are \ldots{}",
}
@Article{Morita:1990:FMM,
author = "Hikaru Morita",
title = "A Fast Modular-Multiplication Algorithm Based on a
Higher Radix",
journal = j-LECT-NOTES-COMP-SCI,
volume = "435",
pages = "387--??",
year = "1990",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon Feb 4 12:01:59 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t0435.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/0435/04350387.htm;
http://link.springer-ny.com/link/service/series/0558/papers/0435/04350387.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@MastersThesis{Mueller:1990:HCA,
author = "Volker M{\"u}ller",
title = "{Hochgenaue CORDIC-Algorithmen f{\"u}r reelle
Standardfunktionen mittels dynamischer
Defektberechnung} \toenglish {High-accuracy CORDIC
Algorithms for Real Elementary Functions by Means of
Dynamic Error Computation} \endtoenglish",
type = "{Diplomarbeit}",
school = "Institut f{\"u}r angewandte Mathematik,
Universit{\"a}t Karlsruhe",
pages = "??",
month = dec,
year = "1990",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Murthy:1990:MPA,
author = "Narayan Murthy and Allen Stix",
title = "Multiple precision arithmetic: a programming
assignment in {CS2} applying linked lists",
journal = j-SIGCSE,
volume = "22",
number = "1",
pages = "129--133",
month = feb,
year = "1990",
CODEN = "SIGSD3",
DOI = "https://doi.org/10.1145/319059.323431",
ISSN = "0097-8418 (print), 2331-3927 (electronic)",
ISSN-L = "0097-8418",
bibdate = "Sat Nov 17 18:57:12 MST 2012",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigcse1990.bib",
acknowledgement = ack-nhfb,
fjournal = "SIGCSE Bulletin (ACM Special Interest Group on
Computer Science Education)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J688",
}
@Article{Ohtomo:1990:FPD,
author = "Hiroyasu Ohtomo and Hisao Ishizuka and Masahiko
Kashimura and Akio Nakajima and Tetsuhiro Hira",
title = "A 32-bit Floating Point Digital Signal Processor for
Graphics Application",
journal = j-NEC-RES-DEV,
volume = "??",
number = "99",
pages = "47--??",
month = oct,
year = "1990",
CODEN = "NECRAU",
ISSN = "0048-0436",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Nippon Electric Company research and development",
}
@InProceedings{Olson:1990:FAA,
author = "T. Olson and B. Stewart",
title = "Floating-point architecture of the Am29050",
crossref = "Wescon:1990:WCR",
pages = "214--217",
year = "1990",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Am29050 is the newest member of Advanced Micro
Devices' 29K family of RISC microprocessors. It is both
binary and pin compatible with the Am29000, and also
incorporates a high-performance floating-point unit
(FPU) on chip. The FPU, which complies with the IEEE
754 standard, consists of parallel add, multiply, and
divide/square-root units, operating on single-precision
and double-precision values. In addition to the
standard operations, the FPU implements two types of
multiply-add functions, which take three operands and
produce one result. A single register file, which is
shared between the integer and floating-point units,
can supply two 64-bit operands and write back both a
32-bit integer result and a 64-bit floating-point
result in a single cycle.",
acknowledgement = ack-nhfb,
affiliation = "Adv. Micro Devices, Austin, TX, USA",
availability = "Western Periodicals Co., 13000 Rayner Street, North
Hollywood, CA 91605, USA",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5220 (Computer architecture);
C5230 (Digital arithmetic methods)",
keywords = "29K family; 64 Bit; Advanced Micro Devices; Am29050;
Double-precision; Floating point architecture; Floating
point arithmetic; Floating-point unit; FPU; IEEE 754
standard; Multiply-add functions; Parallel add; RISC
microprocessors; Single-precision",
numericalindex = "Word length 6.4E+01 bit",
thesaurus = "Computer architecture; Digital arithmetic;
Microprocessor chips; Reduced instruction set
computing",
}
@Article{Owens:1990:BSM,
author = "R. M. Owens and M. J. Irwin",
title = "Being stingy with multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "6",
pages = "809--818",
month = jun,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.53602",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=53602",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Palmore:1990:CAC,
author = "J. Palmore and C. Herring",
title = "Computer arithmetic, chaos and fractals",
journal = j-PHYSICA-D,
volume = "42",
number = "1-3",
pages = "99--110",
month = jun,
year = "1990",
CODEN = "PDNPDT",
ISSN = "0167-2789 (print), 1872-8022 (electronic)",
ISSN-L = "0167-2789",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Ninth Annual International Conference of the Center
for Nonlinear Studies on Self-Organizing, Collective
and Cooperative Phenomena in Natural and Artificial
Networks",
abstract = "The authors explore aspects of computer arithmetic
from the viewpoint of dynamical systems. They
demonstrate the effects of finite precision arithmetic
in three uniformly hyperbolic chaotic dynamical
systems: Bernoulli shifts, cat maps, and pseudorandom
number generators. They show that elementary
floating-point operations in binary computer arithmetic
possess an inherently fractal structure. Each of these
dynamical systems allows us to compare the exact
results in integer arithmetic with those obtained by
using floating-point arithmetic.",
acknowledgement = ack-nhfb,
affiliation = "Department of Math., Illinois University, Urbana, IL,
USA",
classification = "C1160 (Combinatorial mathematics); C5230 (Digital
arithmetic methods)",
confdate = "22-26 May 1989",
conflocation = "Los Alamos, NM, USA",
fjournal = "Physica. D, Nonlinear phenomena",
journal-URL = "http://www.sciencedirect.com/science/journal/01672789",
keywords = "Bernoulli shifts; Binary computer arithmetic; Cat
maps; Chaos; Computer arithmetic; Dynamical systems;
Elementary floating-point operations; Finite precision
arithmetic; Floating-point arithmetic; Fractal
structure; Integer arithmetic; Pseudorandom number
generators; Self-similar structure; Uniformly
hyperbolic chaotic dynamical systems",
pubcountry = "Netherlands",
thesaurus = "Chaos; Digital arithmetic; Fractals; Random number
generation; Roundoff errors",
}
@InProceedings{Pan:1990:FSI,
author = "J. Pan and K. N. Levitz",
title = "A Formal Specification of the {IEEE Floating-Point
Standard} with Application to the Verification of
Floating-Point Coprocessors",
crossref = "Chen:1990:CRT",
pages = "505--510",
year = "1990",
bibdate = "Wed Dec 13 18:41:54 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A description is given of work in progress on
verifying a floating-point coprocessor based on the
MC68881/82, with respect to the IEEE standard
floating-point arithmetic (ANSI-IEEE Std 754-1985). A
complete formalization of the IEEE floating-point
standard using the HOL (high-order-logic) specification
and verification system is presented. The specification
of floating-point numbers, floating-point arithmetic
functions, rounding schemes and post-normalization is
described. In order for the specification to be
adaptable to different implementation, several model
parameters are used in specifying all the functions.
The floating-point coprocessor is specified as a
hierarchy of interpreters. The communication with the
CPU is modeled as standard interprocessor
communication. A technique for verifying hierarchies of
communicating hardware interpreters is described. (11
Refs.)",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Div. of Computer Science, California University,
Berkeley, CA, USA",
availability = "IEEE Computer Society Press, Los Alamitos, CA, USA",
classification = "C5130 (Microprocessor chips); C5230 (Digital
arithmetic methods)",
keywords = "ANSI-IEEE Std 754-1985; Communicating hardware
interpreters; CPU communication; Floating-point
coprocessors; Higher order logic specification; HOL;
IEEE standard floating-point arithmetic; Interpreter
hierarchy; Interprocessor communication; MC68881/82;
Post-normalization; Rounding schemes; Standard
formalization; Verification system",
thesaurus = "Digital arithmetic; Formal specification;
Microprocessor chips; Satellite computers; Standards",
}
@Article{Parhami:1990:GSD,
author = "Behrooz Parhami",
title = "Generalized Signed-Digit Number Systems: a Unifying
Framework for Redundant Number Representations",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "1",
pages = "89--98",
month = jan,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.46283",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Feb 15 15:47:08 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Signed-digit (SD) number representation systems have
been defined for any radix r ?? 3 with digit values
ranging over the set $ ( - \alpha, \ldots {}, - 1, 0,
1, \ldots {}, \alpha) $, where $ \alpha $ is an
arbitrary integer in the range $ 1 / 2 r > \alpha > r
$. Such number representation systems possess
sufficient redundancy to allow for the annihilation of
carry or borrow chains and hence result in fast
propagation-free addition and subtraction. The author
refers to the above as ordinary SD number systems and
defines generalized SD number systems which contain
them as a special symmetric subclass. It is shown that
the generalization not only provides a unified view of
all redundant number systems which have proven useful
in practice (including stored-carry and stored-borrowed
systems), but also leads to new number systems not
examined before. Examples of such new number systems
are stored-carry-or-borrow systems, stored-double-carry
systems, and certain redundant decimal
representations.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Payne:1990:PLCa,
author = "M. Payne and C. Schaffert and B. Wichmann",
title = "Proposal for a language compatible arithmetic
standard",
journal = j-SIGNUM,
volume = "25",
number = "1",
pages = "2--43",
month = jan,
year = "1990",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Describes the proposal for an arithmetic standard
which has been submitted to the American National
Standards Institute and the International Organization
for Standardization. It is being processed by the ANSI
X3T2 committee and the ISO/IEC JTC1/SC22/WG11 working
group. The specifications cover both integer and
floating point arithmetic.",
acknowledgement = ack-nhfb,
affiliation = "Digital Equipment Corp, Maynard, MA, USA",
classification = "C7310 (Mathematics)",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "American National Standards Institute; ANSI X3T2
committee; Floating point arithmetic; Integer
arithmetic; International Organization for
Standardization; Language compatible arithmetic
standard",
thesaurus = "Digital arithmetic; Mathematics computing; Standards",
}
@Article{Payne:1990:PLCb,
author = "M. Payne and C. Schaffert and B. Wichmann",
title = "Proposal for a language compatible arithmetic
standard",
journal = j-SIGPLAN,
volume = "25",
number = "1",
pages = "59--86",
month = jan,
year = "1990",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:15:49 MST 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The proposal for an arithmetic standard has been
submitted to the American National Standard Institute
and the International Organization for Standardization.
The proposal covers both integer and floating point
arithmetic. The underlying goal is to expedite the
production of robust numerical software which is
portable among the diverse arithmetic implementations
currently in wide-spread use. The proposal requires
that a complying system provide error detection
capabilities beyond those currently required by many
language standards. The proposal requires that a
conforming system makes the values of certain
parameters known to users, although the method for
doing so is not specified. It also required a number of
useful operations, beyond those usually implemented. It
is acceptable to implement them by subroutine calls.",
acknowledgement = ack-nhfb,
affiliation = "Digital Equipment Corp., Maynard, MA, USA",
classification = "C5230 (Digital arithmetic methods); C6140D (High
level languages)",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "American National Standard Institute; Error detection
capabilities; Floating point arithmetic; International
Organization for Standardization; Language compatible
arithmetic standard; Robust numerical software;
Subroutine calls",
thesaurus = "Digital arithmetic; High level languages; Standards",
}
@Article{Peter:1990:PZW,
author = "O. Peter",
title = "{Prozessor zieht Wurzeln} \toenglish {Processor
Extracts Roots} \endtoenglish",
journal = j-CT,
volume = "1",
pages = "300--306",
year = "1990",
ISSN = "0724-8679",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "C T: Magazin f{\"u}r Computer Technik (Hannover)",
}
@Article{Piestrak:1990:DHS,
author = "S. J. Piestrak",
title = "Design of high-speed and cost-effective self-testing
checkers for low-cost arithmetic codes",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "3",
pages = "360--374",
month = mar,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.48866",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=48866",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Popov:1990:AFA,
author = "Wladimir Popov",
title = "On the axiomatizations of floating-point arithmetics.
Contributions to computer arithmetic and
self-validating numerical methods ({Basel, 1989})",
journal = "IMACS Ann. Comput. Appl. Math.",
volume = "7",
publisher = pub-BALTZER,
address = pub-BALTZER:adr,
pages = "55--66",
year = "1990",
MRclass = "03B70 (65G05)",
MRnumber = "93g:03024",
bibdate = "Fri Dec 08 12:21:25 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Preparata:1990:PCD,
author = "F. P. Preparata and J. E. Vuillemin",
title = "Practical cellular dividers",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "5",
pages = "605--614",
month = may,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.53574",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:01 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=53574",
abstract = "A discussion is presented of parallel division
algorithms that can be classified among modified higher
radix nonrestoring online division methods, where
redundant representations are extensively utilized to
speed up the operation. The network realizations of
these algorithms are cellular, or even systolic with
exclusively local control; they have both size (area)
and time of $ O(n) $, where $n$ is the length of the
dividend representation. The same structures can also
be used as a signed, digit-serial multiplier. When
suitably equipped with some control and a few
registers, the divider\slash multiplier brings
remarkable performance to large modular arithmetic, RSA
cryptography, and greatest common divisor computations.
They are also of interest for the design of
floating-point units and signal processing
applications.",
acknowledgement = ack-nhfb,
affiliation = "Ecole Normale Superieure, Paris, France",
ajournal = "IEEE Trans. Comput.",
classification = "C5230 (Digital arithmetic methods)",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Digit-serial multiplier; Divider/multiplier;
Floating-point units; Greatest common divisor
computations; Modular arithmetic; Nonrestoring online
division methods; Parallel division algorithms;
Redundant representations; RSA cryptography; Signal
processing; Signed; Systolic",
language = "English",
pubcountry = "USA",
thesaurus = "Digital arithmetic; Dividing circuits; Parallel
algorithms",
}
@Article{Prince:1990:GST,
author = "Timothy Prince",
title = "Generating Source For {{\tt <float.h>}}",
journal = j-CUJ,
volume = "8",
number = "6",
pages = "119--??",
month = jun,
year = "1990",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@Article{Pugh:1990:CBF,
author = "Kenneth Pugh",
title = "Converting {BASIC} Floating Point Files to {C}",
journal = j-CUJ,
volume = "8",
type = "Questions and Answers",
number = "5",
pages = "69--??",
month = may,
year = "1990",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@TechReport{Quach:1990:IAH,
author = "N. T. Quach and M. J. Flynn",
title = "An improved algorithm for high-speed floating-point
addition",
type = "Technical Report",
number = "CSL-TR-90-442",
institution = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
month = aug,
year = "1990",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@Article{Quinn:1990:REL,
author = "T. Quinn and S. Tremaine",
title = "Roundoff error in long-term planetary orbit
integrations",
journal = j-ASTRON-J,
volume = "99",
number = "3",
pages = "1016--1023",
month = mar,
year = "1990",
CODEN = "ANJOAA",
ISSN = "0004-6256 (print), 1538-3881 (electronic)",
ISSN-L = "0004-6256",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The dominant source of error in most long-term
integrations of the solar system is roundoff, which
leads to a fractional energy error of order $ n i_n $
where $n$ is the number of steps and $ i_n $ is the
precision of the floating-point arithmetic. The most
accurate computers are those with optimal
floating-point arithmetic, that is, arithmetic in which
the result of evaluating in arithmetic expression is
the representable number closest to the true value of
that expression. The authors argue that when
floating-point arithmetic is optimal, most of the
roundoff error arises from two sources: the approximate
representation of the numerical coefficients used in
multistep integration formulas, and the additions
required to evaluate these formulas. The authors
present an algorithm that removes these two sources of
error in computers with optimal arithmetic, and appears
to reduce the fractional energy error to of order $
n^{0.5i}_n $ (at least for $ n < $ or approximately $ =
10^7 $) , at the cost of less than a factor of $2$
increase in computing time.",
acknowledgement = ack-nhfb,
affiliation = "Canadian Inst. for Theor. Astrophys., Toronto
University, Ont., Canada",
classification = "A9510C (Celestial mechanics); A9575P (Mathematical
and computer techniques); A9630 (Planets and
satellites); C7350 (Astronomy and astrophysics)",
fjournal = "Astronomical Journal",
journal-URL = "http://iopscience.iop.org/1538-3881",
keywords = "Addition error; Approximate representation; Arithmetic
expression; Celestial mechanics; Computing time;
Floating-point arithmetic precision; Fractional energy
error; Integration steps number; Long-term planetary
orbit integrations; Multistep integration formulas;
Numerical coefficients; Optimal floating-point
arithmetic; Representable number; Roundoff error; Solar
system long-term stability; True value",
thesaurus = "Astronomical techniques; Astronomy computing;
Celestial mechanics; Error correction; Planets; Solar
system; Stability",
}
@InProceedings{Ramamoorthy:1990:MRN,
author = "P. A. Ramamoorthy and P. E. Pace and D. Styer",
booktitle = "Proceedings of the 33rd Midwest Symposium on Circuits
and Systems, 1990",
title = "A modified residue number system with applications to
signal processing",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1018--1021",
year = "1990",
CODEN = "????",
DOI = "https://doi.org/10.1109/MWSCAS.1990.140897",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The authors have developed a number system, the
modified residue number system (MRNS), which is a
direct consequence of considering the need for a more
convenient folding waveform that can be implemented
easily. Through various arrangements of the \ldots{}",
}
@InProceedings{Rao:1990:SAA,
author = "B. D. Rao",
booktitle = "Signals, Systems and Computers, 1990. 1990 Conference
Record Twenty-Fourth Asilomar Conference on. 5--7 Nov
1990",
title = "A systematic approach for the analysis of roundoff
noise in floating point digital filters",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "495",
year = "1990",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Not \ldots{}",
}
@Article{Rauchwerger:1990:MFPa,
author = "Lawrence Rauchwerger and Michael P. Farmwald",
title = "A multiple floating point coprocessor architecture",
journal = j-COMP-ARCH-NEWS,
volume = "18",
number = "2",
pages = "15--24",
month = jun,
year = "1990",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 12 09:40:46 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@InProceedings{Rauchwerger:1990:MFPb,
author = "L. Rauchwerger and P. M. Farmwald",
title = "A multiple floating point coprocessor architecture",
crossref = "IEEE:1990:MMM",
pages = "216--222",
year = "1990",
bibdate = "Tue Dec 12 09:26:54 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "General purpose microprocessor based computers usually
speed their arithmetic processing performance by using
a floating point co-processor. Because adding more
co-processors represents neither a technological nor a
cost problem, the authors investigated a system based
on a MIPS R2000 and 4 floating point units. They show a
block diagram of such an implementation and how two
important scientific operations can be accelerated
using a single unmodified data bus. A large percentage
of the engineering applications are solved with the
help of linear algebra methods like BLAS3 algorithms;
it is precisely for these primitives that the proposed
architecture brings significant performance gains. The
first operation described is a matrix multiplication
algorithm, its timing diagram and some results. Next a
polynomial evaluation technique is examined. Finally
they show how to use the same ideas with various other
microprocessors.",
acknowledgement = ack-nhfb,
affiliation = "Center for Supercomput. Res. and Dev., Illinois
University, Urbana-Champaign, IL, USA",
classification = "C5220 (Computer architecture); C5230 (Digital
arithmetic methods)",
keywords = "Arithmetic processing performance; BLAS3; Engineering
applications; Matrix multiplication algorithm;
Microprocessors; MIPS R2000; Multiple floating point
coprocessor architecture; Polynomial evaluation; RISC",
thesaurus = "Computer architecture; Digital arithmetic; Satellite
computers",
}
@Article{Reemtsen:1990:MFR,
author = "Rembert Reemtsen",
title = "Modifications of the First {Remez} Algorithm",
journal = j-SIAM-J-NUMER-ANAL,
volume = "27",
number = "2",
pages = "507--518",
month = apr,
year = "1990",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0727031",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65D15",
MRnumber = "91a:65039",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Reif:1990:OSI,
author = "John H. Reif and Stephen R. Tate",
title = "Optimal Size Integer Division Circuits",
journal = j-SIAM-J-COMPUT,
volume = "19",
number = "5",
pages = "912--924",
month = oct,
year = "1990",
CODEN = "SMJCAT",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
MRclass = "68Q40 (68Q15 68Q25)",
MRnumber = "91h:68092",
MRreviewer = "Helmut Alt",
bibdate = "Mon Nov 29 11:01:37 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/19/5;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
}
@PhdThesis{Rowan:1990:FSA,
author = "Thomas Harvey Rowan",
title = "Functional stability analysis of numerical
algorithms",
type = "{Ph.D.} thesis",
school = "University of Texas at Austin",
address = "Austin, TX, USA",
pages = "xii + 206",
month = may,
year = "1990",
bibdate = "Mon Oct 21 18:08:52 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://search.proquest.com/pqdtglobal/docview/303865032",
abstract = "The standard technique for detecting instability in
numerical algorithms is backward error analysis. The
analysis is difficult and tedious when performed by
hand, while attempts to automate it have always placed
severe restrictions on the tested numerical algorithms.
A new approach for detecting instability, functional
stability analysis, removes these restrictions by
treating numerical algorithms as black boxes. The
approach consists of two parts. The first part uses the
relationship between the forward error, the backward
error, and a problem's condition to define a function
that estimates a lower bound on the backward error. In
the second part, a new optimization method maximizes
the function. A numerical algorithm is unstable if the
maximization shows that the backward error can become
large. Since numerical algorithms are treated as black
boxes, functional stability analysis normally requires
little more than an executable version of a numerical
algorithm to determine if it is unstable.",
acknowledgement = ack-nhfb,
advisor = "Alan K. Cline",
}
@Article{Sam:1990:GMR,
author = "H. Sam and A. Gupta",
title = "A generalized multibit recoding of two's complement
binary numbers and its proof with application in
multiplier implementations",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "8",
pages = "1006--1015",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57039",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:03 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57039",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Schatte:1990:SBF,
author = "Peter Schatte",
title = "On the stochastic behaviour of the floating point
mantissas of sums",
journal = "J. Inform. Process. Cybernet.",
volume = "26",
number = "4",
pages = "249--254",
year = "1990",
MRclass = "60F99 (11K99)",
MRnumber = "91m:60065",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "Eugenijus Manstavi{\v{c}}ius",
}
@Article{Schimandle:1990:MBC,
author = "James Schimandle",
title = "{Microsoft BASIC}'s and {C}'s Floating Point Formats",
journal = j-CUJ,
volume = "8",
type = "Letter",
number = "7",
pages = "139--??",
month = jul,
year = "1990",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@Article{Sheppard:1990:EYF,
author = "Gene Sheppard",
title = "Evaluating Your Floating Point Library",
journal = j-CUJ,
volume = "8",
number = "8",
pages = "121--??",
month = aug,
year = "1990",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@Article{Silverman:1990:PPA,
author = "Robert D. Silverman",
title = "Parallel polynomial arithmetic over finite rings",
journal = j-J-PAR-DIST-COMP,
volume = "10",
number = "3",
pages = "265--270",
month = nov,
year = "1990",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "MITRE Corp",
affiliationaddress = "Bedford, Ma, USA",
classification = "723; 921; C4130 (Interpolation and function
approximation); C4240 (Programming and algorithm
theory); C5230 (Digital arithmetic methods)",
corpsource = "Mitre Corp., Bedford, MA, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "Alliant FX/8; Chinese remainder; Chinese Remainder
Theorem; Computer Systems, Digital--Parallel
Processing; Computers, Digital--Computational Methods;
Convolution Algorithms; digital arithmetic; Finite
Rings; finite rings; Mathematical Techniques; message
passing; message passing parallel computer;
multiplication; parallel algorithms; parallel
computers; parallel polynomial arithmetic; performance;
polynomial; Polynomial Arithmetic; Polynomials;
polynomials; residue number systems; shared memory;
Symult S2010; theorem",
treatment = "P Practical",
}
@InProceedings{Silverstein:1990:USM,
author = "Joel D. Silverstein and Steven E. Sommars and
Yio-Chian Tao",
title = "The {UNIX} System Math Library, a Status Report",
crossref = "USENIX:1990:PWU",
pages = "117--131",
year = "1990",
bibdate = "Thu Sep 01 11:51:21 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Sips:1990:NML,
author = "Henk J. Sips and Hai Xiang Lin",
title = "A new model for on-line arithmetic with an application
to the reciprocal calculation",
journal = j-J-PAR-DIST-COMP,
volume = "8",
number = "3",
pages = "218--230",
month = mar,
year = "1990",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Delft Univ of Technology",
affiliationaddress = "Delft, Neth",
classification = "722; 723; 921; C4130 (Interpolation and function
approximation); C5230 (Digital arithmetic methods)",
corpsource = "Delft University of Technol., Netherlands",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "adapted Newton--Raphson; approximation method;
Approximation Theory; arithmetic; attainable on-;
computation pipelining; Computational Models; Computer
Systems, Digital--On Line Operation; conditional
on-line; cycle times; delay; delays; Digital
Arithmetic; digital arithmetic; exact function value;
functions; iteration; iteration method; iterative;
Iterative Methods; iterative methods; line delay;
Mathematical Techniques; on-line arithmetic; on-line
computation; on-line digits; online arithmetic;
overlapping computation; pipeline; processing;
reciprocal calculation; seed table; step; table
look-up",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Skelton:1990:GSE,
author = "R. E. Skelton and D. Williamson",
booktitle = "Proceedings of the 29th {IEEE} Conference on Decision
and Control, 1990",
title = "Guaranteed state estimation accuracies with roundoff
error",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "297--298",
year = "1990",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Kalman filter theory is modified to accommodate
roundoff errors in state computation. Two problems are
solved: (i) choosing the wordlength required for each
state computation to guarantee specified estimation
accuracies of multiple output variables \ldots{}",
}
@TechReport{Slishman:1990:FPR,
author = "G. Slishman",
title = "Fast and Perfectly Rounding Decimal\slash Hexadecimal
Conversions",
type = "Research Report",
number = "RC-15683",
institution = pub-IBM-WATSON,
address = pub-IBM-WATSON:adr,
year = "1990",
bibdate = "Fri Apr 21 07:04:09 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Steele:1990:HPF,
author = "Guy L. {Steele Jr.} and Jon L. White",
title = "How to Print Floating-Point Numbers Accurately",
journal = j-SIGPLAN,
volume = "25",
number = "6",
pages = "112--126",
month = jun,
year = "1990",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/93548.93559",
ISBN = "0-89791-364-7",
ISBN-13 = "978-0-89791-364-5",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:15:53 MST 2003",
bibsource = "Compendex database; http://portal.acm.org/;
http://www.acm.org/pubs/contents/proceedings/pldi/93542/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigplan1990.bib",
note = "See also input algorithm in
\cite{Clinger:1990:HRF,Clinger:2004:RHR}, and a faster
output algorithm in \cite{Burger:1996:PFP} and
\cite{Knuth:1990:SPW}, IBM S/360 algorithms in
\cite{Abbott:1999:ASS} for both IEEE 754 and S/360
formats, and a twenty-year retrospective in
\cite{Steele:2004:RHP}. In electronic mail dated Wed,
27 Jun 1990 11:55:36 EDT, Guy Steele reported that an
intrepid pre-SIGPLAN 90 conference implementation of
what is stated in the paper revealed 3 mistakes:
\begin{itemize} \item[1.] Table~5 (page 124):\par
\noindent insert {\tt k <-- 0} after assertion, and
also delete {\tt k <-- 0} from Table~6. \item[2.]
Table~9 (page 125):\par \noindent \begin{tabular} {ll}
for & {\tt -1:USER!({"}{"});} \\
substitute & {\tt -1:USER!({"}0{"});} \end{tabular}\par
\noindent and delete the comment. \item[3.] Table~10
(page 125):\par \noindent \begin{tabular}{ll} for &
{\tt fill(-k, "0")}\\
substitute & {\tt fill(-k-1, "0")} \end{tabular}
\end{itemize}
\def\EatBibTeXPeriod#1{\ifx#1.\else#1\fi}\EatBibTeXPeriod",
URL = "http://www.acm.org:80/pubs/citations/proceedings/pldi/93542/p112-steele/",
abstract = "Algorithms are presented for accurately converting
floating-point numbers to decimal representation. The
key idea is to carry along with the computation an
explicit representation of the required rounding
accuracy. The authors begin with the simpler problem of
converting fixed-point fractions. A modification of the
well-known algorithm for radix-conversion of
fixed-point fractions by multiplication explicitly
determines when to terminate the conversion process; a
variable number of digits are produced. They derive two
algorithms for free-format output of floating-point
numbers. Finally, they modify the free-format
conversion algorithm for use in fixed-format
applications. Information may be lost if the fixed
format provides too few digit positions, but the output
is always correctly rounded. On the other hand, no
`garbage digits' are ever produced, even if the fixed
format specifies too many digit positions (intuitively,
the `4/3 prints as 1.333333328366279602' problem does
not occur).",
acknowledgement = ack-nhfb,
affiliation = "Thinking Machines Corp",
affiliationaddress = "Cambridge, MA, USA",
classification = "722; 723; C5230 (Digital arithmetic methods); C7310
(Mathematics)",
confdate = "20-22 June 1990",
conference = "Proceedings of the ACM SIGPLAN '90 Conference on
Programming Language Design and Implementation",
conferenceyear = "1990",
conflocation = "White Plains, NY, USA",
confsponsor = "ACM",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
journalabr = "SIGPLAN Not",
keywords = "algorithms; computer programming languages; computers,
digital --- computational methods; conversion process;
correct rounding; decimal decimal representation;
design; digit positions; explicit representation;
fixed-format applications; fixed-point fractions;
floating point numbers; floating-point arithmetic;
floating-point numbers; free-format conversion
algorithm; free-format output; garbage digits;
performance; radix-conversion; rounding accuracy;
verification",
remark = "Published as part of the Proceedings of PLDI'90.",
sponsor = "Assoc for Computing Machinery, Special Interest Group
on Programming Languages",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic.",
thesaurus = "Digital arithmetic; Mathematics computing",
xxabstract = "We present algorithms for accurately converting
floating-point numbers to decimal representation. The
key idea is to carry along with the computation an
explicit representation of the required rounding
accuracy. We begin with the simpler problem of
converting fixed-point fractions. A modification of the
well-known algorithm for radix-conversion of
fixed-point fractions by multiplication explicitly
determines when to terminate the conversion process; a
variable number of digits are produced. We then derive
two algorithms for free-format output of floating-point
numbers. Finally, we modify the free-format conversion
algorithm for use in fixed-format applications.",
}
@Article{Su:1990:ASS,
author = "C.-C. Su and H.-Y. Lo",
title = "An algorithm for scaling and single residue error
correction in residue number systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "8",
pages = "1053--1064",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57044",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:03 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57044;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2065",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "An algorithm for scaling and single residue digit
error correction is proposed. This algorithm is fully
based on mixed radix conversion (MRC). The redundant
digits of MRC can be used to establish a lookup table
to correct single residue digit \ldots{}",
}
@InProceedings{Sun:1990:FAM,
author = "Jenn-Dong Sun and H. Krishna",
booktitle = "Conference Record Twenty-Fourth Asilomar Conference on
Signals, Systems and Computers, 5--7 Nov 1990",
title = "Fast Algorithms for Multiple Errors Detection and
Correction in Redundant Residue Number Systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "831",
year = "1990",
CODEN = "????",
DOI = "https://doi.org/10.1109/MWSCAS.1990.140897",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
}
@Book{Tabak:1990:RS,
author = "Daniel Tabak",
title = "{RISC} Systems",
publisher = pub-JW,
address = pub-JW:adr,
pages = "xii + 300",
year = "1990",
ISBN = "0-471-92694-9",
ISBN-13 = "978-0-471-92694-8",
LCCN = "QA76.9.A73.T294 1990",
bibdate = "Wed Aug 10 11:51:06 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$49.95",
acknowledgement = ack-nhfb,
libnote = "Not yet in my library.",
}
@Article{Tang:1990:AET,
author = "Ping Tak Peter Tang",
title = "Accurate and Efficient Testing of the Exponential and
Logarithm Functions",
journal = j-TOMS,
volume = "16",
number = "3",
pages = "185--200",
month = sep,
year = "1990",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65-04 (65G99)",
MRnumber = "1 070 797",
bibdate = "Sun Sep 04 23:14:59 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://doi.acm.org/10.1145/79505.79506;
http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p185-tang/",
abstract = "Table-driven techniques can be used to test highly
accurate implementation of EXP LOG. The largest error
observed in EXP and LOG accurately to within 1/500 unit
in the last place are reported in our tests. Methods to
verify the tests' reliability are discussed. Results of
applying the tests to our own as well as to a number of
other implementations of EXP and LOG are presented.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; languages; verification",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Numerical algorithms. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis. {\bf G.4}: Mathematics of Computing,
MATHEMATICAL SOFTWARE, Certification and testing. {\bf
G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
Portability.",
}
@TechReport{Tang:1990:SSI,
author = "P. T. P. Tang",
title = "Some Software Implementations of the Functions Sine
and Cosine",
number = "Report ANL-90/3",
institution = "Argonne National Laboratory",
address = "Argonne, IL, USA",
pages = "27",
month = apr,
year = "1990",
bibdate = "Mon Sep 12 23:55:17 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Tang:1990:TDIa,
author = "Ping Tak Peter Tang",
title = "Table-Driven Implementation of the Logarithm Function
in {IEEE} Floating-Point Arithmetic",
journal = j-TOMS,
volume = "16",
number = "4",
pages = "378--400",
month = dec,
year = "1990",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sun Sep 04 23:26:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p378-tang/",
abstract = "Algorithms and implementation details for the
logarithm functions in both single and double precision
of IEEE 754 arithmetic are presented here. With a table
of moderate size, the implementation need only working-
precision arithmetic and are provably accurate to
within 0.57 ulp.",
acknowledgement = ack-nj,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; design; performance; reliability;
standardization; theory; verification",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis. {\bf G.1.0}: Mathematics of Computing,
NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
Algorithm analysis.",
}
@TechReport{Tang:1990:TDIb,
author = "P. T. P. Tang",
title = "Table-driven Implementation of the Expm1 Function in
{IEEE} Floating-Point Arithmetic",
number = "Preprint MCS-P144-0390",
institution = "Argonne National Laboratory",
address = "Argonne, IL, USA",
pages = "??",
month = mar,
year = "1990",
bibdate = "Mon Sep 12 23:55:14 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@TechReport{Teetz:1990:SNS,
author = "Ingo Teetz and Thomas Fischer and Walter Issel",
title = "{Die Sprache NBSF fur die strukturelle Beschreibung
von Schaltkreisen.: Eine Darstellung am Beispiel eines
Gleitkomma-Prozessors}",
type = "Report",
number = "R-Math-01/90 0233-2876",
institution = "Akademie der Wissenschaften der DDR,
Karl-Weierstrass-Institut fur Mathematik",
address = "Berlin, Germany",
pages = "vii + 79",
year = "1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer hardware description languages.;
Floating-point arithmetic.; NBSF (Computer hardware
description language)",
remark = "Summary in English and German.",
}
@InCollection{Trefethen:1990:PSP,
author = "L. N. Trefethen and M. H. Gutknecht",
title = "{Pad{\'e}}, Stable {Pad{\'e}}, and
{Chebyshev--Pad{\'e}} Approximation",
crossref = "Mason:1990:AAI",
pages = "??--??",
year = "1990",
bibdate = "Thu Sep 01 12:23:25 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Tricker:1990:ERP,
author = "A. R. Tricker",
title = "The effect of rounding on the power level of certain
normal test statistics",
journal = j-J-APPL-STAT,
volume = "17",
number = "2",
pages = "219--228",
year = "1990",
CODEN = "????",
DOI = "https://doi.org/10.1080/757582833",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Tue Sep 6 11:16:18 MDT 2011",
bibsource = "http://www.tandf.co.uk/journals/routledge/02664763.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
onlinedate = "5 Jun 2011",
}
@Article{Tricker:1990:ERSa,
author = "A. R. Tricker",
title = "The effect of rounding on the significance level of
certain normal test statistics",
journal = j-J-APPL-STAT,
volume = "17",
number = "1",
pages = "31--38",
year = "1990",
CODEN = "????",
DOI = "https://doi.org/10.1080/757582644",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Tue Sep 6 11:16:16 MDT 2011",
bibsource = "http://www.tandf.co.uk/journals/routledge/02664763.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
onlinedate = "18 Jul 2011",
}
@Article{Tricker:1990:ERSb,
author = "A. R. Tricker",
title = "The effect of rounding on the significance level and
power of certain test statistics for non-normal data",
journal = j-J-APPL-STAT,
volume = "17",
number = "3",
pages = "329--340",
year = "1990",
CODEN = "????",
DOI = "https://doi.org/10.1080/02664769000000005",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Tue Sep 6 11:16:20 MDT 2011",
bibsource = "http://www.tandf.co.uk/journals/routledge/02664763.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
onlinedate = "28 Jul 2006",
}
@Article{vanderVorst:1990:CBP,
author = "H. A. {van der Vorst}",
title = "The convergence behaviour of preconditioned {CG} and
{CG-S} in the presence of rounding errors",
journal = j-LECT-NOTES-MATH,
volume = "1457",
pages = "126--136",
year = "1990",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0090905",
ISBN = "3-540-53515-2 (print), 3-540-46746-7 (e-book)",
ISBN-13 = "978-3-540-53515-7 (print), 978-3-540-46746-5
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
MRclass = "65F35",
MRnumber = "1101632 (92a:65141)",
MRreviewer = "Seymour Bachmuth",
bibdate = "Fri May 9 19:07:18 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lnm1990.bib;
MathSciNet database",
URL = "http://link.springer.com/chapter/10.1007/BFb0090905/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/BFb0090897",
book-URL = "http://www.springerlink.com/content/978-3-540-46746-5",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
MRauthor = "H. A. {van der Vorst}",
mynote = "Not copied. No actual error analysis. Just
explanations based on his paper with van der Sluis
(don't reference Greenbaum!).",
}
@MastersThesis{VanElsen:1990:OCL,
author = "Lucien William {Van Elsen}",
title = "An optimizing compiler for low-level floating point
operations",
type = "Thesis ({B.S.})",
school = "Massachusetts Institute of Technology, Dept. of
Electrical Engineering and Computer Science",
address = "Cambridge, MA, USA",
pages = "v + 56",
year = "1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supervised by William J. Dally.",
acknowledgement = ack-nhfb,
}
@Article{Vuillemin:1990:ERC,
author = "J. E. Vuillemin",
title = "Exact real computer arithmetic with continued
fractions",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "8",
pages = "1087--1105",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57047",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57047",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Wallis:1990:IFP,
editor = "Peter J. L. Wallis",
title = "Improving Floating-Point Programming",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xvi + 191",
year = "1990",
ISBN = "0-471-92437-7",
ISBN-13 = "978-0-471-92437-1",
LCCN = "QA76.6 .I446 1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$60.00",
acknowledgement = ack-nhfb,
keywords = "Computation by computer systems --- Floating point
representation; Electronic digital computers ---
Programming.; Floating-point arithmetic.;
Floating-point arithmetic., Compiling (Electronic
computers)",
}
@Article{Weber:1990:EHP,
author = "Ken Weber",
title = "An experiment in high-precision arithmetic on shared
memory multiprocessors",
journal = j-SIGSAM,
volume = "24",
number = "2",
pages = "22--40",
month = apr,
year = "1990",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Wed Oct 5 08:31:59 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIGSAM Bulletin",
issue = "??",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@Article{Wigley:1990:MRR,
author = "N. M. Wigley and G. A. Jullien",
title = "On modulus replication for residue arithmetic
computations of complex inner products",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "8",
pages = "1065--1076",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57045",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:03 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57045",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Wingler:1990:TMI,
author = "Eric Wingler",
title = "The Teaching of Mathematics: An Infinite Product
Expansion for the Square Root Function",
journal = j-AMER-MATH-MONTHLY,
volume = "97",
number = "9",
pages = "836--839",
month = nov,
year = "1990",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:36:09 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@MastersThesis{Wong:1990:PFP,
author = "Kar-pang Wong",
title = "The precision of floating point computation in digital
computer",
type = "Thesis ({M.S. in Computer Science})",
school = "University of Wisconsin, Milwaukee",
address = "Milwaukee, WI, USA",
pages = "vii + 45",
year = "1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.",
}
@Article{Wong:1990:QNF,
author = "P. W. Wong",
title = "Quantization noise, fixed-point multiplicative
roundoff noise, and dithering",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "38",
number = "2",
pages = "286--300",
month = feb,
year = "1990",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "The author considers the characteristics of the error
resulting when a continuous amplitude signal $x_n$ is
quantized and then multiplied by a constant multiplier
a under fixed-point roundoff arithmetic. It is shown
that \ldots{}",
}
@Article{Yager:1990:SNM,
author = "T. Yager",
title = "{Sony NeWS} and {MIPS Magnum}: a double shot of
{RISC}",
journal = j-BYTE,
volume = "15",
number = "13",
pages = "172--175",
month = dec,
year = "1990",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 12 18:39:30 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5430 (Microcomputers)",
fjournal = "BYTE Magazine",
keywords = "20 MHz; 25 MHz; Fast color graphics; Floating-point
acceleration; High-density 3/sup 1///sub 2/-inch floppy
disk; MIPS Magnum 3000; MIPS R3000 RISC CPU chip set;
Quarter-inch cartridge tape drives; RISC/OS; Sony NeWS
3710; System V release 4; Thick-wire Ethernet port;
Unix workstations; X Window System",
numericalindex = "Frequency 2.0E+07 Hz; Frequency 2.5E+07 Hz",
thesaurus = "Computer evaluation; Microcomputers; Workstations",
}
@MastersThesis{Yang:1990:PRN,
author = "George Chia-Jin Yang",
title = "A parametric roundoff noise analysis of second-order
state-space digital filters with floating-point
arithmetic",
type = "Thesis ({M.S.})",
school = "University of Tennessee, Knoxville",
address = "Knoxville, TN, USA",
pages = "vii + 67",
year = "1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Digital filters (Mathematics).; Floating-point
arithmetic.",
}
@Article{Yeh:1990:RTI,
author = "H.-G. Yeh",
title = "Real-Time Implementation of a Narrow-Band {Kalman}
Filter with a Floating-Point Processor {DSP32}",
journal = j-IEEE-TRANS-IND-ELECTRON,
volume = "37",
number = "1",
pages = "13--18",
month = feb,
year = "1990",
CODEN = "ITIED6",
DOI = "https://doi.org/10.1109/41.45838",
ISSN = "0278-0046 (print), 1557-9948 (electronic)",
ISSN-L = "0278-0046",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Industrial Electronics",
summary = "The author presents experimental results from two
studies. First, a real-time narrowband Kalman filter is
implemented with a floating-point digital processor
DSP32. The real-time capability of this narrowband
filter is investigated by varying parameters \ldots{}",
}
@Article{Yoon:1990:MTP,
author = "Hyunsoo Yoon and Kyungsook Y. Lee and Amos Bahiri",
title = "On the modulo {$M$} translators for the prime memory
system",
journal = j-J-PAR-DIST-COMP,
volume = "8",
number = "1",
pages = "72--76",
month = jan,
year = "1990",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Ohio State Univ",
affiliationaddress = "Columbus, OH, USA",
classification = "722; 723; C5230 (Digital arithmetic methods)",
corpsource = "Department of Comput. and Inf. Sci., Ohio State
University, Columbus, OH, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "array processor; binary number system; Burroughs
Scientific Processor; Burroughs Scientific Processor
(bsp); casting out nine rule; Computer Operating
Systems; Computer Systems Programming--Utility
Programs; Computer Systems, Digital--Parallel
Processing; conflict-free access; decimal
floating-point arithmetic; decimal number system;
digital arithmetic; Modulo M Computation; modulo M
translators; parallel algorithms; prime memory system;
Program Translators; SIMD Architecture; SIMD shared
memory parallel processor",
treatment = "P Practical",
}
@Article{Zarowski:1990:AMH,
author = "C. J. Zarowski and H. C. Card",
title = "On addition and multiplication with {Hensel} codes",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "12",
pages = "1417--1423",
month = dec,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.61062",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:05 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=61062",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Zelniker:1990:PBD,
author = "G. S. Zelniker and F. J. Taylor",
booktitle = "Conference Record Twenty-Fourth Asilomar Conference on
Signals, Systems and Computers, 5--7 Nov 1990",
title = "Prime Blocklength Discrete {Fourier} Transforms
Utilising the Polynomial Residue Number System",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "314",
year = "1990",
CODEN = "????",
DOI = "https://doi.org/10.1109/MWSCAS.1990.140897",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
}
@InCollection{Aberth:1991:CHO,
author = "Oliver Aberth",
title = "The Conversion of a High Order Programming Language
from Floating-Point Arithmetic to Range Arithmetic",
crossref = "Meyer:1991:CAP",
pages = "1--4",
year = "1991",
DOI = "https://doi.org/10.1007/978-1-4613-9092-3_1",
bibdate = "Fri Sep 22 18:54:58 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Adali:1991:FPR,
author = "T. Adali and S. H. Ardalan",
booktitle = "Acoustics, Speech, and Signal Processing, 1991.
{ICASSP-91., 1991} International Conference on. 14--17
April 1991",
title = "Fixed-point roundoff error analysis of the {RLS}
algorithm with time-varying channels",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1865--1868",
year = "1991",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The authors derive the steady-state mean square
prediction error expression for the fixed-point RLS
(recursive least squares) algorithm for the case of
time-varying channel estimation, which is modeled as a
first-order Markov tapped delay line. It \ldots{}",
}
@Article{Alia:1991:VMM,
author = "G. Alia and E. Martinelli",
title = "A {VLSI} modulo $m$ multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "40",
number = "7",
pages = "873--878",
month = jul,
year = "1991",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.83626",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 12:52:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=83626",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Alverson:1991:IDU,
author = "Robert Alverson",
title = "Integer Division Using Reciprocals",
crossref = "Kornerup:1991:PIS",
pages = "186--190",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Alverson.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10; correct rounding; floating-point
arithmetic",
remark = "Demonstrates a correctly-rounded algorithm for integer
division that requires six floating-point
multiplications and a table lookup. For comparison,
\cite{Markstein:2000:IEF} shows an algorithm that needs
seven multiply-adds and a reciprocal approximation.",
}
@Article{Anido:1991:IDI,
author = "M. Lois Anido",
title = "Improving the division instruction of
application-specific {RISCs}",
journal = j-MICROPROC-MICROPROG,
volume = "32",
number = "1-5",
pages = "13--21",
month = aug,
year = "1991",
CODEN = "MMICDT",
ISSN = "0165-6074 (print), 1878-7061 (electronic)",
ISSN-L = "0165-6074",
bibdate = "Tue Dec 12 09:26:54 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "17th EUROMICRO Symposium on Microprocessing and
Microprogramming. Hardware and Software Design
Automation.",
abstract = "Presents the development and application of a signed
radix-4 division algorithm to a RISC architecture,
where the internal ALU Manchester carry adder is used
to maintain the partial remainder in irredundant form.
There are division algorithms which are faster than the
one described in this paper, however they usually make
use of a redundant representation of the partial
remainder and require carry-save adders which are not
normally used in the integer execution unit of RISCs.
The method presented in this contribution employs 3x
divisor multiples and uses a reduced next divisor
multiple estimate table which is implemented by a small
and fast logic. Alternative radix-4 schemes with
quotient digits (-2,-1,0,1,2) require large and slow
PLAs for quotient digit generation. Additionally, there
is no need for positive and negative quotient registers
because quotient bits are generated on-the-fly by a
small-sized logic, concurrently with partial remainder
formation. This method also deals directly with signed
two's complement numbers, eliminating the need for
additional instructions for sign conversion. The
application of this radix-4 division algorithm provides
a two-bits-at-a-time division instruction, instead of
the traditional single bit approach used in some RISCs.
The speedup achieved can be very important in many
numerically intensive applications, in which the use of
floating-point units is not essential.",
acknowledgement = ack-nhfb,
affiliation = "Univ. Federal do Rio de Janeiro, Brazil",
classification = "C5220 (Computer architecture); C5230 (Digital
arithmetic methods)",
confdate = "2-5 Sept. 1991",
conflocation = "Vienna, Austria",
fjournal = "Microprocessing and Microprogramming",
keywords = "3X divisor multiples; Application-specific RISCs;
Binary division; Division instruction; Internal ALU
Manchester carry adder; Irredundant form; Logic;
Numerically intensive applications; Partial remainder;
Quotient bits; Quotient digits; Reduced next divisor
multiple estimate table; RISC architecture; Signed
radix-4 division algorithm; Signed two's complement
numbers; Speedup",
pubcountry = "Netherlands",
thesaurus = "Application specific integrated circuits; Digital
arithmetic; Reduced instruction set computing",
}
@Article{Anonymous:1991:FDC,
author = "Anonymous",
title = "{60M-flops}, floating-point {DSP} chip",
journal = j-EDN,
volume = "36",
number = "13",
pages = "80--??",
month = jun,
year = "1991",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "EDN",
}
@Article{Anonymous:1991:SIS,
author = "Anonymous",
title = "{SCAN-1991: International Symposium on Computer
Arithmetic and Scientific Computation}",
journal = j-J-COMPUT-APPL-MATH,
volume = "34",
number = "2",
pages = "N13--N14",
day = "4",
month = apr,
year = "1991",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:20:48 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S037704279190071Q",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Arambepola:1991:CVA,
author = "B. Arambepola",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, 11--14 June 1991",
title = "Common {VLSI} architecture for a practically useful
residue number system",
volume = "5",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2951--2954",
year = "1991",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1991.176164",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "An architecture is presented for carrying out modulo
arithmetic in a practically useful residue number
system. An important feature of this is that it allows
a single hardware design to be used for all moduli. An
application of this architecture is \ldots{}",
}
@Book{Arvo:1991:GGI,
author = "James Arvo",
title = "Graphics gems {II}",
volume = "2",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xxxii + 643",
year = "1991",
ISBN = "0-12-064480-0",
ISBN-13 = "978-0-12-064480-3",
LCCN = "T385 .G6972 1991",
bibdate = "Mon Aug 24 17:12:23 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
series = "Graphics Gems",
URL = "http://www.sciencedirect.com/science/book/9780080507545",
ZMnumber = "0774.68010",
abstract = "\booktitle{Graphics Gems II} is a collection of
articles shared by a diverse group of people that
reflect ideas and approaches in graphics programming
which can benefit other computer graphics programmers.
This volume presents techniques for doing well-known
graphics operations faster or easier. The book contains
chapters devoted to topics on two-dimensional and
three-dimensional geometry and algorithms, image
processing, frame buffer techniques, and ray tracing
techniques. The radiosity approach, matrix techniques,
and numerical and programming techniques are likewise
discussed.",
acknowledgement = ack-nhfb,
libnote = "Not yet in my library.",
tableofcontents = "Foreword / Andrew Glassner \\
The Area of a Simple Polygon / Jon Rokne \\
Intersection of Line Segments / Mukesh Prasad \\
Distance from a Point to a Line / Jack C. Morrison \\
An Easy Bounding Circle / Jon Rokne \\
The Smallest Circle Containing the Intersection of Two
Circles / Jon Rokne \\
Appolonius's 10th Problem / Jon Rokne \\
A Peano Curve Generation Algorithm / Ken Musgrave \\
Space-Filling Curves and a Measure of Coherence /
Douglas Voorhies \\
Scanline Coherent Shape Algebra / Jonathan E. Steinhart
\\
Image Smoothing and Sharpening by Discrete Convolution
/ Dale A. Schumacher \\
A Comparison of Digital Halftoning Techniques / Dale A.
Schumacher \\
Color Dithering / Spencer W. Thomas and Rod G. Bogart
\\
Fast Anamorphic Image Scaling / Dale A. Schumacher \\
Real Pixels / Greg Ward \\
A Fast 90-Degree Bitmap Rotator / Sue-Ken Yap \\
Rotation of Run-Length Encoded Image Data / Jeff Holt
\\
Adaptive Run-Length Encoding / Andrew S. Glassner \\
Image File Compression Made Easy / Alan W. Paeth \\
An Optimal Filter for Image Reconstruction / Nelson Max
\\
Noise Thresholding in Edge Images / John Schlag \\
Computing the Area, the Circumference, and the Genus of
a Binary Digital Image / Hanspeter Bieri and Andreas
Kohler \\
Efficient Inverse Color Map Computation / Spencer W.
Thomas \\
Efficient Statistical Computations for Optimal Color
Quantization / Xiaolin Wu \\
A Random Color Map Animation Algorithm / Ken Musgrave
\\
A Fast Approach to PHIGS PLUS Pseudo Color Mapping /
James Hall and Terence Lindgren \\
Mapping RGB Triples onto 16 Distinct Values / Alan W.
Paeth \\
Television Color Encoding and ``Hot'' Broadcast Colors
/ David Martindale and Alan W. Paeth \\
An Inexpensive Method of Setting the Monitor White
Point / Gary W. Meyer \\
Some Tips for Making Color Hardcopy / Ken Musgrave \\
Area of Planar Polygons and Volume of Polyhedra /
Ronald N. Goldman \\
Getting Around on a Sphere / Clifford A. Shaffer \\
Exact Dihedral Metrics for Common Polyhedra / Alan W.
Paeth \\
A Simple Viewing Geometry / Andrew S. Glassner \\
View Correlation / Rod G. Bogart \\
Maintaining Winged-Edge Models / Andrew S. Glassner \\
Quadtree\slash Octree-to-Boundary Conversion / Claudio
Montani and Roberto Scopigno \\
Three-Dimensional Homogeneous Clipping of Triangle
Strips / Patrick-Gilles Maillot \\
InterPhong Shading / Nadia Magnenat Thalmann, Daniel
Thalmann and Hong Tong Minh \\
Fast Ray-Convex Polyhedron Intersection / Eric Haines
\\
Intersecting a Ray with an Elliptical Torus / Joseph M.
Cychosz \\
Ray-Triangle Intersection Using Binary Recursive
Subdivision / Douglas Voorhies and David Kirk \\
Improved Ray Tagging for Voxel-Based Ray Tracing /
David Kirk and James Arvo \\
Efficiency Improvements for Hierarchy Traversal in Ray
Tracing / Eric Haines \\
A Recursive Shadow Voxel Cache for Ray Tracing / Andrew
Pearce \\
Avoiding Incorrect Shadow Intersections for Ray Tracing
/ Andrew Pearce \\
A Body Color Model: Absorption of Light through
Translucent Media / Mark E. Lee and Samuel P. Uselton
\\
More Shadow Attenuation for Ray Tracing Transparent or
Translucent Objects / Mark E. Lee and Samuel P. Uselton
\\
Implementing Progressive Radiosity with User-Provided
Polygon Display Routines / Shenchang Eric Chen \\
A Cubic Tetrahedral Adaptation of the Hemi-Cube
Algorithm / Jeffrey C. Beran-Koehn and Mark J. Pavicic
\\
Fast Vertex Radiosity Update / Filippo Tampieri \\
Radiosity via Ray Tracing / Peter Shirley \\
Detection of Shadow Boundaries for Adaptive Meshing in
Radiosity / Fran{\c{c}}ois Sillion \\
Decomposing a Matrix into Simple Transformations /
Spencer W. Thomas \\
Recovering the Data from the Transformation Matrix /
Ronald N. Goldman \\
Transformations as Exponentials / Ronald N. Goldman \\
More Matrices and Transformations: Shear and
Pseudo-Perspective / Ronald N. Goldman \\
Fast Matrix Inversion / Kevin Wu \\
Quaternions and $4 \times 4$ Matrices / Ken Shoemake
\\
Random Rotation Matrices / James Arvo \\
Classifying Small Sparse Matrices / James Arvo \\
Bit Picking / Ken Shoemake \\
Faster Fourier Transform / Ken Shoemake \\
Of Integers, Fields, and Bit Counting / Alan W. Paeth
and David Schilling \\
Using Geometric Constructions to Interpolate
Orientation with Quaternions / John Schlag \\
A Half-Angle Identity for Digital Computation: The Joys
of the Halved Tangent / Alan W. Paeth \\
An Integer Square Root Algorithm / Christopher J.
Musial \\
Fast Approximation to the Arctangent / Ron Capelli \\
Fast Sign of Cross Product Calculation / Jack Ritter
\\
Interval Sampling / Ken Shoemake \\
A Recursive Implementation of the Perlin Noise Function
/ Greg Ward \\
Least-Squares Approximations to B{\'e}zier Curves and
Surfaces / Doug Moore and Joe Warren \\
Beyond B{\'e}zier Curves / Ken Shoemake \\
A Simple Formulation for Curve Interpolation with
Variable Control Point Approximation / John Schlag \\
Symmetric Evaluation of Polynomials / Terence Lindgren
\\
Menelaus's Theorem / Hans-Peter Seidel \\
Geometrically Continuous Cubic B{\'e}zier Curves /
Hans-Peter Siedel \\
A Good Straight-Line Approximation of a Circular Arc /
Christopher J. Musial \\
Great Circle Plotting / Alan W. Paeth \\
Fast Anti-Aliased Circle Generation / Xiaolin Wu \\
Graphics Gems C Header File \\
2D and 3D Vector C Library \\
Corrected and Indexed \\
Useful C Macros for Vector Operations / Steve
Hollasch",
xxtableofcontents = "Foreword \\
Preface \\
Mathematical Notation \\
Pseudo-Code \\
Contributors \\
I: 2D Geometry and Algorithms \\
Introduction \\
1: The Area of a Simple Polygon \\
2: Intersection of Line Segments \\
3: Distance from a Point to a Line \\
4: An Easy Bounding Circle \\
5: The Smallest Circle Containing the Intersection of
Two Circles \\
6: Appolonius's 10th Problem \\
7: A Peano Curve Generation Algorithm \\
8: Space-Filling Curves and a Measure of Coherence \\
9: Scanline Coherent Shape Algebra \\
II: Image Processing \\
Introduction \\
1: Image Smoothing and Sharpening by Discrete
Convolution \\
2: A Comparison of Digital Halftoning Techniques \\
3: Color Dithering \\
4: Fast Anamorphic Image Scaling \\
5: Real Pixels \\
6: A Fast 90-Degree Bitmap Rotator \\
7: Rotation of Run-Length Encoded Image Data \\
8: Adaptive Run-Length Encoding \\
9: Image File Compression Made Easy \\
10: An Optimal Filter for Image Reconstruction \\
11: Noise Thresholding in Edge Images \\
12: Computing the Area, the Circumference, and the
Genus of a Binary Digital Image \\
III: Frame Buffer Techniques \\
Introduction \\
1: Efficient Inverse Color Map Computation \\
2. Efficient Statistical Computations for Optimal Color
Quantization \\
3: A Random Color Map Animation Algorithm \\
4: A Fast Approach to PHIGS PLUS Pseudo Color Mapping
\\
5: Mapping RGB Triples onto 16 Distinct Values \\
6: Television Color Encoding and ``Hot'' Broadcast
Colors \\
7: An Inexpensive Method of Setting the Monitor White
Point \\
8: Some Tips for Making Color Hardcopy \\
IV: 3D Geometry and Algorithms \\
Introduction \\
1: Area of Planar Polygons and Volume of Polyhedra \\
2: Getting Around on a Sphere \\
3: Exact Dihedral Metrics for Common Polyhedra \\
4: A Simple Viewing Geometry \\
5: View Correlation \\
6: Maintaining Winged-Edge Models \\
7: Quadtree\slash Octree-to-Boundary Conversion \\
8: Three-Dimensional Homogeneous Clipping of Triangle
Strips \\
9: InterPhong Shading \\
V: Ray Tracing \\
Introduction \\
1: Fast Ray-Convex Polyhedron Intersection \\
2: Intersecting a Ray with an Elliptical Torus \\
3: Ray-Triangle Intersection Using Binary Recursive
Subdivision \\
4: Improved Ray Tagging for Voxel-Based Ray Tracing \\
5: Efficiency Improvements for Hierarchy Traversal in
Ray Tracing \\
6: A Recursive Shadow Voxel Cache for Ray Tracing \\
7: Avoiding Incorrect Shadow Intersections for Ray
Tracing \\
8: A Body Color Model: Absorption of Light through
Translucent Media \\
9: More Shadow Attenuation for Ray Tracing Transparent
or Translucent Objects \\
VI: Radiosity \\
Introduction \\
1: Implementing Progressive Radiosity with
User-Provided Polygon Display Routines \\
2: A Cubic Tetrahedral Adaptation of the Hemi-Cube
Algorithm \\
3: Fast Vertex Radiosity Update \\
4: Radiosity via Ray Tracing \\
5: Detection of Shadow Boundaries for Adaptive Meshing
in Radiosity \\
[data unavailable] \ldots{}",
}
@Article{Balsara:1991:DSM,
author = "Poras T. Balsara and Robert M. Owens and Mary Jane
Irwin",
title = "Digit serial multipliers",
journal = j-J-PAR-DIST-COMP,
volume = "11",
number = "2",
pages = "156--162",
month = feb,
year = "1991",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ of Texas at Dallas",
affiliationaddress = "Richardson, TX, USA",
classification = "713; 723; B2570 (Semiconductor integrated circuits);
C5120 (Logic and switching circuits); C5230 (Digital
arithmetic methods)",
corpsource = "Erik Jonsson Sch. of Eng. and Computer Science, Texas
University, Richardson, TX, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "communication; Computers, Digital; data; digit
pipelined multipliers; digit pipelining; digit serial
multipliers; digital arithmetic; Integrated Circuits,
VLSI; Multiplying Circuits; multiplying circuits;
parallel; pipeline processing; Pipelined Multipliers;
processing; programmable multipliers; semisystolic;
Signal Processing --- Digital Techniques; special
purpose computers; special purpose processors;
systolic; systolic multiplier; Systolic Multipliers;
transmission; VLSI; VLSI signal processing",
treatment = "P Practical",
}
@Article{Barrenechea:1991:NEH,
author = "M. J. Barrenechea",
title = "Numeric exception handling",
journal = j-PROGRAM-J,
volume = "9",
number = "3",
pages = "40--42, 44--49",
month = may # "--" # jun,
year = "1991",
ISSN = "0747-5861",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Numeric exception handling is a facet of compiler
runtime support that is not well understood by many
application programmers, or even by some compiler
vendors. Floating-point errors have puzzled programmers
for too long. The author demystifies the IEEE 754 and
854 floating-point standards and explains how the Intel
80287/80387 and i860 chips fit into the puzzle. He
gives some techniques for handling numeric exceptions
in C++.",
acknowledgement = ack-nhfb,
affiliation = "Microway Inc., Plymouth, MA, USA",
classification = "C6110 (Systems analysis and programming)",
fjournal = "Programmer's Journal",
keywords = "C++; Compiler runtime support; Floating point errors;
Floating-point standards; I860 chips; IEEE 754; IEEE
854; Intel 80287/80387; Numeric exceptions",
thesaurus = "C language; C listings; Standards",
}
@Article{Barsi:1991:MAB,
author = "Ferruccio Barsi",
title = "Mod $m$ arithmetic in binary systems",
journal = j-INFO-PROC-LETT,
volume = "40",
number = "6",
pages = "303--309",
year = "1991",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
MRclass = "68M07 (68Q35)",
MRnumber = "MR1156823 (92m:68009)",
bibdate = "Thu Nov 8 14:50:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@Article{Bartholomew-Biggs:1991:AST,
author = "M. C. Bartholomew-Biggs",
title = "{Ada} Software for Teaching Modern Computer
Arithmetic",
journal = j-SIGNUM,
volume = "26",
number = "3",
pages = "17--26",
month = jul,
year = "1991",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/122649.122651",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:20 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Describes three Ada packages which support the
teaching of some recent and important ideas in
numerical computation. The first is designed to enable
students to write and use applications programs
demonstrating the behavior of floating point arithmetic
with different precisions and roundings. It also
underpins the other two packages which provide simple
computational tools for interval arithmetic and for
accurate arithmetic.",
acknowledgement = ack-nhfb,
affiliation = "Numerical Optimisation Centre, Hatfield Polytech.,
UK",
classification = "C0220 (Education and training); C5230 (Digital
arithmetic methods); C7430 (Computer engineering);
C7810C (Computer-aided instruction)",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "Accurate arithmetic; Ada software; Computer
arithmetic; Floating point arithmetic; Interval
arithmetic; Numerical computation; Precisions;
Roundings; Students; Teaching",
thesaurus = "Computer aided instruction; Computer science
education; Digital arithmetic; Numerical analysis;
Software packages; Teaching",
xxpages = "16--26",
}
@Article{BartholomewBiggs:1991:AST,
author = "M. C. Bartholomew-Biggs",
title = "{Ada} software for teaching modern computer
arithmetic",
journal = j-SIGNUM,
volume = "26",
number = "3",
pages = "16--26",
month = jul,
year = "1991",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Wed Dec 13 13:13:34 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Describes three Ada packages which support the
teaching of some recent and important ideas in
numerical computation. The first is designed to enable
students to write and use applications programs
demonstrating the behavior of floating point arithmetic
with different precisions and roundings. It also
underpins the other two packages which provide simple
computational tools for interval arithmetic and for
accurate arithmetic.",
acknowledgement = ack-nhfb,
affiliation = "Numerical Optimisation Centre, Hatfield Polytech.,
UK",
classification = "C0220 (Education and training); C5230 (Digital
arithmetic methods); C7430 (Computer engineering);
C7810C (Computer-aided instruction)",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "Accurate arithmetic; Ada software; Computer
arithmetic; Floating point arithmetic; Interval
arithmetic; Numerical computation; Precisions;
Roundings; Students; Teaching",
thesaurus = "Computer aided instruction; Computer science
education; Digital arithmetic; Numerical analysis;
Software packages; Teaching",
}
@Article{Bartoloni:1991:MFU,
author = "A. Bartoloni and C. Battista and S. Cabasino and N.
Cabibbo and F. Del Prete and F. Marzano and P. S.
Paolucci and R. Sarno and G. Salina and G. M. Todesco
and M. Torelli and R. Tripiccione and W. Tross and E.
Zanetti",
title = "{MAD}, a floating-point unit for massively-parallel
processors",
journal = "Particle World",
volume = "2",
number = "3",
pages = "65--73",
month = "????",
year = "1991",
ISSN = "1043-6790",
bibdate = "Tue Dec 12 09:26:54 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors describe in detail the architecture and
implementation of the MAD chip. It is a floating point
unit, used as the elementary processing element of the
APE100 array processor. The design has been accurately
tailored to the requirements of a SIMD floating point
intensive machine.",
acknowledgement = ack-nhfb,
affiliation = "Roma University, Italy",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5220P (Parallel architecture);
C5230 (Digital arithmetic methods); C7320 (Physics and
Chemistry)",
keywords = "APE100 array processor; Architecture; Elementary
processing element; Floating-point unit;
Massively-parallel processors; SIMD floating point
intensive machine",
pubcountry = "UK",
thesaurus = "Digital arithmetic; Microprocessor chips; Parallel
architectures; Physics computing",
}
@InProceedings{Beal:1991:GAP,
author = "D. Beal and C. Lambrinoudakis",
title = "{GPFP}: an array processing element for the next
generation of massively parallel supercomputer
architectures",
crossref = "IEEE:1991:PSA",
pages = "348--357",
year = "1991",
bibdate = "Wed Apr 15 16:28:01 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5220P (Parallel architecture); C5230 (Digital
arithmetic methods)",
corpsource = "Department of Computer Science, Queen Mary and
Westfield Coll., London University, UK",
keywords = "1.6 micron; 2.5 GFLOPS; 50 MHz; 50-MHz clock; ALU;
arithmetic and logic unit; array processing element;
CMOS integrated circuits; CMOSIC; cost-effective extra
functionality; digital arithmetic; floating point
arithmetic; general purpose with floating point
support; GPFP; MasPar; massively parallel SIMD arrays;
massively parallel supercomputer architectures;
microprocessor chips; on-chip memory; parallel
architectures; processing element; VLSI",
sponsororg = "IEEE; ACM",
treatment = "P Practical",
}
@TechReport{Beebe:1991:ASR,
author = "Nelson H. F. Beebe",
title = "Accurate Square Root Computation",
institution = inst-CSC,
address = inst-CSC:adr,
pages = "23",
day = "4",
month = feb,
year = "1991",
bibdate = "Sat Feb 8 10:28:55 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supplemental class notes prepared for Mathematics
118.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bohlender:1991:DFP,
author = "G. Bohlender",
title = "Decimal floating-point arithmetic in binary
representation",
crossref = "Kaucher:1991:CAS",
pages = "13--27",
year = "1991",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The binary representation of decimal floating-point
numbers permits an efficient implementation of the
proposed radix independent IEEE standard for
floating-point arithmetic, as far as storage space is
concerned. Unfortunately the left and right shifts
occurring in the arithmetic operations are very
complicated and slow in this representation. The paper
proposes methods which speed up these shifts; in
particular a kind of carry look-ahead technique is used
for division. These methods can be combined to
construct a decimal shifter which is needed in an ALU
for decimal arithmetic.",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "Inst. fur Angewandte Math., Karlsruhe University,
Germany",
classification = "C5230 (Digital arithmetic methods)",
keywords = "ALU; Binary representation; Carry look-ahead; Decimal
arithmetic; decimal floating-point arithmetic; Decimal
floating-point numbers; Decimal shifter; Division;
Floating-point arithmetic; IEEE standard; Left shifts;
Radix independent; Right shifts; Storage space",
thesaurus = "Digital arithmetic; Standards",
}
@InProceedings{Bohlender:1991:SEF,
author = "G. Bohlender and W. Walter and P. Kornerup and D. W.
Matula",
title = "Semantics for exact floating point operations",
crossref = "Kornerup:1991:PIS",
pages = "22--26",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Boldo:2003:RCT} for some special cases that
this paper may have overlooked.",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Bohlender.pdf",
abstract = "Semantics are given for the four elementary arithmetic
operations and the square root, to characterize what
are termed exact floating point operations. The
operands of the arithmetic operations and the argument
of the square root are all floating point numbers in
one format. In every case, the result is a pair of
floating point numbers in the same format with no
accuracy lost in the computation. These semantics make
it possible to realize the following principle: it
shall be a user option to discard any information in
the result of a floating point arithmetic operation.
The reliability and portability previously associated
with only mathematical software implementations in
integer arithmetic can thus be attained exploiting the
generally higher efficiency of floating point
hardware.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Angewandte Math., Karlsruhe University,
Germany",
classification = "C1160 (Combinatorial mathematics); C5230 (Digital
arithmetic methods)",
keywords = "accurate floating-point summation; argument; ARITH-10;
elementary arithmetic operations; exact floating point
operations; floating point arithmetic; floating point
hardware; floating point numbers; integer arithmetic;
mathematical software; operands; portability;
reliability; semantics; square root",
thesaurus = "Digital arithmetic; Number theory",
}
@InProceedings{Bohlender:1991:SPH,
author = "Gerd Bohlender and Andreas Kn{\"o}fel",
title = "A Survey of Pipelined Hardware Support for Accurate
Scalar Products",
crossref = "Kaucher:1991:CAS",
pages = "29--43",
year = "1991",
bibdate = "Sat Sep 17 19:05:23 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bohlender:1991:VEI,
author = "Gerd Bohlender",
title = "A Vector Extension of the {IEEE} Standard for
Floating-Point Arithmetic",
crossref = "Kaucher:1991:CAS",
pages = "3--12",
year = "1991",
bibdate = "Wed Dec 13 18:41:16 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The IEEE standard for floating-point arithmetic aims
at improving security, accuracy, reliability, and
compatibility of floating-point computations. However,
the standard only specifies single, double, and
extended precision operations for real operands.
Therefore, often only these operations are available in
hardware on customary floating-point processors. Vector
and matrix operations, complex operations, and interval
operations, in contrast have to be simulated in the
traditional way, using sequences of rounded operations.
This method leads to an unnecessary loss of accuracy
and efficiency. As floating-point processors more and
more evolve into vector processors for sophisticated
numerical applications, the same aims should be
satisfied for all operations on the customary numerical
data types. The paper proposes a vector extension of
the IEEE standard which leads to improved operations in
higher numerical spaces.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Angewandte Math., Karlsruhe University,
Germany",
classification = "C5220P (Parallel architecture); C5230 (Digital
arithmetic methods)",
keywords = "Floating-point arithmetic; Floating-point processors;
IEEE standard; Numerical data types; Vector
processors",
thesaurus = "Digital arithmetic; Standards; Vector processor
systems",
}
@TechReport{Boughton:1991:CSG,
author = "G. A. {Boughton (editor)}",
title = "{Computation Structures Group} Progress Report
1990--91",
type = "{CSG} Memo",
number = "337",
institution = "MIT Laboratory for Computer Science",
address = "Cambridge, MA, USA",
month = jun,
year = "1991",
bibdate = "Wed Jan 29 16:27:14 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Utilities for accurate reading and printing of double
precision floating point numbers (cited in
\cite{Steele:2004:RHP}).",
}
@Article{Briggs:1991:PCF,
author = "Keith Briggs",
title = "A Precise Calculation of the {Feigenbaum} Constants",
journal = j-MATH-COMPUT,
volume = "57",
number = "195",
pages = "435--439",
month = jul,
year = "1991",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Y60 (39B12 58F14 65Q05)",
MRnumber = "91j:11117",
MRreviewer = "Jeffrey O. Shallit",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "B0290F (Interpolation and function approximation);
B0290K (Nonlinear and functional equations); C4130
(Interpolation and function approximation); C4150
(Nonlinear and functional equations)",
corpsource = "Department of Math., La Trobe University, Bundoora,
Vic., Australia",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Feigenbaum constants; Feigenbaum functional equation;
functional equations; iteration; iterative methods;
multiple precision floating point; period-doubling
bifurcations; real functions",
treatment = "T Theoretical or Mathematical",
}
@Article{Bromley:1991:FAT,
author = "Mark Bromley and Steven Heller and Tim McNerney and
Guy L. {Steele Jr.}",
title = "{Fortran} at ten gigaflops: the {Connection Machine}
convolution compiler",
journal = j-SIGPLAN,
volume = "26",
number = "6",
pages = "145--156",
month = jun,
year = "1991",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Thu May 13 12:37:27 MDT 1999",
bibsource = "http://www.acm.org/pubs/contents/proceedings/pldi/113445/index.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/pldi/113445/p145-bromley/",
abstract = "The authors have implemented a prototype of a
specialized compiler module and associated run-time
support that allows a Fortran user to achieve sustained
floating-point performance of over 10 gigaflops on the
Connection Machine Model CM-2. This improves
substantially over the previous record of 5.6
gigaflops, which was achieved by means of hand-crafted
low-level coding techniques. The compiler module
processes array assignment statements of a certain
form: the right-hand side must be a sum of products and
the products must use the Fortran 90 array shifting
intrinsics in a certain stylized pattern. Such
assignment statements are suitable for expressing array
convolution (stencil) computations and can be executed
efficiently by chained multiply-add operations.",
acknowledgement = ack-nhfb,
affiliation = "Thinking Machines Corp., Cambridge, MA, USA",
classification = "C5440 (Multiprocessor systems and techniques); C6110
(Systems analysis and programming); C6140D (High level
languages); C6150C (Compilers, interpreters and other
processors)",
confdate = "26-28 June 1991",
conflocation = "Toronto, Ont., Canada",
confsponsor = "ACM",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "Array assignment statements; Array convolution;
Chained multiply-add operations; Connection Machine
convolution compiler; Connection Machine Model CM-2;
Fortran 90 array shifting intrinsics; Fortran user;
Hand-crafted low-level coding techniques; languages;
performance; Run-time support; Specialized compiler
module; Sustained floating-point performance",
subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, FORTRAN. {\bf D.3.4} Software,
PROGRAMMING LANGUAGES, Processors, Compilers.",
thesaurus = "FORTRAN; Parallel machines; Parallel programming;
Program compilers",
}
@Book{Brunner:1991:VAR,
editor = "Richard A. Brunner and Dileep P. Bhandarkar and
others",
title = "{VAX} Architecture Reference Manual",
publisher = pub-DP # " and " # pub-PH,
address = pub-DP:adr # " and " # pub-PH:adr,
pages = "xv + 560",
year = "1991",
ISBN = "1-55558-057-2 (Digital Press), 0-13-929522-4
(Prentice-Hall)",
ISBN-13 = "978-1-55558-057-5 (Digital Press), 978-0-13-929522-5
(Prentice-Hall)",
LCCN = "QA76.8.V32 V39 1991",
bibdate = "Wed Nov 01 08:09:54 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Bruss:1991:RMF,
author = "Rolf-J{\"u}rgen Br{\"u}{\ss}",
title = "{RISC}\emdash The {MIPS-R3000} Family",
publisher = pub-SIEMENS,
address = pub-SIEMENS:adr,
pages = "340",
year = "1991",
ISBN = "3-8009-4103-1",
ISBN-13 = "978-3-8009-4103-2",
LCCN = "QA76.5 R48 1991",
bibdate = "Sat Jan 29 23:10:50 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Bryant:1991:CVI,
author = "R. E. Bryant",
title = "On the complexity of {VLSI} implementations and graph
representations of {Boolean} functions with application
to integer multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "40",
number = "2",
pages = "205--213",
month = feb,
year = "1991",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.73590",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 12:52:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=73590",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Calvetti:1991:REF,
author = "Daniela Calvetti",
title = "Roundoff error for floating point representation of
real data",
journal = j-COMMUN-STAT-THEORY-METH,
volume = "20",
number = "8",
pages = "2687--2695",
year = "1991",
CODEN = "CSTMDC",
DOI = "https://doi.org/10.1080/03610929108830658",
ISSN = "0361-0926 (print), 1532-415X (electronic)",
ISSN-L = "0361-0926",
MRclass = "62E99 (65C20)",
MRnumber = "93d:62031",
bibdate = "Wed Jan 27 05:39:04 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/communstattheorymeth1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications in Statistics: Theory and Methods",
journal-URL = "http://www.tandfonline.com/loi/lsta20",
reviewer = "Evdokia Xekalaki",
}
@Article{Calvetti:1991:SRE,
author = "Daniela Calvetti",
title = "A stochastic roundoff error analysis for the {Fast
Fourier Transform}",
journal = j-MATH-COMPUT,
volume = "56",
number = "194",
pages = "755--774",
month = apr,
year = "1991",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65T20 (65G05)",
MRnumber = "91m:65341",
MRreviewer = "Harald E. Krogstad",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "B0290Z (Other numerical methods); B0290B (Error
analysis in numerical methods); C4190 (Other numerical
methods); C4110 (Error analysis in numerical methods)",
corpsource = "Dept. of Math., Southern Colorado Univ., Pueblo, CO,
USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "addition; discrete Fourier transform; error analysis;
expected value; fast Fourier transform; fast Fourier
transforms; linear forms; multiplication; stochastic
roundoff error analysis; variance",
treatment = "T Theoretical or Mathematical",
}
@Book{Catanzaro:1991:STP,
editor = "Ben J. Catanzaro",
title = "The {SPARC} Technical Papers",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 501",
year = "1991",
ISBN = "0-387-97634-5, 3-540-97634-5",
ISBN-13 = "978-0-387-97634-1, 978-3-540-97634-9",
LCCN = "QA76.9.A73 S65 1991",
bibdate = "Wed Feb 9 01:57:02 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Celarier:1991:AML,
author = "Donald A. Celarier and Donald W. Sando",
title = "An {Ada} math library for real-time avionics",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
pages = "274--284",
month = "Fall",
year = "1991",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Sat Aug 9 09:05:43 MDT 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
acknowledgement = ack-nhfb,
classcodes = "C7460 (Aerospace engineering); C7150 (Military); C7310
(Mathematics); C6140D (High level languages)",
corpsource = "Boeing Defense and Space Group, Seattle, WA, USA",
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "accuracy testing; Ada; Ada math library; aerospace
computing; applications; avionics; computing;
implementation; library; mathematics computing;
military; military avionics processor; real-time
avionics; real-time systems; subroutines",
treatment = "P Practical",
}
@Article{Chai:1991:MCF,
author = "P. Chai and T. Chuk and Y. H. Fong and L. Hu and K. Ng
and J. Prabhu and A. Quek and A. Samuels and J. Yeun",
title = "A 120 {MFLOPS CMOS} Floating-Point Processor",
crossref = "IEEE:1991:PIC",
pages = "15.1/1--4",
year = "1991",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Chan:1991:DOC,
author = "Pak K. Chan and Martine D. F. Schlag and Clark D.
Thomborson and Vojin G. Oklobdzija",
title = "Delay optimization of carry-skip adders and block
carry-lookahead adders",
crossref = "Kornerup:1991:PIS",
pages = "154--164",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Chan.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Chance:1991:EPA,
author = "R. J. Chance",
title = "The effect of processor architecture on an efficient
floating point table look-up algorithm",
journal = j-MICROPROC-MICROSYS,
volume = "15",
number = "8",
pages = "411--416 (or 411--415??)",
month = oct,
year = "1991",
CODEN = "MIMID5",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "R J Chance investigates the performance that can be
achieved using linear interpolation and partitioning
techniques in look-up tables",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Microprocessors and Microsystems",
}
@Article{Chang:1991:PLA,
author = "Yuh-Huu Chang and Ching-Kae Tzou and N. J. Bershad",
title = "Postsmoothing for the {LMS} algorithm and a fixed
point roundoff error analysis",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "39",
number = "4",
pages = "959--962",
month = apr,
year = "1991",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "The effect of post-algorithm smoothing on digital
implementations of the least mean square (LMS)
algorithm is studied. An expression is derived for the
mean square error (MSE) with post-algorithm (PA)
smoothing but without finite wordlength effects.
\ldots{}",
}
@Article{Chassaing:1991:DSP,
author = "Chassaing and Horning",
title = "Digital Signal Processing with Fixed- and
Floating-Point Processors",
journal = j-COED,
volume = "II",
number = "1",
pages = "1--4",
month = jan,
year = "1991",
CODEN = "CWLJDP",
ISSN = "0736-8607",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "CoED",
}
@InProceedings{Chatelin:1991:AAA,
author = "F. Chatelin and V. Frayss{\'e}",
title = "Analysis of arithmetic algorithms: a statistical
study",
crossref = "Kornerup:1991:PIS",
pages = "10--16",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Chatelin.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Chen:1991:BDR,
author = "F. Chen and C. S. Chen",
title = "A {20~b} dynamic-range floating-point data acquisition
system",
journal = j-IEEE-TRANS-IND-ELECTRON,
volume = "38",
number = "1",
pages = "10--14",
month = feb,
year = "1991",
CODEN = "ITIED6",
DOI = "https://doi.org/10.1109/41.103477",
ISSN = "0278-0046 (print), 1557-9948 (electronic)",
ISSN-L = "0278-0046",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Industrial Electronics",
summary = "The design and engineering of a floating-point
data-acquisition system are described. The system has
both automatic gain and software-programmable gain
adjustment features. In automatic gain adjustment mode,
the gain is set automatically dependent on \ldots{}",
}
@Article{Chiang:1991:FNR,
author = "Jen-Shiun Chiang and Mi Lu",
title = "Floating-point numbers in residue number systems",
journal = j-COMPUT-MATH-APPL,
volume = "22",
number = "10",
pages = "127--140",
month = "????",
year = "1991",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
MRclass = "65Y10",
MRnumber = "92h:65212",
bibdate = "Wed Dec 13 18:13:40 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Introduce a new type of the residue number system
(RNS), floating-point RNS, which can significantly
increase the range of the numbers represented by RNS.
The concept of the RNS floating-point arithmetics are
presented, and the approaches to perform these
arithmetic operations are proposed. The introduced
methods are simple, efficient and easy to implement. (6
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. Eng., Texas A\&M University,
College Station, TX, USA",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
keywords = "Floating-point RNS; Residue number system; RNS",
pubcountry = "UK",
thesaurus = "Digital arithmetic",
}
@Article{Chiang:1991:FPNa,
author = "Jen-Shiun Chiang and Mi Lu",
title = "Floating-point numbers in residue number systems",
journal = j-COMPUT-MATH-APPL,
volume = "22",
number = "10",
pages = "127--140",
month = "????",
year = "1991",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
MRclass = "65Y10",
MRnumber = "92h:65212",
bibdate = "Wed Dec 13 18:13:40 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Introduce a new type of the residue number system
(RNS), floating-point RNS, which can significantly
increase the range of the numbers represented by RNS.
The concept of the RNS floating-point arithmetics are
presented, and the approaches to perform these
arithmetic operations are proposed. The introduced
methods are simple, efficient and easy to implement. (6
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. Eng., Texas A\&M University,
College Station, TX, USA",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
keywords = "Floating-point RNS; Residue number system; RNS",
pubcountry = "UK",
thesaurus = "Digital arithmetic",
}
@Article{Chiang:1991:FPNb,
author = "Jen-Shiun Chiang and Mi Lu",
title = "Floating-point numbers in residue number systems",
journal = j-COMPUT-MATH-APPL,
volume = "22",
number = "10",
pages = "127--140",
month = "????",
year = "1991",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:11:01 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/089812219190200N",
abstract = "Introduce a new type of the residue number system
(RNS), floating-point RNS, which can significantly
increase the range of the numbers represented by RNS.
The concept of the RNS floating-point arithmetics are
presented, and the approaches to perform these
arithmetic operations are proposed. The introduced
methods are simple, efficient and easy to implement.",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. Eng., Texas A and M University,
College Station, TX, USA",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
keywords = "Floating-point RNS; Residue number system; RNS",
pubcountry = "UK",
thesaurus = "Digital arithmetic",
}
@InProceedings{Chiang:1991:GDA,
author = "J.-S. Chiang and M. Lu",
title = "A general division algorithm for residue number
systems",
crossref = "Kornerup:1991:PIS",
pages = "76--83",
year = "1991",
DOI = "https://doi.org/10.1109/ARITH.1991.145537",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Chiang.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10; residue arithmetic; residue number system",
summary = "A general algorithm for signed number division in
residue number systems (RNSs) is presented. A parity
checking technique is used to accomplish the sign and
overflow detection in this algorithm. Compared with
conventional methods of sign and \ldots{}",
}
@Article{Cmelik:1991:AMS,
author = "Robert F. Cmelik and Shing I. Kong and David R. Ditzel
and Edmund J. Kelly",
title = "An Analysis of {MIPS} and {SPARC} Instruction Set
Utilization on the {SPEC} Benchmarks",
journal = j-SIGPLAN,
volume = "26",
number = "4",
pages = "290--301 (or 290--302??)",
month = apr,
year = "1991",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The dynamic instruction counts of MIPS and SPARC are
compared using the SPEC benchmarks. MIPS typically
executes more user-level instructions than SPARC. This
difference can be accounted for by architectural
differences, compiler differences, and library
differences. The most significant differences are that
SPARC's double-precision floating point load/store is
an architectural advantage in the SPEC floating point
benchmarks while MIPS's compare-and-branch instruction
is an architectural advantage in the SPEC integer
benchmarks. After the differences in the two
architectures are isolated, it appears that although
MIPS and SPARC each have strengths and weaknesses in
their compilers and library routines, the combined
effect of compilers and library routines does not give
either MIPS or SPARC a clear advantage in these
areas.",
acknowledgement = ack-nhfb,
affiliation = "Sun Microsyst. Inc., Mountain View, CA, USA",
classification = "C5220 (Computer architecture); C5470 (Performance
evaluation and testing); C6140B (Machine-oriented
languages)",
confdate = "8-11 April 1991",
conflocation = "Santa Clara, CA, USA",
confsponsor = "IEEE; ACM",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "Architectural differences; Compare-and-branch
instruction; Compiler differences; Double-precision
floating point load/store; Dynamic instruction counts;
Instruction set utilization; Library differences; MIPS;
SPARC; SPEC floating point benchmarks; SPEC integer
benchmarks; User-level instructions",
thesaurus = "Instruction sets; Performance evaluation; Reduced
instruction set computing",
}
@InProceedings{Cody:1991:KAA,
author = "W. J. Cody",
title = "Keynote Address: Arithmetic Standards: The Long Road",
crossref = "Kornerup:1991:PIS",
pages = "ix--ix",
year = "1991",
bibdate = "Sat Nov 17 08:46:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_keynote.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Cody:1991:PEP,
author = "W. J. Cody",
title = "Performance Evaluation of Programs Related to the Real
Gamma Function",
journal = j-TOMS,
volume = "17",
number = "1",
pages = "46--54",
month = mar,
year = "1991",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D20 (65Y20)",
MRnumber = "91m:65052",
bibdate = "Sun Sep 04 23:33:02 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://doi.acm.org/10.1145/103147.103153;
http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p46-cody/",
abstract = "Methods are presented for evaluating the performance
of programs for the functions $ \Gamma (x) $, $ \ln
\Gamma (x) $, and $ \psi (x) $. Accuracy estimates are
based on comparisons using the manipulation theorem.
Ideas for checking robustness are also given, and
details on specific implementations of test programs
are included.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "measurement; performance; reliability",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Numerical algorithms. {\bf G.4}:
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Certification and testing.",
}
@Article{Cody:1991:UTS,
author = "W. J. Cody and L. Stoltz",
title = "The Use of {Taylor} Series to Test Accuracy of
Function Programs",
journal = j-TOMS,
volume = "17",
number = "1",
pages = "55--63",
month = mar,
year = "1991",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D20 (65Y20)",
MRnumber = "91m:65053",
bibdate = "Sun Sep 04 23:36:36 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://doi.acm.org/10.1145/103147.103154;
http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p55-cody/",
abstract = "This paper discusses the use of local Taylor series
expansions for determining the accuracy of computer
programs for special functions. The main example is
testing of programs for exponential integrals.
Additional applications include testing of programs for
certain Bessel functions, Dawson's integral, and error
functions.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; measurement; performance; verification",
subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
SOFTWARE, Certification and testing. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Numerical algorithms.",
}
@Article{Compan:1991:GPS,
author = "A. Compan and P. Debaud and V. Delorme and J. A.
Fran{\c{c}}ois and H. Mehrez and F. Pecheux",
title = "{GAF}: a portable standard-cell floating point adder
generator using the {CXgen} function library",
journal = j-MICROPROC-MICROPROG,
volume = "32",
number = "1",
pages = "637--644",
month = aug,
year = "1991",
CODEN = "MMICDT",
ISSN = "0165-6074 (print), 1878-7061 (electronic)",
ISSN-L = "0165-6074",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Microprocessing and Microprogramming",
}
@Book{Counihan:1991:F,
author = "Martin Counihan",
title = "{Fortran 90}",
publisher = pub-PITMAN,
address = pub-PITMAN:adr,
pages = "309",
year = "1991",
ISBN = "0-273-03073-6",
ISBN-13 = "978-0-273-03073-7",
LCCN = "QA76.73.F25 C68 1991",
bibdate = "Sun May 02 07:48:16 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
note = "See \cite{ANSI:ftn92}.",
acknowledgement = ack-nhfb,
keywords = "Fortran 90 (computer program language); Programming
languages; {Fortran 90} (Computer program language)",
libnote = "Not yet in my library.",
tableofcontents = "1: Introduction \\
1.1: Fortran 90 / 1 \\
1.2: Programs and Programming / 2 \\
2: What is Fortran 90? \\
2.1: Program Structure / 5 \\
2.2: Intrinsic Procedures / 6 \\
2.3: Statement Types / 7 \\
2.4: What Fortran 90 Isn't / 7 \\
2.5: New Features in Fortran 90 / 8 \\
Notes / 10 \\
3: Getting Started \\
3.1: The Character Set / 11 \\
3.2: A Simple Program / 14 \\
3.3: Arithmetic Operators / 18 \\
Exercises 3A / 19 \\
3.4: Names and Other Lexical Tokens / 20 \\
3.5: Fortran Source Form / 21 \\
Exercises 3B / 24 \\
Notes / 25 \\
4: Intrinsic Data Types \\
4.1: Integers / 26 \\
4.2: Real Numbers / 29 \\
Exercises A / 31 \\
4.3: Simple Form of the Type Declaration Statement / 32
\\
4.4: Kinds Real Numbers / 32 \\
4.5: Complex Numbers / 33 \\
4.6: Logical Data; Logical and Relational Operators /
35 \\
4.7: Characters and Strings / 38 \\
Exercises 4B / 40 \\
Notes / 42 \\
5: Some Intrinsic Procedures \\
5.1: An Intrinsic Subroutine / 43 \\
5.2: Mathematical Functions / 44 \\
5.3: Numeric Functions / 46 \\
Exercises 5A / 50 \\
Notes / 52 \\
6: More About Characters \\
6.1: Declaring Character Data / 53 \\
6.2: Character Constants / 54 \\
6.3: Character Operators / 55 \\
6.4: Intrinsic Character Functions / 56 \\
6.5: Substrings / 59 \\
Exercises / 61 \\
Notes / 62 \\
7: Arrays \\
7.1: Declaring Arrays / 63 \\
7.2: Using Arrays / 65 \\
7.3: Array Constructors / 67 \\
7.4: Array Sections / 68 \\
7.5: Array Sections, Character Strings and Substrings /
70 \\
7.6: Where / 72 \\
7.7: Arrays and Intrinsic Functions / 73 \\
Exercises 7B / 74 \\
8: Execution Control \\
8.1: The ``CASE'' Construct / 76 \\
8.2: The ``IF'' Construct / 80 \\
Exercises / 81 \\
8.3: The ``DO'' Construct / 82 \\
8.4: Stop / 88 \\
Exercises 8B / 88 \\
Notes / 89 \\
9: Functions and Subroutines (1) \\
9.1: Functions / 90 \\
Exercises 9A / 93 \\
9.2: Subroutines / 93 \\
9.3: Procedures and Arrays / 96 \\
Exercises 9B / 99 \\
Notes / 100 \\
10: More Intrinsic Procedures; Statement Labels \\
10.1: Intrinsic Subroutines / 102 \\
10.2: Functions for Use with Arrays / 104 \\
Exercises 10A / 110 \\
10.3: Numeric Inquiry Functions and Floating-Point
Manipulation Functions / 110 \\
10.4: Statement Labels and ``GO TO'' / 111 \\
Notes / 114 \\
11: Modules \\
11.1: Data Modules / 116 \\
Module Procedures / 120 \\
11.3: More About ``USE'' Statements / 124 \\
Exercises / 126 \\
Notes / 127 \\
12: Functions and Subroutines (2) \\
12.1: Recursive Procedures / 128 \\
Exercises 12A / 130 \\
12.2: Interface Blocks / 131 \\
12.3: Argument Keywords / 132 \\
12.4: More About Arguments: ``PRESENT'' / 133 \\
12.5: Functions / 134 \\
12.6: Operators / 135 \\
12.7: Generic Names / 138 \\
12.8: Parallel Processing / 141 \\
Exercises 12B / 142 \\
Notes / 143 \\
13: The Type Declaration Statement \\
13.1: General Form of the TDS / 144 \\
13.2: Character Length Selectors / 147 \\
13.3: Attribute Specifications / 149 \\
13.4: Array Specifications / 152 \\
13.5: The Entity Declaration List / 157 \\
13.6: Summary / 158 \\
Exercises 13A / 159 \\
Notes / 161 \\
14: Derived Types \\
14.1: Derived-Type Definition / 164 \\
14.2: Structure Constructors / 166 \\
14.3: Structure Components / 168 \\
Exercises 14A / 169 \\
14.4: Structures of Structures / 170 \\
Exercises 14B / 171 \\
14.5: Functions and Operators with Derived Types / 172
\\
14.6: Defined Assignment / 174 \\
Exercises 14C / 178 \\
Notes / 180 \\
15: Arrays and Pointers \\
15.1: Array Element Order, Array Constructors; RESHAPE
/ 181 \\
15.2: Vector Subscripts / 184 \\
15.3: Allocatable Arrays / 187 \\
Exercises 15A / 190 \\
15.4: LBOUND, SHAPE and SIZE / 190 \\
Exercises 15B / 191 \\
15.5: Simple Pointers / 192 \\
15.6: Pointers as Structures and as Structure
Components / 197 \\
15.7: Pointers and Procedures / 204 \\
15.8: Array Pointers / 205 \\
Exercises 15C / 207 \\
Notes / 208 \\
16: Input and Output; Data Format Specifications \\
16.1: Data Transfer Statements / 209 \\
16.2: The Item List / 210 \\
16.3: List-Directed Input / 212 \\
16.4: List-Directed Output / 216 \\
16.5: Explicit Formats / 217 \\
Exercises 16A / 219 \\
16.6: Data Edit Descriptors and Character Edit
Descriptors / 219 \\
16.7: Control Edit Descriptors / 223 \\
Exercises 16B / 225 \\
16.8: Namelists / 226 \\
16.9: Unformatted / 228 \\
16.10: The TRANSFER Function / 229 \\
16.11: Summary / 231 \\
Notes / 232 \\
17: File Handling \\
17.1: Units, Files and Records / 233 \\
17.2: Opening and Closing Files / 235 \\
17.3: BACKSPACE, ENDFTLE and REWIND / 240 \\
17.4: Control Specifications for / 240 \\
17.5: The ``INQUIRE'' Statement / 242 \\
17.6: Internal Files / 246 \\
Exercises 17A / 248 \\
Notes / 249 \\
18: Bits \\
18.1: Inside Integers / 250 \\
18.2: Bit Logic / 251 \\
18.3: A Warning / 252 \\
Exercises 18A / 253 \\
19: Programming Conventions and Program Architecture:
Putting It All Together \\
19.1: Coding Conventions / 254 \\
19.2: Towards Fortran 90 / 255 \\
Fortran 90 Recommended Statements / 256 \\
Intrinsic Functions / 257 \\
19.3: Program Unit Structure / 258 \\
19.4: Program Structure / 261 \\
19.5: Final Remarks / 262 \\
Answers to Selected Exercises / 263 \\
Appendices \\
A: Fortran 90 Statements \\
B: Intrinsic Procedures / 286 \\
C: Intrinsic Procedures: Names / 292 \\
D: Argument Keywords in Intrinsic Procedures / 294 \\
E: Edit Descriptors / 297 \\
F: The ASCII Character Set / 301 \\
Index / 304",
}
@Article{Cox:1991:TSS,
author = "Christopher L. Cox and James A. Knisely",
title = "A tridiagonal system solver for distributed memory
parallel processors with vector nodes",
journal = j-J-PAR-DIST-COMP,
volume = "13",
number = "3",
pages = "325--331",
month = nov,
year = "1991",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Clemson Univ",
affiliationaddress = "Clemson, SC, USA",
classification = "721; 722; 723; 921; C4140 (Linear algebra); C5220P
(Parallel architecture); C5230 (Digital arithmetic
methods); C5470 (Performance evaluation and testing);
C7310 (Mathematics)",
corpsource = "Department of Math. Sci., Clemson University, SC,
USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "algebraic routine; algorithm; computer; Computer
Programming languages--fortran; Computer
Programming--Algorithms; Computer Systems, Digital;
Cyclic reduction algorithms; Data Storage, Digital;
digital arithmetic; Distributed memories; distributed
memory parallel; divide and conquer strategy; Floating
Point Systems FPS T-20; FORTRAN; Intel iPSC/2-VX;
linear algebra; Mathematical Techniques--Matrix
Algebra; mathematics computing; odd-even cyclic
reduction; parallel architectures; Parallel Processing;
partitioning; performance evaluation; processors;
programs; redundancy; scaled speedup; tridiagonal
system solver; Tridiagonal systems; Vector nodes;
vector nodes; vector processors",
treatment = "A Application; P Practical",
}
@Article{Crenshaw:1991:SRS,
author = "J. W. Crenshaw",
title = "Square roots are simple?",
journal = j-EMBED-SYS-PROG,
volume = "4",
number = "11",
pages = "30--52",
month = nov,
year = "1991",
CODEN = "EYPRE4",
ISSN = "1040-3272",
bibdate = "Wed Sep 14 19:14:52 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Embedded Systems Programming",
}
@Article{Davida:1991:FPA,
author = "George I. Davida and Bruce Litow",
title = "Fast Parallel Arithmetic via Modular Representation",
journal = j-SIAM-J-COMPUT,
volume = "20",
number = "4",
pages = "756--765",
month = aug,
year = "1991",
CODEN = "SMJCAT",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
MRclass = "68Q10",
MRnumber = "92c:68046",
bibdate = "Mon Nov 29 11:01:48 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/20/4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
}
@MastersThesis{Davies:1991:FPS,
author = "Davies, T. C. (Tudor Craddock)",
title = "A floating point systolic array processing element
using serial communication",
type = "Thesis ({M.Eng.})",
school = "Royal Military College of Canada",
address = "Kingston, ON, Canada",
year = "1991",
ISBN = "0-315-60644-4",
ISBN-13 = "978-0-315-60644-9",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "2 microfiches. University Microfilms order no.
UMI00285885",
series = "National Library of Canada = Bibliotheque nationale du
Canada; Canadian theses = Theses canadiennes",
acknowledgement = ack-nhfb,
}
@Article{Davis:1991:CC,
author = "Warren Davis and Kan Yabumoto",
title = "A coprocessor for a coprocessor?",
journal = j-DDJ,
volume = "16",
number = "5",
pages = "16--28, 84--88",
month = may,
year = "1991",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Tue Sep 10 09:11:02 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
UnCover database",
abstract = "When fast graphics aren't fast enough, the TI 34020
graphics coprocessor employs its own coprocessor -- the
34082 FPU -- for even higher system performance.",
acknowledgement = ack-nhfb,
affiliation = "Pixelab Inc., Lisle, IL, USA",
classification = "C5130 (Microprocessor chips); C5540 (Terminals and
graphic displays)",
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "Built-in graphics-related instructions; Floating point
coprocessor; General-purpose microprocessor; Graphics
System Processor; Programmable graphics coprocessor;
Texas Instruments; TMS34020; TMS34082; Video control
circuitry",
thesaurus = "Assembly language listings; C listings; Computer
graphic equipment; Microprocessor chips; Satellite
computers; Texas Instruments computers",
}
@PhdThesis{Deb:1991:BFF,
author = "Kalyanmoy Deb",
title = "Binary and floating-point function optimization using
messy genetic algorithms",
type = "Thesis ({Ph.D.})",
school = "Department of Engineering Mechanics, University of
Alabama",
address = "Tuscaloosa, AL, USA",
pages = "xvii + 166",
year = "1991",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Algorithms.; Combinatorial optimization.",
}
@InProceedings{deLange:1991:DIF,
author = "Alfons A. J. de Lange and Ed F. Deprettere",
title = "Design and implementation of a floating-point
quasi-systolic general purpose {CORDIC} rotator for
high-rate parallel data and signal processing",
crossref = "Kornerup:1991:PIS",
pages = "272--281",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Lange.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Demmel:1991:OIA,
author = "James W. Demmel",
title = "On the odor of {IEEE} arithmetic",
journal = j-NA-DIGEST,
volume = "91",
number = "39",
day = "29",
month = sep,
year = "1991",
bibdate = "Thu Aug 23 06:19:41 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Rebuttal to \cite{Grcar:1991:IAS}.",
URL = "http://www.netlib.org/na-digest/91/v91n39",
acknowledgement = ack-nhfb,
fjournal = "NA Digest",
}
@InProceedings{Dongarra:1991:GBP,
author = "J. J. Dongarra and A. Karp and K. Miura and H. D.
Simon",
title = "{Gordon Bell Prize} lectures (supercomputer
applications)",
crossref = "IEEE:1991:PSA",
pages = "328--337",
year = "1991",
bibdate = "Wed Apr 15 16:28:01 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5440 (Multiprocessor systems and techniques)",
corpsource = "Department of Computer Science, Tennessee University,
Knoxville, TN, USA",
keywords = "128-node Intel iPSC/860; compiler speedup; Connections
Machine; electronic structure; floating point
processors; Fortran 77; Fortran 90; grid generation
program; parallel processing; partial differential
equation; price/performance award; scientific and
engineering problems; supercomputers",
sponsororg = "IEEE; ACM",
treatment = "G General Review; P Practical",
}
@Article{Dunham:1991:ABA,
author = "C. Dunham",
title = "Applications of Best Approximation",
journal = j-SIGNUM,
volume = "26",
number = "2",
pages = "2--10",
month = apr,
year = "1991",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@InProceedings{Duprat:1991:NRR,
author = "Jean Duprat and Yvan Herreros and Sylvanus Kla",
title = "New redundant representations of complex numbers and
vectors",
crossref = "Kornerup:1991:PIS",
pages = "2--9",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Duprat.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Duprat:1991:WND,
author = "J. Duprat and Jean-Michel Muller",
title = "Writing numbers differently for faster calculation",
journal = j-TECHNIQUE-SCI-INFORMATIQUES,
volume = "10",
number = "3",
pages = "211--224",
month = "????",
year = "1991",
CODEN = "TTSIDJ",
ISSN = "0752-4072, 0264-7419",
ISSN-L = "0752-4072",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Instead of Avizienis' or the carry save methods a
borrow save (BS) notation is proposed. Examples are
given of BS addition, subtraction, shifting and
multiplication with the necessary elementary cells
being proposed and circuits for testing zero and sign
being described. Floating point arithmetic is
explained, involving pseudo normalisation and
applications are covered including the Cordic
algorithm.",
acknowledgement = ack-nhfb,
affiliation = "Ecole Normale Superieure de Lyon, France",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "Technique et science informatiques : TSI",
keywords = "Addition; Borrow save; Carry save methods; Cordic
algorithm; Floating point arithmetic; Multiplication;
Pseudo normalisation; Shifting; Subtraction; Zero",
language = "French",
pubcountry = "France",
thesaurus = "Digital arithmetic",
}
@Article{Ercegovac:1991:MPM,
author = "Milo{\v{s}} D. Ercegovac and Tomas Lang",
title = "Module to perform multiplication, division, and square
root in systolic arrays for matrix computations",
journal = j-J-PAR-DIST-COMP,
volume = "11",
number = "3",
pages = "212--221",
month = mar,
year = "1991",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ of California Los Angeles",
affiliationaddress = "Los Angeles, CA, USA",
classification = "722; 723; 921; C4140 (Linear algebra); C5220
(Computer architecture); C5230 (Digital arithmetic
methods)",
corpsource = "Department of Computer Science, California University,
Los Angeles, CA, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "Applications; carry-save; complexity; Computer
Programming --- Algorithms; Computers; digital
arithmetic; division; matrix algebra; Matrix
Computations; matrix computations; module;
multiplication; Multiplication/Division/Square Root
Module; Normalization; On-The-Fly Conversion; radix-2
divider; result-digit selection; Rounding;
signed-digit; square root; Systolic Arrays; systolic
arrays",
treatment = "P Practical",
}
@Article{Even:1991:SMM,
author = "Shimon Even",
title = "Systolic Modular Multiplication",
journal = j-LECT-NOTES-COMP-SCI,
volume = "537",
pages = "619--??",
year = "1991",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Feb 5 11:48:02 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t0537.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/0537/05370619.htm;
http://link.springer-ny.com/link/service/series/0558/papers/0537/05370619.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Ferguson:1991:AMA,
author = "Warren E. {Ferguson, Jr.} and Tom Brightman",
title = "Accurate and Monotone Approximations of Some
Transcendental Functions",
crossref = "Kornerup:1991:PIS",
pages = "237--244",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Ferguson.pdf",
acknowledgement = ack-nj # " and " # ack-nhfb,
keywords = "ARITH-10",
}
@Article{Ferguson:1991:SMC,
author = "Warren E. {Ferguson, Jr.}",
title = "Selecting math coprocessors",
journal = j-IEEE-SPECTRUM,
volume = "28",
number = "7",
pages = "38--41",
month = jul,
year = "1991",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/6.83469",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Thu Sep 01 16:17:34 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "floating-point arithmetic",
remark = "Contains performance-comparison tables for Cyrix,
Intel, Motorola, and Weitek floating-point coprocessor
chips.",
}
@InProceedings{Fleurkens:1991:HLD,
author = "H. Fleurkens and R. Tangelder",
title = "The high level design of the long accumulator chip",
crossref = "IEEE:1991:PFC",
pages = "299--301",
year = "1991",
bibdate = "Wed Dec 13 13:13:34 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors discuss an architecture and its high level
description of a long accumulator chip suited for the
exact calculation of the inner products of floating
point numbers. A highly parallel implementation is
developed using eight independent adder stations, which
add products to two circular long accumulators. A
dispatcher schedules each product to the best available
station. To validate this architecture and to calculate
its performance, a high level description is created.
This description is made with ESCHER+, an interactive
schematic entry tool with a built-in simulator. The
resulting description showed to be the basis for the
further implementation of the chip.",
acknowledgement = ack-nhfb,
affiliation = "Eindhoven University of Technol., Netherlands",
classification = "B1130B (Computer-aided circuit analysis and design);
B1265B (Logic circuits); C5120 (Logic and switching
circuits); C5210B (Computer-aided logic design); C5220P
(Parallel architecture); C5230 (Digital arithmetic
methods); C7410D (Electronic engineering)",
keywords = "Built-in simulator; ESCHER+; Floating point numbers;
High level description; High level design; Highly
parallel implementation; Inner products calculation;
Interactive schematic entry tool; Long accumulator
chip",
thesaurus = "Circuit CAD; Digital arithmetic; Integrated logic
circuits; Logic CAD; Parallel architectures",
}
@Article{Fossmeier:1991:ALH,
author = "R. F{\"o}{\ss}meier",
title = "{Zur Axiomatisierung logarithmischer und
halblogarithmischer Zahlensysteme}. ({German}) [{On}
the axiomatization of logarithmic and semi-logarithmic
number systems]",
journal = j-COMPUTING,
volume = "46",
number = "2",
pages = "175--182",
month = jun,
year = "1991",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G99",
MRnumber = "92e:65064",
bibdate = "Tue Oct 12 16:33:42 MDT 1999",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database; OCLC Contents1st database",
abstract = "In the history of numerical analysis there have been
various approaches to gain stricter control of
numerical computation by axiomatization of
approximative arithmetic systems. In the case of
floating-point-like systems, the limitations to this
approach originate essentially in the fact that
addition is not associative. By suitably weakening the
axiomatic system of the real numbers the author arrives
at a system which can be fulfilled by approximative
arithmetic structures. Comparisons show that structures
fulfilling this system cannot be arbitrarily distant
from reasonable approximative structures. This shows
that it is possible to describe approximative
structures by approximations of the laws of the
original structure.",
acknowledgement = ack-nhfb,
affiliation = "Inst. f{\"u}r Inf., Tech. University of Munchen,
Germany",
classification = "723; 921; C4100 (Numerical analysis)",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Comput Vienna New York",
keywords = "Approximative arithmetic structures; Axiomatization;
computers, digital --- Computational Methods;
Floating-Point Arithmetic; Logarithmic; mathematical
techniques; Number systems; Number Systems; Numerical
analysis; Semi-logarithmic number systems",
language = "German",
pubcountry = "Austria",
thesaurus = "Number theory; Numerical analysis",
}
@Article{Fossmeier:1991:ALS,
author = "R. Fossmeier",
title = "On the axiomatization of logarithmic and
semi-logarithmic number systems",
journal = j-COMPUTING,
volume = "46",
number = "2",
pages = "175--182",
month = "????",
year = "1991",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In the history of numerical analysis there have been
various approaches to gain stricter control of
numerical computation by axiomatization of
approximative arithmetic systems. In the case of
floating-point-like systems, the limitations to this
approach originate essentially in the fact that
addition is not associative. By suitably weakening the
axiomatic system of the real numbers the author arrives
at a system which can be fulfilled by approximative
arithmetic structures. Comparisons show that structures
fulfilling this system cannot be arbitrarily distant
from reasonable approximative structures. This shows
that it is possible to describe approximative
structures by approximations of the laws of the
original structure.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Inf., Tech. University of Munchen, Germany",
classification = "C4100 (Numerical analysis)",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
keywords = "Approximative arithmetic structures; Axiomatization;
Logarithmic; Number systems; Numerical analysis;
Semi-logarithmic number systems",
language = "German",
pubcountry = "Austria",
thesaurus = "Number theory; Numerical analysis",
}
@Article{Foster:1991:PM,
author = "Kenneth R. Foster",
title = "Prepackaged math",
journal = j-IEEE-SPECTRUM,
volume = "28",
number = "11",
pages = "44--50",
month = nov,
year = "1991",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/6.99016",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Wed Jan 15 16:15:28 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1990.bib;
https://www.math.utah.edu/pub/tex/bib/macsyma.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "Chemical analysis; Data engineering; Data
visualization; Differential equations; Graphics; Hard
disks; manipulation; mathematical problems; mathematics
computing; matrices; matrix algebra; Packaging;
Personal communication networks; software packages;
Software packages; Workstations",
}
@InProceedings{Frougny:1991:RNN,
author = "Christiane Frougny",
title = "Representation of numbers in nonclassical numeration
systems",
crossref = "Kornerup:1991:PIS",
pages = "17--21",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Frougny.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Gal:1991:AEM,
author = "Shmuel Gal and Boris Bachelis",
title = "An Accurate Elementary Mathematical Library for the
{IEEE} Floating Point Standard",
journal = j-TOMS,
volume = "17",
number = "1",
pages = "26--45",
month = mar,
year = "1991",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D20 (65-04 65D15)",
MRnumber = "92a:65069",
bibdate = "Sun Sep 04 23:33:02 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://doi.acm.org/10.1145/103147.103151;
http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p26-gal/",
abstract = "The algorithms used by the IBM Israel Scientific
Center for the elementary mathematical library using
the IEEE standard for binary floating point arithmetic
are described. The algorithms are based on the
``accurate tables method.'' This methodology achieves
high performance and produces very accurate results. It
overcomes one of the main problems encountered in
elementary mathematical functions computations:
achieving last bit accuracy. The results obtained are
correctly rounded for almost all argument
values.\par
Our main idea in the accurate tables method is to use
``nonstandard tables,'' which are different from the
natural tables of equally spaced points in which the
rounding error prevents obtaining last bit accuracy. In
order to achieve a small error we use the following
idea: Perturb the original, equally spaced, points in
such a way that the table value (or tables values in
case we need several tables) will be very close to
numbers which can be exactly represented by the
computer (much closer than the usual double precision
representation). Thus we were able to control the error
introduced by the computer representation of real
numbers and extended the accuracy without actually
using extended precision arithmetic.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; correct rounding; floating-point
arithmetic; theory",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf G.1.2}:
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation.",
}
@InProceedings{Gamberger:1991:NAI,
author = "Dragan Gamberger",
title = "New approach to integer division in residue number
systems",
crossref = "Kornerup:1991:PIS",
pages = "84--91",
year = "1991",
DOI = "https://doi.org/10.1109/ARITH.1991.145538",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Gamberger.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10; residue arithmetic; residue number system",
summary = "A novel division algorithm that is especially
appropriate for residue number systems (RNSs) is
presented. It makes use of the fact that the
multiplicative inverse element of a divisor which is
relatively prime to system moduli can be easily
\ldots{}",
}
@Article{Gladshtein:1991:MDD,
author = "M. A. Gladshtein",
title = "A method of designing a decimal arithmetic processor",
journal = j-AUTO-CTL-COMP-SCI,
volume = "25",
number = "6",
pages = "51--56",
month = "????",
year = "1991",
CODEN = "ACCSCE",
ISSN = "0132-4160",
ISSN-L = "0146-4116",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The advantages and drawbacks of binary numeric coding
in digital computers are considered. This type of
coding has is shown to be ineffective in processing
large data arrays especially when represented in the
floating-point form. Also, the low efficiency of
conventionally employed decimal computational
procedures using the so-called corrections is noted. It
is proposed, in designing digital computers, to
renounce the principle of binary computations in favor
of decimal operations on the basis of stored addition
and multiplication tables using binary-decimal numeric
coding. A version of circuit design for a decimal
processor, algorithms and microprograms for addition
and multiplication operations are described. Advantages
inherent in the method proposed are analyzed. (10
Refs.)",
acknowledgement = ack-nhfb,
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5230 (Digital arithmetic
methods)",
fjournal = "Automatic Control and Computer Sciences",
keywords = "Addition tables; BCD code; Binary numeric coding;
Binary-decimal numeric coding; Circuit design; Decimal
arithmetic processor; decimal floating-point
arithmetic; Decimal operations; Digital computers;
Microprograms; Multiplication tables",
pubcountry = "Latvia",
remark = "English translation of: Avtomatika i Vychislitel'naya
Tekhnika",
thesaurus = "Digital arithmetic; Microprocessor chips",
}
@Article{Goldberg:1991:CWE,
author = "David Goldberg",
title = "Corrigendum: {``What Every Computer Scientist Should
Know About Floating-Point Arithmetic''}",
journal = j-COMP-SURV,
volume = "23",
number = "3",
pages = "413--413",
month = sep,
year = "1991",
CODEN = "CMSVAN",
ISSN = "0360-0300 (print), 1557-7341 (electronic)",
ISSN-L = "0360-0300",
bibdate = "Sun Sep 25 09:58:43 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compsurv.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See
\cite{Goldberg:1991:WEC,Dunham:1992:SFW,Wichmann:1992:SFW}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
}
@Article{Goldberg:1991:WEC,
author = "David Goldberg",
title = "What Every Computer Scientist Should Know About
Floating-Point Arithmetic",
journal = j-COMP-SURV,
volume = "23",
number = "1",
pages = "5--48",
month = mar,
year = "1991",
CODEN = "CMSVAN",
DOI = "https://doi.org/10.1145/103162.103163",
ISSN = "0360-0300 (print), 1557-7341 (electronic)",
ISSN-L = "0360-0300",
bibdate = "Thu Jun 19 09:40:16 MDT 2008",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also
\cite{Goldberg:1991:CWE,Dunham:1992:SFW,Wichmann:1992:SFW}.",
URL = "http://www.acm.org/pubs/toc/Abstracts/0360-0300/103163.html",
abstract = "Floating-point arithmetic is considered an esoteric
subject by many people. This is rather surprising,
because floating-point is ubiquitous in computer
systems: almost every language has a floating-point
datatype; computers from PCs to supercomputers have
floating-point accelerators; most compilers will be
called upon to compile floating-point algorithms from
time to time; and virtually every operating system must
respond to floating-point exceptions such as overflow.
This paper presents a tutorial on the aspects of
floating-point that have a direct impact on designers
of computer systems. It begins with background on
floating-point representation and rounding error,
continues with a discussion of the IEEE floating-point
standard, and concludes with examples of how computer
system builders can better support floating point.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Xerox Palo Alto Res. Center, CA, USA",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
keywords = "algorithms; compilers; computer scientist; computer
systems; denormalized number; design; exception;
floating-point; floating-point accelerators;
floating-point algorithms; floating-point datatype;
floating-point exceptions; floating-point
representation; floating-point standard; gradual
underflow; guard digit; IEEE floating-point standard;
languages; NaN; operating system; overflow; PCs;
relative error; rounding error; rounding mode;
standardization; supercomputers; ulp; underflow",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf K.1}:
Computing Milieux, THE COMPUTER INDUSTRY, Standards.
{\bf C.0}: Computer Systems Organization, GENERAL,
Instruction set design. {\bf G.1.0}: Mathematics of
Computing, NUMERICAL ANALYSIS, General, Numerical
algorithms.",
thesaurus = "digital arithmetic; roundoff errors",
}
@TechReport{Golubev:1991:FPM,
author = "Yu. F. Golubev and I. A. Seregin and R. Z.
Kha{\u\i}rullin",
title = "The floating point method in problems of the
optimization of motion during the descent of a
spacecraft into the atmosphere. ({Russian})",
type = "{Inst. Prikl. Mat.} Preprint",
number = "50",
institution = "Akad. Nauk SSSR",
pages = "28",
year = "1991",
MRclass = "65K10 (49N55 70-08 70Q05)",
MRnumber = "166 839",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Gonnella:1991:ACF,
author = "J. Gonnella",
title = "The application of core functions to residue number
systems",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "39",
number = "1",
pages = "69--75",
month = jan,
year = "1991",
CODEN = "ITPRED",
DOI = "https://doi.org/10.1109/78.80766",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2655",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
keywords = "residue arithmetic; residue number system",
summary = "A theory of core functions is presented, and the
application of this theory to the difficult residue
number system (RNS) operations is described. Potential
applications for special-purpose core-based RNS
processors include adaptive array processing,
\ldots{}",
}
@Article{Gotze:1991:SRD,
author = "J. G{\"o}tze and U. Schwiegelshohn",
title = "A Square Root and Division Free {Givens} Rotation for
Solving Least Squares Problems on Systolic Arrays",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "12",
number = "4",
pages = "800--807",
month = jul,
year = "1991",
CODEN = "SIJCD4",
ISSN = "0196-5204",
MRclass = "65F20 (65F25)",
MRnumber = "92a:65125",
bibdate = "Sat Oct 24 13:20:45 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
}
@Article{Grcar:1991:IAS,
author = "Joe Grcar",
title = "{IEEE} Arithmetic Stinks",
journal = j-NA-DIGEST,
volume = "91",
number = "33",
day = "18",
month = aug,
year = "1991",
bibdate = "Thu Aug 23 06:22:13 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See rebuttal \cite{Demmel:1991:OIA}.",
URL = "http://www.netlib.org/na-digest/91/v91n33",
acknowledgement = ack-nhfb,
fjournal = "NA Digest",
}
@Article{Griffin:1991:REA,
author = "C. Griffin and P. Rao and F. Taylor",
title = "Roundoff error analysis of the discrete {Wigner}
distribution using fixed-point arithmetic",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "39",
number = "9",
pages = "2096--2098",
month = sep,
year = "1991",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "The issue of roundoff noise effects in the
implementation of the discrete Wigner distribution
using fixed-point arithmetic is addressed. The
sign-magnitude number representation is assumed
throughout the analysis. The measure of roundoff noise
\ldots{}",
}
@Article{Gusev:1991:NCS,
author = "A. V. Gusev and I. V. Melezhnikov",
title = "Noise in a Constant-Current {SQUID} with a Floating
Operating Point",
journal = j-TELECOMM-RADIO-ENG,
volume = "46",
number = "8",
pages = "125--127",
year = "1991",
CODEN = "TCREAG",
ISSN = "0040-2508 (print), 1943-6009 (electronic)",
ISSN-L = "0040-2508",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Telecommunications and Radio Engineering",
}
@InProceedings{Guyot:1991:OAV,
author = "Alain Guyot",
title = "{OCAPI}: Architecture of a {VLSI} Coprocessor for the
{GCD} and the Extended {GCD} of Large Numbers",
crossref = "Kornerup:1991:PIS",
pages = "226--231",
year = "1991",
bibdate = "Sat Nov 17 08:46:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Guyot.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Hamza:1991:MBD,
author = "K. M. Hamza and M. A. H. Abdul-Karim",
title = "Microprocessor Based Direct Square Root Extractor",
journal = "Modelling",
volume = "34",
number = "1",
pages = "45--48",
month = "????",
year = "1991",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Heidtmann:1991:ASA,
author = "K. D. Heidtmann",
title = "Arithmetic spectrum applied to fault detection for
combinational networks",
journal = j-IEEE-TRANS-COMPUT,
volume = "40",
number = "3",
pages = "320--324",
month = mar,
year = "1991",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.76409",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 12:52:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=76409",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@MastersThesis{Holmes:1991:FSD,
author = "Ian Holmes",
title = "A feasibility study into the design of a 64-bit
floating point processor",
type = "Thesis ({M.Sc. in Electronics})",
school = "University of Southampton, Department of Electronics
and Computer Science",
address = "Southampton, UK",
year = "1991",
bibdate = "Thu May 09 08:35:32 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Horiguchi:1991:HFN,
author = "Hiroshi Horiguchi and Tsutomu Tayama and Kazuaki
Kajitori",
title = "{Hamada} Floating-Point Numbers and Real Numbers",
journal = j-ADV-SOFT-SCI-TECH,
volume = "2",
number = "??",
pages = "123--??",
year = "1991",
ISSN = "1044-7997",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Advances in software science and technology",
}
@Article{Horiguchi:1991:PEP,
author = "Susumu Horiguchi and Takeo Nakada",
title = "Performance Evaluation of Parallel Fast {Fourier}
Transform on a Multiprocessor Workstation",
journal = j-J-PAR-DIST-COMP,
volume = "12",
number = "2",
pages = "158--163",
month = jun,
year = "1991",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 17:13:17 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C4190 (Other numerical methods); C4240 (Programming
and algorithm theory); C5440 (Multiprocessor systems
and techniques)",
corpsource = "Department of Inf. Sci., Tohoku University, Sendai,
Japan",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "algorithms; cache protocols; fast Fourier transform;
fast Fourier transforms; FFT; floating-; multiprocess
operating system; multiprocessing systems;
multiprocessor workstation; multithread operating
system; operating systems; parallel; parallel FFT;
performance; performance evaluation; point
coprocessors",
treatment = "P Practical",
}
@Misc{Hough:1991:TBC,
author = "David G. Hough and Vern Paxson",
title = "Testbase: base conversion test program",
howpublished = "World-Wide Web document",
day = "20",
month = jul,
year = "1991",
bibdate = "Wed May 26 07:22:52 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Paxson:1991:PTI}.",
URL = "http://www.netlib.org/fp/testbase",
acknowledgement = ack-nhfb,
keywords = "floating-point testing",
}
@InProceedings{Hsiao:1991:CHA,
author = "Shen-Fu Hsiao and Jean-Marc Delosme",
title = "The {CORDIC Householder} algorithm",
crossref = "Kornerup:1991:PIS",
pages = "256--263",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Hsiao.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Hu:1991:ERC,
author = "X. Hu and R. G. Harber and S. C. Bass",
title = "Expanding the Range of Convergence of the {CORDIC}
Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "40",
number = "1",
pages = "13--21",
month = jan,
year = "1991",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.67316",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 08 00:50:12 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Hui:1991:DFD,
author = "S. Hui and D. P. Brown",
booktitle = "{IEEE} Pacific Rim Conference on Communications,
Computers and Signal Processing, 9--10 May 1991",
title = "Digital filter design with a combination of fixed
point and residue number systems",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "331--334",
year = "1991",
CODEN = "????",
DOI = "https://doi.org/10.1109/PACRIM.1991.160746",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A new design method using a combination of fixed-point
and RNS (residue number system) arithmetics is
presented. It is proven that an IIR digital filter can
be efficiently implemented in a system that combines
both fixed-point and RNS arithmetics. \ldots{}",
}
@InProceedings{Hull:1991:SVP,
author = "T. E. Hull and M. S. Cohen and C. B. Hall",
title = "Specifications for a variable-precision arithmetic
coprocessor",
crossref = "Kornerup:1991:PIS",
pages = "127--131",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Hull.pdf",
abstract = "The authors have been developing a programming system
intended to be especially convenient for scientific
computing. Its main features are variable precision
(decimal) floating-point arithmetic and convenient
exception handling. The software implementation of the
system has evolved over a number of years, and a
partial hardware implementation of the arithmetic
itself was constructed and used during the early stages
of the project. Based on this experience, the authors
have developed a set of specifications for an
arithmetic coprocessor to support such a system. These
specifications are described. An outline of the
language features and how they can be used is also
provided, to help justify the particular choice of
coprocessor specifications. The authors also indicate
what other hardware features would be most helpful to
the systems programmer, especially for implementation
of the exception handling.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Toronto University,
Ont., Canada",
classification = "B1265B (Logic circuits); B1265F (Microprocessors and
microcomputers); B2570 (Semiconductor integrated
circuits); C5120 (Logic and switching circuits); C5130
(Microprocessor chips); C5230 (Digital arithmetic
methods)",
keywords = "ARITH-10; decimal floating-point arithmetic; Exception
handling; Floating-point arithmetic; Programming
system; Scientific computing; Variable-precision
arithmetic coprocessor",
thesaurus = "Digital arithmetic; Logic circuits; Microprocessor
chips; Satellite computers",
}
@Book{Ince:1991:SQR,
author = "D. (Darrel) Ince",
title = "Software quality and reliability tools and methods",
publisher = "Chapman and Hall",
address = "London, UK",
pages = "178",
year = "1991",
ISBN = "0-442-31314-4, 0-412-37810-8",
ISBN-13 = "978-0-442-31314-2, 978-0-412-37810-2",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Unicom applied information technology reports; [6]",
acknowledgement = ack-nhfb,
keywords = "Computer software --- Quality control.; Computer
software --- Reliability.; Software --- Quality
control",
remark = "Aspects of path testing and mutation testing / M.R.
Woodward --- Quality-- an integrated approach / A.
Smith --- Quality management and software engineering /
R. Hailstone --- The role of verification and
validation tools in the production of critical software
/ J.T. Webb --- The real importance of software quality
and the role of quality systems / A. Voss --- Software
testing tools / E. Fergus \ldots{} [et al.] --- FPV-- a
floating point validation package / J. Du Croz ---
Building in quality through the use of software tools /
P.A.V. Hall --- Software requirements analysis, formal
methods and software prototyping / D. Ince ---
Increasing software quality by objectives and residual
fault prognosis / K. Moller --- Towards a software
quality control environment / M. Adam \ldots{} [et al.]
--- Expert system software quality problems / S. Ronchi
and M. Martignano --- Quality assurance management for
real-time software systems: the experience of the
Spanish Civil Aviation Administration / J.P. Buendia,
C. Bravo --- The PRX/A software reliability
investigation / A.E.J. van Delft.",
}
@InCollection{Iri:1991:HAD,
author = "M. Iri",
editor = "A. Griewank and G. F. Corliss",
booktitle = "Automatic Differentiation of Algorithms: Theory,
Implementation, and Application",
title = "History of automatic differentiation and rounding
error estimation",
crossref = "Griewank:1991:ADA",
pages = "3--16",
year = "1991",
bibdate = "Thu May 27 07:45:02 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Jain:1991:CSN,
author = "Suneel Jain",
title = "Circular scheduling: a new technique to perform
software pipelining",
journal = j-SIGPLAN,
volume = "26",
number = "6",
pages = "219--228",
month = jun,
year = "1991",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:16:07 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/proceedings/pldi/113445/index.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/pldi/113445/p219-jain/",
abstract = "With the advent of deeply pipelined RISC processors,
static instruction scheduling by the compiler has
become extremely important to obtain high processor
performance. This is especially true for floating point
code. The author suggests using a new algorithm called
circular scheduling to perform software pipelining.
Software pipelining has previously been investigated
mostly for VLIW architectures. The algorithm described
is shown to be quite effective for a scalar
architecture. Register renaming, an idea that
originates from dynamic instruction scheduling, is used
in conjunction with this algorithm to augment its
performance. The techniques described here have been
implemented as part of a commercial, production quality
optimizing compiler for a RISC architecture. The
resulting performance improvement has verified the
feasibility and practicality of the techniques.",
acknowledgement = ack-nhfb,
affiliation = "MIPS Comput. Syst. Inc., Sunnyvale, CA, USA",
classification = "C5220 (Computer architecture); C6110 (Systems
analysis and programming); C6150C (Compilers,
interpreters and other processors); C6150J (Operating
systems)",
confdate = "26-28 June 1991",
conflocation = "Toronto, Ont., Canada",
confsponsor = "ACM",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "algorithms; Circular scheduling; Deeply pipelined RISC
processors; Dynamic instruction scheduling;
experimentation; performance; Production quality
optimizing compiler; RISC architecture; Scalar
architecture; Software pipelining; Static instruction
scheduling; VLIW architectures",
subject = "{\bf D.3.4} Software, PROGRAMMING LANGUAGES,
Processors, Compilers. {\bf D.3.4} Software,
PROGRAMMING LANGUAGES, Processors, Optimization.",
thesaurus = "Parallel programming; Pipeline processing; Program
compilers; Reduced instruction set computing;
Scheduling",
}
@InProceedings{Jain:1991:NRS,
author = "V. K. Jain and G. E. Perez and J. M. Wills",
title = "Novel reciprocal and square-root {VLSI} cell:
architecture and application to signal processing",
crossref = "IEEE:1991:VCA",
volume = "2",
pages = "1201--1204",
year = "1991",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
summary = "A novel high-speed cell, capable of performing a
square-root or a reciprocal function in two clock
cycles, is presented. Its performance signifies an
estimated three-fold increase in speed over existing
approaches. Furthermore, since both functions
\ldots{}",
}
@TechReport{Kahan:1991:APL,
author = "William Kahan and J. W. Thomas",
title = "Augmenting a Programming Language with Complex
Arithmetic",
number = "NCEG/91-039, UCB/CSD 91/667",
institution = inst-BERKELEY-CS,
address = inst-BERKELEY-CS:adr,
pages = "8",
day = "15",
month = nov,
year = "1991",
bibdate = "Mon Dec 26 21:13:51 GMT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Manuscript",
acknowledgement = ack-nhfb,
}
@Article{Kahan:1991:ARL,
author = "W. Kahan",
title = "Analysis and Refutation of the {LCAS}",
journal = j-SIGNUM,
volume = "26",
number = "3",
pages = "2--15",
month = jul,
year = "1991",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Fri Jan 5 07:58:42 MST 1996",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/signum.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "LCAS (Language Compatible Arithmetic Standard)",
}
@InProceedings{Kantabutra:1991:DOC,
author = "Vitit Kantabutra",
title = "Designing optimum carry-skip adders",
crossref = "Kornerup:1991:PIS",
pages = "146--153",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Kantabutra.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Kim:1991:ERB,
author = "Jin Yul Kim and Kyu Ho Park and Hwang Soo Lee",
title = "Efficient residue-to-binary conversion technique with
rounding error compensation",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "38",
number = "3",
pages = "315--317",
month = mar,
year = "1991",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "An improved scaled-decoding technique (defined as
residue-to-binary conversion of which outputs are
scaled by a constant) for hardware implementations in
the residue number system (RNS) is presented. The
technique is based on the Chinese remainder \ldots{}",
}
@InProceedings{Kim:1991:NIC,
author = "S. W. Kim and T. Stouraitis",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, 11--14 June 1991",
title = "New implementations of converters for the residue and
quadratic residue number system",
volume = "5",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2959--2962",
year = "1991",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1991.176166",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Full adder (FA)-based converters are proposed for
efficiently performing complex number calculations. The
basic idea is to use FA arrays to decompose 2 i terms
into 2 j terms, where j{$<$}i, by modulo arithmetic.
\ldots{}",
}
@Book{Klatte:1991:PSB,
author = "R. Klatte and U. Kulisch and M. Neaga and D. Ratz and
Ch. Ullrich",
title = "{PASCAL-XSC: Sprachbeschreibung mit Beispielen}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 345",
year = "1991",
ISBN = "0-387-53714-7",
ISBN-13 = "978-0-387-53714-6",
LCCN = "QA76.73.P2 P42 1991",
bibdate = "Mon Dec 18 09:37:18 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "English translation is available as
\cite{Klatte:1991:PXP}.",
acknowledgement = ack-nhfb,
}
@Book{Klatte:1991:PXP,
author = "R. Klatte and U. Kulisch and M. Neaga and D. Ratz and
Ch. Ullrich",
title = "{PASCAL-XSC}: {A PASCAL} Extension for Scientific
Computation",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 344",
year = "1991",
ISBN = "0-387-55137-9 (New York), 3-540-55137-9 (Berlin)",
ISBN-13 = "978-0-387-55137-1 (New York), 978-3-540-55137-9
(Berlin)",
LCCN = "QA76.73.P2 P4213 1992",
bibdate = "Thu Nov 8 14:50:35 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "English translation of \cite{Klatte:1991:PSB}.",
price = "DM64.00",
acknowledgement = ack-nhfb,
referred = "[Corl91a].",
}
@InProceedings{Knofel:1991:FHU,
author = "Andreas Kn{\"o}fel",
title = "Fast hardware units for the computation of accurate
dot products",
crossref = "Kornerup:1991:PIS",
pages = "70--74",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Knofel.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@InProceedings{Knowles:1991:APD,
author = "S. Knowles",
title = "Arithmetic Processor Design for the {T9000}
Transputer",
crossref = "SPIE:1991:PSI",
pages = "230--243",
year = "1991",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Koc:1991:FAG,
author = "Cetin K. Koc and Sarath N. Arachchige",
title = "A fast algorithm for {Gaussian} elimination over
{GF(2)} and its implementation on the {GAPP}",
journal = j-J-PAR-DIST-COMP,
volume = "13",
number = "1",
pages = "118--122",
day = "1",
month = sep,
year = "1991",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ of Houston",
affiliationaddress = "Houston, TX, USA",
classification = "722; 723; 921; C4140 (Linear algebra); C4240
(Programming and algorithm theory)",
corpsource = "Department of Electr. Eng., Houston University, TX,
USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "1s location; Algorithms; algorithms; arithmetic
parallel processor; binary matrix; binary search;
Binary search technique; bit operations; bit-array;
columns; computational complexity; Computer
Programming; Computer Systems, Digital--Parallel
Processing; Galois fields; GAPP; Gaussian elimination;
geometric; Geometric arithmetic parallel processors;
GF(2); Large binary matrices; Mathematical
Techniques--Matrix Algebra; matrix algebra; ones
location; parallel; Triangularization; triangularize;
vertical memory",
treatment = "T Theoretical or Mathematical",
}
@Article{Koc:1991:IAM,
author = "{\c{C}}etin K. Ko{\c{c}}",
title = "An improved algorithm for mixed-radix conversion of
residue numbers",
journal = j-COMPUT-MATH-APPL,
volume = "22",
number = "8",
pages = "63--71",
month = "????",
year = "1991",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:11:04 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/089812219190014U",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@MastersThesis{Kohprasert:1991:FAC,
author = "Teera Kohprasert",
title = "32-bit floating-point arithmetic coprocessor design
using {VHDL}",
type = "Thesis ({M.S.})",
school = "Florida Institute of Technology",
address = "Melbourne, FL, USA",
pages = "xiv + 456",
year = "1991",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units --- Design and
construction.; VHDL (Computer hardware description
language).",
}
@Article{Kostopoulos:1991:ACB,
author = "D. K. Kostopoulos",
title = "An Algorithm for the Computation of Binary
Logarithms",
journal = j-IEEE-TRANS-COMPUT,
volume = "40",
number = "11",
pages = "1267--1270",
month = nov,
year = "1991",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.102831",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Kramer:1991:EFA,
author = "David Kramer and Isaac D. Scherson",
title = "The effect of {FPU} architecture on a dynamic
precision algorithm for the solution of differential
equations",
type = "Technical report",
number = "91-73",
institution = "Information and Computer Science, University of
California, Irvine",
address = "Irvine, CA, USA",
pages = "18",
year = "1991",
LCCN = "Z699 .C3 no. 91-73",
bibdate = "Fri Jan 5 11:51:46 MST 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kuhnel:1991:OPS,
author = "Lars K{\"u}hnel",
title = "Optimal purely systolic addition",
crossref = "Kornerup:1991:PIS",
pages = "172--179",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Kuhnel.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Kurokawa:1991:CGU,
author = "T. Kurokawa and T. Mizukoshi",
title = "Computer graphics using logarithmic number systems",
journal = "IEICE Transactions",
volume = "E74",
number = "2",
pages = "447--451",
month = feb,
year = "1991",
ISSN = "0917-1673",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Logarithmic arithmetic (LA) is a very fast
computational method for real numbers. Its precision is
better than a floating point arithmetic of equivalent
word length and range. This paper shows a method to use
LA in computer graphics-picture generation of almost
any kind. Various experiments are done-from curve
drawing to 3D image generation. The results are all
excellent for quality and speed.",
acknowledgement = ack-nhfb,
affiliation = "Department of Ind. Eng., Aichi Inst. of Technol.,
Toyota, Japan",
classification = "C5230 (Digital arithmetic methods); C6130B (Graphics
techniques)",
keywords = "3D image generation; Computer graphics; Curve drawing;
Fast computational method for real numbers; Logarithmic
arithmetic; Logarithmic number systems; Picture
generation; Precision; Word length",
pubcountry = "Japan",
thesaurus = "Computer graphics; Digital arithmetic",
}
@Article{Lai:1991:HNS,
author = "F.-S. Lai and C.-F. E. Wu",
title = "A hybrid number system processor with geometric and
complex arithmetic capabilities",
journal = j-IEEE-TRANS-COMPUT,
volume = "40",
number = "8",
pages = "952--962",
month = aug,
year = "1991",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.83639",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 12:52:23 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=83639",
abstract = "The architecture, design, and performance of a hybrid
number system processor are described. The processor
performs multiplication, division, square root, and
square in the logarithmic number system (LNS) domain.
However, the input, output, addition, and subtraction
are all executed in the 32-b IEEE standard
floating-point number system. With the LNS multiplier
and pipelined architecture, the processor is able to
perform the geometric and complex arithmetic very
effectively. The processor is also shown to compare
well to an existing 32-b floating-point DSP (digital
signal processor) chip. For the same level of CMOS
technology, the performance ratios between the hybrid
number system and the floating-point processor are
shown to be 6.4:1 and 8:1 for division and square root,
respectively; for the complex FFT (fast Fourier
transform) algorithm, the ratio is around 2:1. (27
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
ajournal = "IEEE Trans. Comput.",
classification = "C5230 (Digital arithmetic methods)",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Complex arithmetic; Division; Floating-point number
system; Geometric; Hybrid number system processor;
Logarithmic number system; Multiplication; Square;
Square root",
thesaurus = "Digital arithmetic",
}
@Article{Lee:1991:FPPa,
author = "Roland L. Lee and Alex Y. Kwok and Fay{\'e} A.
Briggs",
title = "The Floating Point Performance of a superscalar
{SPARC} Processor",
journal = j-COMP-ARCH-NEWS,
volume = "19",
number = "2",
pages = "28--37",
month = apr,
year = "1991",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 12 09:40:40 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Co-published in {\em Operating Systems Review}, {\bf
28}(3S).",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{Lee:1991:FPPb,
author = "Roland L. Lee and Alex Y. Kwok and Fay{\'e} A.
Briggs",
title = "The floating-point performance of a superscalar
{SPARC} processor",
journal = j-OPER-SYS-REV,
volume = "25",
number = "3S",
pages = "28--37",
month = apr,
year = "1991",
CODEN = "OSRED8",
ISSN = "0163-5980 (print), 1943-586X (electronic)",
ISSN-L = "0163-5980",
bibdate = "Sat Aug 26 15:24:15 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Operating Systems Review",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J597",
}
@Article{Lee:1991:FPPc,
author = "Roland L. Lee and Alex Y. Kwok and Fay{\'e} A.
Briggs",
title = "The Floating-Point Performance of a Superscalar
{SPARC} Processor",
journal = j-SIGPLAN,
volume = "26",
number = "4",
pages = "28--37",
month = apr,
year = "1991",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The floating point performance of superscalar SPARC
processors is evaluated based on empirical data from 12
benchmarks. This evaluation is done in the context of
two software instruction scheduling optimizations: loop
unrolling and software pipelining, and for three
machine models: 1-scalar, 2-scalar and 4-scalar. The
authors also consider the effect of the memory system
on the performance improvements. Superscalar hardware
alone exhibit little performance improvement without
software optimization. Of the two scheduling methods,
software pipelining more effectively takes advantage of
increased hardware parallelism, and achieves near
optimal speedup on the 4-scalar machine model. The
performance of loop unrolling is restricted by the
limited number of floating point registers in the SPARC
architecture. The best performance level is obtained by
applying both optimization techniques. A superscalar
SPARC processor can provide improved floating point
performance but with significant software and hardware
development costs.",
acknowledgement = ack-nhfb,
affiliation = "Sun Microsyst. Inc., Mountain View, CA, USA",
classification = "C5220 (Computer architecture); C5470 (Performance
evaluation and testing)",
confdate = "8-11 April 1991",
conflocation = "Santa Clara, CA, USA",
confsponsor = "IEEE; ACM",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "Benchmarks; Development costs; Floating point
performance; Floating point registers; Hardware
parallelism; Loop unrolling; Memory system; N-scalar
machine models; Optimal speedup; Software instruction
scheduling optimizations; Software pipelining; SPARC
architecture; Superscalar SPARC processor",
thesaurus = "Optimisation; Parallel architectures; Performance
evaluation; Pipeline processing; Scheduling",
}
@InProceedings{Lee:1991:SCF,
author = "Jeong-A. Lee and Tom{\'a}s Lang",
title = "{SVD} by constant-factor-redundant-{CORDIC}",
crossref = "Kornerup:1991:PIS",
pages = "264--271",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Lee.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Letcher:1991:GNC,
author = "John H. Letcher",
title = "Getting numeric coprocessors up to speed",
journal = j-DDJ,
volume = "16",
number = "5",
pages = "36, 38, 40, 42",
month = may,
year = "1991",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Tue Sep 10 09:11:02 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
UnCover database",
abstract = "Memory-mapped math coprocessors can boost performance
without sacrificing compatibility.",
acknowledgement = ack-nhfb,
affiliation = "Tulsa University, OK, USA",
classification = "C5130 (Microprocessor chips); C5230 (Digital
arithmetic methods)",
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "80*86 Integer CPU; Floating point coprocessors;
Numeric coprocessors; Processing speeds",
thesaurus = "Digital arithmetic; Microprocessor chips; Satellite
computers",
}
@Article{Lo:1991:BHS,
author = "H.-Y. Lo and T. C. Yang",
title = "Balanced high-speed residue number {VLSI} multiplier
with error detection",
journal = "Circuits, Devices and Systems, IEE Proceedings G",
volume = "138",
number = "3",
pages = "421--423",
month = jun,
year = "1991",
CODEN = "????",
DOI = "https://doi.org/10.1109/78.80821",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=6544",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A balanced residue number VLSI multiplier is proposed
which eliminates the extra delay for an unbalanced
residue multiplier. The number of adding stages used in
the VLSI multiplier is reduced from three to two. The
authors also describe how \ldots{}",
}
@Article{Lyashenko:1991:PAR,
author = "N. N. Lyashenko and M. S. Nikulin",
title = "Probability Analysis of Round-Off Errors in
Floating-Point Arithmetic",
journal = j-THEORY-PROBAB-APPL,
volume = "35",
number = "1",
pages = "66--74",
month = "????",
year = "1991",
CODEN = "TPRBAU",
DOI = "https://doi.org/10.1137/1135006",
ISSN = "0040-585X (print), 1095-7219 (electronic)",
ISSN-L = "0040-585X",
bibdate = "Tue Apr 1 10:40:31 MDT 2014",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/TVP/35/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/theoryprobabappl.bib",
acknowledgement = ack-nhfb,
fjournal = "Theory of Probability and its Applications",
journal-URL = "http://epubs.siam.org/tvp",
onlinedate = "January 1991",
}
@InProceedings{Lynch:1991:RCA,
author = "Tom Lynch and Earl {Swartzlander, Jr.}",
title = "The redundant cell adder",
crossref = "Kornerup:1991:PIS",
pages = "165--170",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Lynch.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@InProceedings{Lyons:1991:FMF,
author = "Ken Lyons",
title = "A fast method for finding an integer square root",
crossref = "Koopman:1991:PST",
pages = "27--30",
year = "1991",
bibdate = "Tue May 4 05:57:50 MDT 1999",
bibsource = "http://www.acm.org/pubs/toc/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/plan/259965/p27-lyons/",
acknowledgement = ack-nhfb,
}
@InProceedings{MacKenzie:1991:FMS,
author = "Donald MacKenzie",
title = "Formal methods and the sociology of proof",
crossref = "Morris:1991:RWP",
pages = "115--124",
year = "1991",
DOI = "https://doi.org/10.1007/978-1-4471-3756-6_6",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The paper begins by asking whether a sociology of
mathematical knowledge is possible. Having answered in
the affirmative (drawing examples from the history of
mathematics), it goes on to discuss the development of
a similar analysis of the mathematical aspects of
computer science. A brief vignette is presented: the
processes of negotiation of the IEEE floating-point
arithmetic specifications. Then the discussion moves on
to the verification of software and hardware. If the
sociology of mathematics is correct, then formal proofs
can be seen as social, not just in the processes of
their acceptance, but also in their internal structure.
Placed in the context of pressure for formal
verification of safety-critical and security-critical
systems, this argument led the author and colleagues to
the prediction that litigation involving the nature of
mathematical proof was bound to occur. That prediction
has now been borne out.",
acknowledgement = ack-nhfb,
affiliation = "Department of Sociol., Edinburgh University, UK",
classification = "C0230 (Economic, social and political aspects);
C4240 (Programming and algorithm theory); C6110B
(Software engineering techniques)",
keywords = "Computer science; Formal proofs; Formal verification;
IEEE floating-point arithmetic specifications;
Litigation; Mathematical aspects; Mathematical
knowledge; Negotiation; Safety-critical systems;
Security-critical systems; Sociology of proof;
Verification",
thesaurus = "Economic and sociologic effects; Formal verification;
Safety; Security of data; Software reliability; Theorem
proving",
}
@Article{MacKenzie:1991:IAL,
author = "Donald MacKenzie",
title = "The Influence of the {Los Alamos} and {Livermore
National Laboratories} on the Development of
Supercomputing",
journal = j-ANN-HIST-COMPUT,
volume = "13",
number = "2",
pages = "179--201",
month = apr # "\slash " # jun,
year = "1991",
CODEN = "AHCOE5",
ISSN = "0164-1239",
bibdate = "Fri Nov 1 15:29:15 MST 2002",
bibsource = "Compendex database;
ftp://ftp.ira.uka.de/pub/bibliography/Parallel/super.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
Contents1st database",
URL = "http://dlib.computer.org/an/books/an1991/pdf/a2179.pdf;
http://www.computer.org/annals/an1991/a2179abs.htm",
acknowledgement = ack-nhfb,
fjournal = "Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
remark = "The author has this remark about Metropolis on page
194: ``What are the architectural consequences of this
kind of influence? [of Los Alamos on computer design]
One apparent in Stretch is that machine's noisy mode
facility (Los Alamos interviews). The inspiration of
these was Los Alamos Nicholas Metropolis, who in the
1950s developed what he called significance arithmetic:
the attempt to determine the consequences, for the
reliability of results, of errors caused by the need to
represent numbers by words of finite length. In noisy
mode the effects of truncation were handled differently
from in normal operation so as to allow errors caused
by truncation to be detected.
By definition of ordinary normalized [floating-point]
operations, numbers are frequently extended on the
right by attaching zeros. During addition the $n$-digit
operand that is not preshifted is extended with n
zeros, so as to provide the extra positions to which
the preshifted operand can be added. Any operand or
result that is shifted left to be normalized requires a
corresponding number of zeros to be shifted in at the
right. Both sets of zeros tend to produce numbers
smaller in absolute value than they would have been if
more digits had been carried. In the noisy mode these
numbers are simply extended with 1s instead of zeros
(1s in a binary machine, 9s in a decimal machine). Now
all numbers tend to be too large in absolute value. The
true value, if there had been no significance loss,
should lie between these two extremes. Hence, two runs,
one made without and one made with the noisy mode,
should show differences in result that indicate which
digits may have been affected by significance loss
(Buchholz 1962, p. 102).''
See \cite{Buchholz:1962:PCS} for more information about
the Stretch noisy mode.",
}
@Book{MacKenzie:1991:NAC,
author = "Donald MacKenzie and Edinburgh Pict",
title = "Negotiating arithmetic, construction proof: the
sociology of mathematics and information technology",
volume = "38",
publisher = "Research Centre for Social Sciences, University of
Edinburgh",
address = "Edinburgh",
pages = "27",
year = "1991",
ISBN = "1-872287-42-5",
ISBN-13 = "978-1-872287-42-3",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Edinburgh PICT working paper",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic; Computer security; Floating-point
arithmetic",
}
@Article{Marcus:1991:HSR,
author = "Marvin Marcus and Markus Sandy",
title = "{Hadamard} Square Roots",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "12",
number = "1",
pages = "49--69",
month = jan,
year = "1991",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A57 (15A18 15A48 15A52 47B15 60H25)",
MRnumber = "92a:15027",
MRreviewer = "Zdzis{\l}aw W. Trzaska",
bibdate = "Tue Jan 21 08:54:30 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@InProceedings{Markstein:1991:WFF,
author = "V. Markstein and P. Markstein and T. Nguyen and S.
Poole",
title = "Wide Format Floating-Point Math Libraries",
crossref = "IEEE:1991:PSA",
pages = "130--138",
year = "1991",
DOI = "https://doi.org/10.1145/125826.125903",
bibdate = "Wed Dec 13 18:34:51 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors present the performance and accuracy
evaluations of eleven transcendental functions found in
64- and 128-bit floating-point formats in math
libraries on the Cray Y-MP, the IBM 3090E/VF, the
Convex C-240, the Hewlett--Packard 9000/720, and the
IBM System/6000. Both architecture and algorithms are
shown to impact the results.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "ISQUARE, Inc., Austin, TX, USA",
classification = "C5230 (Digital arithmetic methods); C5470
(Performance evaluation and testing); C7310
(Mathematics)",
confdate = "18-22 Nov. 1991",
conflocation = "Albuquerque, NM, USA",
confsponsor = "IEEE; ACM",
keywords = "128 Bit; 64 Bit; Accuracy evaluations; Convex C-240;
Cray Y-MP; Floating-point formats; Hewlett--Packard
9000/720; IBM 3090E/VF; IBM System/6000; Math
libraries; Performance; Transcendental functions; Wide
format floating point math libraries",
numericalindex = "Word length 6.4E+01 bit; Word length 1.28E+02 bit",
thesaurus = "Digital arithmetic; Mathematics computing; Parallel
processing; Performance evaluation",
}
@Article{McQuillan:1991:HPV,
author = "S. E. McQuillan and J. V. McCanny and R. F. Woods",
title = "High performance {VLSI} architecture for division and
square root",
journal = j-ELECT-LETTERS,
volume = "27",
number = "1",
pages = "19--21",
day = "3",
month = jan,
year = "1991",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
summary = "A novel high performance bit parallel architecture to
perform square root and division is proposed. Relevant
VLSI design issues have been addressed. By employing
redundant arithmetic and a semisystolic schedule, the
throughput has been made \ldots{}",
}
@InProceedings{McQuillan:1991:VAM,
author = "S. E. McQuillan and J. V. McCanny",
booktitle = "1991 International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP-91, 14--17} April 1991",
title = "A {VLSI} architecture for multiplication, division and
square root",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1205--1208",
year = "1991",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "A high-performance VLSI architecture to perform
combined multiply-accumulate, divide, and square root
operations is proposed. The circuit is highly regular,
requires only minimal control, and can be reconfigured
for every cycle. The execution time \ldots{}",
}
@PhdThesis{Mehrez:1991:AVP,
author = "Habib Mehrez",
title = "Des architectures {VLSI} pipelin{\'e}s pour les
algorithmes num{\'e}riques {\`a} flots de donn{\'e}es
en repr{\'e}sentations arithm{\'e}tiques virgule fixe
et virgule flottante. ({French}) [{Pipelined VLSI}
architectures for numerical algorithms for numerical
data in fixed- and floating-point arithmetic]",
type = "Th{\`e}se Doctoral",
school = "Sciences Appliqu{\'e}es, Universit{\'e} Paris 6",
address = "Paris, France",
year = "1991",
bibdate = "Thu May 09 10:10:32 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Sous la direction de Alain Greiner.",
abstract = "Dans cette th{\`e}se, on se propose d'exposer
certaines reflexions et contributions dans le
d{\'e}veloppement et la recherche en architectures VLSI
pour l'implantation des algorithmes de traitement
num{\'e}rique {\`a} flots des donn{\'e}es. On exposera
en particulier une m{\'e}thodologie g{\'e}n{\'e}rale
d'implantation concr{\'e}tis{\'e}e par des {\'e}tudes
et des r{\'e}alisations des architectures
sp{\'e}cifiques {\`a} la transform{\'e}e de Fourier
rapide (TFR ou FFT). Ces architectures concernent aussi
bien des traitements arithm{\'e}tiques en virgule fixe
qu'en virgule flottante et seront de type pipelin{\'e}s
serie systolique. Des propositions d'implantation des
op{\'e}rateurs arithm{\'e}tiques de base et des chemins
des donn{\'e}es seront developp{\'e}es ainsi que les
{\'e}valuations des performances et de leur
complexit{\'e} correspondantes. Il sera discut{\'e} des
facteurs de classification et d'interactions entre les
aspects fonctionnels et algorithmiques, les aspects
structurels et architecturaux et finalement les aspects
li{\'e}s aux implantations VLSI. Ces derniers aspects
concernent notamment les compromis et les choix
logiques, {\'e}lectriques et topologiques. La
m{\'e}thode de conception est bas{\'e}e sur
l'utilisation d'une biblioth{\`e}que de cellules
standards qui inclut la technique LSSD, de test et
testabilit{\'e}, au moment de la conception des
circuits VLSI.",
acknowledgement = ack-nhfb,
language = "French",
}
@InProceedings{Mehta:1991:HSM,
author = "Mayur Mehta and Vijay Parmar and Earl {Swartzlander,
Jr.}",
title = "High-speed multiplier design using multi-input counter
and compressor circuits",
crossref = "Kornerup:1991:PIS",
pages = "43--50",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Mehta.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Manual{Microsoft:1991:MCC,
author = "{Microsoft Corporation}",
title = "{Microsoft C, C++}: version 7.0: programming
techniques for {MS-DOS} and {Windows} operating
systems",
organization = "Microsoft Corp.",
address = "Redmond, WA, USA",
pages = "xix + 323",
year = "1991",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Microsoft C++.; Microsoft C.; MS - DOS (Computer
file); Windows (Computer programs)",
remark = "Improving program performance: optimizing your
programs; using precompiled header files; reducing
program size with p-code; managing memory in C;
managing memory in C++; using the inline assembler;
controlling floating-point math operations --- Special
environments: compiling with the QuickWin windows
library; communicating with graphics; creating charts
and graphs; programming with mixed languages; writing
portable C programs --- P-code instruction tables. [The
book] describes how to take advantage of the special
features of Microsoft C/C++. The topics covered by this
manual include language extensions, special-purpose
library functions, and the interaction between
programming strategies and compiler options. This
manual is not a reference for the tools included with
Microsoft C/C++. -Introd.",
}
@Article{Montuschi:1991:OAE,
author = "P. Montuschi and M. Mezzalama",
title = "Optimal Absolute Error Starting Values for
{Newton--Raphson} Calculation of Square Root",
journal = j-COMPUTING,
volume = "46",
number = "1",
pages = "67--86",
year = "1991",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65H05 (65G99)",
MRnumber = "92a:65161",
bibdate = "Tue Oct 12 16:33:42 MDT 1999",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database; OCLC Contents1st database",
acknowledgement = ack-nhfb,
affiliation = "Politecnico di Torino",
affiliationaddress = "Torino, Italy",
classification = "723; 921",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Comput Vienna New York",
keywords = "Absolute Error; Computer Programming --- Algorithms;
Mathematical Techniques; Newton--Raphson Method;
Optimization; Square Roots",
}
@InProceedings{Montuschi:1991:SRD,
author = "Paolo Montuschi and Luigi Ciminiera",
title = "Simple radix 2 division and square root with skipping
of some addition steps",
crossref = "Kornerup:1991:PIS",
pages = "202--209",
year = "1991",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Montuschi.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
summary = "The authors present a novel algorithm for shared radix
2 division and square root whose main characteristic is
the ability to avoid any addition when the digit 0 has
been selected. The solution presented uses a redundant
representation of the \ldots{}",
}
@Article{Mulder:1991:AMC,
author = "J. M. Mulder and N. T. Quach and M. J. Flynn",
title = "An area model for on-chip memories and its
application",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "26",
number = "2",
pages = "98--105",
month = feb,
year = "1991",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
}
@InProceedings{Muller:1991:EAF,
author = "Michael M{\"u}ller and Christine R{\"u}b and Wolfgang
R{\"u}lling",
title = "Exact accumulation of floating-point numbers",
crossref = "Kornerup:1991:PIS",
pages = "64--69",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Muller.pdf",
abstract = "The authors present a new idea for designing a chip
which computes the exact sum of arbitrarily many
floating-point numbers, i.e., it can accumulate the
floating-point numbers without cancellation. Such a
chip is needed to provide a fast implementation of
Kulisch arithmetic. This is a new theory of
floating-point arithmetic which makes it possible to
compute least significant bit accurate solutions to
even ill-conditioned numerical problems. The proposed
approach avoids the disadvantages of previously
suggested designs which are too large, too slow, or
consume too much power. The crucial point is a
technique for a fast carry resolution in a long
accumulator. It can also be implemented in software.",
acknowledgement = ack-nhfb,
affiliation = "Max-Planck-Inst., Saarbrucken, Germany",
classification = "B1265B (Logic circuits); C5120 (Logic and switching
circuits); C5230 (Digital arithmetic methods)",
keywords = "Accumulator; ARITH-10; Chip; Exact accumulation; Exact
sum; Fast carry resolution; Floating-point arithmetic;
Floating-point numbers; Ill-conditioned numerical
problems; Kulisch arithmetic; Least significant bit
accurate solutions",
thesaurus = "Adders; Digital arithmetic",
}
@InProceedings{Muller:1991:FSC,
author = "Jean-Michel Muller and Peter Kornerup and David W.
Matula",
title = "Foreword: {10th Symposium on Computer Arithmetic,
Grenoble, France, June 26--28, 1991}",
crossref = "Kornerup:1991:PIS",
pages = "v--v",
year = "1991",
bibdate = "Sat Nov 17 08:46:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_contents.pdf;
http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_foreword.pdf;
http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_preface.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Mundie:1991:OOR,
author = "David A. Mundie and David A. Fisher",
title = "Optimized Overload Resolution and Type Matching for
{Ada}",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "3",
pages = "83--90",
month = "Spring",
year = "1991",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Sat Aug 9 09:05:41 MDT 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
acknowledgement = ack-nhfb,
classcodes = "C6140D (High level languages); C5230 (Digital
arithmetic methods)",
conflocation = "Redondo Beach, CA, USA; 30 April-2 May 1990",
conftitle = "1st International Symposium on Environments and Tools
for Ada",
corpsource = "Incremental Syst. Corp., Pittsburgh, PA, USA; Computer
Sci. Dept., University of Wisconsin, Madison, WI, USA",
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "Ada; computational methods; digital arithmetic;
incremental environment; microprogramming interval
arithmetic; nodes; overload resolution; pruning
heuristics; recursive strategy; tree; type matching",
sponsororg = "IEEE",
treatment = "P Practical; A Application",
}
@PhdThesis{Mutrie:1991:TSS,
author = "Mark P. W. Mutrie",
title = "Towards a Symbolic System for Floating-Point Error
Analysis",
school = "University of Waterloo",
year = "1991",
bibdate = "Thu Nov 8 14:50:35 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Myczkowski:1991:SMA,
author = "J. Myczkowski and G. Steele",
title = "Seismic modeling at {15 Gigaflops} on the {Connection
Machine}",
crossref = "IEEE:1991:PSA",
pages = "316--326",
year = "1991",
bibdate = "Wed Apr 15 16:28:01 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "A9130 (Seismology); C4170 (Differential equations);
C5440 (Multiprocessor systems and techniques); C7340
(Geophysics)",
corpsource = "Thinking Machines Corp., Cambridge, MA, USA",
keywords = "14 GFLOPS; acoustic wave equation; CM-2 supercomputer;
Connection Machine; difference equations; finite
difference algorithm; floating point unit; geophysics
computing; instruction sequence; interprocessor grid
communication; massively parallel machine; memory
interface; parallel processing; seismic modelling code;
seismology; sponge boundary conditions; stencil
compiler",
sponsororg = "IEEE; ACM",
treatment = "A Application; P Practical",
}
@Article{Nagal:1991:PEM,
author = "T. Nagal",
title = "Performance evaluation of mathematical functions",
journal = j-SUPERCOMPUTER,
volume = "8",
number = "8",
pages = "46--56",
month = nov,
year = "1991",
CODEN = "SPCOEL",
ISSN = "0168-7875",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Supercomputer",
}
@InProceedings{Nakano:1991:MBM,
author = "H. Nakano and M. Nakajima and Y. Nakahura and T.
Yoshida and Y. Goi and Y. Nakai and R. Segawa and T.
Kishida and H. Kadora",
title = "A 80 {MFLOPS} 64-bit Microprocessor for Parallel
Computer",
crossref = "IEEE:1991:PIC",
pages = "15.2/1--4",
year = "1991",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Book{Nelson:1991:SPM,
editor = "Greg Nelson",
title = "Systems Programming with {Modula-3}",
publisher = pub-PH,
address = pub-PH:adr,
pages = "ix + 267",
year = "1991",
ISBN = "0-13-590464-1",
ISBN-13 = "978-0-13-590464-0",
LCCN = "QA76.66 .S87 1991",
bibdate = "Mon Sep 12 08:08:01 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "A description of the Modula 3 programming language by
the committee that designed it, with an entertaining
appendix on how various design decisions were made.
Section 3.4 describes three floating-point interfaces
that provide parameters of the underlying
floating-point system, access primitives, and exception
handling.",
acknowledgement = ack-nj,
}
@Article{Ochs:1991:NRU,
author = "T. Ochs",
title = "Numerics for the rest of us",
journal = j-COMP-LANG-MAG,
volume = "8",
number = "10",
pages = "113--127",
month = oct,
year = "1991",
CODEN = "COMLEF",
ISSN = "0749-2839",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Language Magazine",
}
@Article{Ochs:1991:NTR,
author = "T. Ochs",
title = "Numeric types, representations, and other fictions",
journal = j-COMP-LANG-MAG,
volume = "8",
number = "8",
pages = "93--101",
month = aug,
year = "1991",
CODEN = "COMLEF",
ISSN = "0749-2839",
bibdate = "Thu Sep 1 10:14:15 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Language Magazine",
}
@Article{Ochs:1991:RF,
author = "T. Ochs",
title = "A rotten foundation",
journal = j-COMP-LANG-MAG,
volume = "8",
number = "2",
pages = "103--107",
month = feb,
year = "1991",
CODEN = "COMLEF",
ISSN = "0749-2839",
bibdate = "Thu Sep 1 10:15:05 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Language Magazine",
}
@Article{Ochs:1991:SRF,
author = "T. Ochs",
title = "Son of rotten foundation: The sequel",
journal = j-COMP-LANG-MAG,
volume = "8",
number = "3",
pages = "85--91",
month = mar,
year = "1991",
CODEN = "COMLEF",
ISSN = "0749-2839",
bibdate = "Fri Dec 08 13:04:29 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Language Magazine",
}
@Article{OGrady:1991:HOA,
author = "E. Pearse O'Grady and Baek-Kyu K. Young",
title = "A Hardware-Oriented Algorithm for Floating-Point
Function Generation",
journal = j-IEEE-TRANS-COMPUT,
volume = "40",
number = "2",
pages = "237--241",
month = feb,
year = "1991",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.73596",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 12:52:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=73596",
abstract = "An algorithm is presented for performing accurate,
high-speed, floating-point function generation for
univariate functions defined at arbitrary breakpoints.
Rapid identification of the breakdown interval, which
includes the input argument, is the key operation in
the algorithm. A hardware implementation which makes
extensive use of read\slash write memories illustrates
the algorithm.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Okabe:1991:LDC,
author = "Y. Okabe and N. Takagi and S. Yaima",
key = "OTY91",
title = "Log-Depth Circuits for Elementary Functions Using
Residue Number System",
journal = j-ELECTRON-COMMUN-JPN,
volume = "74",
number = "8",
pages = "31--37",
year = "1991",
CODEN = "ECOJAL",
ISSN = "0424-8368",
bibdate = "Mon May 19 15:16:09 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Translated from Denshi Joho Tsushin Gakkai Ronbunshi,
vol.\ 21-DI, no.\ 9, September 1990, pp.\ 723-728",
acknowledgement = ack-nhfb,
fjournal = "Electronics and communications in Japan",
}
@InProceedings{Orup:1991:HRH,
author = "Holger Orup and Peter Kornerup",
title = "{A} high-radix hardware algorithm for calculating the
exponential {$ M^E \bmod N $}",
crossref = "Kornerup:1991:PIS",
pages = "51--56",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Orup.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Ozawa:1991:FND,
author = "K. Ozawa",
title = "A Fast {$ O(n^2) $} Division Algorithm for
Multiple-Precision Floating-Point Numbers",
journal = j-INFO-PROC,
volume = "14",
number = "3",
pages = "354--356",
month = "????",
year = "1991",
bibdate = "Thu Sep 1 10:15:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Ozawa:1991:FOD,
author = "K. Ozawa",
title = "A Fast {$ O(n^2) $} Division Algorithm for
Multiple-Precision Floating-Point Numbers",
journal = j-J-INF-PROCESS,
volume = "14",
number = "3",
pages = "354--356",
month = "????",
year = "1991",
CODEN = "JIPRDE",
ISSN = "0387-6101",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A fast O(n/sup 2/) algorithm is derived for the
division of multiple-precision floating-point numbers,
where $n$ is the number of digits in each of the
numbers. This algorithm, which is a modification of the
conventional pencil-and-paper technique, is as fast as
the conventional $ O(n^2) $ multiplication and 2.67
times faster than the algorithm based on the Newton
method.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Coll. of Gen. Educ.,
Tohoku University, Miyagi, Japan",
classification = "C4240 (Programming and algorithm theory)",
fjournal = "Journal of Information Processing",
keywords = "Fast O(n/sup 2/) division algorithm;
Multiple-precision floating-point numbers; Newton
method",
pubcountry = "Japan",
thesaurus = "Algorithm theory; Digital arithmetic",
}
@InProceedings{Parikh:1991:RBE,
author = "Shrikant N. Parikh and David W. Matula",
title = "A redundant binary {Euclidean GCD} algorithm",
crossref = "Kornerup:1991:PIS",
pages = "220--225",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Parikh.pdf",
abstract = "An efficient implementation of the Euclidean GCD
(greatest common divisor) algorithm employing the
redundant binary number system is described. The time
complexity is O(n), utilizing O(n)4-2 signed 1-b adders
to determine the GCD of two n-b integers. The process
is similar to that used in SRT division. The efficiency
of the algorithm is competitive, to within a small
factor, with floating point division in terms of the
number of shift and add/subtract operations. The
novelty of the algorithm is based on properties derived
from the proposed scheme of normalization of signed bit
fractions. The implementation is well suited for
systolic hardware design.",
acknowledgement = ack-nhfb,
affiliation = "IBM, Westlake, TX, USA",
classification = "C5230 (Digital arithmetic methods)",
keywords = "ARITH-10; Euclidean GCD; Floating point division;
Greatest common divisor; Redundant binary number
system; Signed bit fractions; Systolic hardware design;
Time complexity",
thesaurus = "Computational complexity; Digital arithmetic",
}
@InProceedings{Paterson:1991:SMC,
author = "Michael S. Paterson and Uri Zwick",
title = "Shallow multiplication circuits",
crossref = "Kornerup:1991:PIS",
pages = "28--34",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Peterson.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Misc{Paxson:1991:PTI,
author = "Vern Paxson and W. Kahan",
title = "A Program for Testing {IEEE} Binary--Decimal
Conversion",
howpublished = "World-Wide Web document",
month = may,
year = "1991",
bibdate = "Wed Jan 29 17:59:29 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.ee.lbl.gov/testbase-report.ps.Z;
ftp://ftp.ee.lbl.gov/testbase.tar.Z",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic; floating-point
testing",
}
@InProceedings{Piestrak:1991:DRG,
author = "Stanis{\l}aw J. Piestrak",
title = "Design of Residue Generators and Multioperand Modular
Adders Using Carry-Save Adders",
crossref = "Kornerup:1991:PIS",
pages = "100--107",
year = "1991",
bibdate = "Sat Nov 17 08:46:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Piestrak.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Plauger:1991:AF,
author = "P. J. Plauger",
title = "Approximating functions",
journal = j-COMP-LANG-MAG,
volume = "8",
number = "6",
pages = "17--25",
month = jun,
year = "1991",
CODEN = "COMLEF",
ISSN = "0749-2839",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Language Magazine",
}
@Article{Plauger:1991:EP,
author = "P. J. Plauger",
title = "Economizing polynomials",
journal = j-COMP-LANG-MAG,
volume = "8",
number = "7",
pages = "21--27",
month = jul,
year = "1991",
CODEN = "COMLEF",
ISSN = "0749-2839",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Language Magazine",
}
@Article{Plauger:1991:FPA,
author = "P. J. Plauger",
title = "Floating-Point Arithmetic",
journal = j-EMBED-SYS-PROG,
volume = "4",
number = "8",
pages = "95--99",
month = aug,
year = "1991",
CODEN = "EYPRE4",
ISSN = "1040-3272",
bibdate = "Thu Sep 1 10:14:15 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Embedded Systems Programming",
}
@Article{Plauger:1991:FPP,
author = "P. J. Plauger",
title = "Floating-Point Primitives",
journal = j-JCLT,
volume = "3",
number = "2",
pages = "89--100",
month = sep,
year = "1991",
ISSN = "1042-5721",
bibdate = "Thu Nov 8 14:50:36 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "The Journal of {C} Language Translation",
}
@Article{Plauger:1991:HTF,
author = "P. J. Plauger",
title = "The Header {{\tt <float.h>}}",
journal = j-CUJ,
volume = "9",
type = "{Standard C}",
number = "1",
pages = "9--??",
month = jan,
year = "1991",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@Article{Plauger:1991:WW,
author = "P. J. Plauger",
title = "Washing the watchers",
journal = j-COMP-LANG-MAG,
volume = "8",
number = "9",
pages = "23--32",
month = sep,
year = "1991",
CODEN = "COMLEF",
ISSN = "0749-2839",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Language Magazine",
}
@InProceedings{Priest:1991:AAP,
author = "Douglas M. Priest",
title = "Algorithms for Arbitrary Precision Floating Point
Arithmetic",
crossref = "Kornerup:1991:PIS",
pages = "132--143",
year = "1991",
DOI = "https://doi.org/10.1109/ARITH.1991.145549",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Priest.pdf",
abstract = "The author presents techniques for performing
computations of very high accuracy using only
straightforward floating-point arithmetic operations of
limited precision. The validity of these techniques is
proved under very general hypotheses satisfied by most
implementations of floating-point arithmetic. To
illustrate the applications of these techniques, an
algorithm is presented which computes the intersection
of a line and a line segment. The algorithm is
guaranteed to correctly decide whether an intersection
exists and, if so, to produce the coordinates of the
intersection point accurate to full precision. The
algorithm is usually quite efficient; only in a few
cases does guaranteed accuracy necessitate an expensive
computation.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Department of Math., California University, Berkeley,
CA, USA",
classification = "C1160 (Combinatorial mathematics); C5230 (Digital
arithmetic methods)",
keywords = "accurate floating-point summation; ARITH-10;
coordinates; floating point arithmetic; intersection
point; line intersection; line segment",
thesaurus = "Digital arithmetic; Number theory",
}
@Article{Pugh:1991:TFV,
author = "Kenneth Pugh and Hugo Calleens",
title = "{{\tt float}}s Versus {{\tt double}}s",
journal = j-CUJ,
volume = "9",
type = "Questions and Answers",
number = "6",
pages = "117--??",
month = jun,
year = "1991",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@TechReport{Quach:1991:DIS,
author = "N. Quach and M. Flynn",
title = "Design and implementation of the {SNAP} floating-point
adder",
type = "Technical Report",
number = "CSL-TR-91-501",
institution = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
month = dec,
year = "1991",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@TechReport{Quach:1991:FIR,
author = "N. Quach and N. Takagi and M. J. Flynn",
title = "On Fast {IEEE} Rounding",
type = "Technical Report",
number = "CSL-TR-91-459",
institution = "Stanford University",
address = "Stanford, CA, USA",
pages = "v + 27",
month = jan,
year = "1991",
bibdate = "Sun Dec 10 14:08:33 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://i.stanford.edu/pub/cstr/reports/csl/tr/91/459/CSL-TR-91-459.pdf",
abstract = "A systematic general rounding procedure is proposed.
This procedure consists of 2 steps: constructing a
rounding table and selecting a prediction scheme.
Optimization guidelines are given in each step to
minimize the hardware used. This procedure-based
rounding method has the additional advantage that
verification and generalization are trivial. Two
rounding hardware models are described. The first is
shown to be identical to that reported by Santoro, et
al. The second is more powerful, providing solutions
where the first fails. Applying this approach to the
IEEE rounding modes for high-speed conventional binary
multipliers reveals that round to infinity is more
difficult to implement than the round to nearest mode;
more adders are potentially needed. Round to zero
requires the least amount of hardware. A generalization
of this procedure to redundant binary multipliers
reveals two major advantages over conventional binary
multipliers. First, the computation of the sticky bit
consumes considerably less hardware. Second,
implementing round to positive and minus infinity modes
does not require the examination of the sticky bit,
removing a possible worst-case path. A generalization
of this approach to addition produces a similar
solution to that reported by Quach and Flynn. Although
generalizable to other kinds of rounding as well as
other arithmetic operations, we only treat the case of
IEEE rounding for addition and multiplication; IEEE
rounding because it is the current standard on
rounding, addition and multiplication because they are
the most frequently used arithmetic operations in a
typical scientific computation.",
acknowledgement = ack-nhfb,
keywords = "high-speed floating-point adders; high-speed parallel
multipliers; IEEE rounding; redundant binary
multipliers; redundant binary representation",
}
@TechReport{Quach:1991:LOP,
author = "N. T. Quach and M. J. Flynn",
title = "Leading one prediction --- implementation,
generalization, and application",
type = "Technical Report",
number = "CSL-TR-91-463",
institution = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
month = mar,
year = "1991",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@Article{Raja:1991:NDT,
author = "Paruvachi V. R. Raja",
title = "Novel Design Techniques for {RNS} Systolic {VLSI}
Arrays",
journal = j-LECT-NOTES-COMP-SCI,
volume = "507",
pages = "206--??",
year = "1991",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon May 13 08:51:55 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Rao:1991:ARN,
author = "B. D. Rao",
booktitle = "Acoustics, Speech, and Signal Processing, 1991.
{ICASSP-91., 1991} International Conference on. 14--17
April 1991",
title = "Analysis of roundoff noise in floating point digital
filters",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1893--1896",
year = "1991",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "A systematic approach for the analysis of roundoff
noise in floating point digital filters is presented.
The analysis is based on a high level model developed
to deal with the errors in the inner product operation.
The model consists of an efficient \ldots{}",
}
@Article{Rees:1991:RRA,
author = "Jonathan Rees and William Clinger and others",
title = "The revised$^4$ report on the algorithmic language
{Scheme}",
journal = "ACM SIGPLAN Lisp Pointers",
volume = "4",
number = "3",
pages = "1--55",
month = jul # "\slash " # sep,
year = "1991",
bibdate = "Wed Jan 29 16:50:56 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "From \cite{Steele:2004:RHP}: ``the result [of a
binary-to-decimal conversion] is expressed using the
minimum number of digits\ldots{}''",
}
@Article{Rump:1991:CAI,
author = "Siegfried M. Rump",
title = "A Class of Arbitrarily Ill-Conditioned Floating-Point
Matrices",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "12",
number = "4",
pages = "645--653",
month = oct,
year = "1991",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F35 (15A12 65G05)",
MRnumber = "92d:65076",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Scott:1991:MCS,
author = "T. J. Scott",
title = "Mathematics and computer science at odds over real
numbers",
journal = j-SIGCSE,
volume = "23",
number = "1",
pages = "130--139",
month = mar,
year = "1991",
CODEN = "SIGSD3",
ISSN = "0097-8418 (print), 2331-3927 (electronic)",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "22nd SIGCSE Technical Symposium on Computer Science
Education.",
abstract = "Discusses the `real numbers' data type as implemented
by `floating point' numbers. Floating point
implementations and a theorem that characterizes their
truncations are presented. A teachable floating point
system is presented, chosen so that most problems can
be worked out with paper and pencil. Then major
differences between floating point number systems and
the continuous real number system are presented.
Important floating point formats are next discussed.
Two examples derived from actual computing practice on
mainframes, minicomputers, and PCs are presented. The
paper concludes with a discussion of where floating
point arithmetic should be taught in standard courses
in the ACM curriculum.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Western Illinois
University, Macomb, IL, USA",
classification = "C0220 (Education and training); C5230 (Digital
arithmetic methods)",
confdate = "7-8 March 1991",
conflocation = "San Antonio, TX, USA",
confsponsor = "ACM",
fjournal = "SIGCSE Bulletin (ACM Special Interest Group on
Computer Science Education)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J688",
keywords = "ACM curriculum; Computer science; Floating point
arithmetic; Floating point formats; Floating point
number systems; Real number data types; Standard
courses; Teaching; Truncations",
thesaurus = "Computer science education; Data structures; Digital
arithmetic; Educational courses; Number theory",
}
@TechReport{Seznec:1991:OCE,
author = "Andre Seznec and Karl Courtel",
title = "{OPAC}: a cost-effective floating-point coprocessor =
Le coprocessor num{\'e}rique {OPAC}",
institution = "Institut National de Recherche en Informatique et en
Automatique",
address = "Le Chesnay, France",
pages = "24",
year = "1991",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Rapports de recherche. Institut National de Recherche
en Informatique et en Automatique; 1461 Rapports de
recherche (Institut national de recherche en
informatique et en automatique (France)); 1461.",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Microprocessors.",
remark = "Abstracts in English and French. ``Mai 1991.''
Abstract: ``The effective performance of RISC
microprocessors on numerical applications remains on
the order of a few megaflops/s. In this paper, we show
that the static addressing of the registers in standard
RISC floating-point coprocessors is one of the main
bottleneck [sic] for performance. In the architecture
of the coprocessor OPAC, we propose an alternative
using only FIFO queues for storing intermediate results
and reusable operands. Performance close to
multiplication-accumulation every cycle is expected on
a large set of numerical applications at a reasonable
hardware cost.'' Supported in part by the CNRS PRC-AMN
Supported in part by the French Ministry of Defense.",
}
@TechReport{Seznec:1991:OFP,
author = "Andre Seznec and Karl Courtel",
title = "{OPAC}: a floating-point coprocessor dedicated to
compute-bound kernels = {OPAC}: un coprocesseur
flottant dedi{\'e} au calcul matriciel",
type = "Rapports de recherche",
number = "1555",
institution = "Institut National de Recherche en Informatique et en
Automatique",
address = "Le Chesnay, France",
pages = "27",
year = "1991",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Array processors.; Kernel functions.; Parallel
programming (Computer science)",
remark = "Abstracts in English and French. ``October 7, 1991.''
Abstract: ``In various application domains, programmers
are not specialists of parallel programming, but are
demanding for performance that cannot be reached
without using parallelism. Nevertheless, in many
applications, the main part of the computations may be
encapsulated in compute-bounds kernels with [sic]
exhibit high potential parallelism. Achieving high
performance on compute-bound primitives at a low
hardware cost has became [sic] an important challenge.
In this paper, we present the architecture of the OPAC
floating-point operator. OPAC has been designed in
order to be the basic cell in a multi-cell
floating-point coprocessor dedicated to the execution
of the most useful compute-bound kernels. The peak
performance of one floating-point multiply-add per
cycle per cell obtained on the OPAC prototype may be
approached in a microprocessor environment on a
multi-cell OPAC floating-point coprocessor on a large
set of numerical applications.'' Supported in part by
the French ministry of defense. Supported in part by
the CNRS (PRC-ANM and GCIS)",
}
@Article{Shaeffer:1991:HEP,
author = "D. L. Shaeffer and J. R. Kimbrough and S. M. Denton
and J. L. Kaschmitter and J. W. Wilburn and R. W. Davis
and N. J. Colella and D. B. Holtkamp",
title = "High energy proton {SEU} test results for the
commercially available {MIPS R3000} microprocessor and
{R3010} floating point unit",
journal = j-IEEE-TRANS-NUCL-SCI,
volume = "38",
number = "6",
pages = "1421--1428",
month = dec,
year = "1991",
CODEN = "IRNSAM",
ISSN = "0018-9499 (print), 1558-1578 (electronic)",
ISSN-L = "0018-9499",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Nuclear Science",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23",
keywords = "floating-point testing",
summary = "Proton single event upset (SEU) cross sections and
proton total dose hardness of commercially available
MIPS R3000 microprocessors (CPU) and R3010 floating
point units (FPU) were obtained by exposing these parts
to 256 MeV protons from the linear accelerator
\ldots{}",
}
@Article{Shand:1991:HSL,
author = "M. Shand and P. Bertin and J. Vuillemin",
title = "Hardware speedups in long integer multiplication",
journal = j-COMP-ARCH-NEWS,
volume = "19",
number = "1",
pages = "106--113",
month = mar,
year = "1991",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 12 09:40:33 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Book{Siewiorek:1991:AST,
author = "Daniel P. Siewiorek and Philip John {Koopman, Jr.}",
title = "The Architecture of Supercomputers\emdash Titan, {A}
Case Study",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xvii + 202",
year = "1991",
ISBN = "0-12-643060-8",
ISBN-13 = "978-0-12-643060-8",
LCCN = "QA76.5 S536 1991",
bibdate = "Sun Jan 23 17:54:38 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Skavantzos:1991:PRN,
author = "A. Skavantzos and F. J. Taylor",
title = "On the polynomial residue number system [digital
signal processing]",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "39",
number = "2",
pages = "376--382",
month = feb,
year = "1991",
CODEN = "ITPRED",
DOI = "https://doi.org/10.1109/78.80821",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2656",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
keywords = "residue arithmetic; residue number system",
summary = "The theory of the polynomial residue number system
(PRNS), a system in which totally parallel polynomial
multiplication can be achieved provided that the
arithmetic takes place in some carefully chosen ring,
is examined. Such a system is defined by \ldots{}",
}
@Article{Smith:1991:AFP,
author = "David M. Smith",
title = "{Algorithm 693}: {A FORTRAN} Package for
Floating-Point Multiple-Precision Arithmetic",
journal = j-TOMS,
volume = "17",
number = "2",
pages = "273--283",
month = jun,
year = "1991",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/108556.108585",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Dec 13 18:36:25 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p273-smith/",
abstract = "FM is a collection of FORTRAN-77 routines which
performs floating-point multiple-precision arithmetic
and elementary functions. Results are almost always
correctly rounded, and due to improved algorithms used
for elementary functions, reasonable efficiency is
obtained.",
acknowledgement = ack-nhfb,
affiliation = "Loyola Marymount University, Los Angeles, CA, USA",
classification = "C4130 (Interpolation and function approximation);
C5230 (Digital arithmetic methods); C7310
(Mathematics)",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "Accuracy; correct rounding; Elementary functions;
floating-point arithmetic; Floating-point
multiple-precision arithmetic; FM; FORTRAN-77 routines;
Mathematical library; Portable software; Rounding off",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Numerical algorithms. {\bf D.3.2}:
Software, PROGRAMMING LANGUAGES, Language
Classifications, FORTRAN 77.",
thesaurus = "Digital arithmetic; Function approximation;
Mathematics computing; Software packages; Subroutines",
}
@Article{Sorensen:1991:OEC,
author = "D. C. Sorensen and Ping Tak Peter Tang",
title = "On the Orthogonality of Eigenvectors Computed by
Divide and Conquer Techniques",
journal = j-SIAM-J-NUMER-ANAL,
volume = "28",
number = "6",
pages = "1752--1775",
month = dec,
year = "1991",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F15 (65G05)",
MRnumber = "92h:65065",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database; Parallel/par.lin.alg.bib;
Theory/Matrix.bib",
note = "Pages 1759--1761 discuss implementation of useful
primitives for higher-precision arithmetic: DPAdd2(),
DPAdd3(), DPDiv().",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
kwds = "nla, eig, prll, symmetric matrix",
}
@PhdThesis{Sparmann:1991:SBT,
author = "U. Sparmann",
title = "Structure Based Test Methods for Arithmetic Circuits",
type = "{Ph.D.} thesis",
school = "Computer Science Department, University of Saarland",
address = "Saarbr{\"u}cken, Germany",
year = "1991",
bibdate = "Tue Mar 13 10:30:20 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "In German.",
acknowledgement = ack-nhfb,
keywords = "floating-point testing",
remark = "Cited in \cite{Mueller:2000:CAC}.",
}
@Article{Squire:1991:ANS,
author = "Jon S. Squire",
title = "{Ada} numerics standardization and testing",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
address = "New York, NY, USA",
pages = "1--286",
year = "1991",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "Ada (Computer program language); floating-point
testing",
remark = "A special edition from SIGAda \ldots{} presented by
SIGAda Numerics Working Group and Ada-Europe Numerics
Working Group and ISO- IEC/JTC1/SC22/WG9 Numerics
Rapporteur Group.",
tableofcontents = "Introduction to the proposed standard for the
elementary functions in Ada / Kenneth W. Dritz\\
Proposed standard for a generic package of elementary
functions for Ada / edited by Kenneth W. Dritz\\
Rationale for the proposed standard for a generic
package of elementary functions for Ada; Proposed
standard for a generic package of primitive functions
for Ada; Rationale for the proposed standard for a
generic package of primitive functions for Ada /
Kenneth W. Dritz\\
Proposed standard for packages of real and complex type
declarations and basic operations for Ada (including
vector and matrix types) / edited by Graham S.
Hodgson\\
Rationale for the proposed standard for packages of
real and complex type declarations and basic operations
for Ada (including vector and matrix types) / Graham S.
Hodgson. Proposed standard for a generic package of
complex elementary functions / edited by Jon S. Squire
\\
Rationale for the proposed standard for a generic
package of complex elementary functions / Jon S. Squire
\\
A portable generic elementary function package in Ada
and an accurate test suite / Ping Tak Peter Tang \\
Towards validation of generic elementary functions and
other standard Ada numerics packages / Jon S. Squire\\
Floating point attributes in Ada / Dik T. Winter\\
An Ada math library for real-time avionics / Donald A.
Celarier and Donald W. Sando\\
Predefined floating point type names, uniformity
rapporteur group UI-48 / edited by Jon S. Squire.",
}
@InProceedings{Steidley:1991:FPA,
author = "C. W. Steidley",
title = "Floating point arithmetic basic exercises in
mathematical reasoning for computer science majors",
crossref = "ASEE:1991:CCW",
pages = "191--197 vol.1",
year = "1991",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The author gives examples demonstrating how an
unsuspecting user of floating point arithmetic on
computers may be misled by results. Specifically, there
are cases where the fundamental rules of arithmetic
break down. Thus, it is even more imperative that
fledgling computer scientists have some insight into
the machinations of floating point arithmetic on
computers.",
acknowledgement = ack-nhfb,
affiliation = "Central Washington University, Ellensburg, WA, USA",
classification = "C0220 (Education and training); C5230 (Digital
arithmetic methods)",
keywords = "Computer science majors; Computers; Floating point
arithmetic; Mathematical reasoning",
thesaurus = "Computer science education; Digital arithmetic",
}
@Article{Takagi:1991:RCM,
author = "N. Takagi and T. Asada and S. Yajima",
title = "Redundant {CORDIC} Methods with a Constant Scale
Factor for Sine and Cosine Computation",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-40",
number = "9",
pages = "989--995",
month = sep,
year = "1991",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.83660",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Takagi:1991:RMM,
author = "Naofumi Takagi",
title = "{A} radix-$4$ modular multiplication hardware
algorithm efficient for iterative modular
multiplications",
crossref = "Kornerup:1991:PIS",
pages = "35--42",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Takagi.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@TechReport{Tang:1991:TLAa,
author = "Ping Tak Peter Tang",
title = "Table-Lookup Algorithms for Elementary Functions and
Their Error Analysis",
type = "Technical Report",
number = "MCS-P194-1190",
institution = "Argonne National Laboratory",
address = "Argonne, IL, USA",
pages = "????",
year = "1991",
bibdate = "Thu Jan 30 16:25:10 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Tang:1991:TLAb,
author = "Ping Tak Peter Tang",
title = "Table-Lookup Algorithms for Elementary Functions and
Their Error Analysis",
crossref = "Kornerup:1991:PIS",
pages = "232--236",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Tang.pdf",
acknowledgement = ack-nj # " and " # ack-nhfb,
keywords = "ARITH-10",
}
@InProceedings{Taylor:1991:TFA,
author = "V. E. Taylor and A. Ranade and D. G. Messerschmitt",
title = "Three-dimensional finite-element analyses:
implications for computer architectures",
crossref = "IEEE:1991:PSA",
pages = "786--795",
year = "1991",
bibdate = "Wed Apr 15 16:28:01 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C4140 (Linear algebra); C4185 (Finite element
analysis); C4240P (Parallel programming and algorithm
theory); C5220P (Parallel architecture); C6110P
(Parallel programming); C6120 (File organisation)",
corpsource = "Department of Electr. Eng. and Computer Science,
California University, Berkeley, CA, USA",
keywords = "columns; computer architectures; data path design;
data structure; data structures; finite element
analysis; floating-point units; matrix algebra; memory
bandwidth; parallel architectures; parallel
programming; programming theory; rows; sparse matrices;
sparsity pattern",
sponsororg = "IEEE; ACM",
treatment = "P Practical; T Theoretical or Mathematical",
}
@Article{teRiele:1991:NLB,
author = "H. J. J. {te Riele}",
title = "A new lower bound for the {de Bruijn-Newman}
constant",
journal = j-NUM-MATH,
volume = "58",
number = "6",
pages = "661--667",
year = "1991",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "30D10 (11M26 30D15 65E05)",
MRnumber = "92c:30030",
MRreviewer = "George L. Csordas",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "B0290F (Interpolation and function approximation);
B0290R (Integral equations); C4130 (Interpolation and
function approximation); C4180 (Integral equations)",
corpsource = "Centre for Math. and Computer Science, Amsterdam,
Netherlands",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "complex zeros; de Bruijn-Newman constant;
high-precision floating-point computations; integral
equations; Jensen polynomial; lover bound; polynomials;
Riemann hypothesis; Sturm sequence",
treatment = "T Theoretical or Mathematical",
}
@Manual{TI:1991:TDH,
title = "{TMS34082} designer's handbook",
organization = "{Texas Instruments Incorporated}",
address = "Dallas, TX, USA",
edition = "Revised",
pages = "various",
year = "1991",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer graphics --- Equipment and supplies.;
Floating-point arithmetic --- Computer simulation.;
Integrated circuits --- Very large scale integration
--- Handbooks,; manuals, etc.",
remark = "``Datapath VLSI products''--Cover. ``2564007-9721
revision A, May 1991''--T.p.",
}
@Manual{TI:1991:TFDa,
title = "{TMS320} floating-point {DSP} optimizing {C} compiler
user's guide",
organization = "{Texas Instruments Incorporated}",
address = "Dallas, TX, USA",
edition = "Revised",
pages = "various",
year = "1991",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Compilers (Computer programs).; manuals, etc.; Signal
processing --- Digital techniques --- Equipment and;
supplies.; Texas Instruments TMS320 series
microprocessors --- Handbooks",
remark = "``Microprocessor development systems''--Cover.
``2576391-9721 revision A, October 1991''--T.p.",
}
@Manual{TI:1991:TFDb,
title = "{TMS320} floating-point {DSP} assembly language tools
user's guide",
organization = "{Texas Instruments Incorporated}",
address = "Dallas, TX, USA",
edition = "Revised",
pages = "various",
year = "1991",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Assembler language (Computer program language).;
Handbooks, manuals, etc.; Signal processing --- Digital
techniques --- Equipment and; supplies.; Texas
Instruments TMS320 series microprocessors ---
Programming --",
remark = "``Microprocessor development systems''--Cover.
``2576328-9721 revision A, September 1991''--T.p.",
}
@Manual{TI:1991:TST,
title = "{TMS34082} software tool kit user's guide",
organization = "Texas Instruments Incorporated",
address = "Dallas",
edition = "2547321-9721 revision.",
pages = "various",
year = "1991",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer storage devices.; TMS34082 Floating-Point
Processor.",
remark = "``Datapath VLSI products''--Cover. ``SSCA001''--P. [4]
of cover.",
}
@InProceedings{Tomabechi:1991:DMD,
author = "N. Tomabechi",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, 11--14 June 1991",
title = "Design method of defect-tolerant {WSI} systems based
on the residue number system",
volume = "5",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "3082--3085",
year = "1991",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1991.176199",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A design method is proposed for defect-tolerant WSI
arithmetic systems based on the RNS (residue number
system). The yield analysis has shown that the features
of the RNS are very well suited for the defect recovery
of WSIs. In the RNS, addition and \ldots{}",
}
@TechReport{Tsang:1991:SDC,
author = "Annie Tsang and Manfred Olschanowsky",
title = "A Study of {DataBase 2} Customer Queries",
type = "Technical Report",
number = "TR 03.413",
institution = "IBM Santa Teresa Laboratory",
address = "San Jose, CA, USA",
month = apr,
year = "1991",
bibdate = "Mon Mar 06 08:07:19 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "This report surveys the numeric data types used in
commercial databases by 51 major organizations, and
finds that 98.6\% of the numeric data are decimal.",
}
@Article{Tsubokawa:1991:FEA,
author = "Hiroshi Tsubokawa and Hajime Kubota and Shigeo
Tsujii",
title = "Floating-Point Error Analysis for Recursive
Least-Square Algorithm Using {UD} Factorization",
journal = j-ELECT-COMM-JAPAN-3-FUND-ELECT-SCI,
volume = "74",
number = "6",
pages = "1--10",
year = "1991",
CODEN = "ECJSER",
ISSN = "1042-0967 (print), 1520-6440 (electronic)",
ISSN-L = "1042-0967",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics and communications in Japan. Part 3,
Fundamental electronic science",
}
@InProceedings{Tu:1991:ALA,
author = "Paul K.-G. Tu and Milo{\v{s}} D. Ercegovac",
title = "Application of on-line arithmetic algorithms to the
{SVD} computation: preliminary results",
crossref = "Kornerup:1991:PIS",
pages = "246--255",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Tu.pdf",
abstract = "A scheme for the singular value decomposition (SVD)
problem, based on online arithmetic, is discussed. The
design, using radix-2 floating-point online operations,
implemented in the LSI HCMOS gate-array technology, is
compared with a compatible conventional arithmetic
implementation. The preliminary results indicate that
the proposed online approach achieves a speedup of
2.4-3.2 with respect to the conventional solutions,
with 1.3-5.5 more gates and more than 6 times fewer
interconnections.",
acknowledgement = ack-nhfb,
affiliation = "IBM Corp., Austin, TX, USA",
classification = "C5230 (Digital arithmetic methods)",
keywords = "ARITH-10; Floating-point online operations; Online;
Online arithmetic; Radix-2; Singular value
decomposition",
thesaurus = "Digital arithmetic",
}
@Article{Tu:1991:GAI,
author = "Paul K.-G. Tu and Milo{\v{s}} D. Ercegovac",
title = "Gate Array Implementation of On-Line Algorithms for
Floating-Point Operations",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "3",
number = "4",
pages = "307--318",
month = oct,
year = "1991",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1007/BF00936903",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present gate array designs of on-line arithmetic
units for radix-2 floating-point addition,
multiplication and division operations. Performance and
complexity characteristics of the implementations of
on-line arithmetic units are discussed and compared
with those of the compatible conventional
floating-point algorithms implemented in the same
technology.",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
}
@InProceedings{Turner:1991:IAE,
author = "Peter R. Turner",
title = "Implementation and analysis of extended {SLI}
operations",
crossref = "Kornerup:1991:PIS",
pages = "118--126",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Turner.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Umemura:1991:FNL,
author = "K. Umemura",
title = "Floating-point number {LISP}",
journal = j-SPE,
volume = "21",
number = "10",
pages = "1015--1026",
month = oct,
year = "1991",
CODEN = "SPEXBL",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Tue Dec 12 09:26:54 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A floating-point-number-oriented LISP has been
developed. Though it performs type checking on every
numeric operation, it runs as fast as Fortran for
simple differential-equation problems. The author
describes the implementation, provides some
measurements of its efficiency and discusses the
feasibility of this type of implementation.",
acknowledgement = ack-nhfb,
affiliation = "Software Labs., NTT Corp., Tokyo, Japan",
classification = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques); C6140D (High level languages);
C7310 (Mathematics)",
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
keywords = "Floating-point-number-oriented LISP; Numeric
operation; Simple differential-equation problems; Type
checking",
pubcountry = "UK",
thesaurus = "Digital arithmetic; LISP; Mathematics computing;
Symbol manipulation",
}
@Article{Umemura:1991:FPN,
author = "Kyoji Umemura",
title = "Floating-point Number {LISP}",
journal = j-SPE,
volume = "21",
number = "10",
pages = "1015--1026",
month = oct,
year = "1991",
CODEN = "SPEXBL",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A floating-point-number-oriented LISP has been
developed. Though it performs type checking on every
numeric operation, it runs as fast as Fortran for
simple differential-equation problems. The author
describes the implementation, provides some
measurements of its efficiency and discusses the
feasibility of this type of implementation.",
acknowledgement = ack-nhfb,
affiliation = "Software Labs., NTT Corp., Tokyo, Japan",
classification = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques); C6140D (High level languages);
C7310 (Mathematics)",
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
keywords = "Floating-point-number-oriented LISP; Numeric
operation; Simple differential-equation problems; Type
checking",
pubcountry = "UK",
thesaurus = "Digital arithmetic; LISP; Mathematics computing;
Symbol manipulation",
}
@Article{Vassiliadis:1991:HWM,
author = "S. Vassiliadis and E. M. Schwarz and B. M. Sung",
title = "Hard-wired multipliers with encoded partial products",
journal = j-IEEE-TRANS-COMPUT,
volume = "40",
number = "11",
pages = "1181--1197",
month = nov,
year = "1991",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.102823",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 12:52:24 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=102823",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@MastersThesis{Vishin:1991:FPP,
author = "Sanjay Vishin",
title = "A floating point primitive classifier for the ray
casting machine",
type = "Typescript. Thesis ({M.S.})",
school = "Duke University. Department of Computer Science",
address = "Durham, NC 27708, USA",
pages = "ix + 79",
year = "1991",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer graphics.; Floating-point arithmetic.;
Geometry, Analytic --- Solid --- Data processing.;
Image processing.",
}
@InProceedings{Vuillemin:1991:CTA,
author = "J. E. Vuillemin",
title = "Constant time arbitrary length synchronous binary
counters",
crossref = "Kornerup:1991:PIS",
pages = "180--183",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Vuillemin.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Walter:1991:FMM,
author = "Colin D. Walter",
title = "Faster Modular Multiplication by Operand Scaling",
journal = j-LECT-NOTES-COMP-SCI,
volume = "576",
pages = "313--??",
year = "1991",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Feb 5 11:48:11 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t0576.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/0576/05760313.htm;
http://link.springer-ny.com/link/service/series/0558/papers/0576/05760313.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Wigley:1991:FMR,
author = "N. W. Wigley and G. A. Jullien",
title = "Flexible modulus residue number system for complex
digital signal processing",
journal = j-ELECT-LETTERS,
volume = "27",
number = "16",
pages = "1436--1438",
month = aug,
year = "1991",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2666",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "residue arithmetic; residue number system",
summary = "The quadratic residue number system (QRNS) is often
used for integer calculation on complex data streams. A
finite polynomial ring mapping technique is presented
that removes the $4k + 1$ prime divisor restriction of
the QRNS, albeit with an \ldots{}",
}
@InProceedings{Wigley:1991:SMR,
author = "N. Wigley and G. A. Jullien and D. Reaume and W. C.
Miller",
title = "Small moduli replications in the {MRRNS}",
crossref = "Kornerup:1991:PIS",
pages = "92--99",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Wigley.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@InProceedings{Williams:1991:NBC,
author = "Ted E. Williams and Mark A. Horowitz",
title = "{A} 160 ns 54 bit {CMOS} division implementation using
self-timing and symmetrically overlapped {SRT} stages",
crossref = "Kornerup:1991:PIS",
pages = "210--217",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Williams.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Williams:1991:ZOS,
author = "Ted E. Williams and Mark A. Horowitz",
title = "A zero-overhead self-timed 160-ns 54-b {CMOS}
divider",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "26",
number = "11",
pages = "1651--1661",
month = nov,
year = "1991",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
}
@Article{Winter:1991:FPA,
author = "Dik T. Winter",
title = "Floating point attributes in {Ada}",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
pages = "244--273",
month = "Fall",
year = "1991",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Sat Aug 9 09:05:43 MDT 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
abstract = "The Ada programming language offers a number of
facilities to simplify the writing of portable
programs. One of these is the concept of attributes.
Many types and objects carry with them a set of
attributes that a program may interrogate to get
information about the actual implementation. The author
is concerned with the set of attributes belonging to
floating point types. One should hope that the floating
point attributes give correct results. In fact, they
are compile time constants. A little experimentation
shows that that is not true. Many systems deliver
incorrect attributes in a number of cases. Also, due to
the inappropriate definition of some of the attributes,
many attributes deliver results that are misleading.
The author considers the floating point attributes the
language gives and shows that indeed some definitions
are inappropriate. A program that verifies the validity
of the results given by a system is also presented. (3
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Centrum voor Wiskunde en Inf., Amsterdam,
Netherlands",
classcodes = "C6140D (High level languages); C6110B (Software
engineering techniques); C6150G (Diagnostic, testing,
debugging and evaluating systems); C5230 (Digital
arithmetic methods)",
classification = "C5230 (Digital arithmetic methods); C6110B (Software
engineering techniques); C6140D (High level languages);
C6150G (Diagnostic, testing, debugging and evaluating
systems)",
corpsource = "Centrum voor Wiskunde en Inf., Amsterdam,
Netherlands",
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "Ada; Ada programming language; compile; Compile time
constants; digital arithmetic; Floating point
attributes; floating point attributes; Floating point
types; floating point types; Objects; objects;
portability; Portable programs; portable programs;
program verification; software; time constants; Types;
types; Validity; validity",
thesaurus = "Ada; Digital arithmetic; Program verification;
Software portability",
treatment = "P Practical",
}
@InProceedings{Wong:1991:FDU,
author = "Derek C. Wong and Michael J. Flynn",
title = "Fast division using accurate quotient approximations
to reduce the number of iterations",
crossref = "Kornerup:1991:PIS",
pages = "191--201",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Wong.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Yan:1991:RFA,
author = "Tak W. Yan",
title = "A Rational Function Arithmetic and Simplification
System in {Common Lisp}",
journal = j-SIGSAM,
volume = "25",
number = "4",
pages = "4--6",
month = oct,
year = "1991",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Fri Feb 8 18:27:01 MST 2002",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C7310 (Mathematics); C6140D (High level languages)",
corpsource = "California University, Berkeley, CA, USA",
fjournal = "SIGSAM Bulletin",
issue = "98",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
keywords = "arithmetic simplification; Common Lisp;
exponentiation; freely-distributed computer algebra;
LISP; Lisp prefix form; mathematics computing;
multiplication; multivariate rational function;
rational addition; rational expressions; symbol
manipulation; system",
treatment = "P Practical",
}
@InProceedings{Yassine:1991:FAB,
author = "H. M. Yassine",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, 11--14 June 1991",
title = "Fast arithmetic based on residue number system
architectures",
volume = "5",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2947--2950",
year = "1991",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1991.176163",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A new approach is described for transforming residue
numbers into equivalent decimal numbers. The approach
is based on the periodicity inherent in residue numbers
and uses matrix techniques to achieve high-speed
residue-to-decimal conversion. In \ldots{}",
}
@Article{Yassine:1991:IMR,
author = "H. M. Yassine and W. R. Moore",
title = "Improved mixed-radix conversion for residue number
system architectures",
journal = "Circuits, Devices and Systems, IEE Proceedings G",
volume = "138",
number = "1",
pages = "120--124",
month = feb,
year = "1991",
CODEN = "????",
DOI = "https://doi.org/10.1109/78.80821",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2864",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Processor architectures, based on arithmetic cells
using residue number systems, are inherently parallel,
modular and fault isolating. The fundamental
characteristic of a residue number system is its being
an unweighted numbering system. The authors \ldots{}",
}
@InProceedings{Yokoo:1991:OUF,
author = "Hidetoshi Yokoo",
title = "Overflow\slash underflow-free floating-point number
representations with self-delimiting variable-length
exponent field",
crossref = "Kornerup:1991:PIS",
pages = "110--117",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Yokoo.pdf",
abstract = "A class of new floating-point representations of real
numbers, based on representations of the integers, is
described. In the class, every representation uses a
self-delimiting representation of the integers as a
variable length field, and neither overflow nor
underflow appears in practice. The adopted
representations of the integers are defined
systematically, so that representations of numbers
greater than one have both exponent-significant and
integer-fraction interpretations. Since representation
errors are characterized by the length function of an
underlying representation of the integers, systems
superior in precision can be easily selected from the
proposed class.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Gunma University,
Japan",
classification = "C1160 (Combinatorial mathematics); C5230 (Digital
arithmetic methods)",
keywords = "ARITH-10; Exponent-significant; Floating-point number
representations; Integer-fraction; Integers; Length
function; Real numbers; Representation errors;
Self-delimiting variable-length exponent field",
thesaurus = "Digital arithmetic; Number theory",
}
@Article{Yoshida:1991:PRT,
author = "N. Yoshida and E. Goto and S. Ichikawa",
title = "Pseudorandom Rounding for Truncated Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "40",
number = "9",
pages = "1065--1067",
month = sep,
year = "1991",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.83650",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 12:52:23 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=83650",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "An economical, unbiased, overflow-free rounding scheme
for multiplication of multiple-precision floating-point
numbers is proposed. The scheme, called pseudorandom
rounding, saves multiplications of lower bits and makes
use of statistical properties \ldots{}",
}
@TechReport{Yu:1991:FCF,
author = "Tsung Lun Yu and William B. Ribbens",
title = "A floating-point coprocessor for fault detection and
isolation in electronically controlled internal
combustion engines",
number = "{GLCTTR} 03-91/1",
institution = "Great Lakes Center for Truck Transportation Research",
address = "Ann Arbor, MI, USA",
pages = "68",
month = sep,
year = "1991",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Fault location (Engineering); Floating-point
arithmetic.; Internal combustion engines --- Defects.;
Microprocessors.; Motor vehicles --- Electronic
equipment.",
remark = "Performed in cooperation with the University
Transportation Centers Program by Vehicle Electronics
Laboratory, University of Michigan.",
}
@Article{Zelniker:1991:RCF,
author = "G. Zelniker and F. J. Taylor",
title = "A Reduced Complexity Finite Field {ALU}",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "38",
number = "12",
pages = "1571--1573",
month = dec,
year = "1991",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Jun 24 19:51:42 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "arithmetic logic unit (ALU)",
}
@Article{Zeng:1991:AFP,
author = "B. Zeng and Y. Neuvo",
title = "Analysis of floating point roundoff errors using dummy
multiplier coefficient sensitivities",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "38",
number = "6",
pages = "590--601",
month = jun,
year = "1991",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "A simple method for analyzing roundoff errors in
floating-point digital filters is presented. The method
is based on the coefficient sensitivities of dummy
multipliers with gains of one and connects the roundoff
error analysis to coefficient sensitive \ldots{}",
}
@PhdThesis{Zeng:1991:ARR,
author = "Bing Zeng",
title = "Analysis and reduction of roundoff errors in
floating-point recursive digital filters",
volume = "72",
type = "Avhandling (doktorgrad)",
school = "Tampereen teknillinen korkeakoulu",
address = "Tampere, Finland",
pages = "45 + 80",
year = "1991",
ISBN = "951-721-697-1",
ISBN-13 = "978-951-721-697-5",
bibdate = "Thu May 09 08:15:51 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Julkaisuja",
acknowledgement = ack-nhfb,
}
@InProceedings{Zhang:1991:ADN,
author = "D. Zhang and G. A. Jullien and W. C. Miller and Earl
{Swartzlander, Jr.}",
title = "Arithmetic for digital neural networks",
crossref = "Kornerup:1991:PIS",
pages = "58--63",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Zhang.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@InProceedings{Zhang:1991:HSE,
author = "C. N. Zhang and H. D. Cheng",
booktitle = "Reliable Systems and Applications. 5th Annual European
Computer Conference. Proceedings. {CompEuro 91}.
Advanced Computer Technology, 13--16 May 1991",
title = "A high speed error correcting converter for residue
number processing",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "816--820",
year = "1991",
CODEN = "????",
DOI = "https://doi.org/10.1109/CMPEUR.1991.257495",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A novel pipelined systolic design for residue error
correction using the Chinese remainder theorem (CRT) is
described. This design has a higher throughput compared
to previous methods and minimum time latency. The
design also has overflow detection \ldots{}",
}
@Article{Zhang:1991:HSS,
author = "C. N. Zhang and H. D. Cheng",
title = "High-speed single error correcting convertor for
residue number processing",
journal = j-IEE-PROC-COMPUT-DIGIT-TECH,
volume = "138",
number = "4",
pages = "177--182",
month = jul,
year = "1991",
CODEN = "ICDTEA",
DOI = "https://doi.org/10.1109/78.80821",
ISSN = "1350-2387 (print), 1359-7027 (electronic)",
ISSN-L = "1350-2387",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2686",
acknowledgement = ack-nhfb,
fjournal = "IEE Proceedings. Computers and Digital Techniques",
keywords = "residue arithmetic; residue number system",
summary = "A pipelined systolic design for residue error
correction using the Chinese remainder theorem is
described which has a higher throughput compared with
previous methods and minimum time latency. In addition,
the design has the capability of overflow \ldots{}",
}
@Article{Ziv:1991:FEE,
author = "Abraham Ziv",
title = "Fast Evaluation of Elementary Mathematical Functions
with Correctly Rounded Last Bit",
journal = j-TOMS,
volume = "17",
number = "3",
pages = "410--423",
month = sep,
year = "1991",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/114697.116813",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p410-ziv/",
acknowledgement = ack-nj,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; correct rounding; floating-point
arithmetic; standardization; theory",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Numerical algorithms. {\bf G.1.2}:
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation. {\bf
G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
Efficiency.",
}
@Article{Acha:1992:LOF,
author = "J. I. Acha and J. Calvo",
title = "Low-frequency oscillator for floating-point digital
signal processor chips",
journal = j-ELECT-LETTERS,
volume = "28",
number = "17",
pages = "1582--??",
month = aug,
year = "1992",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}
@Article{Anonymous:1992:FPa,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "11",
number = "8",
pages = "58--??",
month = aug,
year = "1992",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "OpenGL: The NeWs of 3D Graphics?",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Article{Anonymous:1992:FPb,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "11",
number = "11",
pages = "62--??",
month = nov,
year = "1992",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Software with a View.",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Article{Anonymous:1992:FPc,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "11",
number = "10",
pages = "101--??",
month = oct,
year = "1992",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A Helping Hand for FEA.",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Manual{ANSI:ftn92,
title = "{American National Standard Programming Language
Fortran Extended X3.198--1992}",
organization = pub-ANSI,
address = pub-ANSI:adr,
year = "1992",
bibdate = "Sat Feb 8 10:28:55 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
acknowledgement = ack-nhfb,
xxnote = "This US Standard is identical to the international
standard, ISO 1539:1991. See also
\cite{Adams:1992:FHC,Brainerd:1990:PGF,Counihan:1991:F,Metcalf:1990:FE}.",
}
@Article{Arazi:1992:BDC,
author = "B. Arazi and D. Naccache",
title = "Binary-to-Decimal Conversion Based on the Divisibility
of $ 2^8 - 1 $ by 5",
journal = j-ELECT-LETTERS,
volume = "28",
number = "3",
pages = "2151--2152",
month = nov,
year = "1992",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "decimal floating-point arithmetic",
}
@Article{Arnold:1992:AFI,
author = "M. G. Arnold and T. A. Bailey and J. R. Cowles and M.
D. Winkel",
title = "Applying features of {IEEE 754} to sign\slash
logarithm arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "1040--1050",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156547",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156547",
abstract = "Various features found in standard floating point
arithmetic (IEEE 754) are examined in light of their
appropriateness for sign/logarithm arithmetic. The
emphasis is on a 32-b word size comparable to IEEE 754
single precision, although other word sizes are
possible. A multilayer sign/logarithm format is
considered. The lowest layer, similar to previous
implementations, would provide only normalized
representations but would not provide representations
for zero, denormalized values, infinities, and NaNs.
The highest layer would provide most of the features
found in IEEE 754, including zeros, denormalized
values, infinities, and NaNs. Novel algorithms for
implementing logarithmic denormalized arithmetic are
presented. Simulation results show that the error
characteristics of the proposed logarithmic
denormalized arithmetic algorithms are similar to those
of the denormalized floating point arithmetic in IEEE
754.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Wyoming University,
Laramie, WY, USA",
ajournal = "IEEE Trans. Comput.",
classification = "B0250 (Combinatorial mathematics); B1265B (Logic
circuits); C1160 (Combinatorial mathematics); C5230
(Digital arithmetic methods)",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "32 Bit; Denormalized values; IEEE 754; Infinities;
Logarithmic denormalized arithmetic algorithms;
Multilayer sign/logarithm format; NaNs; Sign/logarithm
arithmetic; Standard floating point arithmetic; Zeros",
numericalindex = "Word length 3.2E+01 bit",
thesaurus = "Digital arithmetic; Number theory; Standards",
}
@TechReport{Bailey:1992:ATF,
author = "David H. Bailey",
title = "Automatic Translation of {Fortran} Programs to
Multiprecision",
type = "{RNR} Technical Report",
number = "RNR-91-025",
institution = "NAS Applied Research Branch, NASA Ames Research
Center",
address = "Moffett Field, CA 94035",
day = "17",
month = apr,
year = "1992",
bibdate = "Mon Sep 12 23:55:57 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Bailey:1992:PHP,
author = "David H. Bailey",
title = "A Portable High Performance Multiprecision Package",
type = "{RNR} Technical Report",
number = "RNR-90-022",
institution = "NAS Applied Research Branch, NASA Ames Research
Center",
address = "Moffett Field, CA 94035",
day = "29",
month = may,
year = "1992",
bibdate = "Mon Sep 12 23:56:03 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Baker:1992:LCE,
author = "H. G. Baker",
title = "Less Complex Elementary Functions",
journal = j-SIGPLAN,
volume = "27",
number = "11",
pages = "15--16",
month = nov,
year = "1992",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Thu Sep 08 08:11:27 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@Article{Bakhrakh:1992:NIF,
author = "S. M. Bakhrakh and S. V. Velichko and N. E.
Pilipchatin and V. F. Spiridonov and E. G. Sukhov and
Yu. G. Fedorova and V. I. Kheifets",
title = "Numerical investigation of floating-point arithmetic
operations. ({Russian})",
journal = j-PROGRAMMIROVANIE,
volume = "6",
pages = "13--17",
year = "1992",
CODEN = "PROGD3",
ISSN = "0132-3474, 0361-7688",
MRclass = "65G05",
MRnumber = "1 227 941",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "English translation appears in
\cite{Bakhrakh:1993:NIF}.",
acknowledgement = ack-nhfb,
fjournal = "Programmirovanie",
language = "Russian",
}
@TechReport{Bewick:1992:BMU,
author = "G. Bewick and M. J. Flynn",
title = "Binary multiplication using partially redundant
multiples",
type = "Technical Report",
number = "CSL-TR-92-528",
institution = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
month = jun,
year = "1992",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@TechReport{Blair:1992:PMD,
author = "M. Blair and S. Obenski and P. Bridickas",
title = "{Patriot} missile defense: Software problem led to
system failure at {Dhahran, Saudi Arabia}",
type = "Report",
number = "GAO/IMTEC-92-26",
institution = "Information Management and Technology Division, United
States General Accounting Office",
address = "Washington, DC, USA",
year = "1992",
bibdate = "Sat Apr 01 07:34:33 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.gao.gov/assets/220/215614.pdf;
http://www.gao.gov/products/IMTEC-92-26",
abstract = "Pursuant to a congressional request, GAO reviewed the
facts associated with the failure of a Patriot missile
defense system in Dhahran, Saudi Arabia, during
Operation Desert Storm.\par
GAO found that: (1) the Patriot battery at Dhahran
failed to track and intercept a Scud missile due to a
software problem in the system's weapons control
computer; (2) the software problem caused an inaccurate
tracking calculation which became worse the longer the
system operated; (3) at the time of the incident, the
battery had operated continuously for over 100 hours
and the inaccuracy was serious enough to cause the
system to look in the wrong place for the incoming
Scud; (4) two weeks before the incident, Army officials
received Israeli data indicating some loss in accuracy
after the system had been running for 8 consecutive
hours; (5) the Army had never used the Patriot to
defend against tactical ballistic missiles or expected
the Patriot to operate continuously for long periods of
time; and (6) Army officials modified the software, but
the new software did not reach Dhahran until the day
after the incident. \ldots{} The precision of a
computer's calculations depends on the number of bits
in its registers. Since the Patriot's registers are
only 24 bits long, precision beyond 24 bits is not
possible unless the software is specifically written to
adjust for such hardware limitations. Computers built
today have registers that contain as many as 64 bits,
permitting calculations with far greater precision.
\ldots{} During the conflict the Patriot's software was
modified six times. Patriots had to be shut down for at
least 1 to 2 hours to install each software
modification.",
acknowledgement = ack-nhfb,
remark = "From the report: ``Because of the way the Patriot
computer performs its calculations and the fact that
its registers are only 24 bits long, the conversion of
time from an integer to a real number cannot be any
more precise than 24 bits. This conversion results in a
loss of precision causing a less accurate time
calculation. The effect of this inaccuracy on the range
gate's calculation is directly proportional to the
target's velocity and the length of time the system has
been running. Consequently, performing the conversion
after the Patriot has been running continuously for
extended periods causes the range gate to shift away
from the center of the target, making it less likely
that the target, in this case a Scud, will be
successfully intercepted. \ldots{} On February 25,
Alpha Battery had been in operation for over 100
consecutive hours. Because the system had been on so
long, the resulting inaccuracy in the time calculation
caused the range gate to shift so much that the system
could not track the incoming Scud. Consequently, Alpha
Battery did not engage the Scud, which then struck an
Army barracks and killed 28 American soldiers.''",
xxremark = "Report of integer overflow in a timer that made the
guidance system erroneous; the ultimate solution proved
to be to reboot the guidance computer every few hours,
before the overflow.",
}
@Article{Bohlender:1992:PAF,
author = "G. Bohlender and D. Cordes and A. Kn{\"o}fel and U.
Kulisch and R. Lohner and W. V. Walter",
title = "Proposal for Accurate Floating-Point Vector
Arithmetic",
journal = j-MATH-SCI-ENG,
volume = "189",
number = "??",
pages = "87--104",
year = "1992",
CODEN = "MTSEAT",
ISSN = "0076-5392",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics in Science and Engineering",
}
@Article{Borwein:1992:MHP,
author = "Jonathan M. Borwein and Mark A. Limber",
title = "{Maple} as a High Precision Calculator",
journal = j-MAPLE-TECH-NEWS,
volume = "0",
number = "8",
pages = "39--44",
month = "Fall",
year = "1992",
ISSN = "1061-5733",
ISSN-L = "1061-5733",
bibdate = "Fri May 09 22:33:19 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/maple-tech.bib",
URL = "http://www.can.nl/Systems_and_Packages/Per_Purpose/General/Maple/mtn/mtn8.html",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Maple technical newsletter",
journal-URL = "http://web.mit.edu/maple/www/plibrary/mtn.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Brosgol:1992:ADA,
author = "Benjamin M. Brosgol and Robert I. Eachus and David E.
Emery",
title = "An {Ada} Decimal Arithmetic Capability",
journal = "CrossTalk: The Journal of Defense Software
Engineering",
volume = "36",
publisher = "Software Technology Support Center",
address = "Hill AFB, Odgen, UT, USA",
month = sep,
year = "1992",
bibdate = "Fri Nov 28 16:01:38 2003",
bibsource = "http://www.stsc.hill.af.mil/crosstalk/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.iste.uni-stuttgart.de/ps/AdaBasis/pal_1195/ada/ajpo/work-grp/ev-team/ev-info/summary.txt",
acknowledgement = ack-mfc # " and " # ack-nhfb,
keywords = "decimal floating-point arithmetic",
pagecount = "8 (approx)",
xxCODEN = "none",
xxISSN = "none",
}
@InProceedings{Brosgol:1992:DAA,
author = "Benjamin M. Brosgol and Robert I. Eachus and David E.
Emery",
title = "Decimal arithmetic in {Ada}",
crossref = "Katwijk:1992:AMT",
pages = "138--149",
year = "1992",
DOI = "https://doi.org/10.1007/3-540-55585-4_1",
bibdate = "Thu Aug 07 17:11:50 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Calvetti:1992:SRE,
author = "Daniela Calvetti",
title = "A Stochastic Roundoff Error Analysis for the
Convolution",
journal = j-MATH-COMPUT,
volume = "59",
number = "200",
pages = "569--582",
month = oct,
year = "1992",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65G05 (44A35 65T20)",
MRnumber = "93a:65061",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib;
JSTOR database; Theory/Matrix.bib",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "C4190 (Other numerical methods); C4110 (Error analysis
in numerical methods)",
corpsource = "Dept. of Pure and Appl. Math., Stevens Inst. of
Technol., Hoboken, NJ, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "accuracy; convolution; error analysis; fast Fourier
transforms; Radix-2 fast Fourier transforms; roundoff
errors; stochastic roundoff error analysis",
kwds = "nla, fft, convolution, rounding error, stochastic
analysis",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Clarkson:1992:SED,
author = "K. L. Clarkson",
title = "Safe and effective determinant evaluation",
crossref = "IEEE:1992:ASF",
pages = "387--395",
year = "1992",
bibdate = "Tue Nov 22 05:54:53 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}
@Article{Cosentino:1992:AMJ,
author = "R. J. Cosentino and J. J. Vaccaro",
title = "Adaptation of the {Mactaggart} and {Jack} Complex
Multiplication Algorithm for Floating-Point Operators",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "10",
pages = "1324--1326",
month = oct,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.166608",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=166608",
abstract = "With a suitable treatment of the exponents in the
input operands, a hardware implementation of the
Mactaggart and Jack fixed-point complex multiplication
algorithm can also calculate a floating-point product
with no loss in accuracy from the greater dynamic range
of the floating-point inputs. This floating-point
technique can be extended to any sum to two products
operation, such as encountered in matrix multiplication
and vector cross-products.",
acknowledgement = ack-nhfb,
affiliation = "Mitre Corp., Bedford, MA, USA",
ajournal = "IEEE Trans. Comput.",
classification = "C5230 (Digital arithmetic methods)",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Floating-point operators; Hardware implementation;
Jack complex multiplication algorithm; Mactaggart
complex multiplication; Matrix multiplication; Vector
cross-products",
summary = "With a suitable treatment of the exponents in the
input operands, a hardware implementation of the
Mactaggart and Jack fixed-point complex multiplication
algorithm can also calculate a floating-point product
with no loss in accuracy from the greater \ldots{}",
thesaurus = "Digital arithmetic",
}
@Article{Dao-Trong:1992:SCI,
author = "S. Dao-Trong and K. Helwig",
title = "A single-chip {IBM System}\slash 390 floating-point
processor in {CMOS}",
journal = j-IBM-JRD,
volume = "36",
number = "4",
pages = "733--749",
month = jul,
year = "1992",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Dao-Trong:1992:SIS,
author = "S. Dao-Trong and K. Helwig",
title = "A single-chip {IBM} System\slash 390 floating-point
processor in {CMOS}",
journal = j-IBM-JRD,
volume = "36",
number = "4",
pages = "733--750",
month = jul,
year = "1992",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{DaoTrong:1992:SIS,
author = "S. Dao-Trong and K. Helwig",
title = "A single-chip {IBM} system\slash 390 floating-point
processor in {CMOS}",
journal = j-IBM-JRD,
volume = "36",
number = "4",
pages = "733--749",
month = jul,
year = "1992",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A floating-point processor with the IBM System/390
architecture is implemented in one CMOS VLSI chip
containing over 70000 cells (equivalent inverters),
using a transistor channel length of 0.5 mu m. All
floating-point instructions are hard-wired, including
the binary integer multiplications. The chip is
implemented in a 1- mu m technology with three layers
of metal. All circuits are realized in standard cells
except for a floating-point register and a multiplier
array macro, which are custom designed to save chip
area. Instructions are performed in a five-stage
pipeline with a maximum operating frequency of 37 MHz.
The chip measures 12.7 mm*12.7 mm, and dissipates 2 W.
It is part of the chip set which forms the core of the
IBM Enterprise System/9000 Type 9221 entry-level
models.",
acknowledgement = ack-nhfb,
affiliation = "IBM Germany, Boeblingen, Germany",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5230 (Digital arithmetic methods)",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "37 MHz; Binary integer multiplications; Chip set;
CMOS; Equivalent inverters; Five-stage pipeline; IBM
Enterprise System/9000; Single-chip IBM system/390
floating-point processor; Transistor channel length",
numericalindex = "Frequency 3.7E+07 Hz",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Equipment evaluation; IBM computers; Microprocessor
chips",
}
@MastersThesis{Daumas:1992:BIR,
author = "Marc Daumas",
title = "Basis for the implementation of a reliable dot
product",
type = "{Master}'s Thesis",
school = "Southern Methodist University",
address = "Dallas, Texas",
year = "1992",
bibdate = "Wed Nov 24 12:42:59 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Davarakis:1992:PPA,
author = "C. T. Davarakis and D. G. Maritsas",
title = "A Probabilistic Parallel Associative Search and Query
Set of Algorithms",
journal = j-J-PAR-DIST-COMP,
volume = "14",
number = "1",
pages = "37--49",
month = jan,
year = "1992",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Computer Technology Inst",
affiliationaddress = "Patras, Greece",
classification = "723; 921; 922; C1230 (Artificial intelligence);
C4240P (Parallel programming and algorithm theory);
C5470 (Performance evaluation and testing); C7310
(Mathematics)",
corpsource = "Department of Comput. Eng., Comput. Technol. Inst.,
Patras, Greece",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "Algorithms; arithmetic applications; Associative
searching; Computer Programming; computing; Data
Storage, Digital--Associative; digital arithmetic;
extrema algorithm; extrema queries; generic associative
process; heuristic programming; heuristics; high
performance systems; Mathematical
Techniques--Heuristic; mathematics; multilayer
associative process; parallel algorithms; parallel
associative search; parallel threshold; performance
evaluation; Primitive algorithms; primitive algorithms;
probabilistic; Probability; query set of algorithms;
symbol manipulation; symbolic applications; threshold
searches; time performance",
treatment = "A Application; P Practical",
}
@InProceedings{Dawid:1992:BSC,
author = "H. Dawid and G. Fettweis",
title = "Bit-level systolic carry-save array division",
crossref = "IEEE:1992:GCG",
pages = "484--488 vol.1",
year = "1992",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A bit-level systolic carry-save division array that
allows bit-level pipelining, just as for carry-save
array multipliers, is presented. This architecture
leads to very fast, efficient and regular division
implementations as needed in digital signal processing
(DSP) applications such as speech processing or
cryptography. The architecture is very well suited for
integer division as well as for the division of
normalized fixed-point mantissas used in floating-point
number system implementations.",
acknowledgement = ack-nhfb,
affiliation = "Aachen University of Technol., Germany",
classification = "B1265B (Logic circuits); C5130 (Microprocessor
chips); C5230 (Digital arithmetic methods); C5260
(Digital signal processing)",
keywords = "Bit-level pipelining; Carry-save array multipliers;
Cryptography; Digital signal processing; DSP;
Floating-point number system; Integer division;
Normalized fixed-point mantissas; Speech processing;
Systolic carry-save array division",
thesaurus = "Digital arithmetic; Systolic arrays",
}
@Article{Dawson:1992:RLS,
author = "Jeffrey Dawson and Mary Payne and Craig Schaffert",
title = "The Role of {LIA-1} in Software Portability",
journal = j-SIGNUM,
volume = "27",
number = "4",
pages = "9--12",
month = oct,
year = "1992",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:22 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "LIA is now an International Standard, ISO/IEC
10967-1:1994; it is ``92 pages of small print, densely
mathematical, not counting 8 pages of front matter, and
it is not available electronically.'' Its adoption has
been rather controversial.",
abstract = "The second committee draft of language independent
arithmetic-Part 1: Integer and floating point
arithmetic is now available. This document was formerly
called the Language Compatible Arithmetic Standard
(LCAS) and is now referred to as LIA-1. This draft was
prepared by ISO/IEC JTC1/SC22/WG11, with assistance
from standards committees in several countries. The
authors explain the goals of the standard and methods
for achieving those goals. They present them to clear
up previous misunderstandings, misconceptions, and
misrepresentations of the purpose of the standard. (0
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Digital Equipment Corp., Maynard, MA, USA",
classification = "C0310F (Software development management); C6110B
(Software engineering techniques); C7310
(Mathematics)",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "Floating point arithmetic; Integer arithmetic; ISO/IEC
JTC1/SC22/WG11; Language independent arithmetic; LIA-1;
Software portability; Standard",
thesaurus = "Mathematics computing; Software portability;
Standards",
}
@Book{DEC:1992:AAH,
author = "Digital Equipment Corporation",
title = "{Alpha} Architecture Handbook",
publisher = pub-DP,
address = pub-DP:adr,
year = "1992",
bibdate = "Mon Jan 18 15:08:40 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Demmel:1992:LWN,
author = "James Demmel",
title = "{LAPACK} working note 49 draft: a specification for
floating point parallel prefix",
type = "Technical report",
number = "CS-92-167",
institution = "University of Tennessee, Computer Science Dept.",
address = "Knoxville, TN, USA",
pages = "8 + 1",
month = may,
year = "1992",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Parallel prefix is a useful operation for various
linear algebra operations, including solving bidiagonal
systems of equations and finding the eigenvalues of a
symmetric tridiagonal matrix. However, the simplest
implementations of parallel prefix for the operations
of scalar floating point add and scalar floating point
multiply are inadequate to solve these important
problems. This is because they are too susceptible to
over/underflow, and because they apparently cannot
solve the general two term recurrence needed to find
eigenvalues. In this note we propose a specification
for parallel prefix operations overcoming these
drawbacks.",
acknowledgement = ack-nhfb,
keywords = "Linear algebraic groups.",
}
@TechReport{Demmel:1992:SFP,
author = "J. Demmel",
title = "A Specification for Floating Point Parallel Prefix",
type = "LAPACK Working Note",
number = "49",
institution = inst-UT-CS,
address = inst-UT-CS:adr,
month = may,
year = "1992",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "UT-CS-92-167, May 1992.",
URL = "http://www.netlib.org/lapack/lawns/lawn49.ps;
http://www.netlib.org/lapack/lawnspdf/lawn49.pdf",
acknowledgement = ack-nhfb,
}
@Article{Devine:1992:RTT,
author = "M. L. Devine",
title = "Real time trigonometric function evaluation",
journal = j-MICROPROC-MICROSYS,
volume = "16",
number = "8",
pages = "417--425",
month = aug,
year = "1992",
CODEN = "MIMID5",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Microprocessors and Microsystems",
}
@Article{Dimauro:1992:NMF,
author = "G. Dimauro and S. Impedovo and G. Pirlo",
title = "A new magnitude function for fast numbers comparison
in the residue number system",
journal = j-MICROPROC-MICROPROG,
volume = "35",
number = "1--2",
pages = "97--104",
month = sep,
year = "1992",
CODEN = "MMICDT",
DOI = "https://doi.org/10.1016/0165-6074(92)90300-V",
ISSN = "0165-6074 (print), 1878-7061 (electronic)",
ISSN-L = "0165-6074",
bibdate = "Thu Nov 18 09:52:10 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper a new magnitude function, called the
`diagonal function', has been defined from a Residue
Number System to the integers. The `diagonal function'
provides an efficient technique for fast magnitude
comparison of numbers in the residue representation.
The superiority of this technique with respect to the
approaches based on the Chinese Remainder Theorem and
on the Mixed Radix Transformation is shown.",
acknowledgement = ack-nhfb,
fjournal = "Microprocessing and Microprogramming",
}
@MastersThesis{Du:1992:CAB,
author = "Sihai Du",
title = "Cellular automata based floating-point adder and
multiplier with a single transition rule",
type = "Thesis ({M.S.C.E.})",
school = "Wright State University",
address = "Dayton, OH, USA",
pages = "ix + 68",
year = "1992",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Cellular automata --- Research.; Computer Simulation.;
Floating-point arithmetic --- Research.",
}
@Article{Dunham:1992:SFW,
author = "Charles B. Dunham",
title = "Surveyor's Forum: {``What Every Computer Scientist
Should Know About Floating-Point Arithmetic''}",
journal = j-COMP-SURV,
volume = "24",
number = "3",
pages = "319--319",
month = sep,
year = "1992",
CODEN = "CMSVAN",
ISSN = "0360-0300 (print), 1557-7341 (electronic)",
ISSN-L = "0360-0300",
bibdate = "Sun Sep 25 10:14:37 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compsurv.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See
\cite{Goldberg:1991:WEC,Goldberg:1991:CWE,Wichmann:1992:SFW}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
}
@InProceedings{Duprat:1992:DOF,
author = "J. Duprat and M. Fiallos-Aguilar and Jean-Michel
Muller and H. J. Yeh",
title = "Delays of on-line floating point operators in
borrow-save representation",
crossref = "Quinton:1992:APV",
pages = "273--278",
year = "1992",
bibdate = "Wed Dec 13 13:13:34 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "On-line computation using redundant notations to
represent numbers is an interesting field of computer
arithmetic. In these systems, different operators can
operate together in a digit level pipelining mode. In
integer or fixed-point format, implementations of the
main operations have been proposed. This paper focuses
on a floating point format. The authors show that, more
so in addition than in multiplication, critical loss of
information due to the variation of the length of the
mantissas can be avoided by partial normalizations.
Furthermore, these normalizations do not break the
circulation of the digit though they do delay the
operations even more.",
acknowledgement = ack-nhfb,
affiliation = "Ecole Normale Superieure de Lyon, France",
classification = "C5230 (Digital arithmetic methods); C5440
(Multiprocessor systems and techniques)",
keywords = "Borrow-save representation; Computer arithmetic;
Delays; Digit level pipelining mode; Floating point
format; Mantissas; On-line floating point operators;
Partial normalizations; Redundant notations",
thesaurus = "Delays; Digital arithmetic; Pipeline processing",
}
@Article{Duprat:1992:SPF,
author = "J. Duprat and M. Fiallos Aguilar",
title = "On the Simulation of Pipelining of Fully Digit On-Line
Floating-Point Adder Networks on Massively Parallel
Computers",
journal = j-LECT-NOTES-COMP-SCI,
volume = "??",
number = "634",
pages = "707--712",
year = "1992",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Ercegovac:1992:FRC,
author = "M. D. Ercegovac and T. Lang",
title = "On-the-fly rounding [computing arithmetic]",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "12",
pages = "1497--1503",
month = dec,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.214659",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:21 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=214659",
abstract = "In implementations of operations based on
digit-recurrence algorithms such as division,
left-to-right multiplication and square root, the
result is obtained in digit-serial form, from most
significant digit to least significant. To reduce the
complexity of the result-digit selection and allow the
use of redundant addition, the result-digit has values
from a signed-digit set. As a consequence, the result
has to be converted to conventional representation,
which can be done on-the-fly as the digits are
produced, without the use of a carry-propagate adder.
The authors describe three ways to modify this
conversion process so that the result is rounded. The
resulting operation is fast because no carry-propagate
addition is needed. The schemes described apply also to
online arithmetic operations.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Fagin:1992:LIM,
author = "Barry S. Fagin",
title = "Large Integer Multiplication on Hypercubes",
journal = j-J-PAR-DIST-COMP,
volume = "14",
number = "4",
pages = "426--430",
month = apr,
year = "1992",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 17:13:17 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C4230M (Multiprocessor interconnection); C4240P
(Parallel programming and algorithm theory); C5230
(Digital arithmetic methods)",
corpsource = "Thayer Sch. of Eng., Dartmouth Coll., Hanover, NH,
USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "Connection Machine; digital arithmetic; Fermat Number
Transform; hypercube networks; hypercubes; integer
multiplication; parallel algorithms; polynomial
transforms; transforms",
treatment = "T Theoretical or Mathematical",
}
@Article{Filanovsky:1992:SCA,
author = "I. M. Filanovsky and H. P. Baltes",
title = "Simple {CMOS} analog square-rooting and squaring
circuits",
journal = j-IEEE-TRANS-CIRCUITS-SYST-I-FUNDAM-THEORY-APPL,
volume = "39",
number = "4",
pages = "312--315",
month = apr,
year = "1992",
CODEN = "ITCAEX",
ISSN = "1057-7122 (print), 1558-1268 (electronic)",
ISSN-L = "1057-7122",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems I:
Fundamental Theory and Applications",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=81",
summary = "Two closely related CMOS circuits are described. In
the first circuit, the input signal is a current, and
the output is a voltage proportional to the square root
of input current. In the second circuit, the input is a
voltage, and the output is the \ldots{}",
}
@Article{Fujii:1992:FCL,
author = "H. Fujii and C. Hori and T. Takada and N. Hatanaka and
T. Demura and G. Ootomo",
title = "A Floating-Point Cell Library and a {100-MFLOPS} Image
Signal Processor",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "27",
number = "7",
pages = "1080--1088",
month = jul,
year = "1992",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
}
@Article{Fujii:1992:FPC,
author = "H. Fujii and C. Hori and T. Takada and N. Hatanaka and
T. Demura and G. Ootomo",
title = "A floating-point cell library and a {100-Mflops} image
signal processor",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "27",
number = "7",
pages = "1080--1088",
month = jul,
year = "1992",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "A novel floating-point cell library for image signal
processors that includes a floating-point arithmetic
logic unit (ALU), a floating-point multiplier (MPY), an
instruction RAM, and a data register file is
considered. It has been designed for high-speed
\ldots{}",
}
@Article{Gamberger:1992:IIM,
author = "D. Gamberger",
title = "Inversion of integer matrices in residue number
system",
journal = j-IEE-PROC-COMPUT-DIGIT-TECH,
volume = "139",
number = "5",
pages = "465--468",
month = sep,
year = "1992",
CODEN = "ICDTEA",
DOI = "https://doi.org/10.1109/78.157231",
ISSN = "1350-2387 (print), 1359-7027 (electronic)",
ISSN-L = "1350-2387",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4186",
acknowledgement = ack-nhfb,
fjournal = "IEE Proceedings. Computers and Digital Techniques",
keywords = "residue arithmetic; residue number system",
summary = "The presented algorithm makes use of the recently
introduced incompletely specified residue number
system. This system enables the operations necessary in
the inversion process to be done quickly, completely in
parallel for different moduli, even if \ldots{}",
}
@Article{Goldberg:1992:DFD,
author = "D. Goldberg",
title = "The design of floating-point data types",
journal = j-LOPLAS,
volume = "1",
number = "2",
pages = "138--151",
month = jun,
year = "1992",
CODEN = "ALPSE8",
ISSN = "1057-4514 (print), 1557-7384 (electronic)",
ISSN-L = "1057-4514",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The issues involved in designing the floating-point
part of a programming language are discussed. Looking
at the language specifications for most existing
languages might suggest that this design involves only
trivial issues, such as whether to have one or two
types of REALs or how to name the functions that
convert from INTEGER to REAL. It is shown that there
are more significant semantic issues involved. After
discussing the tradeoffs for the major design
decisions, they are illustrated by presenting the
design of the floating-point part of the Modula-3
language.",
acknowledgement = ack-nhfb,
affiliation = "Xerox Palo Alto Res. Center, CA, USA",
classification = "C6120 (File organisation)",
fjournal = "ACM Letters on Programming Languages and Systems",
keywords = "Design; Floating-point data types; Language
specifications; Modula-3 language; Programming
language; REALs",
thesaurus = "Data structures; Digital arithmetic",
}
@Article{Gray:1992:UMF,
author = "A. Gray and R. Knill",
title = "Using {Mathematica} to Find Closed Form Expressions
for Approximations to the Square Root of $x$",
journal = j-MATHEMATICA-EDUC,
volume = "1",
number = "4",
pages = "12--13",
month = "Summer",
year = "1992",
ISSN = "1065-2965",
bibdate = "Sat Apr 6 16:22:43 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-ble,
fjournal = "Mathematica in Education",
}
@InProceedings{Hartwig:1992:AFQ,
author = "F. Hartwig and A. Lacroix",
title = "Analysis of floating-point quantization errors using
stochastic models",
crossref = "Vandewalle:1992:SPV",
pages = "247--250 vol.1",
year = "1992",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Some results concerning the single quantizer with
limited exponent wordlength are presented. In addition
to roundoff, the authors present a generalization for
magnitude truncation. The method is also applied to
digital filters. The theoretical results are tested in
comparison with simulation results.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Angewandte Phys., J. W. Goethe-University,
Frankfurt am Main, Germany",
classification = "B0240Z (Other and miscellaneous); B0290B (Error
analysis in numerical methods); B1265H (A/D and D/A
convertors); B6140 (Signal processing and detection);
C1140Z (Other and miscellaneous); C5230 (Digital
arithmetic methods); C5240 (Digital filters)",
keywords = "Digital filters; Digital signal processing devices;
Floating-point quantization errors; Limited exponent
wordlength; Magnitude truncation; Roundoff; Simulation
results; Stochastic models; Theoretical results",
thesaurus = "Analogue-digital conversion; Digital arithmetic;
Digital filters; Error analysis; Signal processing;
Stochastic processes",
}
@InProceedings{Hartwig:1992:MFA,
author = "F. Hartwig and A. Lacroix",
title = "Multi-operand floating-point addition utilizing
operand sorting",
crossref = "White:1992:IIS",
pages = "1800--1803 vol.4",
year = "1992",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In many signal processing applications repeated
additions have to be calculated with a considerable
number of operands. It is known that proper sorting of
operands has a positive influence on the precision of
the result of multioperand floating-point additions.
This is investigated for different operand statistics
and for proper sorting strategies. In addition to
successive addition techniques, adder trees are
included in the investigation. The densities of the
addition errors for different floating-point addition
methods are compared.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fuer Angewandte Phys., J. W. Goethe-University,
Frankfurt am Main, Germany",
classification = "C1260 (Information theory); C5230 (Digital
arithmetic methods); C5260 (Digital signal processing);
C6130 (Data handling techniques)",
keywords = "Adder trees; Addition errors densities; Floating-point
addition; Floating-point addition methods; Multioperand
floating-point additions; Operand sorting; Operand
statistics; Repeated additions; Signal processing;
Sorting strategies; Successive addition techniques",
thesaurus = "Digital arithmetic; Signal processing; Sorting",
}
@Article{Hasan:1992:BSS,
author = "M. A. Hasan and V. K. Bhargava",
title = "Bit-serial systolic divider and multiplier for finite
fields {$ \mathrm {GF}(2^m) $}",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "972--980",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156540",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156540",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Hasan:1992:MCL,
author = "M. A. Hasan and M. Wang and V. K. Bhargava",
title = "Modular construction of low complexity parallel
multipliers for a class of finite fields {$ \mathrm
{GF}(2^m) $}",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "962--971",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156539",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156539",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Hegeman:1992:AF,
author = "Frederick W. Hegeman",
title = "Arithmetic In Factorial-Base",
journal = j-CUJ,
volume = "10",
number = "2",
pages = "73--??",
month = feb,
year = "1992",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@Article{Hoehfeld:1992:LLN,
author = "M. Hoehfeld and S. E. Fahlman",
title = "Learning with limited numerical precision using the
cascade-correlation algorithm",
journal = j-IEEE-TRANS-NEURAL-NETW,
volume = "3",
number = "4",
pages = "602--611",
month = jul,
year = "1992",
CODEN = "ITNNEP",
DOI = "https://doi.org/10.1109/72.143374",
ISSN = "1045-9227 (print), 1941-0093 (electronic)",
ISSN-L = "1045-9227",
bibdate = "Fri Sep 22 17:49:00 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Neural Networks",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=72",
}
@InProceedings{Hoff:1992:FCH,
author = "J. R. Hoff and G. W. Foster",
title = "A full custom, high speed, floating point adder",
crossref = "Alley:1992:CRI",
pages = "450 vol.1",
year = "1992",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Summary form only. A high-speed pipelined floating
point adder for use by the Solenoidal Detector
Collaboration (SDC) at the Superconducting Super
Collider (SSC) is discussed. The adder uses a unique
floating point format. The chip is designed to be a
two-stage pipeline and to operate at a peak speed of at
least 63 MHz. Static rather than dynamic logic was
desired, to permit operation at lower speeds and to
ease system testing. The chip is implemented using
Orbit Semiconductor's 1.2 mu m n-well process.
Simulations indicate that the device will operate at 63
MHz. Initial testing performed at Fermilab, limited by
test equipment, indicates speeds of at least 63 MHz,
with some tests demonstrating speeds in excess of 150
MHz.",
acknowledgement = ack-nhfb,
affiliation = "Fermilab, Batavia, IL, USA",
classification = "A2980C (Computer systems); B1265B (Logic circuits);
B7430 (Counting circuits and electronics); C5120 (Logic
and switching circuits); C5230 (Digital arithmetic
methods); C7320 (Physics and Chemistry)",
keywords = "150 MHz; 63 MHz; Fermilab; Floating point adder; High
speed; Orbit Semiconductor; Pipelined; SDC; Simulation;
Static logic; System testing; Testing; Two-stage
pipeline",
numericalindex = "Frequency 6.3E+07 Hz; Frequency 1.5E+08 Hz",
thesaurus = "Adders; Digital arithmetic; Nuclear electronics;
Physics computing; Pipeline processing",
}
@Article{Hohfeld:1992:PRN,
author = "Markus H{\"o}hfeld and Scott E. Fahlman",
title = "Probabilistic rounding in neural network learning with
limited precision",
journal = j-NEUROCOMPUTING,
volume = "4",
number = "6",
pages = "291--299",
month = dec,
year = "1992",
CODEN = "NRCGEO",
DOI = "https://doi.org/10.1016/0925-2312(92)90014-g",
ISSN = "0925-2312 (print), 1872-8286 (electronic)",
ISSN-L = "0925-2312",
bibdate = "Fri Sep 22 17:46:22 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Neurocomputing",
journal-URL = "http://www.sciencedirect.com/science/journal/09252312",
}
@Article{Horiguchi:1992:FNR,
author = "Hiroshi Horiguchi and Tsutomu Tayama",
title = "Floating-Point Numbers and Real Numbers {II}",
journal = j-ADV-SOFT-SCI-TECH,
volume = "3",
number = "??",
pages = "151--156",
year = "1992",
ISSN = "1044-7997",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Advances in software science and technology",
}
@MastersThesis{Hoyt:1992:MFP,
author = "Brian S. Hoyt",
title = "The {Macintosh} floating point arithmetic
visualization system",
type = "Thesis ({M.S.--Electrical Engineering})",
school = "Bucknell University",
address = "Lewisburg, PA, USA",
pages = "ix + 88",
year = "1992",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supervised by Richard J. Zaccone. Describes the
design, development, implementation, and use of MacFavs
(Macintosh Floating point arithmetic visualization
system). MacFavs uses simulation, visual displays, and
animations to allow students to see actual machine
representations of floating point numbers.",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Macintosh (Computer);
Numerical analysis --- Computer-assisted instruction.",
}
@Article{Hudak:1992:RPL,
author = "Paul Hudak and Simon Peyton Jones and Philip Wadler
and Brian Boutel and Jon Fairbairn and Joseph Fasel and
Mar{\'\i}a M. Guzm{\'a}n and Kevin Hammond and John
Hughes and Thomas Johnsson and Dick Kieburtz and
Rishiyur Nikhil and Will Partain and John Peterson",
title = "Report on the programming language {Haskell}: a
non-strict, purely functional language (Version 1.2)",
journal = j-SIGPLAN,
volume = "27",
number = "5",
pages = "Ri--Rx, R1--R163",
month = may,
year = "1992",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:16:21 MST 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Haskell is a general purpose, purely functional
programming language incorporating many recent
innovations in programming language research, including
higher-order functions, non-strict semantics, static
polymorphic typing, user-defined algebraic datatypes,
pattern-matching, list comprehensions, a module system,
and a rich set of primitive datatypes, including lists,
arrays, arbitrary and fixed precision integers, and
floating-point numbers. Haskell is both the culmination
and solidification of many years of research on
functional languages-the design has been influenced by
languages as old as ISWIM and as new as Miranda. The
report defines the syntax for Haskell programs and an
informal abstract semantics for the meaning of such
programs.",
acknowledgement = ack-nhfb,
affiliation = "Yale University, New Haven, CT, USA",
classification = "C6140D (High level languages)",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "Abstract semantics; Arrays; Fixed precision integers;
Floating-point numbers; Functional programming
language; Haskell; Higher-order functions; List
comprehensions; Lists; Module system; Non-strict
semantics; Pattern-matching; Primitive datatypes;
Static polymorphic typing; Syntax; User-defined
algebraic datatypes",
thesaurus = "Functional programming; High level languages",
}
@Article{IFIF:1992:CVD,
author = "{IFIP Working Group 2.5 (Numerical Software)}",
title = "Comments on version 3.1 of draft {ISO\slash IEC
10967:1991 Language Compatible Arithmetic}",
journal = j-SIGNUM,
volume = "27",
number = "1",
pages = "2--3",
month = jan,
year = "1992",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:21 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@InProceedings{Jackson:1992:DTF,
author = "P. B. Jackson",
title = "Developing a toolkit for floating-point hardware in
the {Nuprl} proof development system",
crossref = "Prinetto:1992:CHD",
pages = "401--419",
year = "1992",
bibdate = "Wed Dec 13 13:13:34 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Describes current work in building a toolkit of
theorems, definitions and tactics in the Nuprl proof
development system for the verification of
floating-point hardware designs. The approach
emphasizes reasoning over a wide range of levels of
abstraction within a single system. For example the
specification of the IEEE's floating point standard
makes free use of rational arithmetic, as well as
talking explicitly about the input and output
bit-vectors of floating-point circuits.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Cornell University,
Ithaca, NY, USA",
classification = "C4210 (Formal logic); C5230 (Digital arithmetic
methods); C6110B (Software engineering techniques);
C6115 (Programming support)",
keywords = "Floating-point hardware; Nuprl proof development
system; Rational arithmetic; Reasoning; Toolkit;
Verification",
thesaurus = "Digital arithmetic; Formal specification; Software
tools; Theorem proving",
}
@Article{Jacobson:1992:ETF,
author = "David Jacobson",
title = "Engineer's Toolbox: Floating Point in {Mathematica}",
journal = j-MATHEMATICA-J,
volume = "2",
number = "3",
pages = "42--46",
month = "Summer",
year = "1992",
CODEN = "????",
ISSN = "1047-5974 (print), 1097-1610 (electronic)",
ISSN-L = "1047-5974",
bibdate = "Sat Nov 6 13:33:40 MDT 2010",
bibsource = "http://www.mathematica-journal.com/issue/v2i3/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.mathematica-journal.com/issue/v2i3/tutorials/toolbox/index.html",
abstract = "Mathematica provides both traditional machine-level
floating point numbers and software-implemented
variable-precision floating-point numbers. There are
two different notions of precision: an estimate of the
maximum possible relative error, which is propagated
through arithmetic operations based on the precision of
the operands; and the number of digits used to
represent the significand (mantissa). Mathematica links
the first notion to the second, throwing away digits
that it cannot prove are significant. In iterative
calculations the precision can ratchet down a little
each iteration, until there is nothing left.",
acknowledgement = ack-nhfb,
fjournal = "Mathematica Journal",
journal-URL = "http://www.mathematica-journal.com/",
}
@Article{Jaffar:1992:AMC,
author = "Joxan Jaffar and Peter J. Stuckey and Spiro Michaylov
and Roland H. C. Yap",
title = "An abstract machine for {CLP$ (\mathcal {R}) $}",
journal = j-SIGPLAN,
volume = "27",
number = "7",
pages = "128--139",
month = jul,
year = "1992",
CODEN = "SINODQ",
ISBN = "0-89791-475-9",
ISBN-13 = "978-0-89791-475-8",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
LCCN = "QA76.7.S53 1992",
bibdate = "Sun Dec 14 09:16:22 MST 2003",
bibsource = "Compendex database; http://portal.acm.org/;
http://www.acm.org/pubs/contents/proceedings/pldi/143095/index.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/pldi/143095/p128-jaffar/",
abstract = "An abstract machine is described for the CLP$
(\mathcal {R}) $ programming language. It is intended
as a first step toward enabling CLP$ (\mathcal {R}) $
programs to be executed with efficiency approaching
that of conventional languages. The core Constraint
Logic Arithmetic Machine (CLAM) extends the Warren
Abstract Machine (WAM) for compiling Prolog with
facilities for handling real arithmetic constraints.
The full CLAM includes facilities for taking advantage
of information obtained from global program analysis.",
acknowledgement = ack-nhfb,
affiliation = "IBM T. J. Watson Research Cent",
affiliationaddress = "Yorktown Heights, NY, USA",
annote = "Published as part of the Proceedings of PLDI'92.",
classification = "723.1",
conference = "Proceedings of the ACM SIGPLAN '92 Conference on
Programming Language Design and Implementation",
conferenceyear = "1992",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
journalabr = "SIGPLAN Not",
keywords = "Abstract machine; algorithms; Computer programming;
Computer programming languages; Constraint logic
arithmetic machine; design; Global program analysis;
languages; Program compilers; prolog (programming
language)",
meetingaddress = "San Francisco, CA, USA",
meetingdate = "Jun 17--19 1992",
meetingdate2 = "06/17--19/92",
sponsor = "ACM",
subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, Prolog. {\bf D.1.6} Software,
PROGRAMMING TECHNIQUES, Logic Programming. {\bf D.3.3}
Software, PROGRAMMING LANGUAGES, Language Constructs
and Features, Data types and structures. {\bf D.3.4}
Software, PROGRAMMING LANGUAGES, Processors,
Optimization.",
}
@InProceedings{Jain:1992:AEA,
author = "V. K. Jain and G. E. Perez and E. E. Swartzlander",
title = "Arithmetic Error Analysis of a New Reciprocal Cell",
crossref = "IEEE:1992:IIC",
pages = "106--109",
year = "1992",
bibdate = "Thu Sep 08 00:34:18 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@MastersThesis{James:1992:DRC,
author = "Shelton L. James",
title = "A distributed remote computational server",
type = "Thesis ({M.S.})",
school = "University of Missouri, Columbia",
address = "Columbia, MO, USA",
pages = "vi + 183",
year = "1992",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Distributed operating systems (Computers); Electronic
networks.; Floating-point systems.; OSI (Computer
network standard)",
}
@InProceedings{Johnstone:1992:RNA,
author = "P. Johnstone and F. E. Petry",
title = "Rational number approximation in higher radix floating
point systems",
crossref = "IEEE:1992:PIS",
pages = "501--504 vol.2",
year = "1992",
bibdate = "Wed Dec 13 13:13:34 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Recent research has shown that hybrid non-binary
floating point bases, particularly decimal-based
systems, can match or exceed the error performance of
more traditional binary systems. The authors address a
more general question of whether such bases offer any
further advantages in the domain of rational number
approximation. They consider the effect of the choice
of floating point base on rational number approximation
in systems which exhibit the typical characteristics of
floating point representations, normalized encodings,
limited exponent range, and storage allocated in a
fixed number of bits per datum. The frequency with
which terminating and representable results can be
expected is considered for binary, decimal, and other
potentially interesting bases (base 30 and base 210).",
acknowledgement = ack-nhfb,
affiliation = "Telerate Syst. Inc., New Orleans, LA, USA",
classification = "C5230 (Digital arithmetic methods)",
keywords = "Base 10; Base 2; Base 210; Base 30; Bits per datum;
decimal floating-point arithmetic; Error performance;
Floating point representations; Fractions; Higher radix
floating point systems; Limited exponent range;
Normalized encodings; Rational number approximation;
Storage allocated",
thesaurus = "Digital arithmetic",
}
@Article{Kahan:1992:ARL,
author = "W. Kahan",
title = "Analysis and Refutation of the {LCAS}",
journal = j-SIGPLAN,
volume = "27",
number = "1",
pages = "61--74",
month = jan,
year = "1992",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Thu Aug 18 02:37:25 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "LCAS (Language Compatible Arithmetic Standard)",
}
@Unpublished{Kahan:1992:FPE,
author = "W. Kahan",
title = "Floating-Point Exception-Handling",
institution = inst-BERKELEY-CS,
address = inst-BERKELEY-CS:adr,
pages = "2",
day = "31",
month = jul,
year = "1992",
bibdate = "Mon Apr 25 18:24:02 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Manuscript",
acknowledgement = ack-nhfb,
}
@Article{Kahaner:1992:SJC,
author = "D. K. Kahaner and U. Wattenberg",
title = "{Supercomputing-Japan}: a competitive assessment",
journal = j-IEEE-SPECTRUM,
volume = "29",
number = "9",
pages = "42--47",
month = sep,
year = "1992",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/6.155708",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Thu Jan 16 07:37:23 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1990.bib;
https://www.math.utah.edu/pub/tex/bib/super.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "5 to 8 GFLOPS; Arithmetic; Central Processing Unit;
Computer industry; Hardware; high-speed single
processor systems; Home computing; Information
technology; intuitive information processing; Japanese
supercomputers; Manufacturing industries; Ministry of
International Trade and Industry; National electric
code; parallel machines; Real-World Computing Program;
research initiatives; Supercomputers; Telephony; US
machines; vector processing functions",
}
@InProceedings{Kalliojarvi:1992:DRN,
author = "K. Kalliojarvi and Y. Neuvo",
title = "Distribution of roundoff noise in binary
floating-point addition",
crossref = "White:1992:IIS",
volume = "4",
bookpages = "3028",
pages = "1796--1799",
year = "1992",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A method for deriving the distribution of relative
round off error in addition of two binary
floating-point numbers is introduced. The distribution
is needed in the calculation of variance of the
relative roundoff error in floating-point addition. The
resulting distribution depends on the statistics of the
addends and the rounding strategy chosen. As an
example, the distribution is derived for the addition
of two uncorrelated numbers from Gaussian distribution.
The result was verified by simulation.",
acknowledgement = ack-nhfb,
affiliation = "Signal Process. Lab., Tampere University of Technol.,
Finland",
classification = "C1260 (Information theory); C5230 (Digital
arithmetic methods); C5260 (Digital signal
processing)",
keywords = "Addends; Binary floating-point addition; Calculation
of variance; Distribution of relative round off error;
Gaussian distribution; Relative roundoff error;
Rounding strategy; Roundoff noise; Simulation; Two
uncorrelated numbers",
thesaurus = "Digital arithmetic; Digital simulation; Roundoff
errors; Signal processing",
}
@Book{Kane:1992:MRA,
author = "Gerry Kane and Joe Heinrich",
title = "{MIPS RISC} Architecture",
publisher = pub-PH,
address = pub-PH:adr,
year = "1992",
ISBN = "0-13-590472-2",
ISBN-13 = "978-0-13-590472-5",
LCCN = "QA76.8.M52 K37 1992",
bibdate = "Wed Dec 15 10:35:45 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/microchip.bib",
acknowledgement = ack-nhfb,
keywords = "computer architecture; MIPS R2000 series
microprocessors; reduced instruction set computers",
tableofcontents = "RISC Architecture: An Overview \\
MIPS Processor Architecture Overview \\
CPU Instruction Set Summary \\
Memory Management System \\
Caches \\
Exception Processing \\
FPU Overview \\
FPU Instruction Set Summary and Instruction Pipeline
\\
Floating Point Exceptions \\
Appendixes \\
Index",
}
@Book{Klatte:1992:PXP,
author = "Rudi Klatte and Ulrich Kulisch and Michael Neaga and
Dietmar Ratz and Christian Ullrich",
title = "{PASCAL-XSC}: language reference with examples",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 344",
year = "1992",
DOI = "https://doi.org/10.1007/978-3-642-77277-1",
ISBN = "3-540-55137-9 (Berlin), 0-387-55137-9 (New York)",
ISBN-13 = "978-3-540-55137-9 (Berlin), 978-0-387-55137-1 (New
York)",
LCCN = "QA76.73.P2 P4213 1992",
bibdate = "Thu Jan 21 17:16:51 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "Translated by G. F. Corliss and others.",
price = "DM 64.00",
abstract = "The programming language PASCAL-XSC (PASCAL eXtension
for Scientific Computation) significantly simplifies
programming in the area of scientific and technical
computing. PASCAL-XSC provides a large number of
predefined data types with arithmetic operators and
predefined functions of highest accuracy for real and
complex numbers, for real and complex intervals, and
for the corresponding vectors and matrices. Thus
PASCAL-XSC makes the computer more powerful concerning
the arithmetic. Through an implementation in C,
compilers for PASCAL-XSC are available for a large
variety of computers such as personal computers,
workstations, mainframes, and supercomputers.
PASCAL-XSC provides a module concept, an operator
concept, functions and operators with general result
type, overloading of functions, procedures, and
operators, dynamic arrays, access to subarrays,
rounding control by the user, and accurate evaluation
of expressions. The language is particularly suited for
the development of numerical algorithms that deliver
highly accurate and automatically verified results. A
number of problem-solving routines with automatic
result verification have already been implemented.
PASCAL-XSC contains Standard PASCAL. It is immediately
usable by PASCAL programmers. PASCAL-XSC is easy to
learn and ideal for programming education. The book can
be used as a textbook for lectures on computer
programming. It contains a major chapter with sample
programs, exercises, and solutions. A complete set of
syntax diagrams, detailed tables, and indices complete
the book.",
acknowledgement = ack-nhfb,
language = "English.",
remark = "Translation of: PASCAL-XSC.",
subject = "Pascal (Computer program language)",
tableofcontents = "1 Introduction \\
1.1 Typography \\
1.2 Historical Remarks and Motivation \\
1.3 Advanced Computer Arithmetic \\
1.4 Connection with Programming Languages \\
1.5 Survey of PASCAL-XSC \\
2 Language Reference \\
2.1 Basic Symbols \\
2.2 Identifiers \\
2.3 Constants, Types, and Variables \\
2.4 Expressions \\
2.5 Statements \\
2.6 Program Structure \\
2.7 Subroutines \\
2.8 Modules \\
2.9 String Handling and Text Processing \\
2.10 How to Use Dynamic Arrays \\
3 The Arithmetic Modules \\
3.1 The Module C\_ARI \\
3.2 The Module I\_ARI \\
3.3 The Module CI\_ARI \\
3.4 The Module MV\_ARI \\
3.5 The Module MVC\_ARI \\
3.6 The Module MVI\_ARI \\
3.7 The Module MVCI\_ARI \\
3.8 The Hierarchy of the Arithmetic Modules \\
3.9 A Complete Sample Program \\
4 Problem-Solving Routines \\
5 Exercises with Solutions \\
5.1 Test of Representability \\
5.2 Summation of Exponential Series \\
5.3 Influence of Rounding Errors \\
5.4 Scalar Product \\
5.5 Boothroyd/Dekker Matrices \\
5.6 Complex Functions \\
5.7 Surface Area of a Parallelepiped \\
5.8 Parallelism and Intersection of Lines \\
5.9 Transposed Matrix, Symmetry \\
5.10 Rail Route Map \\
5.11 Inventory Lists \\
5.12 Complex Numbers and Polar Representation \\
5.13 Complex Division \\
5.14 Electric Circuit \\
5.15 Alternating Current Measuring Bridge \\
5.16 Optical Lens \\
5.17 Interval Evaluation of a Polynomial \\
5.18 Calculations for Interval Matrices \\
5.19 Differentiation Arithmetic \\
5.20 Newton's Method with Automatic Differentiation \\
5.21 Measurement of Time \\
5.22 Iterative Method \\
5.23 Trace of a Product Matrix \\
5.24 Calculator for Polynomials \\
5.25 Interval Newton Method \\
5.26 Runge-Kutta Method \\
5.27 Rational Arithmetic \\
5.28 Evaluation of Polynomials \\
A Syntax Diagrams \\
B Indices and Lists \\
B.1 Syntax Diagrams \\
B.2 Reserved Words \\
B.3 Predefined Identifiers \\
B.4 Operators \\
B.4.1 Basic Operators \\
B.4.2 Arithmetic Operators \\
B.4.3 Relational Operators for the Arithmetic Types \\
B.4.4 Assignment Operators \\
B.5 Predefined Functions \\
B.6 Transfer Functions \\
B.7 Predefined Procedures \\
B.8 \#-Expressions \\
B.8.1 Real and Complex \#-Expressions \\
B.8.2 Real and Complex Interval \#-Expressions \\
Bibliography \\
Index",
}
@Article{Koc:1992:AAS,
author = "{\c{C}}etin K. Ko{\c{c}} and Ching-Yu Hung",
title = "Adaptive $m$-ary segmentation and canonical recoding
algorithms for multiplication of large binary numbers",
journal = j-COMPUT-MATH-APPL,
volume = "24",
number = "3",
pages = "3--12",
month = aug,
year = "1992",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:11:08 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/089812219290209Z",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Kola:1992:MQP,
author = "M. Kol{\'a}r and T. Sasaki",
title = "Multivariate quotient by power-series division",
journal = j-SIGSAM,
volume = "26",
number = "3",
pages = "17--20",
month = aug,
year = "1992",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Fri Feb 8 18:27:02 MST 2002",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIGSAM Bulletin",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@InProceedings{Kontro:1992:FAS,
author = "J. Kontro and K. Kalliojarvi and Y. Neuvo",
title = "Floating-point arithmetic in signal processing",
crossref = "White:1992:IIS",
pages = "1784--1791 vol.4",
year = "1992",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The use of floating-point arithmetic in digital signal
processing is considered. An introduction to
floating-point arithmetic based on the IEEE
floating-point standards is given. Finite wordlength
effects of these arithmetic systems are presented.
Floating-point hardware is discussed. The emphasis is
on audio applications. As an example, amplitude
distributions and signal-to-noise ratios of quantized
music are considered, and audio standards using
floating-point arithmetic are presented.",
acknowledgement = ack-nhfb,
affiliation = "Signal Process. Lab., Tampere University of Technol.,
Finland",
classification = "B1265F (Microprocessors and microcomputers); B6140
(Signal processing and detection); B6450 (Audio
equipment and systems); C1260 (Information theory);
C5130 (Microprocessor chips); C5230 (Digital arithmetic
methods); C5260 (Digital signal processing)",
keywords = "Amplitude distributions; Audio applications; Audio
standards; Digital signal processing; Finite wordlength
effects; Floating-point arithmetic; Hardware; IEEE
floating-point standards; Quantized music;
Signal-to-noise ratios",
thesaurus = "Audio equipment; Audio signals; Digital arithmetic;
Digital signal processing chips; Roundoff errors;
Signal processing",
}
@Article{Kontro:1992:USF,
author = "J. Kontro and K. Kalliojarvi and Y. Neuvo",
title = "Use of Short Floating-Point Formats in Audio
Applications",
journal = j-IEEE-TRANS-CONSUMER-ELECTRONICS,
volume = "38",
number = "3",
pages = "200--207",
month = aug,
year = "1992",
CODEN = "ITCEDA",
ISSN = "0098-3063 (print), 1558-4127 (electronic)",
ISSN-L = "0098-3063",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Consumer Electronics",
summary = "Use of short floating-point formats that are shorter
than the IEEE floating-point standard (ANSI/IEEE S+A
754-1985), 24+8-b, in digital audio applications is
studied. The performance of these formats is analyzed
in different parts of the digital audio \ldots{}",
}
@Article{Krishna:1992:CTA,
author = "H. Krishna and K.-Y. Lin and J.-D. Sun",
title = "A coding theory approach to error control in redundant
residue number systems. {I}. Theory and single error
correction",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "39",
number = "1",
pages = "8--17",
month = jan,
year = "1992",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.204106",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5240",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems. 2, Analog
and Digital Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
keywords = "residue arithmetic; residue number system",
summary = "A coding theory approach to error control in redundant
residue number systems (RRNSs) is presented. The
concepts of Hamming weight, minimum distance, weight
distribution, and error detection and correction
capabilities in redundant residue number \ldots{}",
}
@Article{Krishnan:1992:CGF,
author = "R. Krishnan and G. A. Jullien and W. C. Miller",
title = "Computation of generalized {FIR} filter structure
using the modified quadratic residue number system",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "39",
number = "1",
pages = "58--62",
month = jan,
year = "1992",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.204110",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5240",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems. 2, Analog
and Digital Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
keywords = "residue arithmetic; residue number system",
summary = "The systematic approach for generating the generalized
number theoretic FIR filter structure based on the
complex number theoretic z-transform is presented. A
step-by-step computational method that can be used in
the implementation and \ldots{}",
}
@InProceedings{Kubosawa:1992:BFP,
author = "H. Kubosawa and A. Katsuno and H. Takahashi and T.
Sato and A. Suga and G. Goto",
title = "A 64-bit floating point processing unit for a {RISC}
microprocessor",
crossref = "Anonymous:1992:EAP",
pages = "270--273",
year = "1992",
DOI = "https://doi.org/10.1109/EUASIC.1992.228042",
bibdate = "Thu Mar 02 09:45:28 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/iel2/416/5911/00228042.pdf",
acknowledgement = ack-nhfb,
keywords = "25MHz SPARC S-25 microprocessor; CMOS; PGA; RISC",
}
@InProceedings{Kutuso:1992:EMO,
author = "K. N. Kutuso and H. M. Yassine",
booktitle = "Proceedings of the 35th Midwest Symposium on Circuits
and Systems, 1992",
title = "Effect of moduli ordering of mixed radix conversion
methods in residue number systems",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "678--680",
year = "1992",
CODEN = "????",
DOI = "https://doi.org/10.1109/MWSCAS.1992.271232",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The effect of moduli ordering in different methods for
converting residue numbers to decimal numbers using the
mixed radix approach is investigated. The number of
operations involved in the conversion process of
residue numbers to their decimal \ldots{}",
}
@InProceedings{Lacroix:1992:DDM,
author = "A. Lacroix and F. Hartwig",
title = "Distribution densities of the mantissa and exponent of
floating point numbers",
crossref = "White:1992:IIS",
pages = "1792--1795 vol.4",
year = "1992",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "6 vol.",
abstract = "The relations between the probability densities of
real numbers and the corresponding mantissa and
exponent densities in the floating point number format
are investigated. Assumptions about continuity of the
probability density of real numbers lead to certain
restrictions in terms of the density of the mantissa. A
few real number densities of practical importance were
treated analytically and experimentally. During
arithmetic operations like addition and multiplication
which are essential for signal processing the operand
density is altered. The effect concerning the densities
of mantissa and exponent of the result is discussed.
The reciprocal density of the mantissas plays a central
role. Applications in roundoff-noise-analysis of signal
processing with finite wordlength are considered. (5
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Inst. fuer Angewandte Phys., J. W. Goethe-University,
Frankfurt am Main, Germany",
classification = "B1270F (Digital filters); B6140 (Signal processing
and detection); C1260 (Information theory); C5230
(Digital arithmetic methods); C5240 (Digital filters);
C5260 (Digital signal processing)",
keywords = "Addition; Arithmetic operations; Exponent densities;
Finite wordlength; Floating point number format;
Floating point numbers; Mantissa densities;
Multiplication; Operand density; Probability densities;
Real numbers; Reciprocal density;
Roundoff-noise-analysis; Signal processing",
thesaurus = "Digital arithmetic; Digital filters; Roundoff errors;
Signal processing",
}
@Article{Lang:1992:HRS,
author = "T. Lang and P. Montuschi",
title = "Higher radix square root with prescaling",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "996--1009",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156542",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156542",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "A scheme for performing higher radix square root based
on prescaling of the radicand is presented to reduce
the complexity of the result-digit selection. The
scheme requires several steps, namely multiplication
for prescaling the radicand, square \ldots{}",
}
@Article{Lee:1992:ACR,
author = "J. H. M. Lee and M. H. {van Emden}",
title = "Adapting {$ {\rm CLP}(\sc {R}) $} to floating-point
arithmetic",
journal = "Fifth generation computer systems, vol 1",
volume = "2",
publisher = "Ohm",
address = "Tokyo, Japan",
pages = "996--1003",
year = "1992",
MRclass = "68N15 (68N17 68Q40)",
MRnumber = "93m:68027",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Lee:1992:FPP,
author = "K. Lee",
title = "On the Floating Point Performance of the i860
Microprocessor",
journal = j-INT-J-HIGH-SPEED-COMPUTING,
volume = "4",
number = "4",
pages = "251--268",
month = dec,
year = "1992",
CODEN = "IHSCEZ",
ISSN = "0129-0533",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of High Speed Computing",
journal-URL = "http://www.worldscientific.com/worldscinet/ijhsc",
}
@Book{Leighton:1992:IPA,
author = "Frank Thomson Leighton",
title = "Introduction to Parallel Algorithms and Architectures:
Arrays, Trees, Hypercubes",
publisher = pub-MORGAN-KAUFMANN,
address = pub-MORGAN-KAUFMANN:adr,
pages = "xviii + 831",
year = "1992",
ISBN = "1-55860-117-1",
ISBN-13 = "978-1-55860-117-8",
LCCN = "QA76.5 .L45 1992",
bibdate = "Mon Sep 16 16:21:01 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$54.95",
acknowledgement = ack-nhfb,
}
@Article{Li:1992:CSC,
author = "Zhenyu Li and Victor Milenkovic",
title = "Constructing Strongly Convex Hulls Using Exact or
Rounded Arithmetic",
journal = j-ALGORITHMICA,
volume = "8",
number = "5--6",
pages = "345--364",
year = "1992",
CODEN = "ALGOEJ",
ISSN = "0178-4617 (print), 1432-0541 (electronic)",
ISSN-L = "0178-4617",
MRclass = "68U05 (52B55)",
MRnumber = "MR1195157 (93k:68104)",
MRreviewer = "Nikolaj M. Korneenko",
bibdate = "Mon Jan 22 05:31:33 MST 2001",
bibsource = "dblp-journals-algorithmica.bib;
http://dblp.uni-trier.de/db/journals/algorithmica/algorithmica8.html#LiM92;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/index-table-a.html#algorithmica;
MathSciNet database",
note = "1990 Computational Geometry Symposium (Berkeley, CA,
1990)",
acknowledgement = ack-nhfb,
fjournal = "Algorithmica. An International Journal in Computer
Science",
journal-URL = "http://link.springer.com/journal/453",
keywords = "exact arithmetic; floating-point arithmetic; rounding
errors",
oldlabel = "LiM92",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/algorithmica/LiM92",
}
@Article{Lim:1992:SPM,
author = "Y. C. Lim",
title = "Single-precision multiplier with reduced circuit
complexity for signal processing applications",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "10",
pages = "1333--1336",
month = oct,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.166611",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=166611",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Liu:1992:QBS,
author = "K. J. R. Liu and E. Frantzeskakis",
booktitle = "Workshop on {VLSI} Signal Processing, V, 1992",
title = "Qrd-based Square Root Free and Division Free
Algorithms and Architectures",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "459--468",
year = "1992",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Not \ldots{}",
}
@Article{Lozier:1992:RPC,
author = "D. W. Lozier and P. R. Turner",
title = "Robust Parallel Computation in Floating-Point and
{SLI} Arithmetic. {Robuste Parallel-Verarbeitung in
Gleitkomma-und SLI-Arithmetik}",
journal = j-COMPUTING,
volume = "48",
number = "3-4",
pages = "239--258 (or 239--257??)",
year = "1992",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65Y05 (65-04 65G05)",
MRnumber = "93e:65161",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Lozier:1992:RPV,
author = "D. W. Lozier and P. R. Turner",
title = "{Robuste Parallel-Verarbeitung in Gleitkomma- und
SLI-Arithmetik}. ({German}) [{Robust} Parallel
Computation in Floating-Point and {SLI} Arithmetic]",
journal = j-COMPUTING,
volume = "48",
number = "3--4",
pages = "239--257",
month = sep,
year = "1992",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65Y05 (65-04 65G05)",
MRnumber = "93e:65161",
bibdate = "Mon Oct 11 20:38:38 MDT 1999",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database; OCLC Contents1st database",
acknowledgement = ack-nhfb,
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
language = "German",
}
@Article{Lozier:1992:SLI,
author = "Daniel W. Lozier and P. R. Turner",
title = "Symmetric Level-Index Arithmetic in Simulation and
Modeling",
journal = j-J-RES-NATL-BUR-STAND,
volume = "97",
number = "4",
pages = "471--485",
month = jul,
year = "1992",
CODEN = "JRNBAG",
DOI = "https://doi.org/10.6028/jres.097.020",
ISSN = "0091-0635 (print), 2376-5305 (electronic)",
ISSN-L = "0091-0635",
bibdate = "Fri Jul 09 07:24:16 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://nvlpubs.nist.gov/nistpubs/jres/097/jresv97n4p471_A1b.pdf",
abstract = "This paper begins with a general introduction to the
symmetric level-index, SLI, system of number
representation and arithmetic. This system provides a
robust framework in which experimental computation can
be performed without the risk of failure due to
overflow/underflow or to poor scaling of the original
problem. There follows a brief summary of some existing
computational experience with this system to illustrate
its strengths in numerical, graphical and parallel
computational settings. An example of the use of SLI
arithmetic to overcome graphics failure in the modeling
of a turbulent combustion problem is presented. The
main thrust of this paper is to introduce the idea of
SLI-linear least squares data fitting. The use of
generalized logarithm and exponential functions is seen
to offer significant improvement over the more
conventional linear regression tools for fitting data
from a compound exponential decay such as the decay of
radioactive materials.",
acknowledgement = ack-nhfb,
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
keywords = "computer graphics; generalized logarithms and
exponentials; least-squares data-fitting; overflow,
underflow, and scaling; parallel computing; symmetric
level-index arithmetic.",
}
@Article{Lu:1992:NDA,
author = "M. Lu and J.-S. Chiang",
title = "A novel division algorithm for the residue number
system",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "1026--1032",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156545",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156545;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4052",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "A novel general algorithm for signed number division
in the residue number system (RNS) is presented. The
parity checking technique used for sign and overflow
detection in this algorithm is more efficient and
practical than conventional methods. \ldots{}",
}
@InProceedings{Lynch:1992:FCA,
author = "Thomas W. Lynch and Earl E. {Swartzlander, Jr.}",
title = "A Formalization for Computer Arithmetic",
crossref = "Atanassova:1992:CAE",
pages = "137--145",
year = "1992",
bibdate = "Sat Sep 17 19:09:42 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "From the abstract: ``The formalism, when applied to
IEEE Std 754 shows that the non-trapping mode can
produce incorrect numeric and non-numeric results.''",
acknowledgement = ack-nhfb,
}
@Misc{Lynch:1992:HSD,
author = "T. Lynch and S. McIntyre and K. Tseng and S. Shaw and
T. Hurson",
title = "High speed divider with square root capability",
year = "1992",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "U.S. Patent No. 5,128,891.",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@InProceedings{Maguire:1992:MD,
author = "J. Maguire",
title = "{MC8810}: Datapath",
crossref = "Juj:1992:NCR",
pages = "193--197",
year = "1992",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@MastersThesis{Makhdumi:1992:CCS,
author = "Shazia Makhdumi",
title = "Comparison of current switch bipolar circuits for high
performance floating point arithmetic",
type = "Thesis ({M.S.})",
school = "Massachusetts Institute of Technology, Dept. of
Electrical Engineering and Computer Science",
address = "Cambridge, MA, USA",
pages = "107",
year = "1992",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Mar:1992:DSP,
editor = "Amy Mar",
title = "Digital signal processing applications using the
{ADSP}-2100 family",
publisher = pub-PH,
address = pub-PH:adr,
pages = "????",
year = "1992",
ISBN = "0-13-219726-X (vol. 1), 0-13-178567-2 (vol. 2)",
ISBN-13 = "978-0-13-219726-7 (vol. 1), 978-0-13-178567-0 (vol.
2)",
LCCN = "TK5102.9 .D53 1992",
bibdate = "Sat Jan 15 05:58:58 MST 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Vol. 2: edited by Jere Babst. System requirements for
computer disks: IBM-compatible PC; DOS 3.0 or higher;
high-density disk drive.",
subject = "Signal processing; Digital techniques;
Microprocessors",
}
@Article{McQuillan:1992:VMH,
author = "S. E. McQuillan and J. V. McCanny",
title = "{VLSI} module for high-performance multiply, square
root and divide",
journal = j-IEE-PROC-COMPUT-DIGIT-TECH,
volume = "139",
number = "6",
pages = "505--510",
month = nov,
year = "1992",
CODEN = "ICDTEA",
ISSN = "1350-2387 (print), 1359-7027 (electronic)",
ISSN-L = "1350-2387",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEE Proceedings. Computers and Digital Techniques",
summary = "A high-performance VLSI architecture to perform
multiply-accumulate, division and square root
operations is proposed. The circuit is highly regular,
requires only minimal control and ean be pipelined
right down to the bit level. The system can also
\ldots{}",
}
@TechReport{MenissierMorain:1992:CNR,
author = "V. M{\'e}nissier-Morain",
title = "{CAML} numbers reference manual",
number = "141",
institution = "Inst. Nat. Recherche Inf. Autom.",
address = "Le Chesnay, France",
pages = "157",
month = jul,
year = "1992",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An overview is given of the arithmetic of the
functional language CAML V3.1. This arithmetic includes
floating point numbers, arbitrary large integers and
rationals and a complete set of primitives. Its
implementation relies on the efficient BigNum package
(J.-C. Herve et al., 1989).",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods); C6110 (Systems
analysis and programming); C6140D (High level
languages); C7310 (Mathematics)",
keywords = "Arbitrary large integers; Arithmetic; BigNum package;
Floating point numbers; Functional language CAML;
Primitives; Rationals",
pubcountry = "France",
thesaurus = "Digital arithmetic; Functional programming; High level
languages; Mathematics computing",
}
@Book{Menninger:1992:NWN,
author = "Karl Menninger",
title = "Number Words and Number Symbols: a Cultural History of
Numbers",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xiii + 480",
year = "1992",
ISBN = "0-486-27096-3",
ISBN-13 = "978-0-486-27096-8",
LCCN = "QA141.2 .M4513 1992",
bibdate = "Fri Nov 28 18:29:23 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@Article{Meredith:1992:NPF,
author = "Roger W. Meredith",
title = "Numeric precision in {FORTRAN} computing",
journal = j-COMPUT-PHYS,
volume = "6",
number = "5",
pages = "506--512",
month = sep # "\slash " # oct,
year = "1992",
CODEN = "CPHYE2",
DOI = "https://doi.org/10.1063/1.168438",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Wed Apr 10 08:45:36 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://aip.scitation.org/doi/10.1063/1.168438",
acknowledgement = ack-nhfb,
ajournal = "Comput. Phys",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
}
@Article{Mikami:1992:NDO,
author = "N. Mikami and M. Kobayashi and Y. Yokoyama",
title = "A New {DSP}-Oriented Algorithm for Calculation of the
Square Root Using a Nonlinear Digital Filter",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "40",
number = "7",
pages = "1663--1669",
month = jul,
year = "1992",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "A high-speed algorithm for calculating the square root
is proposed. This algorithm, which can be regarded as
calculation of the step response of a kind of nonlinear
IIR filter, requires no divisions. Therefore, it is
suitable for a VLSI digital \ldots{}",
}
@Article{Mitchell:1992:VFA,
author = "H. B. Mitchell",
title = "Very fast accurate square-root algorithm for use with
gradient edge operators",
journal = j-ELECT-LETTERS,
volume = "28",
number = "10",
pages = "922--923",
day = "7",
month = may,
year = "1992",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
summary = "Commonly used gradient edge operators such as the
Sobel, Prewitt and Roberts operators all required a
square root operation; this is, however,
computationally intensive and, consequently, simple but
very inaccurate approximations are often used
\ldots{}",
}
@InProceedings{Montuschi:1992:DAC,
author = "P. Montuschi and L. Ciminiera and A. Giustina",
title = "A Division Architecture Combining {Newton--Raphson}
Approximations and Direct Methods Iterations",
crossref = "Singh:1992:CRT",
pages = "376--380",
year = "1992",
bibdate = "Wed Dec 13 18:19:38 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors consider the possibility of designing
architectures which combine in the best possible way
the convergence with the square advantages of the
Newton--Raphson method with the precision
characteristics of the digit-by-digit algorithms so as
to obtain units which satisfy the IEEE 754 floating
point standard requirements. This is a general method
which can be extended with simple and minor changes
also to square root. Attention is focused on a possible
implementation of this design methodology for division.
The evaluation shows that the proposed unit offers an
alternative architecture for division which provides
interesting performances.",
acknowledgement = ack-nj,
affiliation = "Dipartimento di Autom. e Inf., Politecnico di Torino,
Italy",
classification = "B0290F (Interpolation and function approximation);
B1265B (Logic circuits); C4130 (Interpolation and
function approximation); C5230 (Digital arithmetic
methods)",
keywords = "Convergence; Digit-by-digit algorithms; Direct methods
iterations; Division architecture; IEEE 754 floating
point standard; Newton--Raphson method; Square
advantages; Square root",
thesaurus = "Convergence of numerical methods; Digital arithmetic;
Dividing circuits; Iterative methods",
}
@Article{Montuschi:1992:DRD,
author = "P. Montuschi and L. Ciminiera",
title = "Design of a radix $4$ division unit with simple
selection table",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "12",
pages = "1606--1611",
month = dec,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.214670",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=214670",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Moore:1992:PRP,
author = "David L. Moore",
title = "Programming the 29050 ({RISC} programming)",
journal = j-DDJ,
volume = "17",
number = "1",
pages = "34, 36, 38, 40, 42",
month = jan,
year = "1992",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Tue Sep 10 10:06:23 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5220 (Computer architecture); C6110 (Systems
analysis and programming); C6140B (Machine-oriented
languages)",
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "29000 Family; AM29050; Assembly language programming;
Flat address space; Floating-point operations;
Registers; RISC processors",
thesaurus = "Assembly language; Microprogramming; Reduced
instruction set computing",
}
@Book{Morgan:1992:NM,
author = "Don Morgan",
title = "Numerical Methods: Real-time and Embedded Systems
Programming",
publisher = pub-MT,
address = pub-MT:adr,
pages = "496",
year = "1992",
ISBN = "1-55851-232-2 (book only), 1-55851-233-0 (disk only),
1-55851-234-9 (book and disk set)",
ISBN-13 = "978-1-55851-232-0 (book only), 978-1-55851-233-7 (disk
only), 978-1-55851-234-4 (book and disk set)",
LCCN = "QA76.6 .M669 1992",
bibdate = "Wed Sep 14 19:16:35 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$34.95",
acknowledgement = ack-nj,
}
@Article{Mou:1992:OSA,
author = "Z.-J. Mou and F. Jutand",
title = "{`Overturned-stairs'} adder trees and multiplier
design",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "940--948",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156536",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156536",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Mutrie:1992:AFE,
author = "Mark P. W. Mutrie and Richard H. Bartels and Bruce W.
Char",
title = "An approach for floating-point error analysis using
computer algebra",
crossref = "Wang:1992:PII",
pages = "284--293",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p284-mutrie/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, Maple. {\bf G.2.2} Mathematics
of Computing, DISCRETE MATHEMATICS, Graph Theory, Graph
algorithms.",
}
@PhdThesis{Mutrie:1992:TSS,
author = "Mark P. W. Mutrie",
title = "Towards a symbolic system for floating-point error
analysis",
type = "Thesis ({Ph.D.})",
publisher = "National Library of Canada = Bibliotheque nationale du
Canada",
school = "University of Waterloo",
address = "Waterloo, ON, Canada",
year = "1992",
ISBN = "0-315-72486-2",
ISBN-13 = "978-0-315-72486-0",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "8 microfiches. University Microfilms order no.
UMI00359027",
series = "Canadian theses = Theses canadiennes",
acknowledgement = ack-nhfb,
}
@Article{Nakano:1992:AHS,
author = "H. Nakano and M. Nakajima and Y. Nakakura and T.
Yoshida and Y. Goi and Y. Nakai and R. Segawa and T.
Kishida",
title = "An accurate, high speed implementation of division by
the quasi-unity divisor method",
journal = j-IFIP-TRANS-A,
volume = "A-12",
pages = "261--267",
month = "????",
year = "1992",
CODEN = "ITATEC",
ISSN = "0926-5473",
bibdate = "Thu Dec 14 15:33:50 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Algorithms, Software, Architecture. Information
Processing 92. IFIP 12th World Computer Congress.",
abstract = "A first-order convergent division algorithm is
generally thought to be accurate but slow. Using a
large look-up table and a multiplier improves speed.
Since a partial quotient is not negative and iterations
use only one formula, an iteration is carried out in
the form of a partial carry and a partial sum. This
paper describes a new developed division algorithm with
the above-mentioned characteristics. This algorithm is
compared to other similar algorithms. In a hardware
implementation, this algorithm is applied to the 53-bit
significand part of a floating-point double precision
divider. The execution time is division of 8 or 9
cycles.",
acknowledgement = ack-nhfb,
affiliation = "Corporate R and D, Matsushita Electric Industrial Co.
Ltd., Osaka, Japan",
classification = "C5230 (Digital arithmetic methods)",
confdate = "7-11 Sept. 1992",
conflocation = "Madrid, Spain",
confsponsor = "IFIP",
fjournal = "IFIP Transactions. A. Computer Science and
Technology",
keywords = "53-Bit significand part; First-order convergent
division algorithm; Floating-point double precision
divider; Look-up table; Multiplier; Partial carry;
Partial sum; Quasi-unity divisor method",
pubcountry = "Netherlands",
thesaurus = "Digital arithmetic; Table lookup",
}
@Article{Nakano:1992:FPB,
author = "H. Nakano and M. Nakajima and Y. Nakakura and T.
Yoshida and Y. Goi and Y. Nakai and R. Segawa and T.
Kishida and H. Kadota",
title = "An 80-{FLOPS} (Peak) 64-b Microprocessor for Parallel
Computer",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "27",
number = "3",
pages = "365--372",
month = mar,
year = "1992",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Journal of Solid-State Circuits",
}
@Article{Ng:1992:ARH,
author = "K. C. Ng",
title = "Argument Reduction for Huge Arguments: Good to the
Last Bit",
journal = "SunPro",
volume = "??",
number = "??",
day = "13",
month = jul,
year = "1992",
bibdate = "Thu Sep 1 10:16:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Work in progress.",
URL = "http://www.validlab.com/arg.pdf",
acknowledgement = ack-nj,
keywords = "range reduction",
}
@InProceedings{Nishimura:1992:FPR,
author = "S. Nishimura",
booktitle = "Proceedings of the 35th Midwest Symposium on Circuits
and Systems, 1992",
title = "A fixed-point roundoff error analysis of adaptive
notch filters",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "373--376",
year = "1992",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Methods to analyze the convergence and steady-state
characteristics of an adaptive notch filter when the
effects of fixed-point arithmetic are taken into
account are presented. The adaptive detection of a
sinusoid with white Gaussian noise is \ldots{}",
}
@Article{Obaidat:1992:DMA,
author = "Mohammad S. Obaidat and Saleh A. Bleha",
title = "A Decimal Multiplication Algorithm for
Microcomputers",
journal = j-COMPUT-ELECTR-ENG,
volume = "18",
number = "5",
pages = "357--363",
month = sep,
year = "1992",
CODEN = "CPEEBQ",
ISSN = "0045-7906 (print), 1879-0755 (electronic)",
ISSN-L = "0045-7906",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computers and Electrical Engineering",
keywords = "decimal floating-point arithmetic",
}
@Article{Ochs:1992:SIR,
author = "T. Ochs",
title = "This sine is also right!",
journal = j-COMP-LANG-MAG,
volume = "9",
number = "1",
pages = "89--93",
month = jan,
year = "1992",
CODEN = "COMLEF",
ISSN = "0749-2839",
bibdate = "Thu Sep 01 10:44:04 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Language Magazine",
}
@Article{Okada:1992:AQE,
author = "Kazuho Okada and Yasuaki Kuroe",
title = "Analysis of Quantization Errors in Digital Control
Systems Using Floating-Point Arithmetic--Considering
Computational Order in Controller",
journal = j-ELECT-COMM-JAPAN-3-FUND-ELECT-SCI,
volume = "75",
number = "6",
pages = "1--??",
month = jun,
year = "1992",
CODEN = "ECJSER",
ISSN = "1042-0967 (print), 1520-6440 (electronic)",
ISSN-L = "1042-0967",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics and communications in Japan. Part 3,
Fundamental electronic science",
}
@Article{Orton:1992:NFT,
author = "G. A. Orton and L. E. Peppard and S. E. Tavares",
title = "New fault tolerant techniques for residue number
systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "11",
pages = "1453--1464",
month = nov,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.177315",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:21 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=177315;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4475",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "Previously proposed error detection algorithms for the
residue number system require a complete recombination.
A weighted approximation via the Chinese remainder
theorem is shown to be sufficient to detect 100\% of
single errors. This makes real-time \ldots{}",
}
@InProceedings{Paliouras:1992:SDP,
author = "V. Paliouras and D. Soudris and T. Stouraitis",
booktitle = "{IEEE} International Symposium on Circuits and
Systems. {ISCAS '92}. Proceedings, 3--6 May 1992",
title = "Systematic derivation of the processing element of a
systolic array based on residue number system",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "815--818",
year = "1992",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1992.230097",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A systematic methodology for synthesizing optimal VLSI
residue number system architectures using full adders
(FAs) as the basic building block is introduced. The
design methodology derives array architectures starting
from the algorithmic level. \ldots{}",
}
@TechReport{Pan:1992:CWU,
author = "V. Y. Pan",
title = "Can we utilize the cancellation of the most
significant digits?",
type = "Report",
number = "TR 92 061",
institution = "The International Computer Science Institute",
address = "Berkeley, CA, USA",
year = "1992",
bibdate = "Mon Mar 06 17:00:31 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Park:1992:MED,
author = "Haesun Park",
title = "On Multiple Error Detection in Matrix
Triangularizations Using Checksum Methods",
journal = j-J-PAR-DIST-COMP,
volume = "14",
number = "1",
pages = "90--97",
month = jan,
year = "1992",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
MRclass = "65F05 (65F25)",
MRnumber = "92i:65060",
bibdate = "Mon Apr 14 08:15:42 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ of Minnesota",
affiliationaddress = "Minneapolis, MN, USA",
classification = "722; 723; 921; 922; C4110 (Error analysis in
numerical methods); C5220P (Parallel architecture);
C5230 (Digital arithmetic methods); C5470 (Performance
evaluation and testing)",
corpsource = "Department of Computer Science, Minnesota University,
Minneapolis, MN, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "Checksum methods; checksum methods; Codes,
Symbolic--Error Detection; Computer Systems,
Digital--Fault Tolerant Capability; correct rounding;
detection; digital arithmetic; error; error analysis;
error correction; errors; floating-point arithmetic;
floating-point error analysis; Gaussian elimination; LU
decomposition; Mathematical Techniques; matrix; Matrix
Algebra; Matrix triangularizations; multiple error
correction; multiple error detection; pairwise
pivoting; parallel architectures; performance
evaluation; QR decomposition; rounding; transient
errors; triangularizations",
treatment = "P Practical",
}
@Article{Parker:1992:OVN,
author = "A. Parker and J. O. Hamblen",
title = "Optimal value for the {Newton--Raphson} division
algorithm",
journal = j-INFO-PROC-LETT,
volume = "42",
number = "3",
pages = "141--144",
day = "25",
month = may,
year = "1992",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Wed Nov 11 07:31:13 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
keywords = "fast division; floating-point arithmetic",
}
@Article{Pichat:1992:SFR,
author = "Mich{\`e}le Pichat",
title = "Sets of floating-point results associated with an
algebraic algorithm",
journal = "Computational and applied mathematics, I (Dublin,
1991)",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "409--418",
year = "1992",
MRclass = "68M07 (65G05)",
MRnumber = "93m:68010",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Plauger:1992:SCL,
author = "P. J. Plauger",
title = "The {Standard C} Library",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xiv + 498",
year = "1992",
ISBN = "0-13-838012-0",
ISBN-13 = "978-0-13-838012-0",
LCCN = "QA76.73.C15 P563 1991",
bibdate = "Wed Dec 15 10:40:47 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ansistd.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/litprog.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/unix.bib",
abstract = "\booktitle{The Standard C Library} shows you how to
use all of the library functions mandated by the ANSI
and ISO Standards for the programming language C. To
help you understand how to use the library, this book
also shows you how to implement it. You see
approximately 9,000 lines of tested, working code that
is highly portable across diverse computer
architectures. \booktitle{The Standard C Library}
explains how the library was meant to be used and how
it can be used. It places particular emphasis on
features added to C as part of the C Standard. These
features include support for multiple locales (cultural
conventions) and very large character sets (such as
Kanji). The code presented in this book has been tested
with C compilers from Borland, Saber, Project Gnu, Sun,
UNIX, and VAX, ULTRIX. It has passed the widely used
Plum Hall Validation Suite tests for library functions.
It has also survived an assortment of public-domain
programs designed to stress C implementations and
illuminate their darker corners. The mathematical
functions are particularly well-engineered and tested.
Finally, \booktitle{The Standard C Library} shows you
many principles of library design in general. You learn
how to design and implement libraries that are highly
cohesive and reusable.",
acknowledgement = ack-nhfb,
tableofcontents = "Preface / ix \\
Introduction / 1 \\
<assert.h> / 17 \\
<ctype.h> / 25 \\
<errno.h> / 47 \\
<float.h> / 57 \\
<limits.h> / 73 \\
<locale.h> / 81 \\
<math.h> / 127 \\
<setjmp.h> / 181 \\
<signal.h> / 193 \\
<stdarg.h> / 205 \\
<stddef.h> / 215 \\
<stdio.h> / 225 \\
<stdlib.h> / 333 \\
<string.h> / 387 \\
<time.h> / 415 \\
Interfaces / 445 \\
Names / 453 \\
Terms / 463 \\
Index / 475",
}
@TechReport{Posch:1992:MRR,
author = "K. C. Posch and R. Posch",
title = "Modulo reduction in residue number systems",
institution = "Inst., TU, Ges.",
address = "????",
pages = "16",
year = "1992",
bibdate = "Thu Nov 18 09:44:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "IIG-report-series",
URL = "http://books.google.com/books?id=YPLKHAAACAAJ",
abstract = "Residue number systems provide a good means for
extremely long integer arithmetic. Their carry-free
operations make parallel implementations feasible. Some
applications involving very long integers, such as
public key encryption, rely heavily on fast modulo
reductions. This paper shows a new combination of
residue number systems with efficient modulo reduction
methods. Two methods are compared, and the faster one
is scrutinized in detail. Both methods have the same
order of complexity, $ O(\log n) $, with $n$ denoting
the amount of registers involved.",
acknowledgement = ack-nhfb,
}
@InProceedings{Posch:1992:RNS,
author = "K. C. Posch and R. Posch",
booktitle = "Proceedings of the Fourth {IEEE} Symposium on Parallel
and Distributed Processing 1992",
title = "Residue number systems: a key to parallelism in public
key cryptography",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "432--435",
year = "1992",
CODEN = "????",
DOI = "https://doi.org/10.1109/SPDP.1992.242713",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Public key cryptography and parallel algorithms are
considered. Special attention is paid to algorithms
using long integer modulo arithmetic. A modification of
the commonly known RSA algorithm is taken as a
candidate. So far all implementations have \ldots{}",
}
@Book{Press:1992:NRC,
author = "W. H. Press and B. P. Flannery and S. A. Teukolsky and
W. T. Vetterling",
title = "Numerical Recipes in {C}: The Art of Scientific
Computing",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
edition = "Second",
pages = "xxvi + 994",
year = "1992",
ISBN = "0-521-43108-5, 0-521-43720-2",
ISBN-13 = "978-0-521-43108-8, 978-0-521-43720-2",
LCCN = "QA297 .N864 1992",
bibdate = "Thu Sep 01 22:12:07 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@PhdThesis{Priest:1992:PFP,
author = "Douglas M. Priest",
title = "On Properties of Floating Point Arithmetics: Numerical
Stability and the Cost of Accurate Computations",
type = "Thesis ({Ph.D.} in Mathematics)",
school = "Department of Computer Science, University of
California, Berkeley",
address = "Berkeley, CA, USA",
pages = "iv + 136",
month = dec,
year = "1992",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "UMI order number GAX93-30692.",
URL = "ftp://ftp.icsi.berkeley.edu/pub/theory/priest-thesis.ps.Z",
abstract = "Floating point arithmetics generally possess many
regularity properties in addition to those that are
typically used in roundoff error analyses; these
properties can be exploited to produce computations
that are more accurate and cost effective than many
programmers might think possible. Furthermore, many of
these properties are quite simple to state and to
comprehend, but few programmers seem to be aware of
them (or at least willing to rely on them).\par
This dissertation presents some of these properties and
explores their consequences for computability,
accuracy, cost, and portability. For example, we
consider several algorithms for summing a sequence of
numbers and show that under very general hypotheses, we
can compute a sum to full working precision at only
somewhat greater cost than a simple accumulation, which
can often produce a sum with no significant figures at
all. This example, as well as others we present, can be
generalized further by substituting still more complex
algorithms; consequently, examples such as these oblige
us to consider more carefully the tradeoffs between
cost and accuracy.\par
At one end of the accuracy spectrum we find one of the
least obvious consequences of the properties of
floating point arithmetic: the accuracy of a
computation consisting of rational arithmetic
operations and comparisons need not be limited by the
precision of the floating point arithmetic in which it
is carried out. Of course, the more accuracy desired,
the greater the cost of the computation, and the cost
of computing a very accurate result may be quite high;
we illustrate this possibility in the case of
polynomial evaluation. At the other end of the
spectrum, however, we give an example of a problem for
which simply computing a result to a modest guaranteed
accuracy costs far less than the contortions required
to accommodate inaccurate results. As a consequence of
examples such as these, we conclude that programmers
and theorists alike must be willing to adopt a more
sophisticated view of floating point arithmetic, even
if only to consider that more accurate and reliable
computations than those presently in common use might
be possible based on stronger hypotheses than are
customarily assumed.",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; Dept. of
Mathematics; Dissertations; floating-point arithmetic;
University of California, Berkeley",
}
@Article{Quach:1992:HSA,
author = "N. T. Quach and M. J. Flynn",
title = "High-speed addition in {CMOS}",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "12",
pages = "1612--1615",
month = dec,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.214671",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Quach:1992:RFP,
author = "N. Quach and M. Flynn",
title = "A radix-64 floating-point divider",
type = "Technical Report",
number = "CSL-TR-92-529",
institution = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
month = jun,
year = "1992",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@Article{Rao:1992:FPA,
author = "B. D. Rao",
title = "Floating point arithmetic and digital filters",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "40",
number = "1",
pages = "85--95",
month = jan,
year = "1992",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "The roundoff noise properties of floating point
digital filters are examined. To make the analysis
tractable, a high level model to deal with the errors
in the inner product operation is developed. This model
establishes a broad connection between \ldots{}",
}
@InProceedings{Rix:1992:CFA,
author = "B. Rix and D. Timmermann and H. Hahn and B. J.
Hosticka",
title = "A {CORDIC}-based floating-point arithmetic unit",
crossref = "IEEE:1992:PIC",
bookpages = "766",
pages = "30.3/1--4",
year = "1992",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A floating-point arithmetic unit based on the CORDIC
algorithm is described. It computes a wide range of
arithmetic, trigonometric, and hyperbolic functions and
achieves a normalized peak performance of 220 MFLOPS.
The unit is implemented in 1.6- mu m double-metal CMOS
technology and packaged in a 280-pin PGA.",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. Eng., Duisburg University,
Germany",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5135 (Digital signal
processing chips); C5230 (Digital arithmetic methods);
C5260 (Digital signal processing)",
keywords = "1.6 Micron; 220 MFLOPS; 280-Pin PGA; CORDIC algorithm;
Double-metal CMOS technology; DSP; Floating-point
arithmetic unit; Hyperbolic functions; Trigonometric
functions",
numericalindex = "Computer speed 2.2E+08 FLOPS; Size 1.6E-06 m",
thesaurus = "CMOS integrated circuits; Digital arithmetic; Digital
signal processing chips",
}
@InProceedings{Sanz-Gonzalez:1992:OFP,
author = "J. L. Sanz-Gonzalez and F. Lopez-Ferreras",
booktitle = "Proceedings of the 3rd {AFRICON} Conference: {AFRICON
'92}",
title = "Optimal floating-point structures for low roundoff
noise digital filters",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "194--197",
year = "1992",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "A theoretical analysis of roundoff noise power in
floating-point realizations of digital filters is
presented. Formulas are given for single-length and
double-length accumulators. The minimal-noise
floating-point structure is found to be identical
\ldots{}",
}
@Article{Scherson:1992:BPA,
author = "I. D. Scherson and D. A. Kramer and B. D. Alleyne",
title = "Bit-parallel arithmetic in a massively-parallel
associative processor",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "10",
pages = "1201--1210",
month = oct,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.166599",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=166599",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Schwarz:1992:ASF,
author = "E. M. Schwarz and M. J. Flynn",
title = "Approximating the Sine Function With Combinational
Logic",
crossref = "Singh:1992:CRT",
pages = "386--390",
year = "1992",
bibdate = "Thu Sep 08 08:02:20 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Seznec:1992:CSH,
author = "Andr{\'e} Seznec and Karl Courtel",
title = "Controlling and sequencing a heavily pipelined
floating-point operator",
journal = j-SIGMICRO,
volume = "23",
number = "1--2",
pages = "111--114",
month = dec,
year = "1992",
CODEN = "SIGMDJ",
DOI = "https://doi.org/10.1145/144965.145008",
ISSN = "0163-5751, 1050-916X",
ISSN-L = "0163-5751",
bibdate = "Fri Apr 16 10:27:43 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
URL = "https://dl.acm.org/doi/10.1145/144965.145008",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMICRO Newsletter",
journal-URL = "https://dl.acm.org/loi/sigmicro",
}
@Article{Seznec:1992:OAF,
author = "Andr{\'e} Seznec and Karl Courtel",
title = "{OPAC} (abstract): a floating-point coprocessor
dedicated to compute-bound kernels",
journal = j-COMP-ARCH-NEWS,
volume = "20",
number = "2",
pages = "427--427",
month = may,
year = "1992",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 12 09:40:43 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{Seznec:1992:OFC,
author = "A. Seznec and K. Courtel",
title = "{OPAC}: a Floating-Point Coprocessor Dedicated to
Compute-Bound Kernels",
journal = j-COMP-ARCH-NEWS,
volume = "20",
number = "2",
pages = "427--427",
month = may,
year = "1992",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{Simar:1992:FPP,
author = "Ray {Simar, Jr.} and Peter Koeppen and Jerald Leach
and Steve Marshall and Dave Francis and Greg Mekras and
Jeffrey Rosenstrauch and Scott Anderson",
title = "Floating-Point Processors Join Forces in Parallel
Processing Architectures",
journal = j-IEEE-MICRO,
volume = "12",
number = "4",
pages = "60--69",
month = jul # "\slash " # aug,
year = "1992",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.149737",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Achieving cost-effective design performance goals with
parallel DSP building blocks supported by extensive
software",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
summary = "The hardware architecture and software capabilities of
the TMS320C40 floating-point digital signal processor
are described. The C40 operates at 275 million
operations per second (MOPS) and transfers data at a
rate of 320 Mbytes/s with a 40-ns cycle time \ldots{}",
}
@Book{Sites:1992:AAR,
author = "Richard L. Sites and Richard Witek and others",
title = "Alpha Architecture Reference Manual",
publisher = pub-DP # " and " # pub-PH,
address = pub-DP:adr # " and " # pub-PH:adr,
year = "1992",
ISBN = "0-13-033663-7 (PH), 1-55558-098-X (DP: print)",
ISBN-13 = "978-0-13-033663-7 (PH), 978-1-55558-098-8 (DP:
print)",
LCCN = "QA76.9.A73 A46 1992",
bibdate = "Wed Jan 23 08:49:36 MST 2019",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/microchip.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Foreword \\
Preface \\
Common Architecture \\
Introduction \\
Basic Architecture \\
Instruction Formats \\
Instruction Descriptions \\
System Architecture and Programming Implications \\
Common PALcode Architecture \\
Console Subsystem Overview \\
Input/Output \\
OpenVMS Alpha Software \\
Introduction to OpenVMS Alpha \\
OpenVMS PALcode Instruction Descriptions \\
OpenVMS Memory Management \\
OpenVMS Process Structure \\
OpenVMS Internal Processor Registers \\
OpenVMS Exceptions, Interrupts, and Machine Checks \\
DEC OSF/1 Alpha Software \\
Introduction to DEC OSF/1 Alpha \\
OSF/1 PALcode Instruction Descriptions \\
OSF/1 Memory Management \\
OSF/I Process Structure \\
OSF/1 Exceptions and Interrupts \\
Appendix A: Software Considerations \\
Appendix B: IEEE Floating-Point Conformance \\
Appendix C: Instruction Encodings \\
Index",
xxauthor = "{Alpha Architecture Committee}",
}
@Article{Skavantzos:1992:DCM,
author = "A. Skavantzos and T. Stouraitis",
title = "Decomposition of complex multipliers using polynomial
encoding",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "10",
pages = "1331--1333",
month = oct,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.166610",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
note = "See comments \cite{Katti:1994:CDC}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=166610",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Skavantzos:1992:NMM,
author = "A. Skavantzos and P. B. Rao",
title = "New multipliers modulo {$ 2^N - 1 $}",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "957--961",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156538",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156538",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Skavantzos:1992:TII,
author = "A. Skavantzos and N. Mitash",
booktitle = "{IEEE} Southeastcon '92, Proceedings, 12--15 April
1992",
title = "Theory and implementation issues of the 2-dimensional
polynomial residue number system",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "226--233",
year = "1992",
CODEN = "????",
DOI = "https://doi.org/10.1109/SECON.1992.202342",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The authors present 2D polynomial residue number
system techniques for parallel polynomial
multiplication in modular rings and discuss array
implementation issues of such 2D polynomial
multipliers. A specific example design is presented.
The \ldots{}",
}
@Article{Skeel:1992:REP,
author = "R. Skeel",
title = "Roundoff error and the {Patriot} missile",
journal = j-SIAM-NEWS,
volume = "25",
number = "4",
pages = "11--1",
month = jul,
year = "1992",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Sat Apr 28 19:10:25 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.siam.org/siamnews/general/patriot.htm",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "https://sinews.siam.org/",
}
@Article{Smith:1992:FPR,
author = "L. Montgomery Smith and B. W. Bomar and R. D. Joseph
and G. C. J. Yang",
title = "Floating-Point Roundoff Noise Analysis of Second-Order
State-Space Digital Filter Structures",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "39",
number = "2",
pages = "90--98",
month = feb,
year = "1992",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.205812",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE transactions on circuits and systems. 2, Analog
and digital signal processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
summary = "A parametric approach is used to determine the
roundoff noise in all real second-order floating-point
state-space realizations of a transfer function having
complex conjugate poles. The parametric roundoff noise
analysis is then verified by experiment \ldots{}",
}
@InProceedings{Soudris:1992:SDAa,
author = "D. Soudris and V. Paliouras and T. Stouraitis",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing. {ICASSP-92, 23--26} March 1992",
title = "Systematic development of architectures for
multidimensional {DSP} using the residue number
system",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "397--400",
year = "1992",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1992.226192",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A systematic methodology for mapping multidimensional
algorithms onto array processor architectures based on
the quadratic residue number system is presented. A
class of algorithms with separable functions, which can
be reduced to the computation of \ldots{}",
}
@InProceedings{Soudris:1992:SDAb,
author = "D. Soudris and V. Paliouras and T. Stouraitis",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing. {ICASSP-92, 23--26} March 1992",
title = "Systematic development of architectures for
multidimensional {DSP} using the residue number
system",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "397--400",
year = "1992",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1992.226192",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A systematic methodology for mapping multidimensional
algorithms onto array processor architectures based on
the quadratic residue number system is presented. A
class of algorithms with separable functions, which can
be reduced to the computation of \ldots{}",
}
@Book{SPARC:1992:SAM,
author = "{SPARC International, Inc.}",
title = "The {SPARC} Architecture Manual\emdash{}Version 8",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xxix + 316",
year = "1992",
ISBN = "0-13-825001-4",
ISBN-13 = "978-0-13-825001-0",
LCCN = "QA76.9.A73 S647 1992",
bibdate = "Thu Dec 16 09:12:32 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Sparmann:1992:DHQ,
author = "Uwe Sparmann",
title = "Derivation of high quality tests for large
heterogeneous circuits: floating-point operations",
journal = "Informatik",
volume = "1",
publisher = pub-TEUBNER,
address = pub-TEUBNER:adr,
pages = "425--439",
year = "1992",
MRclass = "94C12 (93C05)",
MRnumber = "93j:94039",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Teubner-Texte Inform.",
acknowledgement = ack-nhfb,
keywords = "floating-point testing",
reviewer = "Adrian Ad{\u{a}}sc{\u{a}}li{\c{t}}ei",
}
@Article{Srinivas:1992:SFV,
author = "S. Srinivas and K. Dybvig",
title = "Superscalar Floating-Point Vector Computation in
Scheme",
journal = j-LECT-NOTES-COMP-SCI,
volume = "??",
number = "634",
pages = "811--812",
year = "1992",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Steidley:1992:FPA,
author = "C. W. Steidley",
title = "Floating point arithmetic basic exercises in
mathematical reasoning for computer science majors",
journal = j-COMP-EDU-J,
volume = "2",
number = "4",
pages = "1--6",
month = oct # "--" # dec,
year = "1992",
CODEN = "CEJOE7",
ISSN = "1069-3769",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Efficient mathematical (numerical) computing requires
floating point computation since fixed point arithmetic
limits the range of the numbers being manipulated.
Fixed point arithmetic also adds to the complexity of
operation by demanding a great deal of scaling among
numbers with different `implicit' radix (base) points.
Thus, floating point arithmetic has become a modern
computing necessity. In 1988, Central Washington
University introduced CPSC 321 Systems Programming into
the curriculum. The course was intended to give
students an opportunity to learn more about the
hardware, architecture, and organization of computing
machines by studying and writing systems software. Some
topics considered for the initial offering of the
course included: a simple assembler, a basic loader, or
a simple compiler. However, many of these topics are
covered in other courses and after discussions with
many colleagues in the Department of Mathematics
regarding the coverage of representation and use of
decimal arithmetic on computers, it was decided that
the fundamentals of some systems programs could be
covered by introducing the basic aspects of doing
mathematics on a computer from the systems point of
view.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Southeastern Louisiana
University, Hammond, LA, USA",
classification = "C0220 (Education and training); C5230 (Digital
arithmetic methods); C6110 (Systems analysis and
programming); C7310 (Mathematics)",
fjournal = "Computers in education journal",
keywords = "Computer science majors; Computing machines; Computing
necessity; CPSC 321 Systems Programming; Curriculum;
decimal floating-point arithmetic; Floating point
arithmetic; Floating point computation; Mathematical
reasoning; Students; Systems software",
thesaurus = "Computer science education; Digital arithmetic;
Educational courses; Mathematics computing; Systems
analysis; Teaching",
}
@Article{Stetter:1992:ICR,
author = "F. Stetter",
title = "Internal computer representation of integer numbers",
journal = j-INFORMATIK-SPEKTRUM,
volume = "15",
number = "6",
pages = "352--354",
month = dec,
year = "1992",
CODEN = "INSKDW",
ISSN = "0170-6012 (print), 1432-122X (electronic)",
ISSN-L = "0170-6012",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Compares floating point and integer representations
and presents a proposal for a unified integer
representation which allows for sign. Definitions are
given of two's complement and one's complement
representations and rules are proposed for integer
addition and subtraction, multiplication and division
with various translation algorithms.",
acknowledgement = ack-nhfb,
affiliation = "Mannheim University, Germany",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "Informatik Spektrum",
journal-URL = "http://link.springer.com/journal/287",
keywords = "Division; Floating point; Integer addition; Integer
numbers; Integer representations; Multiplication;
Subtraction; Unified integer representation",
language = "German",
pubcountry = "Germany",
thesaurus = "Digital arithmetic",
}
@Article{Stouraitis:1992:ECR,
author = "T. Stouraitis",
title = "Efficient convertors for residue and quadratic-residue
number systems",
journal = "Circuits, Devices and Systems, IEE Proceedings G",
volume = "139",
number = "6",
pages = "626--634",
month = dec,
year = "1992",
CODEN = "????",
DOI = "https://doi.org/10.1109/78.157231",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4741",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The quadratic-residue number system (QRNS) is known to
be efficient for complex-number calculations, since it
eliminates the need for cross-product terms and offers
high speed with small hardware complexity. However, the
conversion overhead between \ldots{}",
}
@Article{Sun:1992:CTA,
author = "J.-D. Sun and H. Krishna",
title = "A coding theory approach to error control in redundant
residue number systems. {II}. Multiple error detection
and correction",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "39",
number = "1",
pages = "18--34",
month = jan,
year = "1992",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.204107",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5240",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems. 2, Analog
and Digital Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
keywords = "residue arithmetic; residue number system",
summary = "For pt.I see ibid., vol.39, no.1, p.8-17 (1992). The
coding theory approach to error control in redundant
residue number systems (RRNSs) is extended by deriving
computationally efficient algorithms for correcting
multiple errors, single-burst-error, \ldots{}",
}
@Article{Takagi:1992:MMH,
author = "N. Takagi and S. Yajima",
title = "Modular multiplication hardware algorithms with a
redundant representation and their application to {RSA}
cryptosystem",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "7",
pages = "887--891",
month = jul,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.256444",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:18 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=256444",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Takagi:1992:RMM,
author = "N. Takagi",
title = "A radix-$4$ modular multiplication hardware algorithm
for modular exponentiation",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "949--956",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156537",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156537",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Tang:1992:TDI,
author = "Ping Tak Peter Tang",
title = "Table-Driven Implementation of the {{\tt Expm1}}
Function in {IEEE} Floating-Point Arithmetic",
journal = j-TOMS,
volume = "18",
number = "2",
pages = "211--222",
month = jun,
year = "1992",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/146847.146928",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D15",
MRnumber = "1 167 891",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See independent analysis and accuracy confirmation of
this algorithm in \cite{Kramer:1998:PWC}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p211-tang/",
abstract = "Algorithms and implementation details for the function
$ e^x - 1 $ in both single and double precision of IEEE
754 arithmetic are presented here. With a table of
moderate size, the implementations need only
working-precision arithmetic and are provably accurate
to within 0.58 ulp.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis. {\bf G.1.0}: Mathematics of Computing,
NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
Algorithm analysis.",
}
@InProceedings{Teufel:1992:IFP,
author = "Thomas Teufel",
title = "Implementation of a floating-point arithmetic with an
accurate scalar product for digital signal processing",
crossref = "Atanassova:1992:CAE",
pages = "147--156",
year = "1992",
bibdate = "Sat Sep 17 19:12:26 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Thirumalaiswamy:1992:DSB,
author = "Vijayashree Thirumalaiswamy",
title = "Design and simulation of bit-serial floating point
arithmetic co-processor",
type = "Thesis ({M.S.})",
school = "University of Texas at El Paso",
address = "El Paso, TX, USA",
pages = "xii + 113",
year = "1992",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Array processors --- Design.; Floating-point
arithmetic.",
}
@Article{Timmermann:1992:LLT,
author = "D. Timmermann and H. Hahn and B. J. Hosticka",
title = "Low Latency Time {CORDIC} Algorithms",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "1010--1015",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156543",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 08 00:52:02 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Vowels:1992:D,
author = "R. A. Vowels",
title = "Division by 10",
journal = j-AUSTRALIAN-COMP-J,
volume = "24",
number = "3",
pages = "81--85",
month = aug,
year = "1992",
CODEN = "ACMJB2",
ISSN = "0004-8917",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Division of a binary integer and a binary
floating-point mantissa by 10 can be performed with
shifts and adds, yielding a significant improvement in
hardware execution time, and in software execution time
if no hardware divide instruction is available. Several
algorithms are given, appropriate to specific machine
word sizes, hardware and hardware instructions
available, and depending on whether a remainder is
required. The integer division algorithms presented
here contain a new strategy that produces the correct
quotient directly, without the need for the
supplementary correction required of
previously-published algorithms. The algorithms are
competitive in time with binary coded decimal (BCD)
divide by 10. Both the integer and floating-point
algorithms are an order of magnitude faster than
conventional division.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, R. Melbourne Inst. of
Technol. Ltd., Vic., Australia",
classification = "C7310 (Mathematics)",
fjournal = "Australian Computer Journal",
keywords = "Binary integer; decimal floating-point arithmetic;
Floating-point algorithms; Hardware execution time;
Integer division algorithms; Software execution time",
pubcountry = "Australia",
thesaurus = "Digital arithmetic; Mathematics computing",
}
@MastersThesis{Wang:1992:RAF,
author = "Jie Wang",
title = "Response analysis for floating point implementations
of linear discrete systems",
type = "Thesis ({M.S.E.E.})",
school = "University of Notre Dame",
address = "Notre Dame, IN 46556, USA",
pages = "xi + 83",
year = "1992",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Weber-Wulff:1992:REC,
author = "Debora Weber-Wulff",
title = "Rounding error changes {Parliament} makeup",
journal = "The Risks Digest",
volume = "13",
number = "37",
pages = "8--8",
year = "1992",
bibdate = "Sat Apr 28 19:12:42 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://catless.ncl.ac.uk/Risks/13.37.html#subj4",
acknowledgement = ack-nhfb,
}
@Article{Werter:1992:SLC,
author = "M. J. Werter",
title = "Suppression of limit cycles in the first-order
two-dimensional direct form digital filter with a
controlled rounding arithmetic",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "40",
number = "6",
pages = "1599--1601",
month = jun,
year = "1992",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "The first-order two-dimensional direct-form digital
filter with magnitude truncation is known to be free
from limit cycles for a limited range of allowed filter
coefficients. In this correspondence, the quantization
technique of controlled rounding \ldots{}",
}
@Article{Wesner:1992:TS,
author = "J. Wesner",
title = "{Ein Tick schneller} \toenglish {A Tick Faster}
\endtoenglish",
journal = j-MC,
volume = "2",
pages = "80--86",
year = "1992",
ISSN = "0720-4442, 0941-777x , 0943-5409",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "MC: Die Mikrocomputer-Zeitschrift",
}
@Article{Wichmann:1992:NUF,
author = "Brian A. Wichmann",
title = "A Note on the Use of Floating Point in Critical
Systems",
journal = j-COMP-J,
volume = "35",
number = "1",
pages = "41--44",
month = feb,
year = "1992",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www3.oup.co.uk/computer_journal/Volume_35/Issue_01/Vol35_01.index.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/Volume_35/Issue_01/Vol35_01.body.html#AbstractWichmann",
abstract = "Floating point is a well tried technology which, it
might seem, can be used without reservation.
Unfortunately, there are dangers which arise from
faults in implementation and incorrect use. These are
often hard to locate. The paper addresses these
dangers.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "NPL, Teddington, UK",
author-1-adr = "National Physical Laboratory, Teddington, Middlesex
TW11 OLW",
classcodes = "C5230 (Digital arithmetic methods)",
classification = "C5230 (Digital arithmetic methods)",
corpsource = "NPL, Teddington, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "critical systems; digital arithmetic; faults; floating
point; Floating point; safety systems",
pubcountry = "UK",
thesaurus = "Digital arithmetic; Safety systems",
treatment = "P Practical",
}
@Article{Wichmann:1992:SFW,
author = "Brian A. Wichmann",
title = "{Surveyor's Forum}: ``{What} Every Computer Scientist
Should Know About Floating-Point Arithmetic''",
journal = j-COMP-SURV,
volume = "24",
number = "3",
pages = "319--319",
month = sep,
year = "1992",
CODEN = "CMSVAN",
ISSN = "0360-0300 (print), 1557-7341 (electronic)",
ISSN-L = "0360-0300",
bibdate = "Sun Sep 25 10:14:37 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See
\cite{Goldberg:1991:WEC,Goldberg:1991:CWE,Dunham:1992:SFW}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
}
@Article{Wilkes:1992:E,
author = "Maurice V. Wilkes",
title = "{EDSAC 2}",
journal = j-IEEE-ANN-HIST-COMPUT,
volume = "14",
number = "4",
pages = "49--56",
month = oct # "--" # dec,
year = "1992",
CODEN = "IAHCEX",
DOI = "https://doi.org/10.1109/85.194055",
ISSN = "1058-6180 (print), 1934-1547 (electronic)",
ISSN-L = "1058-6180",
bibdate = "Thu Jul 12 06:22:54 MDT 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeeannhistcomput.bib",
URL = "http://dlib.computer.org/an/books/an1992/pdf/a4049.pdf;
http://www.computer.org/annals/an1992/a4049abs.htm",
acknowledgement = ack-nhfb,
fjournal = "IEEE Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
remark = "From page 54: ``When the machine was initialized for a
new program to be run, every bit in the memory was set
to a 1, rather than to a 0. Since, according to the
format used for floating numbers, no floating number
could consist entirely of 1's, any attempt to read a
floating-point number from part of the memory that had
not been written into caused the machine to stop. Many
a programmer must have been grateful to [David J.]
Wheeler for his foresight in making this happen.''",
}
@Article{Wilt:1992:ALP,
author = "Nicholas Wilt",
title = "Assembly language programming for the 80*87",
journal = j-DDJ,
volume = "17",
number = "3",
pages = "36, 38, 40, 42, 88",
month = mar,
year = "1992",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Tue Sep 10 10:06:23 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5130 (Microprocessor chips); C5230 (Digital
arithmetic methods); C6110 (Systems analysis and
programming)",
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "80*87 Coprocessor; Assembly language programming;
Floating point arithmetic; Numeric coprocessors;
Optimization",
thesaurus = "Assembly language listings; Digital arithmetic;
Microprocessor chips; Optimisation; Programming;
Satellite computers",
}
@Article{Wong:1992:DSR,
author = "W. F. Wong and E. Goto",
title = "Division and square-rooting using a split multiplier",
journal = j-ELECT-LETTERS,
volume = "28",
number = "18",
pages = "1758--1759",
day = "27",
month = aug,
year = "1992",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Wed Dec 13 13:13:34 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A modification is proposed to the traditional design
of a fast floating point multiplication circuit such
that instead of just performing $ A * B $ where $A$ and
$B$ are $m$ bits long, it is also capable of performing
$ C * x_0$ and $ D * x_1$ where $C$ and $D$ are still m
bits long but $ x_0$ and $ x_1$ are $ m / 2$ bits long
using about the same amount of hardware resources but
in two thirds of the time. Such a circuit is called a
split multiplier. The authors show how such a split
multiplier can be used to compute division and $ Y
\sqrt {X}$ accurately and quickly.",
acknowledgement = ack-nhfb,
affiliation = "Goto Lab., Inst. of Phys. and Chem. Res., Saitama,
Japan",
classification = "B1265B (Logic circuits); C5120 (Logic and switching
circuits); C5230 (Digital arithmetic methods)",
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "Division; Fast floating point multiplication circuit;
Split multiplier; Square-rooting",
pubcountry = "UK",
thesaurus = "Digital arithmetic; Dividing circuits; Logic circuits;
Multiplying circuits",
}
@Article{Wong:1992:FDU,
author = "D. Wong and M. Flynn",
title = "Fast Division Using Accurate Quotient Approximations
to Reduce the Number of Iterations",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "981--995",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156541",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156541",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Woods:1992:HPD,
author = "R. F. Woods and S. E. McQuillan and J. Dowling and J.
V. McCanny",
booktitle = "Proceedings of Fifth Annual {IEEE} International
{ASIC} Conference and Exhibit, 1992",
title = "High performance {DSP} {ASIC} for multiply, divide and
square root",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "209--213",
year = "1992",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The design of a high-speed ASIC that combines the
operations of multiplication, division and square root
is described. The chip is based on a systolic array
architecture that uses a redundant number system and
allows multiplication, division, and \ldots{}",
}
@Article{Yeyios:1992:TSA,
author = "A. K. Yeyios",
title = "On two sequences of algorithms for approximating
square roots",
journal = j-J-COMPUT-APPL-MATH,
volume = "40",
number = "1",
pages = "63--72",
month = jun,
year = "1992",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Yokoo:1992:OUF,
author = "H. Yokoo",
title = "Overflow\slash Underflow-Free Floating-Point Number
Representations with Self-Delimiting Variable-Length
Exponent Field",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "1033--1039",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156546",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156546",
abstract = "A class of new floating-point representations of real
numbers, based on representations of the integers, is
described. In the class, every representation uses a
self-delimiting representation of the integers as a
variable length field of the exponent, and neither
overflow nor underflow appears in practice. The adopted
representations of the integers are defined
systematically, so that representation's of numbers
greater than one have both exponent-significant and
integer-fraction interpretations. Since representation
errors are characterized by the length function of an
underlying representation of the integers, superior
systems in precision can be easily selected from the
proposed class.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Gunma University,
Kiryu, Japan",
ajournal = "IEEE Trans. Comput.",
classification = "B0250 (Combinatorial mathematics); B1265B (Logic
circuits); C1160 (Combinatorial mathematics); C5230
(Digital arithmetic methods)",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Floating-point number representations; Integer
representation; Real numbers; Self-delimiting
variable-length exponent field",
summary = "A class of new floating-point representations of real
numbers, based on representations of the integers, is
described. In the class, every representation uses a
self-delimiting representation of the integers as a
variable length field of the exponent \ldots{}",
thesaurus = "Digital arithmetic; Number theory",
}
@Article{Zelniker:1992:RMC,
author = "G. S. Zelniker and F. J. Taylor",
title = "On the reduction in multiplicative complexity achieved
by the polynomial residue number system",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "40",
number = "9",
pages = "2318--2320",
month = sep,
year = "1992",
CODEN = "ITPRED",
DOI = "https://doi.org/10.1109/78.157231",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4075",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
keywords = "residue arithmetic; residue number system",
summary = "The polynomial residue number system is known to
reduce the complexity of polynomial multiplication from
O(N 2) to O(N). A new interpretation of this complexity
reduction is given in the context of \ldots{}",
}
@Article{Alam:1993:RTO,
author = "M. S. Alam and M. A. Karim",
title = "Real-Time Optical Arithmetic\slash Logical
Processing",
journal = j-J-PAR-DIST-COMP,
volume = "17",
number = "3",
pages = "251--258",
month = mar,
year = "1993",
CODEN = "JPDCER",
DOI = "https://doi.org/10.1006/jpdc.1993.1024",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Thu Mar 9 09:18:51 MST 2000",
bibsource = "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.idealibrary.com/links/doi/10.1006/jpdc.1993.1024/production;
http://www.idealibrary.com/links/doi/10.1006/jpdc.1993.1024/production/pdf",
acknowledgement = ack-nhfb,
classification = "B4180 (Optical logic devices and optical computing
techniques); C5110D (Optical logic elements)C5120
(Logic and switching circuits); C5230 (Digital
arithmetic methods); C5270 (Optical computing
techniques)",
corpsource = "Department of Eng., Purdue University, Fort Wayne, IN,
USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "autocorrelation peaks; binary; coding scheme; digital
arithmetic; full adder; input joint image; joint
transform correlator; minterms; multiple outputs;
optical logic; real time logical processing; real-time
optical arithmetic; real-time systems",
treatment = "P Practical",
}
@Book{Albrecht:1993:VNT,
editor = "R. (Rudolf F.) Albrecht and G. (G{\"o}tz) Alefeld and
H. (Hans) J. Stetter",
title = "Validation numerics: theory and applications",
volume = "9",
publisher = pub-SV,
address = pub-SV:adr,
pages = "291",
year = "1993",
ISBN = "3-211-82451-0 (Wien), 0-387-82451-0 (New York)",
ISBN-13 = "978-3-211-82451-1 (Wien), 978-0-387-82451-2 (New
York)",
LCCN = "QA297 .V27 1993",
bibdate = "Thu Apr 02 09:18:32 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "This volume is dedicated to Professor Dr. Ulrich
Kulisch, \ldots{} on the occasion of his 60th
birthday.",
series = "Computing (Springer-Verlag). Supplementum",
acknowledgement = ack-nhfb,
}
@MastersThesis{Alqeisi:1993:FPF,
author = "Yousuf Alqeisi",
title = "A 16-bit floating point fast {Fourier} transform
processor using {Xlinx}'s {FPGA's}",
type = "Thesis ({M.S.})",
school = "Department of Electrical Engineering, Southern
Illinois University at Carbondale",
address = "Carbondale, IL, USA",
pages = "v + 60",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Anonymous:1993:FPa,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "12",
number = "1",
pages = "56--??",
month = jan,
year = "1993",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Making a Case for Pencil Plotters.",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Article{Anonymous:1993:FPb,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "12",
number = "5",
pages = "67--??",
month = may,
year = "1993",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Component Technology.",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Article{Anonymous:1993:FPc,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "12",
number = "9",
pages = "48--??",
month = sep,
year = "1993",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "ProStep.",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Article{Anonymous:1993:FPd,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "12",
number = "10",
pages = "98--??",
month = oct,
year = "1993",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Open Modeling Still Going Strong.",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Article{Anonymous:1993:FPe,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "12",
number = "11",
pages = "42--??",
month = nov,
year = "1993",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Cost Benefits CAD/CAM.",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Article{Anonymous:1993:FSB,
author = "Anonymous",
title = "The ``fastest system on the block'' label must be
qualified with new multiplatform, floating-point
benchmarks",
journal = j-PC-WEEK,
volume = "10",
number = "22",
pages = "85--??",
month = jun,
year = "1993",
ISSN = "0740-1604",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "PC Week",
}
@Book{Anonymous:1993:SRT,
author = "Anonymous",
title = "The Square Root of Two to 100,000 digits",
volume = "52",
publisher = pub-PROJECT-GUTENBERG,
address = pub-PROJECT-GUTENBERG:adr,
year = "1993",
bibdate = "Sun Jan 24 10:00:27 MST 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-PROJECT-GUTENBERG,
URL = "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext93/2sqrt10.zip",
acknowledgement = ack-nhfb # " and " # ack-st,
subject = "Mathematical constants.",
}
@Article{Asprey:1993:PFP,
author = "T. Asprey and G. Averill and E. DeLano and R. Mason
and B. Weiner and J. Yetter",
title = "Performance features of the {PA7100} microprocessor",
journal = j-IEEE-MICRO,
volume = "13",
number = "3",
pages = "22--35",
month = may # "\slash " # jun,
year = "1993",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.216746",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Book{ASTM:1993:AES,
author = "{ASTM}",
title = "{ASTM E29-08}: Standard Practice for Using Significant
Digits in Test Data to Determine Conformance with
Specifications",
publisher = "ASTM International",
address = "West Conshohocken, PA, USA",
year = "1993",
bibdate = "Mon May 21 17:19:21 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Superseded by \cite{ASTM:2008:AES}.",
URL = "https://www.astm.org/DATABASE.CART/HISTORICAL/E29-08.htm",
acknowledgement = ack-nhfb,
remark = "Cited in \cite[ref. 32]{Carter:2013:ESF}.",
}
@Article{Bailey:1993:AMT,
author = "David H. Bailey",
title = "{Algorithm 719}: Multiprecision Translation and
Execution of {FORTRAN} Programs",
journal = j-TOMS,
volume = "19",
number = "3",
pages = "288--319",
month = sep,
year = "1993",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/155743.155767",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Dec 13 18:37:31 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p288-bailey/",
abstract = "This paper describes two Fortran utilities for
multiprecision computation. The first is a package of
Fortran subroutines that perform a variety of
arithmetic operations and transcendental functions on
floating point numbers of arbitrarily high precision.
This package is in some cases over 200 times faster
than that of certain other packages that have been
developed for this purpose.\par
The second utility is a translator program, which
facilitates the conversion of ordinary Fortran programs
to use this package. By means of source directives
(special comments) in the original Fortran program, the
user declares the precision level and specifies which
variables in each subprogram are to be treated as
multiprecision. The translator program reads this
source program and outputs a program with the
appropriate multiprecision subroutine calls.\par
This translator supports multiprecision integer, real,
and complex datatypes. The required array space for
multiprecision data types is automatically allocated.
In the evaluation of computational expressions, all of
the usual conventions for operator precedence and mixed
mode operations are upheld. Furthermore, most of the
Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP
are supported and produce true multiprecision values.",
abstract-2 = "The author describes two Fortran utilities for
multiprecision computation. The first is a package of
Fortran subroutines that perform a variety of
arithmetic operations and transcendental functions on
floating point numbers of arbitrarily high precision.
This package is in some cases over 200 times faster
than that of certain other packages that have been
developed for this purpose. The second utility is a
translator program, which facilitates the conversion of
ordinary Fortran programs to use this package. By means
of source directives (special comments) in the original
Fortran program, the user declares the precision level
and specifies which variables in each subprogram are to
be treated as multiprecision. The translator program
reads this source program and outputs a program with
the appropriate multiprecision subroutine calls. This
translator supports multiprecision integer, real, and
complex datatypes. The required array space for
multiprecision data types is automatically allocated.
In the evaluation of computational expressions, all of
the usual conventions for operator precedence and mixed
mode operations are upheld. Furthermore, most of the
Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP
are supported and produce true multiprecision values.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "NASA Ames Res. Center, Moffett Field, CA, USA",
classification = "C5230 (Digital arithmetic methods); C6120 (File
organisation); C6140D (High level languages); C6150C
(Compilers, interpreters and other processors); C7310
(Mathematics)",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "Algorithm 719; Arithmetic operations; Array space;
Complex data types; Computational expressions; Floating
point numbers; Fortran programs; Fortran subroutines;
Fortran utilities; Fortran-77 intrinsics; Mixed mode
operations; Multiprecision computation; Multiprecision
data types; Multiprecision subroutine calls;
Multiprecision translation; Operator precedence; Source
directives; Transcendental functions; Translator
program",
subject = "F.2.1 [Analysis of Algorithms and Problem Complexity]:
Numerical Algorithms and Problems; G.1.0 [Numerical
Analysis]: General; G.1.2 [Numerical Analysis];
Approximation",
thesaurus = "Data structures; Digital arithmetic; FORTRAN;
Mathematics computing; Program interpreters;
Subroutines",
}
@InProceedings{Bailey:1993:MPM,
author = "David H. Bailey and Robert Krasny and Richard Pelz",
title = "Multiple precision, multiple processor vortex sheet
roll-up computation",
crossref = "Sincovec:1993:PSS",
pages = "52--56",
year = "1993",
bibdate = "Thu Nov 25 10:04:31 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bajard:1993:BNH,
author = "J. C. Bajard and S. Kla and Jean-Michel Muller",
title = "{BKM}: a New Hardware Algorithm for Complex Elementary
Functions",
crossref = "Swartzlander:1993:SCA",
pages = "146--153",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Bajard.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Article{Baker:1993:SLR,
author = "Henry G. {Baker, Jr.}",
title = "Safe and leakproof resource management using {Ada83}
limited types",
journal = j-SIGADA-LETTERS,
volume = "13",
number = "5",
pages = "32--42",
month = sep # "\slash " # oct,
year = "1993",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Sat Aug 9 09:05:49 MDT 2003",
bibsource = "Compendex database; http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
abstract = "Safe, leakproof and automatic resource managers are
essential to the implementation of every embedded
system, yet the standard examples of Ada83 resource
managers are either unsafe: they risk allocating the
same resource for two different purposes, leaky: they
risk permanently losing track of some resources, or
non-automatic: they require explicit deallocation,
which allows for a host of opportunities for
single-point system failures. Nevertheless, it is
possible to construct a safe, leakproof and automatic
resource manager --- at least for systems with only a
single task --- by a careful combination of certain
features of Ada83, and a careful avoidance of other
features. We illustrate our scheme with a safe,
leakproof and fully automatic dynamic-string package.
The same techniques also work for an arbitrary
precision arithmetic package [Fisher83] and for
managing the `roots' of a real-time garbage-collected
heap [Baker78] [Baker91SP] [Baker92Tread]. Suggestions
are offered to improve the use of limited private types
in Ada9X for automatic, safe and leakproof resource
management.",
acknowledgement = ack-nhfb,
affiliation = "Nimble Computer Corp",
affiliationaddress = "Encino, CA, USA",
classcodes = "C6150J (Operating systems); C6110B (Software
engineering techniques); C6120 (File organisation);
C6140D (High level languages)",
classification = "722.1; 722.4; 723.1; 723.1.1; 723.2",
conferenceyear = "1993",
corpsource = "Nimble Comput. Corp., Encino, CA, USA",
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
journalabr = "Ada Lett",
keywords = "Ada; Ada (programming language); Ada listings; Ada83
limited types; Ada83 resource; Ada9X; arbitrary
precision; Arbitrary precision arithmetic package;
arithmetic package; Automatic resource manager;
automatic resource managers; Computer operating
systems; Computer system recovery; Computer systems
programming; Data collection; data structures;
Deallocation; dynamic-string package; Embedded system;
embedded system; explicit deallocation; failures;
Information management; Interfaces (computer); Large
scale systems; leakproof resource management; limited
private types; management; managers; Program debugging;
Real time garbage collected heap; Real time systems;
real-time garbage-collected heap; real-time systems;
Resource allocation; resource allocation; Resource
management; Single point system failures; single-point
system; software reliability; storage; Storage
allocation (computer); Supervisory and executive
programs; System failure",
treatment = "P Practical; T Theoretical or Mathematical",
}
@Article{Bakhrakh:1993:NIF,
author = "S. M. Bakhrakh and S. V. Velichko and N. E.
Pilipchatin and V. F. Spiridonov and E. G. Sukhov and
Yu. G. Fedorova and V. I. Kheifets",
title = "Numerical investigation of floating-point arithmetic
operations",
journal = j-PROG-COMP-SOFT,
volume = "18",
number = "6",
pages = "255--258",
year = "1993",
CODEN = "PCSODA",
ISSN = "0361-7688 (print), 1608-3261 (electronic)",
ISSN-L = "0361-7688",
bibdate = "Wed Dec 13 18:18:07 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Original Russian language paper in
\cite{Bakhrakh:1992:NIF}.",
abstract = "This article analyzes the sources of accumulated
computational error in certain computers (of ES and PS
types) in floating-point mode. Results of numerical
experiments are given. These experiments demonstrate
the influence of rounding on accumulated error. (5
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Inst. for Control Sci., Acad. of Sci., Russia",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "Programming and Computer Software; translation of
Programmirovaniye (Moscow, USSR) Plenum",
journal-URL = "http://link.springer.com/journal/11086",
keywords = "Accumulated error rounding; Computational error;
Digital arithmetic; ES computers; Floating-point
arithmetic; Numerical investigation; PS computers",
pubcountry = "Russia",
remark = "English translation of: Programmirovanie",
thesaurus = "Digital arithmetic",
}
@Article{Barrera:1993:IBS,
author = "Tony Barrera and Pelle Olsson",
title = "An Integer Based Square Root Algorithm",
journal = j-BIT,
volume = "33",
number = "2",
pages = "253--261",
month = jun,
year = "1993",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01989748",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "68M07",
MRnumber = "1 326 017",
bibdate = "Wed Dec 13 18:20:52 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.mai.liu.se/BIT/contents/bit33.html;
http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=33&issue=2&spage=253",
abstract = "The authors propose a fast integer based method for
computing square roots of floating point numbers. This
implies high accuracy and robustness, since no
precision will be lost during the computation. Only
integer addition and shifts are necessary to obtain the
square root. Comparisons made with the modified Newton
method indicate that the suggested method is twice as
fast for computing floating point square roots. (5
Refs.)",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "AB Consonant, Uppsala, Sweden",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "Floating point numbers; floating-point arithmetic;
Integer based square root algorithm; Modified Newton
method; Robustness",
pubcountry = "Denmark",
thesaurus = "Digital arithmetic",
xxpages = "254--261",
}
@Article{Bauer:1993:LCB,
author = "P. H. Bauer and J. Wang",
title = "Limit cycle bounds for floating point implementations
of second-order recursive digital filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "40",
number = "8",
pages = "493--501",
month = aug,
year = "1993",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.242338",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems. 2, Analog
and Digital Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
summary = "It is shown that floating point realizations of
linearly stable systems can exhibit four fundamental
types of free responses. Sufficient conditions for the
existence or nonexistence of some of these periodic
response types in a given system are presented
\ldots{}",
}
@Article{Beckmann:1993:FFTa,
author = "P. E. Beckmann and B. R. Musicus",
title = "Fast fault-tolerant digital convolution using a
polynomial residue number system",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "41",
number = "7",
pages = "2300--2313",
month = jul,
year = "1993",
CODEN = "ITPRED",
DOI = "https://doi.org/10.1109/78.224241",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5864",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
keywords = "residue arithmetic; residue number system",
summary = "A fault-tolerant convolution algorithm that is an
extension of residue-number-system fault-tolerance
schemes applied to polynomial rings is described. The
algorithm is suitable for implementation on
multiprocessor systems and is able to concurrently
\ldots{}",
}
@Article{Beckmann:1993:FFTb,
author = "P. E. Beckmann and B. R. Musicus",
title = "Fast fault-tolerant digital convolution using a
polynomial residue number system",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "41",
number = "7",
pages = "2300--2313",
month = jul,
year = "1993",
CODEN = "ITPRED",
DOI = "https://doi.org/10.1109/78.224241",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5864",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
keywords = "residue arithmetic; residue number system",
summary = "A fault-tolerant convolution algorithm that is an
extension of residue-number-system fault-tolerance
schemes applied to polynomial rings is described. The
algorithm is suitable for implementation on
multiprocessor systems and is able to concurrently
\ldots{}",
}
@InProceedings{Benouamer:1993:LEA,
author = "M. O. Benouamer and P. Jaillon and D. Michelucci and
J.-M. Moreau",
title = "A Lazy Exact Arithmetic",
crossref = "Swartzlander:1993:SCA",
pages = "242--249",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Benouamer.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@InProceedings{Bickerstaff:1993:RAM,
author = "K'Andrea C. Bickerstaff and Michael J. Schulte and
Earl E. {Swartzlander, Jr.}",
title = "Reduced Area Multipliers",
crossref = "Wah:1993:ICA",
pages = "478--489",
year = "1993",
bibdate = "Sun Mar 04 10:43:38 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1993-03.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Bizzan:1993:IMA,
author = "S. S. Bizzan and G. A. Jullien and N. M. Wigley and W.
C. Miller",
title = "Integer Mapping Architectures for the Polynomial Ring
Engine",
crossref = "Swartzlander:1993:SCA",
pages = "44--51",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Bizzan.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@InCollection{Bohlender:1993:PAF,
author = "G. Bohlender and D. Cordes and A. Kn{\"o}fel and U.
Kulisch and R. Lohner and W. V. Walter",
title = "Proposal for accurate floating-point vector
arithmetic",
crossref = "Adams:1993:SCA",
pages = "87--102",
year = "1993",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Many computers provide accurate and reliable scalar
arithmetic for floating point numbers. An accurate
definition of the four elementary floating-point
operations +, -, *, / is given in the IEEE standards
for floating-point arithmetic and was well established
long before. An increasing number of computers
(especially PC's and workstations) feature IEEE
arithmetic. In many numerical algorithms, however,
compound operations such as the summation of a sequence
of numbers or the dot product of two vectors are highly
common. A simulation of these compound operations by
means of elementary floating-point operations leads to
accumulation of rounding errors and may suffer from
catastrophic cancellation of leading digits. Existing
standards for floating-point arithmetic do not improve
this situation. The goal of the proposal is to define
vector operations in a manner consistent with the
elementary scalar arithmetic operations. The rounding
modes and accuracy requirements as well as the data
formats of the operands and results of the vector
operations described in the proposal are chosen to be
fully consistent with the existing scalar
floating-point arithmetic.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Angewandte Math., Karlsruhe University,
Germany",
classification = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques); C7310 (Mathematics)",
keywords = "Accuracy requirements; Catastrophic cancellation;
Compound operations; Data formats; Dot product;
Elementary floating-point operations; Elementary scalar
arithmetic operations; Floating point numbers; IEEE
arithmetic; IEEE standards; Leading digits; Numerical
algorithms; Operands; Rounding errors; Rounding modes;
Scalar floating-point arithmetic; Sequence; Standards;
Summation; Vector operations",
thesaurus = "Digital arithmetic; Mathematics computing; Roundoff
errors; Standards",
}
@InProceedings{Booth:1993:ECA,
author = "Andrew D. Booth",
title = "Early Computer Arithmetic",
crossref = "Swartzlander:1993:SCA",
pages = "ix--ix",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_keynote.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
remark = "The author developed ``Booth's Algorithm'' for two's
complement multiplication, the APEXC computer at the
University of London (one of the world's first three
electronic digital computers), and the M3 series of
computers at the University of Saskatchewan (the first
all Canadian electronic computer).",
}
@InProceedings{Briggs:1993:XBM,
author = "W. S. Briggs and D. W. Matula",
title = "A $ 17 \times 69 $ Bit Multiply and Add Unit with
Redundant Binary Feedback and Single Cycle Latency",
crossref = "Swartzlander:1993:SCA",
pages = "163--170",
year = "1993",
bibdate = "Thu Jun 20 10:16:11 2002",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Briggs.pdf",
acknowledgement = ack-nj,
keywords = "ARITH-11",
}
@InProceedings{Callaway:1993:EPC,
author = "Thomas K. Callaway and Earl E. {Swartzlander, Jr.}",
title = "Estimating the Power Consumption of {CMOS} Adders",
crossref = "Swartzlander:1993:SCA",
pages = "210--216",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Callaway.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Article{Chang:1993:REP,
author = "Long-Wen Chang",
title = "Roundoff Error Problem of the Systolic Array for
{DFT}",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "41",
number = "1",
pages = "395",
month = jan,
year = "1993",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "Not \ldots{}",
}
@InProceedings{Choi:1993:FPR,
author = "H. Choi and W. P. Burleson and D. S. Phatak",
booktitle = "Proceedings of 1993 International Joint Conference on
Neural Networks. {IJCNN '93-Nagoya}",
title = "Fixed-point roundoff error analysis of large
feedforward neural networks",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1947--1950",
year = "1993",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Digital implementations of neural nets must consider
finite wordlength effects. For large sized nets, it is
particularly important to investigate the roundoff
errors in order to realize low-cost hardware
implementations while satisfying precision \ldots{}",
}
@Misc{Chu:1993:FPA,
author = "Tan V. Chu and Faraydon O. Karim and Christopher H.
Olson",
title = "Floating point arithmetic unit with size efficient
pipelined multiply-add architecture",
howpublished = "US Patent 5,241,493",
day = "31",
month = aug,
year = "1993",
bibdate = "Thu Oct 17 10:40:01 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://patents.google.com/patent/US5241493A",
abstract = "An architecture and method relating to a floating
point operation which performs the mathematical
computation of A * B + C. The multiplication is
accomplished in two or more stages, each stage
involving corresponding sets of partial products and
concurrently accomplished incremental summations. A
pipelined architecture provides for the summation of
the least significant bits of an intermediate product
with operand C at a stage preceding entry into a full
adder. Thereby, a significant portion of the full adder
can be replaced by a simpler and smaller incrementer
circuit. Partitioning of the multiplication operation
into two or more partial product operations
proportionally reduces the size of the multiplier
required. Pipelining and concurrence execution of
multiplication and addition operation in the multiplier
provides in two cycles the results of the mathematical
operation A * B + C while using a full adder of
three-quarters normal size.",
acknowledgement = ack-nhfb,
remark = "Patent filed 16 December 1991, granted to IBM on 31
August 1993, possibly expired 16 December 2011.",
}
@Article{Cody:1993:ACP,
author = "W. J. Cody",
title = "{Algorithm 714}: {CELEFUNT}: a Portable Test Package
for Complex Elementary Functions",
journal = j-TOMS,
volume = "19",
number = "1",
pages = "1--21",
month = mar,
year = "1993",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/151271.151272",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Sep 05 09:15:25 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p1-cody/",
abstract = "This paper discusses CELEFUNT, a package of Fortran
programs for testing complex elementary functions.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; measurement; performance",
subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
SOFTWARE, Certification and testing. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Numerical algorithms.",
}
@Article{Cody:1993:AFS,
author = "W. J. Cody and Jerome T. Coonen",
title = "{Algorithm 722}: Functions to Support the {IEEE}
Standard for Binary Floating-Point Arithmetic",
journal = j-TOMS,
volume = "19",
number = "4",
pages = "443--451",
month = dec,
year = "1993",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/168173.168185",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p443-cody/",
abstract = "This paper describes C programs for the support
functions {\em copysign(x,y), logb(x), scalb(x,n),
nextafter(x,y), finite(x)}, and {\em isnan(x)}
recommended in the Appendix to the {\em IEEE Standard
for Binary Floating-Point Arithmetic.} In the case of
{\em logb}, the modified definition given in the later
{\em IEEE Standard for Radix-Independent Floating-Point
Arithmetic} is followed. These programs should run
without modification on most systems conforming to the
binary standard.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Argonne Nat. Lab., IL, USA",
classification = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques); C7310 (Mathematics)",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "C programs; Copysign(x,y); Finite(x); IEEE Standard
for Binary Floating-point arithmetic; Isnan(x);
Logb(x); Nextafter(x,y); Numerical software;
Scalb(x,n)",
subject = "G.1.0 [Numerical Analysis]: General -- numerical
algorithms; G.4 [Numerical Analysis]: Mathematical
Software -- certification and testing",
thesaurus = "Data handling; Digital arithmetic; Mathematics
computing; Standards",
}
@Article{Cody:1993:ASE,
author = "W. J. Cody",
title = "{Algorithm 715}: {SPECFUN}\emdash {A} Portable
{FORTRAN} Package of Special Function Routines and Test
Drivers",
journal = j-TOMS,
volume = "19",
number = "1",
pages = "22--32",
month = mar,
year = "1993",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/151271.151273",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Mar 09 10:23:18 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See remark \cite{Price:1996:RA}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p22-cody/",
abstract = "SPECFUN is a package containing transportable FORTRAN
special function programs for real arguments and
accompanying test drivers. Components include Bessel
functions, exponential integrals, error functions and
related functions, and gamma functions and related
functions.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms",
subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
SOFTWARE, Certification and testing. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Numerical algorithms.",
}
@Article{Cole:1993:SAA,
author = "T. J. Cole",
title = "Statistical Algorithms: {Algorithm AS 281}: Scaling
and Rounding Regression Coefficients to Integers",
journal = j-APPL-STAT,
volume = "42",
number = "1",
pages = "261--268",
year = "1993",
CODEN = "APSTAG",
ISSN = "0035-9254 (print), 1467-9876 (electronic)",
ISSN-L = "0035-9254",
bibdate = "Sat Apr 21 10:26:43 MDT 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
URL = "http://lib.stat.cmu.edu/apstat/281",
acknowledgement = ack-nhfb,
fjournal = "Applied Statistics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}
@InProceedings{Cortadella:1993:DSQ,
author = "Jordi Cortadella and Tom{\'a}s Lang",
title = "Division with Speculation of Quotient Digits",
crossref = "Swartzlander:1993:SCA",
pages = "87--94",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Cortadella.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@InProceedings{Dadda:1993:MPC,
author = "Luigi Dadda and Vincenzo Piuri and Renato Stefanelli",
title = "Multi-Parallel Convolvers",
crossref = "Swartzlander:1993:SCA",
pages = "70--77",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Dadda.pdf",
acknowledgement = ack-nhfb,
author-dates = "29 April 1923--26 October 2012",
keywords = "ARITH-11",
}
@InProceedings{Daumas:1993:DFV,
author = "M. Daumas and D. W. Matula",
title = "Design of a Fast Validated Dot Product Operation",
crossref = "Swartzlander:1993:SCA",
pages = "62--69",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Daumas.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@MastersThesis{Delgado:1993:DSP,
author = "Maria Luisa Delgado",
title = "Design and simulation of a pipeline floating-point
adder",
type = "Thesis ({M.S.})",
school = "University of Texas at El Paso",
address = "El Paso, TX, USA",
pages = "x + 90",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Parallel processing
(Electronic computers)",
}
@InProceedings{Demmel:1993:FNA,
author = "James W. Demmel and Xiaoye Li",
title = "Faster numerical algorithms via exception handling",
crossref = "Swartzlander:1993:SCA",
pages = "234--241",
year = "1993",
bibdate = "Thu Jun 20 10:16:21 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Demmel.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@TechReport{Desaulniers:1993:BEA,
author = "H. Desaulniers and Stewart, N. F. (Neil Frederick)",
title = "Backward error analysis for floating-point operations
on rectilinear $r$-sets",
type = "Publication",
number = "816",
institution = "Universit{\'{e}} de Montr{\'{e}}al, Departement
d'informatique et de recherche operationnelle",
address = "Montr{\'{e}}al, Qu{\'{e}}bec, Canada",
pages = "64",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer-aided design.",
remark = "``January 5, 1993.'' Supported in part by the Natural
Sciences and Engineering Research Council of Canada",
}
@Article{DiClaudio:1993:SRR,
author = "E. D. {Di Claudio} and G. Orlandi and F. Piazza",
title = "A systolic redundant residue arithmetic error
correction circuit",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "4",
pages = "427--432",
month = apr,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.214689",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:48 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=214689",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{DiLecce:1993:CES,
author = "V. Di Lecce and E. Di Sciascio",
title = "A comparative evaluation of solutions for inner
product",
journal = j-INT-J-MINI-MICROCOMPUTERS,
volume = "15",
number = "2",
pages = "71--77",
month = "????",
year = "1993",
CODEN = "IJMMDE",
ISSN = "0702-0481",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper proposes the design and performance
evaluation of a bit-serial processing element for inner
product computation in fine-grain architectures. Some
solutions proposed in the scientific literature for
inner product are presented and evaluated. The
processing element architecture and its operating mode
are described; a single floating-point inner product
computation can be accomplished in e*(n+1) clock cycles
(2*(n+1) in pipelined mode), supposing that mantissas
and exponents have the same length n. The VLSI
implementation of the processing element is discussed
with reference to both standard cell and full custom
design styles. A comparative evaluation with the
previously described solutions is proposed, relative to
some particularly significant parameters.",
acknowledgement = ack-nhfb,
affiliation = "Department of Electron. Eng., Politecnico di Bari,
Italy",
classification = "B1265F (Microprocessors and microcomputers); C5135
(Digital signal processing chips); C5220 (Computer
architecture); C5230 (Digital arithmetic methods);
C5260 (Digital signal processing)",
fjournal = "International Journal of Mini and Microcomputers",
keywords = "Bit-serial processing element; Comparative evaluation;
DSP chips; Exponents; Fine-grain architectures; Full
custom design styles; Inner product; Mantissas;
Operating mode; Performance evaluation; VLSI
implementation",
thesaurus = "Digital arithmetic; Digital signal processing chips;
Performance evaluation",
}
@Article{Dimauro:1993:NTF,
author = "G. Dimauro and S. Impedovo and G. Pirlo",
title = "A new technique for fast number comparison in the
residue number system",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "5",
pages = "608--612",
month = may,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.223680",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:49 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=223680;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5840",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "A technique for number comparison in the residue
number system is presented, and its theoretical
validity is proved. The proposed solution is based on
using a diagonal function to obtain a magnitude order
of the numbers. In a first approach the \ldots{}",
}
@Article{Dittmer:1993:EUC,
author = "Ingo Dittmer",
title = "Error in {Unix} commands {\tt dc} and {\tt bc} for
multiple-precision-arithmetic",
journal = j-SIGNUM,
volume = "28",
number = "2",
pages = "8--11",
month = apr,
year = "1993",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:23 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@Book{Dowd:1993:HPC,
author = "Kevin Dowd",
title = "High Performance Computing",
publisher = pub-ORA,
address = pub-ORA:adr,
pages = "xxv + 371",
year = "1993",
ISBN = "1-56592-032-5",
ISBN-13 = "978-1-56592-032-3",
LCCN = "QA76.88 .D6 1993; QA76.9.A73 D68 1993",
bibdate = "Mon Jan 3 18:34:37 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/hpfortran.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/ora.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$25.95",
series = "RISC architectures, optimization and benchmarks; A
Nutshell handbook",
URL = "http://www.oreilly.com/catalog/9781565920323",
acknowledgement = ack-nhfb,
subject = "Computer architecture; Electronic digital computers;
Parallel processing (Electronic computers);
Supercomputers",
tableofcontents = "Preface / xxi \\
Who Should Buy This Book? / xxii \\
What's in This Book / xxii \\
Conventions / xxiv \\
Acknowledgments / xxv \\
1 Modern Computer Architectures / 1 \\
1: What is High Performance Computing? / 3 \\
Why Worry About Performance? / 3 \\
Measuring Performance / 5 \\
The Next Step / 6 \\
2: RISC Computers / 9 \\
Why CISC? / 10 \\
Space and Time / 10 \\
Beliefs About Complex Instruction Sets / 11 \\
Memory Addressing Modes / 12 \\
Microcode / 14 \\
Making the Most of a Clock Tick / 17 \\
Pipelines / 18 \\
Instruction Pipelining / 19 \\
Why RISC? / 21 \\
Characterizing RISC / 22 \\
A Few More Words About Pipelining / 27 \\
Memory References / 27 \\
Floating Point Pipelines / 28 \\
Classes of Processors / 29 \\
Superscalar Processors / 30 \\
Superpipelined Processors / 32 \\
Long Instruction Word (LIW) / 34 \\
Other Advanced Features / 35 \\
Register Bypass / 36 \\
Register Renaming / 36 \\
Reducing Branch Penalties / 37 \\
Closing Notes / 40 \\
3: Memory / 43 \\
Memory Technology / 44 \\
Random Access Memory / 45 \\
Access Time / 47 \\
Caches / 48 \\
Direct Mapped Cache / 50 \\
Fully Associative Cache / 52 \\
Set Associative Cache / 52 \\
Uses of Cache / 54 \\
Virtual Memory / 54 \\
Page Tables / 55 \\
Translation Lookaside Buffer / 56 \\
Page Faults / 57 \\
Improving Bandwidth / 59 \\
Large Caches / 60 \\
Interleaved Memory Systems / 60 \\
Software Managed Caches / 64 \\
Memory Reference Reordering / 64 \\
Multiple References / 66 \\
Closing Notes / 67 \\
IL Porting and Tuning Software / 91 \\
4: What an Optimizing Compiler Does / 69 \\
Optimizing Compiler Tour / 70 \\
Intermediate Language Representation / 70 \\
Basic Blocks / 72 \\
Forming a DAG / 74 \\
Uses and Definitions / 76 \\
Loops / 78 \\
Object Code Generation / 80 \\
Classical Optimizations / 81 \\
Copy Propagation / 81 \\
Constant Folding / 82 \\
Dead Code Removal / 83 \\
Strength Reduction / 84 \\
Variable Renaming / 84 \\
Common Subexpression Elimination / 85 \\
Loop Invariant Code Motion / 86 \\
Induction Variable Simplification / 87 \\
Register Variable Detection / 88 \\
Closing Notes / 88 \\
5: Clarity / 93 \\
Under Construction / 94 \\
Comments / 94 \\
Clues in the Landscape / 95 \\
Variable Names / 96 \\
Variable Types / 98 \\
Named Constants / 99 \\
INCLUDE Statements / 100 \\
Use of COMMON / 101 \\
The Shape of Data / 102 \\
Closing Notes / 104 \\
6: Finding Porting Problems / 105 \\
Problems in Argument Lists / 106 \\
Aliasing / 106 \\
Argument Type Mismatch / 108 \\
Storage Issues / 110 \\
Equivalenced Storage / 111 \\
Memory Reference Alignment Restrictions / 112 \\
Closing Notes / 115 \\
7: Timing and Profiling / 119 \\
Timing / 120 \\
Timing a Whole Program / 120 \\
Timing a Portion of the Program / 124 \\
Using Timing Information / 126 \\
Subroutine Profiling / 127 \\
prof / 130 \\
gprof / 133 \\
gprofs Flat Profile / 138 \\
Accumulating the Results of Several gprof Runs / 139
\\
A Few Words About Accuracy / 140 \\
Basic Block Profilers / 140 \\
tcov / 141 \\
!prof / 142 \\
pixie / 143 \\
Closing Notes / 144 \\
8: Understanding Parallelism / 147 \\
A Few Important Concepts / 148 \\
Constants / 148 \\
Scalars / 150 \\
Vectors and Vector Processing / 150 \\
Dependencies / 153 \\
Data Dependencies / 154 \\
Control Dependencies / 159 \\
Ambiguous References / 161 \\
Closing Notes / 162 \\
9: Eliminating Clutter / 165 \\
Subroutine Calls / 166 \\
Macros / 168 \\
Procedure Inlining / 170 \\
Branches / 171 \\
Wordy Conditionals / 171 \\
Redundant Tests / 172 \\
Branches Within Loops / 173 \\
Loop Invariant Conditionals / 174 \\
Loop Index Dependent Conditionals / 175 \\
Independent Loop Conditionals / 176 \\
Dependent Loop Conditionals / 177 \\
Reductions / 178 \\
Conditionals That Transfer Control / 179 \\
A Few Words About Branch Probability / 180 \\
Other Clutter / 181 \\
Data Type Conversions / 181 \\
Doing Your Own Common Subexpression Elimination / 182
\\
Doing Your Own Code Motion / 183 \\
Handling Array Elements in Loops / 184 \\
Closing Notes / 185 \\
10: Loop Optimizations / 187 \\
Basic Loop Unrolling / 188 \\
Qualifying Candidates for Loop Unrolling / 189 \\
Loops with Low Trip Counts / 190 \\
Fat Loops / 191 \\
Loops Containing Procedure Calls / 191 \\
Loops with Branches in Them / 193 \\
Recursive Loops / 194 \\
Negatives of Loop Unrolling / 195 \\
Unrolling by the Wrong Factor / 196 \\
Register Thrashing / 196 \\
Instruction Cache Miss / 197 \\
Other Hardware Delays / 197 \\
Outer Loop Unrolling / 197 \\
Outer Loop Unrolling to Expose Computations / 199 \\
Associative Transformations / 200 \\
Reductions / 202 \\
Dot Products and daxpys / 204 \\
Matrix Multiplication / 206 \\
Loop Interchange / 208 \\
Loop Interchange to Move Computations to the Center /
208 \\
Operation Counting / 209 \\
Closing Notes / 211 \\
11: Memory Reference Optimizations / 213 \\
Memory Access Patterns / 214 \\
Loop Interchange to Ease Memory Access Patterns / 215
\\
Blocking to Ease Memory Access Patterns / 216 \\
Ambiguity in Memory References / 223 \\
Ambiguity in Vector Operations / 224 \\
Pointer Ambiguity in Numerical C Applications / 225 \\
Programs That Require More Memory Than You Have / 227
\\
Software-Managed, Out-of-Core Solutions / 227 \\
Virtual Memory / 228 \\
Instruction Cache Ordering / 231 \\
Closing Notes / 232 \\
12: Language Support for Performance / 235 \\
Subroutine Libraries / 235 \\
Vectorizing Preprocessors / 237 \\
Explicitly Parallel Languages / 243 \\
Fortran 90 / 244 \\
High Performance Fortran (HPF) / 250 \\
Explicitly Parallel Programming Environments / 251 \\
Closing Notes / 253 \\
1/L Evaluating Performance / 255 \\
13: Industry Benchmarks / 257 \\
What is a MIP? / 258 \\
VAX MIPS / 259 \\
Dhrystones / 259 \\
Floating Point Benchmarks / 261 \\
Linpack / 262 \\
Whetstone / 264 \\
The SPEC Benchmarks / 265 \\
Individual SPEC Benchmarks / 266 \\
030.matrix300 Was Deleted / 272 \\
Transaction Processing Benchmarks / 272 \\
TPC-A / 273 \\
TPC-B / 273 \\
TPC-C / 273 \\
Closing Notes / 273 \\
14: Running Your Own Benchmarks / 275 \\
Choosing What to Benchmark / 275 \\
Benchmark Run Time / 276 \\
Benchmark Memory Size / 277 \\
Kernels and Sanitized Benchmarks / 277 \\
Benchmarking Third Party Codes / 278 \\
Types of Benchmarks / 279 \\
Single Stream Benchmarks / 280 \\
Throughput Benchmarks / 282 \\
Interactive Benchmarks / 283 \\
Preparing the Code / 285 \\
Portability / 285 \\
Making a Benchmark Kit / 286 \\
Benchmarking Checklist / 287 \\
Closing Notes / 288 \\
IV. Parallel Computing / 291 \\
15: Large Scale Parallel Computing / 293 \\
Problem Decomposition / 294 \\
Data Decomposition / 295 \\
Control Decomposition / 299 \\
Distributing Work Fairly / 300 \\
Classes of Parallel Architectures / 302 \\
Single Instruction, Multiple Data / 303 \\
SIMD Architecture / 305 \\
Mechanics of Programming a SIMD Machine / 309 \\
Multiple Instruction, Multiple Data / 312 \\
Distributed Memory MIMD Architecture / 314 \\
Programming a Distributed Memory MIMD Machine / 315 \\
A Few Words About Data Layout Directives / 319 \\
Virtual Shared Memory / 320 \\
Closing Notes / 323 \\
16: Shared-Memory Multiprocessors / 325 \\
Symmetric Multiprocessing / 326 \\
Operating System Support for Multiprocessing / 327 \\
Multiprocessor Architecture / 329 \\
Shared Memory / 330 \\
Conservation of Bandwidth / 330 \\
Coherency / 332 \\
Data Placement / 334 \\
Multiprocessor Software Concepts / 334 \\
Fork and Join / 335 \\
Synchronization with Locks / 337 \\
Synchronization with Barriers / 340 \\
Automatic Parallelization / 341 \\
Loop Splitting / 341 \\
Subroutine Calls in Loops / 342 \\
Nested Loops / 342 \\
Manual Parallelism / 344 \\
Closing Notes / 345 \\
A: Processor Overview / 347 \\
B: How to Tell When Loops Can Be Interchanged / 351 \\
C: Obtaining Sample Programs and Problem Set Answers /
357 \\
FTP / 357 \\
FTPMAIL / 358 \\
BITFTP / 359 \\
UUCP / 359 \\
Figures \\
2: RISC Computers / 9 \\
2-1 Registers, a single common data path, and an adder
/ 15 \\
2-2 A pipeline / 18 \\
2-3 Three instructions in flight through one pipeline /
20 \\
2-4 Variable length instructions make pipelining
difficult / 23 \\
2-5 Variable length CISC versus fixed length RISC
instructions / 23 \\
2-6 Processor encounters a branch / 26 \\
2-7 The Branch Delay Slot --- ZERO R3 executes either
way / 27 \\
2-8 Memory references scheduled early to account for
pipeline depth / 28 \\
2-9 Decomposing a serial stream / 30 \\
2-10 RS/ 6000 functional blocks / 31 \\
2-11 MIPS R4000 Instruction Pipeline / 33 \\
2-12 Intel i860 transition between modes / 35 \\
3: Memory / 43 \\
3-1 Row--Column memory address / 46 \\
3-2 Direct mapping of memory address to RAM / 46 \\
3-3 Cache lines can come from different parts of memory
/ 49 \\
3-4 Many memory addresses map to same cache line / 51
\\
3-5 Two -way set associative cache / 53 \\
3-6 Virtual to physical address mapping / 55 \\
3-7 Simple memory system / 59 \\
3-8 Page mode cache refill / 60 \\
3-9 Multi-banked memory system / 62 \\
3-10 Cache refill from interleaved memory / 63 \\
4: What an Optimizing Compiler Does / 69 \\
4-1 Example 4-1 divided into basic blocks / 73 \\
4-2 Tuple mapped into a DAG / 74 \\
4-3 Basic Block B / 75 \\
4-4 DAG for Block B / 75 \\
4-5 Revised Basic Block B / 76 \\
4-6 Flow graph for data flow analysis / 77 \\
4-7 Flow graph with a loop in it / 79 \\
5: Clarity / 93 \\
5-1 Array C in two -dimensional memory / 103 \\
6: Finding Porting Problems / 105 \\
6-1 IEEE 754 floating point formats / 109 \\
6-2 IBM 370 floating point formats / 110 \\
6-3 Equivalence storage relationship on most computers
/ 111 \\
6-4 Misaligned variables / 113 \\
7: Timing and Pro.filing / 119 \\
7-1 The built-in csh time function / 123 \\
7-2 Sharp profile --- dominated by routine 1 / 128 \\
7-3 Flat profile --- no routine predominates / 129 \\
7-4 Simple call graph / 134 \\
7-5 FORTRAN example / 135 \\
7-6 Quantization Errors in Profiling / 140 \\
8: Understanding Parallelism / 147 \\
8-1 Vector Computer / 152 \\
8-2 A little section of your program / 159 \\
8-3 Expensive operation moved so that it's rarely
executed / 160 \\
11: Memory Reference Optimizations / 213 \\
11-1 Arrays A and B / 217 \\
11-2 How array elements are stored / 218 \\
11-3 2x2 squares / 219 \\
11-4 Picture of unblocked versus blocked references /
220 \\
11-5 Optimization performance for various sized loops /
222 \\
11-6 Vector machine memory access / 223 \\
12: Language Support for Performance / 235 \\
12-1 Linda's Tuple Space Bulletin Board / 252 \\
14: Running Your Own Benchmarks / 275 \\
14-1 Kernel benchmark / 278 \\
14-2 Single stream benchmarks / 280 \\
14-3 Computing an overall benchmark score / 281 \\
14-4 Wrong way to run a throughput benchmark / 282 \\
14-5 Benchmark stone wall / 283 \\
14-6 Interactive use benchmark / 284 \\
_15:Large Scale Parallel Computing / 293 \\
15-1 Domain decomposition / 295 \\
15-2 Cells with X's have life / 296 \\
15-3 One iteration later / 297 \\
15-4 Two examples of division of cells between four
CPUs / 298 \\
15-5 Each processor with a piece of the domain / 300
\\
15-6 Duplicated data domain / 301 \\
15-7 Iterations mapped onto SIMD nodes / 304 \\
15-8 Mapping a route through a strictly Cartesian mesh
/ 306 \\
15-9 Four nodes / 307 \\
15-10 A 3-cube and a 4-cube / 307 \\
15-11 Front-end and SIMD machine / 309 \\
15-12 KSR-1 ring of rings architecture / 322 \\
16: Shared-Memory Multiprocessors / 325 \\
16-1 A typical bus architecture / 329 \\
16-2 A $4 \times 4$ crossbar / 330 \\
16-3 High cache hit rate reduces main memory traffic /
331 \\
16-4 Multiple copies of variable A / 332 \\
16-5 Fork and join / 335 \\
16-6 Integration / 337 \\
16-7 Implementation of a spinlock / 339 \\
B: How to Tell When Loops Can Be Interchanged / 351 \\
B-1 $4 \times 4$ matrix / 352 \\
B-2 One iteration complete / 353 \\
B-3 All iterations completed / 354 \\
B-4 Movement of data in array A / 355 \\
Examples \\
4: What an Optimizing Compiler Does / 69 \\
4-1 Intermediate Language for a Single Loop / 72 \\
5: Clarity / 93 \\
5-1 Comments, asterisks, and pretty printing / 95 \\
5-2 Variable names count / 97 \\
5-3 Parameter statements \\
5-4 Declarations / 100 \\
5-5 Routine using both INCLUDE files / 100 \\
5-6 Changing the Shape of an Array / 100 \\
/ 102 \\
6: Finding Porting Problems / 105 \\
6-1 Program for creating misaligned references \\
6-2 Misaligned reference in C / 114 \\
/ 115 \\
7: Timing and Profiling / 119 \\
7-1 FORTRAN program using etime / 125 \\
7-2 etime implemented in C / 126 \\
7-3 loops.c --- a program for testing profilers / 131
\\
7-4 Profile of loops.c / 132 \\
7-5 A portion of gprof output / 135 \\
7-6 gprof flat profile / 138 \\
8: Understanding Parallelism / 147 \\
8-1 Vector Addition / 150 \\
9: Eliminating Clutter / 165 \\
9-1 Macro definition and use / 168 \\
10: Loop Optimizations / 187 \\
10-1 Loop containing a procedure call / 192 \\
10-2 Matrix multiply with daxpy inner loop / 206 \\
10-3 Matrix multiply with dot product inner loop / 206
\\
11: Memory Reference Optimizations / 213 \\
11-1 Two-dimensional vector sum / 216 \\
11-2 Outer and inner loop unrolled / 217 \\
B: How to Tell When Loops Can Be Interchanged / 351 \\
B-1 Each iteration is independent / 351 \\
B-2 Can we interchange these loops? / 352 \\
B-3 Legal alternate loop nests / 354 \\
B-4 More complicated references / 355 \\
B-5 More complicated references / 356 \\
Tables \\
6: Finding Porting Problems / 105 \\
6-1 Preferred Alignment Boundaries on Most Computers /
113 \\
15: Large Scale Parallel Computing / 293 \\
15-1 Worst Case Communication / 308 \\
A: Processor Overview / 347 \\
A-1 CPU Characteristics / 347 \\
A-2 Cache and Branch Architecture / 348 \\
A-2 Cache and Branch Architecture (continued) / 349",
}
@Article{Duncan:1993:CES,
author = "Roy Duncan and John Tunstall and Brian T. Smith and
Richard Brankin",
title = "Correspondence: Expert Systems for Re-ordering
Arithmetic Expressions?",
journal = j-FORTRAN-FORUM,
volume = "12",
number = "3",
pages = "12--14",
month = sep,
year = "1993",
CODEN = "????",
ISSN = "1061-7264 (print), 1931-1311 (electronic)",
ISSN-L = "1061-7264",
bibdate = "Tue Apr 23 14:50:51 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Fortran Forum",
issue = "35",
journal-URL = "http://portal.acm.org/toc.cfm?id=J286",
}
@Article{Duprat:1993:CAN,
author = "J. Duprat and J. Muller",
title = "The {CORDIC} Algorithm: New Results for Fast {VLSI}
Implementation",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "2",
pages = "168--178",
month = feb,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.204786",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Eisig:1993:DBI,
author = "David Eisig and Josh Rotstain and Israel Koren",
title = "The Design of a 64-bit Integer Multiplier\slash
Divider Unit",
crossref = "Swartzlander:1993:SCA",
pages = "171--178",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Eisig.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Article{Eldridge:1993:HIM,
author = "S. E. Eldridge and C. D. Walter",
title = "Hardware implementation of {Montgomery}'s modular
multiplication algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "6",
pages = "693--699",
month = jun,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.277287",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:49 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=277287",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Ercegovac:1993:VHR,
author = "Milo{\v{s}} D. Ercegovac and Tom{\'a}s Lang and Paolo
Montuschi",
title = "Very high radix division with selection by rounding
and prescaling",
crossref = "Swartzlander:1993:SCA",
pages = "112--119",
year = "1993",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Ercegovac.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
summary = "A division algorithm in which the quotient-digit
selection is performed by rounding the shifted residual
in carry-save form is presented. To allow the use of
this simple function, the divisor (and dividend) is
prescaled to a range close to one. The \ldots{}",
}
@InProceedings{Etiemble:1993:AMV,
author = "D. Etiemble and K. Navi",
title = "Algorithms and Multi-Valued Circuits for the
Multioperand Addition in the Binary Stored-Carry Number
System",
crossref = "Swartzlander:1993:SCA",
pages = "194--201",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Etiemble.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@InProceedings{Fortune:1993:EEA,
author = "Steven Fortune and Christopher J. {Van Wyk}",
editor = "{ACM}",
booktitle = "{Proceedings of the 9th ACM Symposium on Computational
Geometry, May 19--21, 1993, San Diego, CA, USA}",
title = "Efficient Exact Arithmetic for Computational
Geometry",
publisher = pub-ACM,
address = pub-ACM:adr,
bookpages = "vii + 406",
pages = "163--172",
year = "1993",
DOI = "https://doi.org/10.1145/160985.161015",
ISBN = "0-89791-582-8",
ISBN-13 = "978-0-89791-582-3",
LCCN = "QA448.D38 S96 1993",
bibdate = "Tue Nov 13 21:44:58 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Fowkes:1993:HEA,
author = "R. E. Fowkes",
title = "Hardware Efficient Algorithms for Trigonometric
Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "3",
pages = "235--239",
month = feb,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.204796",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Fox:1993:HLS,
author = "J. R. Fox",
title = "A higher level of synthesis ({CAD})",
journal = j-IEEE-SPECTRUM,
volume = "30",
number = "3",
pages = "43--47",
month = mar,
year = "1993",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/6.211955",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Thu Jan 16 07:37:23 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1990.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "abstraction; Arithmetic; CAD; Circuit synthesis;
Clocks; design automation; Design automation; Design
engineering; design synthesis systems; Fabrication;
Hardware; hardware description languages; Logic
circuits; Logic design; Microarchitecture; software
tools; specification languages; testability; top-down
design",
}
@MastersThesis{Geraminejad:1993:DIC,
author = "Mohsen Geraminejad",
title = "Design and implementation of a 16-bit {CMOS} floating
point multiplier",
type = "Research paper ({M.S.})",
school = "Department of Electrical Engineering, Southern
Illinois University at Carbondale",
address = "Carbondale, IL, USA",
pages = "vii + 54",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gibbons:1993:FMW,
author = "Jeremy Gibbons",
editor = "John Hosking",
booktitle = "{Proceedings of the 13th New Zealand Computer Society
Conference: Applying the future today, Aotea Centre,
Auckland, 18--20 August 1993}",
title = "Formal Methods: {Why} Should {I} Care? {The}
development of the {T800} transputer floating-point
unit",
publisher = "New Zealand Computer Society",
address = "Wellington, NZ",
pages = "207--217",
year = "1993",
ISBN = "0-9597657-6-X; 0-9597657-5-1",
ISBN-13 = "978-0-9597657-6-2; 978-0-9597657-5-5",
LCCN = "????",
bibdate = "Tue Nov 13 21:37:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The term `formal methods' is a general term for
precise mathematically-based techniques used in the
development of computer systems, both hardware and
software. This paper discusses formal methods in
general, and in particular describes their successful
role in specifying, constructing and proving correct
the floating-point unit of the Inmos T800 transputer
chip.",
acknowledgement = ack-nhfb,
keywords = "Inmos T800 transputer",
}
@TechReport{Goldberg:1993:DFP,
author = "David Goldberg",
title = "The design of floating-point data types",
type = "Technical report",
number = "CSL-93-3",
institution = "Xerox Corp., Palo Alto Research Center",
address = "Palo Alto, CA, USA",
pages = "19",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Abstract data types (Computer science)",
remark = "``A version of this paper will appear in Letters on
Programming Languages and Systems.'' ``February 1993.''
Abstract: ``We discuss the issues involved in designing
the floating-point part of a programming language.
Looking at the language specifications for most
existing languages might suggest that this design
involves only trivial issues such as whether to have
one or two types of REALs or how to name the functions
that convert from INTEGER to REAL. We show that there
are more significant semantic issues involved. After
discussing the tradeoffs for the major design
decisions, we illustrate them by presenting the design
of the floating-point part of the Modula-3
language.''",
}
@TechReport{Gudeman:1993:RTI,
author = "David Gudeman",
title = "Representing Type Information in Dynamically Typed
Languages",
type = "Technical report",
number = "TR 93-27",
institution = "Department of Computer Science, The University of
Arizona",
address = "Tucson, AZ 85721, USA",
pages = "40",
month = oct,
year = "1993",
bibdate = "Wed Oct 13 08:12:36 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.cs.arizona.edu/reports/1993/TR93-27.ps;
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.4394",
abstract = "This report is a discussion of various techniques for
representing type information in dynamically typed
languages, as implemented on general-purpose machines
(and costs are discussed in terms of modern RISC
machines). It is intended to make readily available a
large body of knowledge that currently has to be
absorbed piecemeal from the literature or re-invented
by each language implementer. This discussion covers
not only tagging schemes but other forms of
representation as well, although the discussion is
strictly limited to the representation of type
information. It should also be noted that this report
does not purport to contain a survey of the relevant
literature. Instead, this report gathers together a
body of folklore, organizes it into a logical
structure, makes some generalizations, and then
discusses the results in terms of modern hardware.",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic; integer arithmetic; Lisp;
Prolog; typed objects",
remark = "Discusses implementation of fast arithmetic for typed
integer and floating-point data.",
}
@Misc{Gupta:1993:NPF,
author = "S. Gupta and R. Periman and T. Lynch and B. McMinn",
title = "Normalizing pipelined floating point processing
units",
day = "30",
month = nov,
year = "1993",
bibdate = "Fri Nov 28 15:27:34 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "U.S. Patent No. 5,267,186.",
acknowledgement = ack-nhfb,
}
@InCollection{Hammer:1993:PXN,
author = "R. Hammer and M. Neaga and D. Ratz",
title = "{PASCAL-XSC}: New Concepts for Scientific Computation
and Numerical Data Processing",
crossref = "Adams:1993:SCA",
pages = "15--44",
year = "1993",
bibdate = "Wed Oct 13 22:38:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Hasan:1993:MMO,
author = "M. A. Hasan and M. Z. Wang and V. K. Bhargava",
title = "A modified {Massey--Omura} parallel multiplier for a
class of finite fields",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "10",
pages = "1278--1280",
month = oct,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.257715",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=257715",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Hatzinakos:1993:AFP,
author = "D. Hatzinakos",
title = "Analysis of floating point roundoff errors in the
estimation of higher-order statistics",
journal = "IEE proceedings. F, Radar and signal processing",
volume = "140",
number = "6",
pages = "371--379",
month = dec,
year = "1993",
ISSN = "0956-375X",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "A floating point roundoff error analysis in the
estimation of higher-order statistics, moments or
cumulants of real stationary processes from single data
records is provided. Closed form expressions or upper
bounds are derived for the mean and \ldots{}",
}
@Book{Heinrich:1993:MRM,
author = "Joe Heinrich",
title = "{MIPS R4000} Microprocessor User's Manual",
publisher = pub-PHPTR,
address = pub-PHPTR:adr,
pages = "xxvi + 438 + A182 + B62 + C6 + D4 + E4",
year = "1993",
ISBN = "0-13-105925-4",
ISBN-13 = "978-0-13-105925-2",
LCCN = "QA76.8.M523H45 1993",
bibdate = "Wed Aug 10 11:02:27 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\$34.00",
acknowledgement = ack-nhfb,
libnote = "Not yet in my library.",
tableofcontents = "Introduction \\
CPU Instruction Set Summary \\
The CPU Pipeline \\
Memory Management \\
CPU Exception Processing \\
Floating-Point Unit \\
Floating-Point Exceptions \\
R4000 Processor Signal Descriptions \\
Initialization Interface \\
Clock Interface \\
Cache Organization, Operation, and Coherency \\
System Interface \\
Secondary Cache Interface \\
JTAG Interface \\
R4000 Processor Interrupts \\
Error Checking and Correcting \\
CPU Instruction Set Details \\
FPU Instruction Set Details \\
Subblock Ordering \\
Output Buffer \ldots{} Di \ldots{} Dt Control Mechanism
\\
PLL Passive Components \\
R4000 Coprocessor 0 Hazards",
}
@InProceedings{Hekstra:1993:FPC,
author = "Gerben J. Hekstra and Ed F. A. Deprettere",
title = "Floating Point Cordic",
crossref = "Swartzlander:1993:SCA",
pages = "130--137",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Hekstra.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@InProceedings{Hemkumar:1993:ECM,
author = "Nariankadu D. Hemkumar and Joseph R. Cavallaro",
title = "Efficient Complex Matrix Transformations with
{CORDIC}",
crossref = "Swartzlander:1993:SCA",
pages = "122--129",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Hemkumar.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Article{Hendtlass:1993:MNIa,
author = "T. Hendtlass",
title = "Math-who needs it?",
journal = j-FORTH-DIMENSIONS,
volume = "14",
number = "6",
pages = "27--38",
month = mar # "--" # apr,
year = "1993",
CODEN = "FODMD5",
ISSN = "0884-0822",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A thorough treatment of integer, double-precision,
fixed-point, and floating-point mathematics. A
mathematician's toolbox of code is presented, and
tables compare the benefits bestowed and the penalties
extracted by the routines.",
acknowledgement = ack-nhfb,
classification = "C6140D (High level languages); C7310 (Mathematics)",
fjournal = "Forth Dimensions",
keywords = "Code toolbox; Double precision arithmetic; Fixed-point
arithmetic; Floating-point mathematics; Integer",
thesaurus = "FORTH; FORTH listings; Mathematics computing",
}
@Article{Hendtlass:1993:MNIb,
author = "T. Hendtlass",
title = "Math---who needs it?",
journal = j-FORTH-DIMENSIONS,
volume = "15",
number = "1",
pages = "38--39",
month = may # "--" # jun,
year = "1993",
CODEN = "FODMD5",
ISSN = "0884-0822",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The continuation of the source code for a Forth
program is presented (see ibid., vol.14, no.6, 1993).
The software is a math professor's toolbox of integer,
double-precision, fixed-point and floating-point
routines.",
acknowledgement = ack-nhfb,
classification = "C6110 (Systems analysis and programming); C7310
(Mathematics)",
fjournal = "Forth Dimensions",
keywords = "Double-precision; Fixed-point; Floating-point
routines; Forth program; Math; Source code; Toolbox",
thesaurus = "Digital arithmetic; FORTH listings; Mathematics
computing; Programming",
}
@Article{Higginbotham:1993:ISR,
author = "T. F. Higginbotham",
title = "The integer square root of {N} via a binary search",
journal = j-SIGCSE,
volume = "25",
number = "4",
pages = "41--45",
month = dec,
year = "1993",
CODEN = "SIGSD3",
DOI = "https://doi.org/10.1145/164205.164229",
ISSN = "0097-8418 (print), 2331-3927 (electronic)",
ISSN-L = "0097-8418",
bibdate = "Sat Nov 17 18:57:24 MST 2012",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigcse1990.bib",
abstract = "An algorithm is presented which may be used to find
the integer square root of N. The method is intended
for use on a binary computer, where only addition,
subtraction, multiplication, or division by 2 is
required. The problem arose when the author was working
on factoring large numbers, where the machine, the
Honeywell DPS 8, had double precision integer addition
and subtraction, and the simulation of multiplication
was easy. The actual factoring of the large number was
to be Fermat's Method, requiring only addition and
subtraction, but the integer square root is required in
order to test for termination. The algorithm is
implemented in FORTRAN for ease of reading. Students
enjoy the unconventional approach to solving this
problem. It isn't long before some of them think of
other unusual solutions.",
acknowledgement = ack-nhfb,
fjournal = "SIGCSE Bulletin (ACM Special Interest Group on
Computer Science Education)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J688",
}
@Article{Higham:1993:AFP,
author = "Nicholas J. Higham",
title = "The accuracy of floating point summation",
journal = j-SIAM-J-SCI-COMP,
volume = "14",
number = "4",
pages = "783--799",
month = jul,
year = "1993",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/0914050",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65G05 (65B10)",
MRnumber = "94a:65025",
bibdate = "Thu Aug 23 06:36:53 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://citeseer.nj.nec.com/higham93accuracy.html;
http://www.maths.man.ac.uk/~nareports/narep198.pdf;
http://www.maths.man.ac.uk/~nareports/narep198.ps.gz",
abstract = "The usual recursive summation technique is just one of
several ways of computing the sum of $n$ floating point
numbers. Five summation methods and their variations
are analyzed. The accuracy of the methods is compared
using rounding error analysis and numerical
experiments. Four of the methods are shown to be
special cases of a general class of methods, and an
error analysis is given for this class. No one method
is uniformly more accurate than the others, but some
guidelines are given on the choice of method in
particular cases.",
acknowledgement = ack-nhfb,
affiliation = "Department of Math., Manchester University, UK",
classification = "C4110 (Error analysis in numerical methods); C5230
(Digital arithmetic methods)",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "accurate floating-point summation; floating point
numbers; numerical experiments; recursive summation
technique; rounding error analysis",
thesaurus = "Digital arithmetic; Error analysis",
}
@MastersThesis{Holler:1993:IFP,
author = "Paul T. Holler",
title = "Integrating a floating point unit into the {AT\&T
Hobbit} microprocessor",
type = "Thesis ({M.S.})",
school = "Lehigh University",
address = "Bethlehem, PA, USA",
pages = "viii + 85",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Microprocessors.",
}
@Article{Hopkins:1993:CEM,
author = "Tim Hopkins and John Slater",
title = "A Comment on the {Eispack} Machine Epsilon Routine",
journal = j-SIGNUM,
volume = "28",
number = "4",
pages = "2--6",
month = oct,
year = "1993",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/165639.165641",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:24 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors analyze the algorithm used to generate the
value for the machine epsilon in the Eispack suite of
routines and show that it can fail on a binary
floating-point system. The comments in the code
describing the conditions under which this method will
work are not restrictive enough and the authors provide
a replacement set of assumptions. They conclude by
suggesting how the algorithm may be modified to
overcome most of the shortcomings.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Comput. Lab., Kent University, Canterbury, UK",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "Binary floating-point system; Eispack machine epsilon
routine",
thesaurus = "Digital arithmetic",
}
@TechReport{Horning:1993:SUM,
author = "Jim Horning and Bill Kalsow and Paul McJones and Greg
Nelson",
title = "Some Useful {Modula-3} Interfaces",
type = "Memo",
number = "113",
institution = "Digital Equipment Corporation, Systems Research
Center",
address = "Palo Alto, CA, USA",
month = dec,
year = "1993",
bibdate = "Wed Jan 29 16:39:06 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "From \cite{Steele:2004:RHP}: ``The floating-point
reader has been implemented in \ldots{} to
Modula-3''.",
}
@Article{Hu:1993:EIS,
author = "X. Hu and S. C. Bass and R. G. Harber",
title = "An Efficient Implementation of Singular Value
Decomposition Rotation Transformations with {CORDIC}
Processors",
journal = j-J-PAR-DIST-COMP,
volume = "17",
number = "4",
pages = "360--362",
month = apr,
year = "1993",
CODEN = "JPDCER",
DOI = "https://doi.org/10.1006/jpdc.1993.1034",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Thu Mar 9 09:18:52 MST 2000",
bibsource = "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.idealibrary.com/links/doi/10.1006/jpdc.1993.1034/production;
http://www.idealibrary.com/links/doi/10.1006/jpdc.1993.1034/production/pdf",
acknowledgement = ack-nhfb,
classification = "C4140 (Linear algebra); C5230 (Digital arithmetic
methods); C7310 (Mathematics)",
corpsource = "General Motors Res. Labs., Warren, MI, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "2*2 matrices; CORDIC processors; digital arithmetic;
mathematics computing; matrix algebra; singular value
decomposition rotation transformations",
treatment = "A Application; P Practical",
}
@Book{IBM:1993:IPA,
author = "{IBM Corporation}",
title = "The {IBM PowerPC} Architecture: a New Family of {RISC}
Processors",
publisher = pub-MORGAN-KAUFMANN,
address = pub-MORGAN-KAUFMANN:adr,
year = "1993",
ISBN = "1-55860-316-6",
ISBN-13 = "978-1-55860-316-5",
LCCN = "QA76.8.P67P68 1994",
bibdate = "Sat Oct 15 12:26:00 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$49.95",
acknowledgement = ack-nhfb,
}
@Article{Ide:1993:CFP,
author = "N. Ide and H. Fukuhisa and Y. Kondo and T. Yoshida and
M. Nagamatsu and J. Mori and I. Yamazaki and K. Ueno",
title = "A {320-MFLOPS} {CMOS} Floating-Point Processing Unit
for Superscalar Processors",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "28",
number = "3",
pages = "352--361",
month = mar,
year = "1993",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
}
@Article{Ide:1993:MCF,
author = "Nobuhiro Ide and Hiroto Fukuhisa and Yoshihisa Kondo
and Takeshi Yoshida and Masato Nagamatsu and Junji Mori
and Itaru Yamazaki and Kiyoji Ueno",
title = "A 320-{MFLOPS CMOS} Floating-Point Processing Unit for
Superscalar Processors",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "28",
number = "3",
pages = "352--361",
month = mar,
year = "1993",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "A CMOS pipelined floating-point processing unit (FPU)
for superscalar processors is described. It is
fabricated using a 0.5 $\mu$m CMOS triple-metal-layer
technology on a 61 mm 2 die. The FPU has two execution
modes to meet precise scientific computations and
real-time applications. It can start two FPU operations
in each cycle, and this achieves a peak performance of
160 MFLOPS double or single precision with an 80 MHz
clock. Furthermore, the original computation mode, twin
single-precision computation, double the peak
performance and delivers 320 MFLOPS single precision.
Its full bypass reduces the latency of operations,
including load and store, and achieves an effective
throughput even in nonvectorizable computations. An
out-of-order completion is provided by using a new
exception prediction method and a pipeline stall
technique.",
}
@Article{Jahn:1993:LIF,
author = "K.-U. Jahn",
title = "Loop Invariants in Floating Point Algorithms.
{Schleifen-Invarianten in Gleitpunktalgorithmen}",
journal = j-COMPUTING,
volume = "50",
number = "3",
pages = "255--264",
year = "1993",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G05 (65G10)",
MRnumber = "94f:65052",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "It is shown that by using directed roundings with
respect to enclosure sets for the exact values, the
loop conditions and loop invariants of numerical
algorithms can be generalized for computing in a
discrete screen. It is possible to verify the received
results. Thereby only inherent properties of the
algorithms are used, which moreover guarantee that the
loops terminate.",
acknowledgement = ack-nhfb,
classification = "C4240P (Parallel programming and algorithm theory);
C6150G (Diagnostic, testing, debugging and evaluating
systems)",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
keywords = "Directed roundings; Enclosure sets; Floating point
algorithms; Loop conditions; Loop invariants",
pubcountry = "Austria",
thesaurus = "Program verification",
}
@Article{Jahn:1993:SIG,
author = "K.-U. Jahn",
title = "{Schleifen-Invarianten in Gleitpunktalgorithmen}.
({German}) [{Loop} Invariants in Floating Point
Algorithms]",
journal = j-COMPUTING,
volume = "50",
number = "3",
pages = "255--264",
month = sep,
year = "1993",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G05 (65G10)",
MRnumber = "94f:65052",
bibdate = "Mon Oct 11 20:38:38 MDT 1999",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database; OCLC Contents1st database",
abstract = "It is shown that by using directed roundings with
respect to enclosure sets for the exact values, the
loop conditions and loop invariants of numerical
algorithms can be generalized for computing in a
discrete screen. It is possible to verify the received
results. Thereby only inherent properties of the
algorithms are used, which moreover guarantee that the
loops terminate.",
acknowledgement = ack-nhfb,
classification = "C4240P (Parallel programming and algorithm theory);
C6150G (Diagnostic, testing, debugging and evaluating
systems)",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
keywords = "Directed roundings; Enclosure sets; Floating point
algorithms; Loop conditions; Loop invariants",
language = "German",
pubcountry = "Austria",
thesaurus = "Program verification",
}
@InProceedings{Jebelean:1993:CSG,
author = "T. Jebelean",
title = "Comparing Several {GCD} Algorithms",
crossref = "Swartzlander:1993:SCA",
pages = "180--185",
month = jun,
year = "1993",
bibdate = "Wed Nov 14 18:46:15 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Jebelean.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@InProceedings{Jenkins:1993:CSL,
author = "W. K. Jenkins and B. A. Schnaufer and A. J. Mansen",
title = "Combined System-Level Redundancy and Modular
Arithmetic for Fault Tolerant Digital Signal
Processing",
crossref = "Swartzlander:1993:SCA",
pages = "28--35",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Jenkins.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Article{Johnstone:1993:RNA,
author = "P. Johnstone and F. E. Petry",
title = "Rational number approximation in higher radix floating
point systems",
journal = j-COMPUT-MATH-APPL,
volume = "25",
number = "6",
pages = "103--108",
month = mar,
year = "1993",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Mathematical researchers have long recognized that
some bases offer some representational advantages in
that they generate fewer nonterminate values when
representing arbitrary rational numbers. While such
results are true for abstract number systems, little
attention has been paid to machine based computation
and its finite resources. In the paper, such results
are considered in an environment more typical of
computer based models of number systems. Specifically,
the authors consider the effect of the choice of
floating point base on rational number approximation in
systems which exhibit the typical characteristics of
floating point representations-normalized encodings,
limited exponent range and storage allocated in a fixed
number of `bits' per datum. The frequency with which
terminate and representable results can be expected is
considered for binary, decimal, and other potentially
interesting bases.",
acknowledgement = ack-nhfb,
affiliation = "New Orleans Tech. Dev. Group, Telerate Systems Inc.,
LA, USA",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
keywords = "Computer based models; decimal floating-point
arithmetic; Floating point base; Floating point
systems; Number systems; Rational number
approximation",
pubcountry = "UK",
thesaurus = "Digital arithmetic",
}
@InProceedings{Ju:1993:WCB,
author = "Chwen-Jye Ju",
title = "What can block floating-point arithmetic do for {DSP}
applications",
crossref = "Anonymous:1993:IPF",
bookpages = "1675",
pages = "641--650 vol.1",
year = "1993",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Block floating-point arithmetic for filtering was
proposed by Oppenheim two decades ago. Although it has
the advantages of both integer and floating-point
arithmetic, it is scarcely used in DSP applications
because the required signal reference level adjustment
(scaling) usually offsets its advantages. To conquer
the scaling problem, the unified indexing concept has
been proposed by the author for the M-D FFT
implementation. This paper will extend the concept to
derive the general block-oriented block floating-point
DSP algorithms. Therefore, the block floating-point
processors such as the LH9124/LH9320 can provide
self-contained solutions for some classes of DSP
applications.",
acknowledgement = ack-nhfb,
affiliation = "Sharp Microelectron. Technol. Inc., Camas, WA, USA",
classification = "B1265F (Microprocessors and microcomputers); B6140
(Signal processing and detection); C5135 (Digital
signal processing chips); C5230 (Digital arithmetic
methods); C5260 (Digital signal processing)",
keywords = "Block floating-point arithmetic; Block floating-point
processors; DSP applications; General block-oriented
block floating-point DSP algorithms; LH9124/LH9320; M-D
FFT implementation; Oppenheim; Scaling problem; Signal
reference level adjustment; Unified indexing concept",
thesaurus = "Array signal processing; Digital arithmetic; Digital
filters; Digital signal processing chips; Fast Fourier
transforms",
}
@TechReport{Karp:1993:HPD,
author = "A. H. Karp and P. Markstein",
title = "High precision division and square root",
number = "HPL-93-42",
institution = "Hewlett--Packard Lab.",
address = "Palo Alto, CA, USA",
pages = "20",
month = jun,
year = "1993",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors present division and square root
algorithms for calculations with more bits than are
handled by the floating point hardware. These
algorithms avoid the need to multiply two high
precision numbers, speeding up the last iteration by as
much as a factor of ten.",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
keywords = "Division; Floating point hardware; Square root
algorithms",
thesaurus = "Digital arithmetic",
}
@InProceedings{Kim:1993:FABa,
author = "S. W. Kim and T. Stouraitis and A. Skavantzos",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, {ISCAS '93}, 3--6 May 1993",
title = "Full adder-based inner product step processors for
residue and quadratic residue number systems",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1821--1824",
year = "1993",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1993.394100",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A full adder-based arithmetic unit of a modulus $m$,
called an FA-based AU$_m$, is proposed. It performs
both addition and multiplication at the same time.
Since the proposed AU$_m$'s use full adders as their
basic units, they lead to modular and regular designs
which result in lower cost and easier implementation in
VLSI.",
}
@InProceedings{Kim:1993:FABb,
author = "Seon Wook Kim and T. Stouraitis and A. Skavantzos",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, {ISCAS '93}, 3--6 May 1993",
title = "Full adder-based inner product step processors for
residue and quadratic residue number systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1821--1824",
year = "1993",
CODEN = "????",
DOI = "https://doi.org/10.1109/EDAC.1993.386412",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
}
@InProceedings{Kim:1993:FABc,
author = "S. W. Kim and T. Stouraitis and A. Skavantzos",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, {ISCAS '93}, 3--6 May 1993",
title = "Full adder-based inner product step processors for
residue and quadratic residue number systems",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1821--1824",
year = "1993",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1993.394100",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A full adder-based arithmetic unit of a modulus m,
called an FA-based AU m, is proposed. It performs both
addition and multiplication at the same time. Since the
proposed AU m's use full adders as their basic units,
they \ldots{}",
}
@InProceedings{Kim:1993:FABd,
author = "Seon Wook Kim and T. Stouraitis and A. Skavantzos",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, {ISCAS '93}, 3--6 May 1993",
title = "Full adder-based inner product step processors for
residue and quadratic residue number systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1821--1824",
year = "1993",
CODEN = "????",
DOI = "https://doi.org/10.1109/EDAC.1993.386412",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
}
@InProceedings{Kirsch:1993:ABU,
author = "Bary J. Kirsch and Peter R. Turner",
title = "Adaptive Beamforming Using {RNS} Arithmetic",
crossref = "Swartzlander:1993:SCA",
pages = "36--43",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Kirsch.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11; residue number system",
}
@Book{Klatte:1993:CXC,
editor = "Rudi Klatte and Ulrich Kulisch and Christian Lawo and
Michael Rauch and Andreas Wiethoff",
title = "{C-XSC}: a {C++} class library for extended scientific
computing",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xii + 269",
year = "1993",
ISBN = "3-540-56328-8 (Berlin), 0-387-56328-8 (New York)",
ISBN-13 = "978-3-540-56328-0 (Berlin), 978-0-387-56328-2 (New
York)",
LCCN = "QA76.73.C153 C9 1993",
bibdate = "Fri Jun 24 20:05:29 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
price = "DM74.00",
abstract = "C-XSC is a tool for the development of numerical
algorithms delivering highly accurate and automatically
verified results. It provides a large number of
predefined numerical data types and operators. These
types are implemented as C++ classes. Thus, C-XSC
allows high-level programming of numerical applications
in C and C++. The most important features of C-XSC are:
real, complex, interval, and complex interval
arithmetic; dynamic vectors and matrices; subarrays of
vectors and matrices; dotprecision data types,
predefined arithmetic operators with maximum accuracy;
standard functions of high accuracy; multiple precision
arithmetic and standard functions; rounding control for
I/O data; error handling, and library of problem
solving routines with automatic result verification.
Thus, C-XSC makes the computer more powerful concerning
the arithmetic. C-XSC is immediately usable by C
programmers, easy to learn, user-extendable, and may
also be combined with other tools. The book can be used
as a textbook and as a reference manual. It consists of
an introduction to advanced computer arithmetic, a
chapter describing the programming languages C and C++,
the major chapter ``C-XSC Reference'', sample programs,
and indices.",
acknowledgement = ack-nhfb,
remark = "This book is a translation of an unpublished German
manuscript.",
subject = "C++ (Computer program language); C-XSC; Mathematics;
Numerical analysis; Mathematics.; Numerical analysis.",
tableofcontents = "1 Introduction \\
1.1 Typography \\
1.2 C-XSC: A Class Library in the Programming Language
C++ \\
1.3 C-XSC: A Programming Environment for Scientific
Computing with Result Verification \\
1.4 Survey of C-XSC \\
2 The Programming Languages C and C++ \\
2.1 A Short Introduction to C \\
2.2 Additional Features in C++ \\
3 C-XSC Reference \\
3.1 Constants, Data Types, and Variables \\
3.2 Expressions \\
3.3 Statements \\
3.4 Error Handling \\
3.5 Pitfalls for Programming with C XSC \\
A Syntax Diagrams \\
A.1 Data Types \\
A.2 Management of Vectors and Matrices \\
A.3 Definition of Variables \\
A.4 Expressions \\
A.5 Logical Expressions \\
A.6 Type Castings \\
A.7 Assignments \\
A.8 Arithmetic Standard Functions \\
A.9 Other Functions \\
A.10 Input and Output \\
A.11 Extension of a Syntax Diagram of C++ \\
B The Structure of the C-XSC Package \\
B.1 Header Files \\
B.2 Module Libraries \\
C Error List \\
D Sample Programs \\
D.1 Rounding Control of Arithmetic Operations \\
D.2 Rounding Control of Input and Output \\
D.3 Scalar Product \\
D.4 Transpose of a Matrix \\
D.5 Trace of a Product Matrix \\
D.6 Inverse of a Matrix \\
D.7 Multiple-Precision Arithmetic \\
D.8 Interval Newton Method \\
D.9 Runge-Kutta Method \\
D.10 Complex Polynomial Arithmetic \\
D.11 Automatic Differentiation \\
E Scientific Computation with Verified Results \\
E.1 Evaluation of Polynomials \\
E.2 Matrix Inversion \\
E.3 Linear Systems of Equations \\
E.4 Eigenvalues of Symmetric Matrices \\
E.5 Fast Fourier Transform \\
E.6 Zeros of a Nonlinear Equation \\
E.7 System of Nonlinear Equations \\
E.8 Ordinary Differential Equations",
}
@Book{Koren:1993:CAA,
author = "Israel Koren",
title = "Computer Arithmetic Algorithms",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xiii + 210",
year = "1993",
ISBN = "0-13-151952-2",
ISBN-13 = "978-0-13-151952-7",
LCCN = "76.9.C62 K67 1993",
bibdate = "Thu Sep 1 10:12:51 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Kornerup:1993:HRM,
author = "Peter Kornerup",
title = "High-Radix Modular Multiplication for Cryptosystems",
crossref = "Swartzlander:1993:SCA",
pages = "277--283",
year = "1993",
bibdate = "Wed Nov 14 18:46:45 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Kornerup.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Book{Kortemeyer:1993:CPT,
author = "Gerd Kortemeyer and others",
title = "{Coprozessoren Programmierung mit Turbo Pascal und
C++: eine grundlegende Einf{\"u}hrung in die
mathematischen Coprozessoren ab 80387 und deren
Programmierung} \toenglish Coprocessor Programming with
{Turbo Pascal} and {C++}\relax \endtoenglish",
publisher = pub-IWT,
address = pub-IWT:adr,
pages = "391",
year = "1993",
ISBN = "3-88322-439-1",
ISBN-13 = "978-3-88322-439-8",
LCCN = "????",
bibdate = "Mon Sep 16 17:08:22 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Kota:1993:NAH,
author = "K. Kota and J. R. Cavallaro",
title = "Numerical Accuracy and Hardware Tradeoffs for {CORDIC}
Arithmetic for Special-Purpose Processors",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "7",
pages = "769--779",
month = jul,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.237718",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:50 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=237718",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Krandick:1993:EMF,
author = "Werner Krandick and Jeremy R. Johnson",
title = "Efficient multiprecision floating point multiplication
with optimal directional rounding",
crossref = "Swartzlander:1993:SCA",
pages = "228--233",
year = "1993",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Krandick.pdf",
abstract = "An algorithm is described for multiplying
multiprecision floating-point numbers. The algorithm
can produce either the smallest floating-point number
greater than or equal to the true product, or the
greatest floating-point number smaller than or equal to
the true product. Software implementations of
multiprecision floating-point multiplication can reduce
the computation time by a factor of two if they do not
compute the low-order digits of the product of the two
mantissas. However, these algorithms do not necessarily
provide optimally rounded results. The algorithms
described here is guaranteed to produce optimally
rounded results and typically obtains the same
savings.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
University, Linz, Austria",
classification = "C5230 (Digital arithmetic methods)",
confdate = "29 June-2 July 1993",
conflocation = "Windsor, Ont., Canada",
confsponsor = "IEEE Comput. Soc.; IEEE Tech. Committee on VLSI;
Natural Sci. and Eng. Res.; Council of Canada",
keywords = "ARITH-11; Floating-point numbers; Multiprecision
floating point multiplication; Optimal directional
rounding; Optimally rounded results",
thesaurus = "Floating point arithmetic",
}
@Article{Krishna:1993:TFA,
author = "H. Krishna and J.-D. Sun",
title = "On theory and fast algorithms for error correction in
residue number system product codes",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "7",
pages = "840--853",
month = jul,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.237724",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:50 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=237724;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=6095",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "The authors develop a coding theory approach to error
control in residue number system product codes. Based
on this coding theory framework, computationally
efficient algorithms are derived for correcting single
errors, double errors, and multiple \ldots{}",
}
@Article{Lee:1993:DAE,
author = "Joong-Eon Lee and Oh-Young Kwon and Tack-Don Han",
title = "Design of an area efficient unit for floating-point
division and square root",
journal = j-J-KOREA-INFO-SCI-SOCIETY,
volume = "20",
number = "7",
pages = "1060--1071",
month = jul,
year = "1993",
CODEN = "HJKHDC",
ISSN = "0258-9125",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors propose an algorithm for a high
performance floating point division and square root
unit that uses a parallel multiplier. The basic
algorithm used in the design is the continued-product
normalization method. In this method, an arbitrary
number is constantly multiplied to the divisor and
dividend and dividend/divisor ends up with quotient/1
and the desired result attained. However this method
requires computation of x*(2-x) and x*(3-x)/2 and this
is quite an overhead. Therefore they propose a new
algorithm to compute (2-x) and (3-x)/2 by using the
modified Booth algorithm. When applied to the
continued-product normalization method, this algorithm
can maximize the inherent parallelism of the
continued-product normalization method, and reduce
computation time by effectively applying pipelining,
and also achieve area efficient design by eliminating
one register and one carry propagate adder needed for
computing (2-x) and (3-x)/2. When the designed unit is
used with the seed generator which has the accuracy of
2/sup -7/, division can be executed in eight cycles and
the square root operation in 13 cycles.",
acknowledgement = ack-nhfb,
classification = "B1265B (Logic circuits); C4240P (Parallel
programming and algorithm theory); C5120 (Logic and
switching circuits); C5230 (Digital arithmetic
methods)",
fjournal = "Journal of the Korea Information Science Society =
Chongbo Kwahakhoe nonmunji",
keywords = "Area efficient unit; Continued-product normalization
method; Floating-point division; Modified Booth
algorithm; Parallel multiplier; Pipelining; Seed
generator; Square root",
language = "Korean",
pubcountry = "South Korea",
thesaurus = "Adders; Digital arithmetic; Parallel algorithms",
}
@InProceedings{Lewis:1993:ALA,
author = "D. M. Lewis",
title = "An accurate {LNS} arithmetic unit using interleaved
memory function interpolator",
crossref = "Swartzlander:1993:SCA",
pages = "2--9",
year = "1993",
bibdate = "Sat Jul 16 16:14:38 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Lewis.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
summary = "A logarithmic number system (LNS) arithmetic unit
using a new method for polynomial interpolation in
hardware is described. The use of an interleaved memory
reduces storage requirements by allowing each stored
function value to be used in \ldots{}",
}
@Misc{Lindsley:1993:DME,
author = "Brett L. Lindsley",
title = "Device and method for evaluating exponentials",
howpublished = "United States Patent 5,177,702",
day = "5",
month = jan,
year = "1993",
bibdate = "Tue Jan 08 22:31:05 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.freepatentsonline.com/5177702.html",
abstract = "A method and apparatus are described for processing an
input value to provide an output exponential value of a
desired base raised to the power of the input value.
The method includes, and the apparatus included
hardware for implementing, the steps of adjusting the
input value relative to the input value, a
predetermined base of a first exponential value, and
the desired base of the output exponential value to
obtain a first scaled value, modifying the scaled value
to obtain an approximation value, determining the first
exponential value of the approximation value,
generating an adjusted error value relative to the
first scaled value, the approximation value, and a
logarithm of the predetermined base of the first
exponential value, determining a correction value for
the first exponential value and combining the first
exponential value with the correction value to obtain,
substantially, the output exponential value having the
desired base raised to the power of the input value.",
acknowledgement = ack-nhfb,
}
@Article{Linzer:1993:IEF,
author = "E. N. Linzer and E. Feig",
title = "Implementation of Efficient {FFT} Algorithms on Fused
Multiply-Add Architectures",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "41",
number = "1",
year = "1993",
CODEN = "ITPRED",
DOI = "https://doi.org/10.1109/TSP.1993.193130",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sun Feb 20 10:11:17 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
}
@Article{Lo:1993:BCP,
author = "J.-C. Lo and S. Thanawastien and T. R. N. Rao",
title = "{Berger} check prediction for array multipliers and
array dividers",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "7",
pages = "892--896",
month = jul,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.237731",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:50 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
note = "See correction \cite{Lo:1996:CBC}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=237731",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Louie:1993:DRD,
author = "M. E. Louie and M. D. Ercegovac",
title = "On Digit-Recurrence Division Implementations for Field
Programmable Gate Arrays",
crossref = "Swartzlander:1993:SCA",
pages = "202--209",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Louie.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@InProceedings{Louie:1993:DRS,
author = "M. E. Louie and M. D. Ercegovac",
booktitle = "Proceedings of the {IEEE} Workshop on {FPGAs} for
Custom Computing Machines, 5--7 April 1993",
title = "A digit-recurrence square root implementation for
field programmable gate arrays",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "178--183",
year = "1993",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Creating efficient arithmetic processors requires a
pairing of high speed arithmetic algorithms with
optimal mapping strategies for a given technology. The
authors propose bit reduction as key to an efficient
pairing process for lookup table based \ldots{}",
}
@InProceedings{Lozier:1993:UGF,
author = "D. W. Lozier",
title = "An underflow-induced graphics failure solved by {SLI}
arithmetic",
crossref = "Swartzlander:1993:SCA",
pages = "10--17",
year = "1993",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Lozier.pdf",
abstract = "Floating-point underflow is often regarded as either
harmless or as an indication that the computational
algorithm is in need of scaling. A counterexample to
this view is given of a function for which contour
plotting is difficult due to floating-point underflow.
The function arose as an asymptotic solution to a model
problem in turbulent combustion in which two chemical
species (fuel and oxidizer) mix and react in a vortex
field. Scaling is not a viable option because of
extreme sensitivity to a small physical parameter.
Standard graphics software packages produce erroneous
contours without any indication of difficulty. This
example provides support for considering symmetric
level-index arithmetic, a new form of computer
arithmetic which is immune to underflow and overflow.",
acknowledgement = ack-nhfb,
affiliation = "Nat. Inst. of Stand. and Technol., Gaithersburg, MD,
USA",
classification = "C5230 (Digital arithmetic methods); C6130B (Graphics
techniques)",
confdate = "29 June-2 July 1993",
conflocation = "Windsor, Ont., Canada",
confsponsor = "IEEE Comput. Soc.; IEEE Tech. Committee on VLSI;
Natural Sci. and Eng. Res.; Council of Canada",
keywords = "ARITH-11; Asymptotic solution; Computer arithmetic;
Contour plotting; Floating point underflow; Graphics
failure; Graphics software packages; Turbulent
combustion",
thesaurus = "Computer graphics; Floating point arithmetic",
}
@Article{Mandelbaum:1993:SRS,
author = "D. M. Mandelbaum",
title = "Some results on a {SRT} type division scheme",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "1",
pages = "102--106",
month = jan,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.192218",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:46 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=192218",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@MastersThesis{Maryoung:1993:DBP,
author = "James Maryoung",
title = "Development of a binary phase shift keying modem
receiver with a floating point processor {TMS320C30}",
type = "Thesis ({M.S.})",
school = "California State University, Long Beach",
address = "Long Beach, CA, USA",
pages = "xi + 265",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Signal processing --- Algorithms.; Signal processing
--- Digital techniques.",
}
@Article{Masotti:1993:FNE,
author = "G. Masotti",
title = "Floating-point numbers with error estimates",
journal = j-CAD,
volume = "25",
number = "9",
pages = "524--538",
month = sep,
year = "1993",
CODEN = "CAIDA5",
ISSN = "0010-4485 (print), 1879-2685 (electronic)",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Addresses the problem of precision in floating-point
computations. A method for estimating the errors which
affect intermediate and final results is presented, and
a synthesis of many software simulations is discussed.
The basic idea is to represent floating-point numbers
by means of a data-structure collecting value and
estimated error information. It has been found that,
under certain circumstances, the estimate of the
absolute error is accurate and has a compact
statistical distribution. It is also shown that, by
monitoring the estimated relative error during a
computation (an ad hoc definition of relative error is
used), the validity of results can be ensured. The
error estimates enable robust algorithms to be
implemented and ill-conditioned problems to be
detected. A hardware implementation of the method by
means of a special floating-point processor is
outlined. A dynamic extension of number precision,
under the control of error estimates, is also
advocated, in order to compute results within given
error bounds.",
acknowledgement = ack-nhfb,
affiliation = "Dept. di Elettr. Inf. e Sistem., Universita degli
Studi di Bologna, Bologna, Italy",
classification = "C5230 (Digital arithmetic methods)",
keywords = "Compact statistical distribution; Computer arithmetic;
Data-structure collecting value; Dynamic extension;
Dynamic precision extension; Error bounds; Error
estimates; Final results; Floating-point numbers;
Floating-point processor; Hardware implementation;
Ill-conditioned problems; Intermediate results;
Numerical accuracy; Relative error; Robust algorithms;
Software simulations; Validity",
pubcountry = "UK",
thesaurus = "Digital arithmetic; Error statistics; Roundoff
errors",
}
@Article{Mazenc:1993:CFU,
author = "Christophe Mazenc and Xavier Merrheim and Jean-Michel
Muller",
title = "Computing functions $ \cos^{-1} $ and $ \sin^{-1} $
using {Cordic}",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "1",
pages = "118--122",
month = jan,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.192222",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:47 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=192222",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{McClellan:1993:AFP,
author = "Scott McClellan",
title = "Alternatives to floating point representation",
type = "Honors paper",
number = "4",
institution = "United States Naval Academy Honors Paper. Dept. of
Mathematics",
pages = "various",
year = "1993",
bibdate = "Sat May 04 17:18:52 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.",
remark = "Honors paper--United States Naval Academy, 1993.",
}
@Article{McKeeman:1993:AOC,
author = "W. M. McKeeman",
title = "Avoiding Overflow in Constant Expression Evaluation",
journal = j-JCLT,
volume = "5",
number = "1",
pages = "27--31",
month = sep,
year = "1993",
ISSN = "1042-5721",
bibdate = "Fri Nov 21 14:40:20 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "The Journal of {C} Language Translation",
remark = "Predicting overflow before it occurs",
}
@InProceedings{McQuillan:1993:NAV,
author = "S. E. McQuillan and J. V. McCanny and R. Hamill",
title = "New algorithms and {VLSI} architectures for {SRT}
division and square root",
crossref = "Swartzlander:1993:SCA",
pages = "80--86",
year = "1993",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_McQuillan.pdf",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "ARITH-11",
summary = "Radix two algorithms for SRT division and
square-rooting are developed. For these schemes, the
result digits and the residuals are computed
concurrently and the computations in adjacent rows are
overlapped. Consequently, their performance should
\ldots{}",
}
@Article{Meier:1993:EMC,
author = "Willi Meier and Othmar Staffelbach",
title = "Efficient Multiplication on Certain Nonsupersingular
Elliptic Curves",
journal = j-LECT-NOTES-COMP-SCI,
volume = "740",
pages = "333--344",
year = "1993",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Feb 5 11:48:51 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t0740.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/0740/07400333.htm;
http://link.springer-ny.com/link/service/series/0558/papers/0740/07400333.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
keywords = "CRYPTO; cryptology",
}
@InProceedings{Mellott:1993:GMG,
author = "Jonathon D. Mellott and Jeremy C. Smith and Fred J.
Taylor",
title = "The {Gauss} Machine: a {Galois}-Enhanced Quadratic
Residue Number System Systolic Array",
crossref = "Swartzlander:1993:SCA",
pages = "156--162",
year = "1993",
DOI = "https://doi.org/10.1109/ARITH.1993.378097",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Mellott.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11; residue arithmetic; residue number system",
summary = "The Gauss machine is a SIMD systolic array
architecture that takes advantage of the
Galois-enhanced residue number system (GEQRNS) to form
reduced-complexity arithmetic elements. The Gauss
machine is targeted at front-end signal and image
processing applications. A discrete prototype that
achieves a peak rating of 320 million complex
arithmetic operations per second while operating at 10
MHz has been constructed. A VLSI implementation of the
Gauss machine's processor cell has been created. The
VLSI implementation is implemented in 2.0-$\mu$m CMOS
and achieves greater than 20-MHz performance, using
less than 2.0-mm$^2$ die area. It is shown that
techniques for defect tolerance in RNS systolic arrays
can result in substantial yield enhancement, thereby
making larger than conventional (ULSI) systems
possible",
}
@InProceedings{Merrheim:1993:FEP,
author = "Xavier Merrheim and Jean-Michel Muller and Hong-Jin
Yeh",
title = "Fast Evaluation of Polynomials and Inverses of
Polynomials",
crossref = "Swartzlander:1993:SCA",
pages = "186--192",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Merrheim.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@MastersThesis{Mesfin:1993:IHP,
author = "Biniam Mesfin",
title = "Implementation of a high performance floating point
unit multiplier",
type = "Thesis ({M.A.Sc.})",
school = "University of Windsor",
address = "Windsor, ON, Canada",
year = "1993",
ISBN = "0-315-78864-X",
ISBN-13 = "978-0-315-78864-0",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "National Library of Canada = Bibliotheque nationale du
Canada; Canadian theses = Theses canadiennes",
acknowledgement = ack-nhfb,
remark = "3 microfiches. University Microfilms order no.
UMI00399117",
}
@Article{Metzger:1993:IFR,
author = "D. Metzger",
title = "Investigation of Finite Register Length Effects on
{Winograd} {FFT} Computation Using Floating Point
Math",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "41",
number = "1",
pages = "449",
month = jan,
year = "1993",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
}
@Manual{MicrosoftCorporation:1993:PGM,
author = "{Microsoft Corporation}",
title = "Programmer's guides: {Microsoft Visual C++}
development system for {Windows}: version 1.0",
organization = "Microsoft Corp.",
address = "Redmond, WA, USA",
pages = "various",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "C++ (Computer program language); Microsoft Visual
C++.",
remark = "C++ tutorial: introduction to C++: a first look at
C++; C++ enhancements to C; references; classes:
introduction to classes; classes and dynamic memory
allocation; more features of classes; inheritance and
polymorphism; operator overloading and conversion
functions; object-oriented design: fundamentals of
object-oriented design; design example, a windowing
class --- Class library user's guide for the Microsoft
Foundation Class Library: introducing the class
library; creating a new application with AppWizard;
creating the document, view; constructing the user
interface with App Studio; binding visual objects to
code using ClassWizard; adding a dialog box; enhancing
views, printing; adding context-sensitive help;
general-prupose classes; CObject class; collections;
files and serialization; diagnostics; exceptions;
programming with VBX controls; OLE support ---
Programming techniques: improving program performance:
using precompiled headers; managing memory for 16-bit C
programs; controlling floating-point math operations;
special environments: programming for Windows;
programming with mixed languages; writing portable C
programs. [Section one of the book], the C++ tutorial,
provides an introduction to the C++ language and
object-oriented programming. [It] assumes [the reader
is] familiar with C \ldots{} [Section two] contains a
tutorial for the Microsoft Foundation Class Library.
The class library is a set of C++ classes that
encapsulate the functionality of applications written
for the Microsoft Windows operating system \ldots{}
[Section three], programming techniques, describes how
to take advantage of the special features of Microsoft
Visual C++. The topics covered \ldots{} include
language extensions, special-purpose library functions,
and the interaction between programming strategies and
compiler options. [This section] is divided into two
parts. Part I, ``Improving Program Performance,'' helps
[the reader] write more efficient programs \ldots{}
Part 2, ``Special Environments,'' covers techniques
specific to certain programming situations. -Introds.",
}
@Article{Mikami:1993:RER,
author = "N. Mikami and M. Kobayashi and Y. Yokoyama",
title = "Roundoff-error reduction for evaluation of a function
by polynomial approximation with error feedback in
fixed-point arithmetic",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "41",
number = "5",
pages = "1953--1955",
month = may,
year = "1993",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "The relationship between Hornor's method for
polynomial evaluation and a first-order recursive
filter with error feedback (EFB) is described. It is
shown that EFB is a useful technique for reducing the
roundoff errors that occur in evaluating a \ldots{}",
}
@InProceedings{Montuschi:1993:CSM,
author = "Paolo Montuschi and Luigi Ciminiera",
title = "$ n \times n $ Carry-Save Multipliers without Final
Addition",
crossref = "Swartzlander:1993:SCA",
pages = "54--61",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Montuschi.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Article{Montuschi:1993:RIT,
author = "P. Montuschi and L. Ciminiera",
title = "Reducing iteration time when result digit is zero for
radix $2$ {SRT} division and square root with redundant
remainders",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "2",
pages = "239--246",
month = feb,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.204797",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:47 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
note = "See remark \cite{Montuschi:1995:RRI}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=204797",
acknowledgement = ack-sfo # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "A new architecture is presented for shared radix 2
division and square root whose main characteristic is
the ability to avoid any addition/subtraction, when the
digit 0 has been selected. The solution presented uses
a redundant representation of the \ldots{}",
}
@Article{Motteler:1993:APF,
author = "Frederick C. Motteler",
title = "Arbitrary Precision Floating-Point Arithmetic",
journal = j-DDJ,
volume = "18",
number = "9",
pages = "28, 30, 32, 34, 84, 86--87",
month = sep,
year = "1993",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Tue Sep 03 09:15:43 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
UnCover database",
abstract = "The C library presented was developed with IEEE-754
compatibility and portability as its primary goals. Its
first application was as part of a portable cross
compiler. It is a general-purpose library that supports
single, double, double-extended, and longer IEEE-754
like formats. The library has been ported to and tested
on a variety of systems including CP/M, PCs running
MS-DOS, PCs running Coherent, Sun 3s, Sparcstations
(Sun's C compiler), and the IBM RS/6000 under AIX. The
package is K and R, ANSI C, and C++ compatible. A
table-driven tester included with the library checks if
it has compiled properly. The tester also gives an idea
of what the package is capable of doing.",
acknowledgement = ack-nhfb,
affiliation = "Zetron Inc., Redmond, WA, USA",
classification = "C5230 (Digital arithmetic methods); C7310
(Mathematics)",
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "C library; Coherent; CP/M; Double-extended;
Floating-point arithmetic; General-purpose library; IBM
RS/6000; IEEE-754 compatibility; IEEE-754 like formats;
MS-DOS; PCs; Portability; Portable cross compiler;
Sparcstations; Sun 3s; Table-driven tester",
thesaurus = "C listings; Digital arithmetic; Mathematics computing;
Software portability; Subroutines",
}
@Misc{Ng:1993:FV,
author = "K-C Ng",
title = "{FDLIBM} Version 5.3",
howpublished = "Web site",
year = "1993",
bibdate = "Thu Oct 17 06:21:14 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.netlib.org/fdlibm/readme",
acknowledgement = ack-nhfb,
keywords = "FDLIBM (Freely Distributable Math Library)",
}
@InProceedings{Nguyen:1993:LDR,
author = "Q. H. Nguyen and I. Kollar",
booktitle = "Instrumentation and Measurement Technology Conference,
1993. {IMTC/93}. Conference Record., {IEEE. 18--20} May
1993",
title = "Limited dynamic range of spectrum analysis due to
roundoff errors of the {FFT}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "47--50",
year = "1993",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Roundoff errors of the block-float fast Fourier
transform (FFT) are treated. Special emphasis is given
to the case when signals containing sine waves are
analyzed. In the detection and analysis of sine waves,
root-mean-square values and overall \ldots{}",
}
@Article{North:1993:FPA,
author = "R. C. North and J. R. Zeidler and W. H. Ku and T. R.
Albert",
title = "A floating-point arithmetic error analysis of direct
and indirect coefficient updating techniques for
adaptive lattice filters",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "41",
number = "5",
pages = "1809--1823",
month = may,
year = "1993",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "The ways in which finite precision arithmetic effects
can deleteriously manifest themselves in both the
stochastic gradient and the recursive least squares
adaptive lattice filters are discussed. closed form
expressions are derived for the steady-state \ldots{}",
}
@Article{Ozawa:1993:SAE,
author = "K. Ozawa and M. Miyazaki",
title = "A summation algorithm with error correction for
parallel computers",
journal = j-SYS-COMP-JAPAN,
volume = "24",
number = "7",
pages = "62--68",
month = "????",
year = "1993",
CODEN = "SCJAEP",
ISSN = "0882-1666 (print), 1520-684X (electronic)",
ISSN-L = "0882-1666",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Proposes an algorithm to accurately compute the sum of
floating-point numbers on parallel computers. This
algorithm is an extension of the well-known recursive
doubling technique which computes the sum of n
floating-point number in log/sub 2/n parallel steps.
The time complexity of the present algorithm also is
O(logn), and the space complexity is O(n). This
algorithm enables a highly accurate result to be
obtained with guarantee. The theoretical analysis and
the numerical experiments on a parallel computer show
that this algorithm is as accurate as Kahan's, which is
the fastest and an accurate serial algorithm for the
summation of the numbers, and also that the present
algorithm is faster than Kahan's provided that two or
more processors are available.",
acknowledgement = ack-nhfb,
affiliation = "Coll. of Gen. Educ., Tohoku University, Sendai,
Japan",
classification = "C4110 (Error analysis in numerical methods); C4240P
(Parallel programming and algorithm theory)",
fjournal = "Systems and computers in Japan",
keywords = "accurate floating-point summation; correct rounding;
error correction; floating-point numbers; guaranteed
accuracy; parallel computation; parallel computers;
recursive doubling; recursive doubling technique;
round-off error analysis; space complexity; summation;
summation algorithm; time complexity",
thesaurus = "computational complexity; error correction; parallel
algorithms",
}
@PhdThesis{Pan:1993:TFVa,
author = "Jing Pan",
title = "Toward a formal verification of a floating-point
coprocessor and its composition with a central
processing unit",
type = "Thesis ({Ph.D.})",
school = "Computer Science Department, University of California,
Davis",
address = "Davis, CA, USA",
pages = "221",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Pan:1993:TFVb,
author = "Jing Pan and K. N. Levitt and M. Archer and S.
Kalvala",
title = "Towards a formal verification of a floating point
coprocessor and its composition with a central
processing unit",
journal = j-IFIP-TRANS-A,
volume = "A20",
pages = "427--447",
month = "????",
year = "1993",
CODEN = "ITATEC",
ISSN = "0926-5473",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Higher Order Logic Theorem Proving and its
Applications IFIP TC\slash WG10.2 International
Workshop - HOL '92.",
abstract = "The authors discuss verification (ultimately down to
the microcode level) of a microprocessor that consists
of a central processing unit that is the master of a
floating point coprocessor; the design is drawn from
the MC68881 floating point coprocessor slaved to the
MC68000, but greatly simplified. The coprocessor in
isolation is verified with respect to a specification
that captures the IEEE floating point standard. In the
authors system, CPU and floating point instructions are
allowed to execute concurrently, but the appearance to
the programmer of the composed system is that of a
sequentially executing instruction stream. The CPU and
floating point coprocessor communicate through the
four-phase handshaking protocol. The verification
involves reasoning about a form of behavioural
abstraction wherein concurrently executing instruction
steams are mapped to a sequential stream.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, California University,
Davis, CA, USA",
classification = "C4210 (Formal logic); C5130 (Microprocessor chips);
C5230 (Digital arithmetic methods); C6110B (Software
engineering techniques)",
confdate = "21-24 Sept. 1992",
conflocation = "Leuven, Belgium",
fjournal = "IFIP Transactions. A. Computer Science and
Technology",
keywords = "Behavioural abstraction; Central processing unit;
Concurrently executing instruction steams; Floating
point coprocessor; Formal verification; Four-phase
handshaking protocol; MC68000; MC68881; Microprocessor;
Reasoning; Sequentially executing instruction stream;
Specification",
pubcountry = "Netherlands",
thesaurus = "Digital arithmetic; Formal verification;
Microprocessor chips; Theorem proving",
}
@InProceedings{Panneerselvam:1993:MAF,
author = "G. Panneerselvam and B. Nowrouzian",
title = "Multiply-add fused {RISC} architectures for {DSP}
applications",
crossref = "IEEE:1993:PIP",
volume = "1",
pages = "108--111",
year = "1993",
DOI = "https://doi.org/10.1109/PACRIM.1993.407210",
bibdate = "Sun Feb 20 10:47:10 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The development of a fixed-point bit-parallel
multiply-add fused (MAF) architecture together with a
corresponding VLSI implementation is presented. The
proposed MAF implementation employs 1.2 CMOS
technology. This MAF implementation finds a variety of
practical applications in high-speed real-time digital
signal processing. The MAF implementation employs a
parallel modified Booth multiplier incorporating an
array of carry-save adders for the addition of the
intermediate partial products, and a hardware efficient
carry-skip adder for carry propagation. The performance
characteristics of the MAF implementation have been
successfully verified by an HSPICE simulation at speeds
of up to 100 MHz.",
acknowledgement = ack-nhfb,
}
@Article{Parhami:1993:IAS,
author = "B. Parhami",
title = "On the implementation of arithmetic support functions
for generalized signed-digit number systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "3",
pages = "379--384",
month = mar,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.210182",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:48 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=210182",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Parker:1993:OHS,
author = "A. Parker",
title = "Optimization of high speed function generation using
table-lookup",
journal = j-TRANS-SOC-COMP-SIM,
volume = "10",
number = "2",
pages = "105--114",
month = jun,
year = "1993",
CODEN = "TSCSEV",
ISSN = "0740-6797",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A process is presented for the use of generic operator
optimization for the evaluation of unary floating point
functions using table lookup. The process involves the
identification of an underlying architecture and the
symbolic-numeric optimization of operators to minimize
a least-squares representation of total error. The
approach is illustrated for the case of floating point
division.",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. and Comput. Eng., Alabama
University, Huntsville, AL, USA",
classification = "C1160 (Combinatorial mathematics); C4120 (Functional
analysis); C6130 (Data handling techniques)",
fjournal = "Transactions of the Society for Computer Simulation",
keywords = "Floating point division; High speed function
generation; Least-squares representation;
Symbolic-numeric optimization; Table lookup",
thesaurus = "Equivalence classes; Function evaluation; Symbol
manipulation; Table lookup",
}
@Book{Pichat:1993:IDC,
author = "Mich{\`e}le Pichat and Jean Vignes",
title = "Ing{\'e}nierie du contr{\^o}le de la pr{\'e}cision des
calculs sur ordinateur",
publisher = "Editions Technip",
address = "Paris, France",
pages = "xvii + 233",
year = "1993",
ISBN = "2-7108-0653-3",
ISBN-13 = "978-2-7108-0653-0",
LCCN = "TJ213 .P478 1993",
bibdate = "Wed Nov 24 12:28:18 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "Collection Informatique",
acknowledgement = ack-nhfb,
subject = "Automatic control; Microcomputers",
}
@Article{Plauger:1993:FCE,
author = "P. J. Plauger",
title = "Floating-Point {C} Extensions",
journal = j-CUJ,
volume = "11",
type = "{Standard C}",
number = "9",
pages = "10--??",
month = sep,
year = "1993",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@Book{Plauger:1993:PPIc,
author = "P. J. Plauger",
title = "Programming on Purpose {III}: Essays on Software
Technology",
volume = "3",
publisher = pub-PHPTR,
address = pub-PHPTR:adr,
pages = "viii + 224",
year = "1993",
ISBN = "0-13-328113-2",
ISBN-13 = "978-0-13-328113-2",
LCCN = "QA76.76.D47 P53 1994",
bibdate = "Wed Jul 6 14:26:01 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\$19.95",
acknowledgement = ack-nhfb,
libnote = "Not yet in my library.",
remark = "Originally published in the author's monthly column in
Computer language magazine, 1986-1992. Contents: Volume
I: Essays on software design -- volume II: Essays on
software people -- volume III: Essays on software
technology.",
tableofcontents = "You Must Be Joking \\
Computer Arithmetic \\
Floating-Point Arithmetic \\
The Central Folly \\
Safe Math \\
Do-It-Yourself Math Functions \\
Locking the Barn Door \\
Half a Secret \\
It's (Almost) Alive \\
The (Almost) Right Stuff \\
Instant Lies \\
What Meets the Eye \\
Technicolor and Cinemascope \\
What Meets the Ear \\
Warm Fuzzies \\
Font Follies \\
Text Editors \\
Approximating Functions \\
Economizing Polynomials \\
Technical Writing \\
All I Want to Do Is \\
Programming for the Billions \\
All Sorts of Sorts \\
Transforming Strings \\
Books for Our Times \\
Through the Grapevine \\
List of Columns \\
Bibliography \\
Index",
}
@Article{Posch:1993:BKR,
author = "K. C. Posch and R. Posch",
title = "{Basiserweiterung mit einer Konvolutionssumme in
Restklassenzahlensystemen}. ({German}) [{Base}
Extension Using a Convolution Sum in Residue Number
Systems]",
journal = j-COMPUTING,
volume = "50",
number = "2",
pages = "93--104",
year = "1993",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "68M07 (11Y16)",
MRnumber = "94e:68024",
bibdate = "Mon Oct 11 20:38:38 MDT 1999",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database; OCLC Contents1st database",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
language = "German",
}
@Article{Pugh:1993:FPC,
author = "Kenneth Pugh",
title = "Floating Point Constants",
journal = j-CUJ,
volume = "11",
type = "Questions and Answers",
number = "10",
pages = "130--??",
month = oct,
year = "1993",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@Article{Reid:1993:LIA,
author = "John Reid",
title = "{Language Independent Arithmetic} ({LIA}) --- a {Draft
International Standard} ({DIS})",
journal = j-SIGNUM,
volume = "28",
number = "1",
pages = "2--7",
month = jan,
year = "1993",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:23 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "LIA is now an International Standard, ISO/IEC
10967-1:1994; it is ``92 pages of small print, densely
mathematical, not counting 8 pages of front matter, and
it is not available electronically.'' Its adoption has
been rather controversial.",
abstract = "The UK and US votes have been decided on the draft
international standard ISO/IEC CD 10967-1:1992:
language independent arithmetic-part 1: integer and
floating point arithmetic. The stated goals of the
draft are: to enhance the portability of numeric
programs across a wide range of numeric architectures.
To help programming languages express the semantics of
their numerical types. It defines integer and
(normalized and denormalized) floating point types. It
defines integer and (normalized and denormalized)
floating point types. It specifies the primitive
computational operations with source and destination
operands of the same type, comparison operations on two
operands of the same type, and conversions from any
arithmetic type to any other arithmetic type. The
values of parameters define the exact arithmetic
behaviour of any particular platform.",
acknowledgement = ack-nhfb,
affiliation = "Rutherford Appleton Lab., Didcot, UK",
classification = "C5230 (Digital arithmetic methods); C6140D (High
level languages)",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "International standard; Language independent
arithmetic; Numeric architectures; Numeric programs;
Portability; Programming languages",
thesaurus = "Digital arithmetic; High level languages; Standards",
}
@InProceedings{Richardson:1993:ETR,
author = "S. E. Richardson",
title = "Exploiting trivial and redundant computation",
crossref = "Swartzlander:1993:SCA",
pages = "220--227",
year = "1993",
bibdate = "Thu Jun 20 10:16:15 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Richardson.pdf",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "ARITH-11",
}
@Article{Ris:1993:WFP,
author = "Fred Ris and Ed Barkmeyer and Craig Schaffert and
Peter Farkas",
title = "When Floating-Point Addition Isn't Commutative",
journal = j-SIGNUM,
volume = "28",
number = "1",
pages = "8--13",
month = jan,
year = "1993",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/156301.156303",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:23 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In the early 1980s, the IEEE floating-point standards
(754 for binary formats adopted in 1985 and 854 for
more general situations adopted in 1987) were
developed. There are now many more-or-less IEEE 754
conformant products on the market. A fully compliant
implementation must provide conforming representations
of floating-point values, perform arithmetic operations
as specified by the standard, provide four rounding
modes and five exception flags defined by the standard,
support infinities, NaNs, signed zeros, and unordered
comparisons, and provide access to all these features
from programming languages (as supported by the
compiler and runtime library). Not surprisingly, very
few implementations comply fully with the IEEE 754
standard in all respects. But one might imagine that if
there were such compliance one could expect bit-for-bit
identical results for a given algorithm executed on any
conforming implementation. The paper explains why this
is not always the case.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "IBM Federal Syst. Co., Boulder, CO, USA",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "Arithmetic operations; Conforming implementation;
Exception flags; Floating-point addition;
Floating-point values; IEEE 754; IEEE floating-point
standards; Rounding modes",
thesaurus = "Digital arithmetic; Standards",
}
@InProceedings{Samani:1993:SVP,
author = "D. M. Samani and J. Ellinger and E. J. Powers and E.
E. Swartzlander",
title = "Simulation of variable precision {IEEE} floating point
using {C}++ and its application in digital signal
processor design",
crossref = "IEEE:1993:PMS",
pages = "1509--1514 vol.2",
year = "1993",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We use a C++ class to transparently emulate
variable-precision floating point arithmetic using
standard arithmetic. This allows the determination of
an algorithm's susceptibility to errors produced by
finite-precision arithmetic and the determination of
the minimum precision necessary for stability. The
class, called Real, offers several advantages for many
applications, e.g., ALU design, signal processing,
systolic and lattice filter design, etc. Since it
supports the IEEE floating point standard, it produces
identical results on any compliant platform. An
algorithm can be adapted for simulation with minimal
effort and without interfering with normal operation.
We also consider how the acceptance of the IEEE
standard and the development of fast hardware for
microcomputers have changed common assumptions about
algorithm timing. Finally, we examine the potential use
of the new floating point DSP chips for adaptive
filtering. Historically, the computational requirements
of adaptive filters confined implementations to
specialized hardware or supercomputers. Today's DSP
chips offer a relatively inexpensive alternative. We
have implemented several adaptive filtering algorithms
that are based on Least Squares estimation criterion on
Motorola's DSP96002. Our experience indicates that the
DSP96K is a viable medium for such algorithms and one
can expect a ten-fold speed improvement over a i486
running at 50 MHz.",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. and Comput. Eng., Texas
University, Austin, TX, USA",
classification = "B1265F (Microprocessors and microcomputers); B1270F
(Digital filters); B6140 (Signal processing and
detection); C5135 (Digital signal processing chips);
C5220P (Parallel architecture); C5230 (Digital
arithmetic methods); C5240 (Digital filters); C5260
(Digital signal processing); C6140D (High level
languages)",
keywords = "Adaptive filtering; Algorithm timing; ALU design; C++
language; Digital signal processor design; DSP chips;
Floating point arithmetic; IEEE standard; Lattice
filter; Least squares estimation criterion; Motorola
DSP96002; Real; Systolic filter; Variable precision
IEEE floating point",
thesaurus = "Adaptive filters; C language; Digital signal
processing chips; Floating point arithmetic; Lattice
filters; Least squares approximations; Systolic
arrays",
}
@InProceedings{Sarma:1993:MAR,
author = "D. D. Sarma and D. W. Matula",
title = "Measuring the Accuracy of {ROM} Reciprocal Tables",
crossref = "Swartzlander:1993:SCA",
pages = "95--102",
year = "1993",
bibdate = "Wed Nov 14 18:47:17 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Sarma.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Article{Scannell:1993:DMM,
author = "Robert K. Scannell and John K. Hagge",
title = "Development of a Multichip Module {DSP}",
journal = j-COMPUTER,
volume = "26",
number = "4",
pages = "13--21",
month = apr,
year = "1993",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Tue May 14 16:20:44 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A highly modular processor architecture based on
off-the-shelf components supports an MCM design
implementation that delivers 400 million floating-point
operations per second in a 75-gram package.",
acknowledgement = ack-nhfb,
affiliation = "Rockwell Int., Anaheim, CA, USA",
classification = "B0170J (Product packaging); B1265F (Microprocessors
and microcomputers); B2220J (Hybrid integrated
circuits); B2570 (Semiconductor integrated circuits);
C5135 (Digital signal processing chips)",
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
keywords = "Cost; Highly modular processor architecture;
Interconnect-substrate design; MCM package assembly;
Multichip module DSP; Signal processor packaging
design; Size; Weight",
thesaurus = "Digital signal processing chips; Multichip modules",
}
@Article{Schorn:1993:AAR,
author = "Peter Schorn",
title = "An Axiomatic Approach to Robust Geometric Programs",
journal = j-J-SYMBOLIC-COMP,
volume = "16",
number = "2",
pages = "155--166 (or 155--165??)",
month = aug,
year = "1993",
CODEN = "JSYCEH",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
MRclass = "68U07",
MRnumber = "94k:68196",
bibdate = "Sat May 10 15:54:09 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C4260 (Computational geometry); C1180 (Optimisation
techniques)",
corpsource = "Inst. fur Theor. Inf., Eidgenossische Tech.
Hochschule, Zurich, Switzerland",
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
keywords = "axiomatic approach; computational geometry; digital
arithmetic; floating point arithmetic; geometric;
imprecise primitives; non-trivial; plane sweep
algorithm; primitives; programming; robust geometric
programs",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Schulte:1993:ERC,
author = "M. Schulte and E. Swartzlander",
title = "Exact rounding of certain elementary functions",
crossref = "Swartzlander:1993:SCA",
pages = "138--145",
year = "1993",
bibdate = "Thu Jun 20 10:16:17 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1993-01.pdf;
http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Schulte.pdf",
abstract = "An algorithm is described which produces exactly
rounded results for the functions of reciprocal, square
root, 2/sup x/, and log 2/sup x/. Hardware designs
based on this algorithm are presented for floating
point numbers with 16- and 24-b significands. These
designs use a polynomial approximation in which
coefficients are originally selected based on the
Chebyshev series approximation and are then adjusted to
ensure exactly rounded results for all inputs. To
reduce the number of terms in the approximation, the
input interval is divided into subintervals of equal
size and different coefficients are used for each
subinterval. For floating point numbers with 16-b
significands, the exactly rounded value of the function
can be computed in 51 ns on a 20-mm/sup 2/ chip. For
floating point numbers with 24-b significands, the
functions can be computed in 80 ns on a 98-mm/sup 2/
chip.",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. and Comput. Eng., Texas
University, Austin, TX, USA",
classification = "C4120 (Functional analysis); C5230 (Digital
arithmetic methods)",
confdate = "29 June--2 July 1993",
conflocation = "Windsor, Ont., Canada",
confsponsor = "IEEE Comput. Soc.; IEEE Tech. Committee on VLSI;
Natural Sci. and Eng. Res.; Council of Canada",
keywords = "ARITH-11; Elementary functions; Exact rounding;
Floating point numbers; Polynomial approximation;
Reciprocal; Rounded results; Square root",
thesaurus = "Floating point arithmetic; Function evaluation",
}
@InProceedings{Schulte:1993:PHD,
author = "M. J. Schulte and E. E. {Swartzlander, Jr.}",
title = "Parallel Hardware Designs for Correctly Rounded
Elementary Functions",
crossref = "Corliss:1993:AIC",
pages = "65--87 (or 65--88??)",
year = "1993",
bibdate = "Tue Oct 22 13:37:58 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Schulte:1993:TMC,
author = "M. J. Schulte and E. E. {Swartzlander, Jr.}",
title = "Truncated Multiplication with Correction Constant",
crossref = "Eggermont:1993:VSP",
pages = "388--396",
year = "1993",
bibdate = "Sun Mar 04 10:38:15 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1993-02.pdf",
acknowledgement = ack-nhfb,
}
@TechReport{Schwarz:1993:HRAa,
author = "E. Schwarz",
title = "High-radix algorithms for high-order arithmetic
operations",
type = "Technical Report",
number = "CSL-TR-93-559",
institution = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
month = jan,
year = "1993",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@PhdThesis{Schwarz:1993:HRAb,
author = "Eric Mark Schwarz",
title = "High-radix algorithms for high-order arithmetic
operations",
type = "Thesis ({Ph.D.})",
school = "Department of Electrical Engineering, Stanford
University",
address = "Stanford, CA, USA",
pages = "224",
month = apr,
year = "1993",
bibdate = "Mon Jan 07 22:38:06 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Many common algorithms for high-order arithmetic
operations require an initial approximation. The
Newton--Raphson algorithm starts with an approximation
and then quadratically converges on the solution. The
initial approximation determines the number of
iterations of the algorithm and is typically
implemented as a look-up table in the form of a ROM or
PLA. A novel method is suggested which describes
high-order arithmetic operations with a partial product
array. This method applies to the operations of
division, reciprocal, square root, natural logarithm,
exponential, and trigonometric functions. The partial
product array of Boolean elements which describes the
operation can be summed on an existing floating-point
multiplier. The hardware needed is only the logic gates
to create the Boolean elements in the array and a
multiplexor, and the latency is that of the multiplier.
Thus, by reusing a floating-point multiplier, a
high-precision approximation to a high-order arithmetic
operation can be implemented with a low marginal
cost.\par
This dissertation describes the implementation and
shows a method for deriving partial product arrays to
approximate arithmetic operations. Then the proposed
method is applied and evaluated for several operations.
The proposed method yields a minimum approximation of
twelve bits correct for the reciprocal operation and
sixteen bits for the square root operation. The
proposed method is shown to be as small as 0.05\% the
size (in gates) of an equivalent precision look-up
table and has up to four times the accuracy (in bits)
as an equivalent latency polynomial approximation.
Also, three new iterative algorithms to increase the
precision of the approximations and a theoretical
analysis of the partial product array representation
are detailed. Thus, high-radix algorithms of many
arithmetic operations are possible at low cost.",
acknowledgement = ack-nhfb,
keywords = "division; elementary functions; exponential;
logarithm; PPA (partial product array); reciprocal
square root; square root",
remark = "AAT 9317816. ProQuest document ID 746798521.",
}
@InProceedings{Schwarz:1993:HSA,
author = "Eric M. Schwarz and Michael J. Flynn",
title = "Hardware starting approximation for the square root
operation",
crossref = "Swartzlander:1993:SCA",
pages = "103--111",
year = "1993",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Schwarz.pdf",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "ARITH-11",
summary = "A method for obtaining high-precision approximations
of high-order arithmetic operations is presented. These
approximations provide an accurate starting
approximation for high-precision iterative algorithms,
which translates into few iterations and \ldots{}",
}
@Article{Schwarz:1993:PHR,
author = "E. M. Schwarz and M. J. Flynn",
title = "Parallel high-radix nonrestoring division",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "10",
pages = "1234--1246",
month = oct,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.257709",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=257709",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Schwarz:1993:UFM,
author = "Eric Mark Schwarz and M. J. (Michael J.) Flynn",
title = "Using a floating-point multiplier's internals for
high-radix division and square root",
type = "Technical report",
number = "CSL-TR-93-554",
institution = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
pages = "iv + 45",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic.",
remark = "``January 1993.'' Abstract: ``A method for obtaining
high-precision approximations of high-order arithmetic
operations at low-cost is presented in this study.
Specifically, high-precision approximations of the
reciprocal (12 bits worst case) and square root (16
bits) operations are obtained using the internal
hardware of a floating-point multiplier without the use
of look-up tables. The additional combinatorial logic
necessary is very small due to the reuse of existing
hardware. These low-cost high-precision approximations
are used by iterative algorithms to perform the
operations of division and square root. The method
presented also applies to several other high-order
arithmetic operations. Thus, high-radix algorithms for
high-order arithmetic operations such as division and
square root are possible at low-cost.''",
}
@InProceedings{Shanbhag:1993:REAa,
author = "N. R. Shanbhag and K. K. Parhi",
booktitle = "{IEEE} International Symposium on Circuits and
Systems: {ISCAS '93}, 3--6 May 1993",
title = "Roundoff error analysis of the pipelined {ADPCM}
coder",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "886--889",
year = "1993",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Not \ldots{}",
}
@InProceedings{Shanbhag:1993:REAb,
author = "N. R. Shanbhag and K. K. Parhi",
booktitle = "{IEEE} International Symposium on Circuits and
Systems: {ISCAS '93}, 3--6 May 1993",
title = "Roundoff error analysis of the pipelined {ADPCM}
coder",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "886--889",
year = "1993",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Roundoff error analysis of a pipelined adaptive
differential pulse code modulation (ADPCM) coder is
presented. The pipelined coder has been developed by
employing the relaxed look-ahead technique. It is shown
that the precision of the quantized \ldots{}",
}
@InProceedings{Shand:1993:FIR,
author = "M. Shand and J. Vuillemin",
title = "Fast Implementations of {RSA} Cryptography",
crossref = "Swartzlander:1993:SCA",
pages = "252--259",
year = "1993",
bibdate = "Wed Nov 14 18:47:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Shand.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Book{Shannon:1993:CES,
author = "Claude Elwood Shannon and N. J. A. (Neil James
Alexander) Sloane and A. D. (Aaron D.) Wyner",
title = "{Claude Elwood Shannon}: collected papers",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xliv + 924",
year = "1993",
ISBN = "0-7803-0434-9",
ISBN-13 = "978-0-7803-0434-5",
LCCN = "TK5101 .S448 1993",
bibdate = "Sat Nov 20 09:04:51 MST 2010",
bibsource = "catalog.princeton.edu:7090/voyager;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
author-dates = "Claude Elwood Shannon (1916--2001)",
subject = "telecommunication; information theory; computers",
}
@Article{Sharp:1993:PRN,
author = "W. E. Sharp and Carter Bays",
title = "A portable random number generator for
single-precision floating-point arithmetic",
journal = j-COMP-GEOSCI,
volume = "19",
number = "4",
pages = "593--??",
month = apr,
year = "1993",
CODEN = "CGEODT, CGOSDN",
ISSN = "0098-3004 (print), 1873-7803 (electronic)",
ISSN-L = "0098-3004",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computers and Geosciences",
}
@InProceedings{Shirayanagi:1993:MCM,
author = "Kiyoshi Shirayanagi",
title = "An algorithm to compute floating point {Gr{\"o}bner}
bases",
crossref = "Lee:1993:MCM",
pages = "95--106",
year = "1993",
MRclass = "68Q40 (13P10 68Q25)",
MRnumber = "94j:68129",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Shute:1993:AAB,
author = "Malcolm J. Shute",
title = "{Abotec}: an automatic back-of-the-envelope
calculator",
journal = j-SIGPLAN,
volume = "28",
number = "8",
pages = "90--98",
month = aug,
year = "1993",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:16:40 MST 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The trial-and-error method, iteratively applied, is
invariably involved in any kind of design work, with
much back-of-the-envelope calculation to guide the
process. In this, the `what-if' game is a very useful
tactic in the search for unexpected solutions in
complex design spaces, made all the more effective by
the availability of automated interpreters. These are
needed to perform the tedious re-calculation of the
model each time a change is made to a small part. In
the financial world, the interpreter generally takes
the form of the spread-sheet, of which Quattro is a
fine example; in mathematics it takes the form of
packages such as Mathematica. Neither of these is
ideally tailored for engineering design, and so Abotec
was developed when the author had need of such a tool.
There are four main characteristics which fit Abotec
for its purpose: it works with floating-point numbers
throughout; it uses a richer than normal set of
arithmetic operators and functions; it uses mnemonic
labelling throughout; and, most importantly it treats
all variables as having an upper and lower bound.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Manchester University,
UK",
classification = "C6140D (High level languages); C7310 (Mathematics);
C7400 (Engineering)",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "Abotec; Arithmetic operators; Automated interpreters;
Automatic back-of-the-envelope calculator;
Back-of-the-envelope calculation; Complex design
spaces; Design work; Engineering design; Floating-point
numbers; Mnemonic labelling; Re-calculation;
Trial-and-error method; Unexpected solutions; What-if",
thesaurus = "CAD; High level languages; Mathematics computing",
}
@Article{Smith:1993:PFC,
author = "Ross Smith and Gerald Sobelman and George Luk and
Koichi Suda and Jeff Bracken",
title = "A Programmable Floating-Point Cell for Systolic Signal
Processing",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "5",
number = "1",
pages = "75--84",
month = jan,
year = "1993",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1007/BF01880273",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The FPC controller and the AMD Am29325 32-bit
floating-point mathematics processor form a two-chip
cell designed for one- or two-dimensional systolic
arrays which can be used to implement a wide variety of
signal processing applications. The FPC controls the
Am29325, routes data to and from it, and routes data
and control to other cells in the array. Unique
architectural features include two interchangeable data
memories, an input port which can be used as either a
local or global port, and a 32-bit instruction word
that allows concurrent use of all cell resources.
Additional features include a program memory, two data
streams, and three control streams.",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
}
@Article{Smith:1993:VFP,
author = "William Smith",
title = "Varying Floating-Point Precision",
journal = j-CUJ,
volume = "11",
number = "7",
pages = "87--??",
month = jul,
year = "1993",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@Article{Smith:1993:WDF,
author = "William Smith",
title = "Windows, {DLLs}, and Floating Point Types",
journal = j-CUJ,
volume = "11",
number = "9",
pages = "21--??",
month = sep,
year = "1993",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@InProceedings{Soulas:1993:AMC,
author = "T. Soulas and D. Villeger and V. G. Oklobdzija",
title = "An {ASIC} macro cell multiplier for complex numbers",
crossref = "IEEE:1993:PEC",
pages = "589--593",
year = "1993",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An architecture for ASIC macro cell implementing a
complex number multiplier with applications in a
digital signal processing ASIC chip is described. The
complex numbers are packed into one 32-bit word. The
design is unique and combines shared Booth encoding for
the real and imaginary parts including only one
combined modified Wallace tree. The regular Wallace
tree and the tree of 4:2 adders for the complex
multiplier implementation are compared. The authors
took advantage of 4:2 adders in implementing the
combined bit compression tree for each part. This
design resulted in a more compact wiring structure and
balanced delays resulting in faster multiplier circuit.
The number of adders was also decreased.",
acknowledgement = ack-nhfb,
affiliation = "Ecole Superieure d'Ingenieurs en Electrotech. et
Electron., Noisy le Grand, France",
classification = "B1130B (Computer-aided circuit analysis and design);
B1265B (Logic circuits); B1265F (Microprocessors and
microcomputers); B2570D (CMOS integrated circuits);
C5120 (Logic and switching circuits); C5135 (Digital
signal processing chips); C5210B (Computer-aided logic
design); C5230 (Digital arithmetic methods); C7410D
(Electronic engineering computing)",
confsponsor = "IEEE; EDA Assoc.; AEIA, Spain; AFCET, France; AICA,
Italy; Bull SA, France; CEC ESPRIT Basic Research",
keywords = "32 Bit; ASIC macro cell multiplier; Balanced delays;
CMOS; Combined bit compression tree; Compact wiring
structure; Complex numbers; Digital signal processing
ASIC chip; Floating point number representation; Shared
Booth encoding; Wallace tree",
numericalindex = "Word length 3.2E+01 bit",
thesaurus = "Application specific integrated circuits; Cellular
arrays; CMOS logic circuits; Digital signal processing
chips; Floating point arithmetic; Integrated circuit
design; Logic arrays; Logic CAD; Multiplying circuits",
}
@Article{Subramaniam:1993:PPP,
author = "Ramesh Subramaniam and Kiran Kundargi and J. Dahms",
title = "Programming The {Pentium} Processor",
journal = j-DDJ,
volume = "18",
number = "6",
pages = "34, 36, 38, 40--42",
month = jun,
year = "1993",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Tue Sep 03 09:15:41 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
UnCover database",
abstract = "Intel's recent entry into the 32-bit microprocessor
race ups the performance ante. Our authors discuss the
Pentium's superscalar, pipelined architecture, focusing
on floating-point code. John Dahms shares some of his
experiences in writing a Pentium-aware compiler.",
acknowledgement = ack-nhfb,
affiliation = "Intel, Santa Clara, CA, USA",
classification = "C5130 (Microprocessor chips); C5220 (Computer
architecture); C6110 (Systems analysis and
programming); C6150C (Compilers, interpreters and other
processors)",
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "32 Bit; 32-Bit microprocessor; Floating-point code;
High performance architecture; Intel Pentium;
Pentium-aware compiler; Programming; Superscalar
pipelined architecture",
thesaurus = "Computer architecture; Microprocessor chips;
Microprogramming; Pipeline processing; Program
compilers",
}
@InProceedings{Swartzlander:1993:FSC,
author = "Earl Swartzlander and Mary Jane Irwin and Graham
Jullien",
title = "Foreword: {11th Symposium on Computer Arithmetic,
Windsor, Ontario, Canada, June 29--July 2, 1993}",
crossref = "Swartzlander:1993:SCA",
pages = "v--v",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_contents.pdf;
http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_foreword.pdf;
http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_preface.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@InProceedings{Takagi:1993:MMA,
author = "N. Takagi",
title = "Modular Multiplication Algorithm with Triangle
Addition",
crossref = "Swartzlander:1993:SCA",
pages = "272--276",
year = "1993",
bibdate = "Wed Nov 14 18:48:15 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Takagi.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Article{Thompson:1993:CCQ,
author = "William J. Thompson",
title = "Cutting Corners: Quick Square Roots and Trig
Functions",
journal = j-COMPUT-PHYS,
volume = "7",
number = "1",
pages = "18--??",
month = jan,
year = "1993",
CODEN = "CPHYE2",
DOI = "https://doi.org/10.1063/1.4823136",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Wed Apr 10 08:45:39 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://aip.scitation.org/doi/10.1063/1.4823136",
acknowledgement = ack-nhfb,
ajournal = "Comput. Phys",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
}
@Manual{TI:1993:ITC,
title = "Interfacing {TI} clocked {FIFOs} with {TI}
floating-point digital signal processors: first-in,
first-out technology",
organization = "Texas Instruments Incorporated",
address = "S.l",
pages = "iv + 15",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer input-output equipment.; Signal processing
--- Digital techniques --- Equipment and; supplies.",
remark = "``SCAA005'' --- back cover.",
}
@Misc{TI:1993:ITT,
key = "TI '1993",
title = "Inside technology today 32-bit floating point
multi-port {DSP} \slash{} produced by {Texas
Instruments}",
howpublished = "VHS format. High-speed, multi-port DSPs can be used in
parallel processing applications to really enhance
computation time and power. A popular 6-port floating
point DSP and high speed design integration and
applications are described in this tape.",
address = "Dallas, TX, USA",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "1 videocassette",
acknowledgement = ack-nhfb,
keywords = "Computer --- Circuits.; Electronic calculating
machines circuits.",
publication = "Texas Instruments Inc.",
}
@Article{Timmermann:1993:GFR,
author = "D. Timmermann and B. Rix and B. Hosticka",
title = "{Gleitkommaprozessor f{\"u}r rechenintensive
Echtzeitanwendungen} \toenglish {Floating-point
Processor for Computationally Intensive Real-Time Use}
\endtoenglish",
journal = j-ELECTRONIK,
volume = "20",
number = "??",
pages = "142--146",
month = "????",
year = "1993",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Dec 08 13:05:00 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronik",
}
@Article{Tiwari:1993:NCP,
author = "Neeraj Tiwari and A. K. Nigam",
title = "A note on constructive procedure for unbiased
controlled rounding",
journal = j-STAT-PROB-LETT,
volume = "18",
number = "5",
pages = "415--420",
day = "2",
month = dec,
year = "1993",
CODEN = "SPLTDC",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
bibdate = "Sun Jun 1 11:14:48 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/statproblett1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/016771529390036I",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
}
@Article{Tsuji:1993:FNS,
author = "Kumiko Tsuji",
title = "Floating-point number solutions in a simple linear
equation with addition algorithm. Numerical calculation
methods with guaranteed accuracy and their applications
({Japanese}) ({Kyoto}, 1992)",
journal = "S{\=u}rikaisekikenky{\=u}sho K{\=o}ky{\=u}roku",
volume = "831",
pages = "33--45",
year = "1993",
MRclass = "65G05",
MRnumber = "95a:65083",
bibdate = "Fri Dec 8 08:24:11 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Turner:1993:CSA,
author = "P. R. Turner",
title = "Complex {SLI} arithmetic: Representation, algorithms
and analysis",
crossref = "Swartzlander:1993:SCA",
pages = "18--25",
year = "1993",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Turner.pdf",
abstract = "The extension of the SLI (symmetric level index)
system to complex numbers and arithmetic is discussed.
The natural form for representation of complex
quantities in SLI is in the modulus-argument form, and
this can be sensibly packed into a single 64-b word for
the equivalent of the 32-b real SLI representation. The
arithmetic algorithms prove to be very slightly more
complicated than for real SLI arithmetic. The
representation, the arithmetic algorithms, and the
control of errors within these algorithms are
described.",
acknowledgement = ack-nhfb,
affiliation = "Department of Math., US Naval Acad., Annapolis, MD,
USA",
classification = "C5230 (Digital arithmetic methods)",
keywords = "ARITH-11; Arithmetic algorithms; Complex numbers;
Modulus-argument form; Representation; SLI; SLI
arithmetic; Symmetric level index",
thesaurus = "Floating point arithmetic",
}
@Article{Vassiliadis:1993:CHW,
author = "S. Vassiliadis and E. M. Schwarz",
title = "Correction to {``Hard-wired multipliers with encoded
partial products''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "1",
pages = "127--127",
month = jan,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.192224",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:47 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=192224",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Veselic:1993:FPH,
author = "Kre{\v{s}}imir Veseli{\'c} and Ivan Slapni{\v{c}}ar",
title = "Floating-Point Perturbations of {Hermitian} Matrices",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "195",
number = "??",
pages = "81--116",
month = dec,
year = "1993",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15 (15A18 15A57)",
MRnumber = "94m:65066",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Vignes:1993:SAR,
author = "J. Vignes",
title = "A stochastic arithmetic for reliable scientific
computation",
journal = j-MATH-COMP-SIM,
volume = "35",
number = "3",
pages = "233--261",
month = sep,
year = "1993",
CODEN = "MCSIDR",
DOI = "https://doi.org/10.1016/0378-4754(93)90003-D",
ISSN = "0378-4754 (print), 1872-7166 (electronic)",
ISSN-L = "0378-4754",
bibdate = "Thu Mar 24 20:56:34 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://portal.acm.org/citation.cfm?id=165789.165792",
acknowledgement = ack-nhfb,
fjournal = "Mathematics and Computers in Simulation",
journal-URL = "http://www.sciencedirect.com/science/journal/03784754",
}
@Article{vonNeumann:1993:FDR,
author = "John von Neumann",
title = "First Draft of a Report on the {EDVAC}",
journal = j-IEEE-ANN-HIST-COMPUT,
volume = "15",
number = "4",
pages = "28--75",
month = oct # "\slash " # dec,
year = "1993",
CODEN = "IAHCEX",
ISSN = "1058-6180 (print), 1934-1547 (electronic)",
ISSN-L = "1058-6180",
bibdate = "Thu Jul 12 06:22:55 MDT 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeeannhistcomput.bib",
note = "Edited and corrected by Michael D. Godfrey.",
URL = "http://dlib.computer.org/an/books/an1993/pdf/a4027.pdf;
http://www.computer.org/annals/an1993/a4027abs.htm",
acknowledgement = ack-nhfb,
ajournal = "IEEE Ann. Hist. Comput.",
fjournal = "IEEE Annals of the History of Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
xxpages = "27--??",
keywords = "floating-point arithmetic; rounding",
}
@Article{Vornberger:1993:BBM,
author = "Cal Vornberger",
title = "Beyond Bit Maps: Multiple floating objects deliver new
power and flexibility to bit-map image processing.
{Micrografx Picture Publisher} 4.0 and {Fractal Design
Painter X2} feature object layers and other useful
innovations",
journal = j-BYTE,
volume = "18",
number = "13",
pages = "165--166, 168",
month = dec,
year = "1993",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 12 16:34:03 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "D2010 (Business and professional); D2020 (Design and
graphics)",
fjournal = "BYTE Magazine",
keywords = "Bit maps; Ease of use; Fractal design painterX2;
Functionality; Micrografx; Object technology; Picture
Publisher 4.0",
thesaurus = "Business graphics; Desktop publishing",
}
@Article{Walter:1993:SMM,
author = "C. D. Walter",
title = "Systolic modular multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "3",
pages = "376--378",
month = mar,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.210181",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:48 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=210181",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Wang:1993:SAC,
author = "Chin-Liang Wang and Jung-Lung Lin",
title = "A systolic architecture for computing inverses and
divisions in finite fields {$ \mathrm {GF}(2^m) $}",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "9",
pages = "1141--1146",
month = sep,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.241603",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=241603",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Wei:1993:CTA,
author = "D.-Y. D. Wei and J. H. Kim and T. R. N. Rao",
title = "Complete tests in algorithm-based fault-tolerant
matrix operation on processor arrays",
crossref = "Lombardi:1993:PII",
pages = "255--262",
year = "1993",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Recently, F. T. Assaad and S. Dutt (1992) proposed the
hybrid checksum test method for the floating-point
matrix-matrix multiplication in ABFT environment, by
which the error coverage can be greatly increased.
However, the thresholded test in their approach is
still not avoidable in the floating-point additions
involved in matrix multiplication and the number of
error detections decrease with the increase in the
dynamic range of data, which is not totally
satisfactory. The authors present an effective method,
called concurrent floating-point checksum (CFPC) test,
which provides very convincing error
detection/correction capabilities for the part of
floating-point addition with a minimum time latency and
hardware overhead.",
acknowledgement = ack-nhfb,
affiliation = "Center for Adv. Comput. Studies, University of
Southwestern Louisiana, Lafayette, LA, USA",
classification = "B0290H (Linear algebra); B1265 (Digital
electronics); B6120B (Codes); C4140 (Linear algebra);
C5210 (Logic design methods); C5230 (Digital arithmetic
methods); C6130 (Data handling techniques)",
keywords = "concurrent floating-point checksum; error correction;
error detections; fault-tolerant matrix; floating-point
additions; floating-point matrix-matrix multiplication;
floating-point testing; hardware overhead; hybrid
checksum test; minimum time latency; processor arrays;
thresholded test",
thesaurus = "Computational complexity; Error correction; Error
detection; Fault tolerant computing; Floating point
arithmetic; Logic arrays; Logic testing; Matrix
multiplication",
}
@Book{Weste:1993:PCV,
author = "Neil H. E. Weste and Kamran Eshraghian",
title = "Principles of {CMOS VLSI} Design: a Systems
Perspective",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Second",
pages = "xxii + 713",
year = "1993",
ISBN = "0-201-53376-6",
ISBN-13 = "978-0-201-53376-7",
LCCN = "TK7874 .W46 1993",
bibdate = "Mon Sep 16 16:32:31 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Williams:1993:BFM,
author = "Al Williams",
title = "Bit Floating-Point Math",
journal = j-DDJ,
volume = "18",
number = "6",
pages = "70--??",
month = jun,
year = "1993",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This approach to floating-point math uses 32-bit
instructions. Although Al uses the 80386 as an example,
these techniques can be applied to other 32-bit
processors as well.",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Williams:1993:FM,
author = "Al Williams",
title = "32-bit floating-point math",
journal = j-DDJ,
volume = "18",
number = "6",
pages = "70, 72, 74, 76, 80",
month = jun,
year = "1993",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Tue Sep 10 08:57:56 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
UnCover database",
abstract = "This approach to floating-point math uses 32-bit
instructions. Although Al uses the 80386 as an example,
these techniques can be applied to other 32-bit
processors as well.",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "32 Bit; 32-Bit instructions; 32-Bit processors; 386
Instruction set; 80386; Floating-point mathematics",
thesaurus = "Digital arithmetic; Microprocessor chips",
}
@InProceedings{Wrzyszcz:1993:DDCa,
author = "A. Wrzyszcz and D. Caban and E. L. Dagless",
booktitle = "Proceedings. [4th] European Conference on Design
Automation, 1993, with the European Event in {ASIC}
Design",
title = "Design of a discrete cosine transform circuit using
the residue number system",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "584--588",
year = "1993",
CODEN = "????",
DOI = "https://doi.org/10.1109/EDAC.1993.386412",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The design of an integrated circuit aimed at efficient
discrete cosine transform computation is presented.
High performance is obtained through the use of
pipelining and residue arithmetic. An approach to
high-speed modular multiplication employing \ldots{}",
}
@InProceedings{Wrzyszcz:1993:DDCb,
author = "A. Wrzyszcz and D. Caban and E. L. Dagless",
booktitle = "Proceedings. [4th] European Conference on Design
Automation, 1993, with the European Event in {ASIC}
Design",
title = "Design of a discrete cosine transform circuit using
the residue number system",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "584--588",
year = "1993",
CODEN = "????",
DOI = "https://doi.org/10.1109/EDAC.1993.386412",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The design of an integrated circuit aimed at efficient
discrete cosine transform computation is presented.
High performance is obtained through the use of
pipelining and residue arithmetic. An approach to
high-speed modular multiplication employing \ldots{}",
}
@Article{Zeng:1993:CFA,
author = "Chuan-Qing Zeng and Kousuke Tsukamoto and Takeo
Miyata",
title = "Charge-balancing floating-point analogue-to-digital
converter using acyclic conversion",
journal = j-INT-J-ELECTRON,
volume = "74",
number = "5",
pages = "705--??",
month = may,
year = "1993",
CODEN = "IJELA2",
ISSN = "0020-7217 (print), 1362-3060 (electronic)",
ISSN-L = "0020-7217",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Electronics Theoretical \&
Experimental",
}
@Article{Zhang:1993:EAP,
author = "C. N. Zhang and B. Shirazi and D. Y. Y. Yun",
title = "An Efficient Algorithm and Parallel Implementations
for Binary and Residue Number Systems",
journal = j-J-SYMBOLIC-COMP,
volume = "15",
number = "4",
pages = "451--462",
month = apr,
year = "1993",
CODEN = "JSYCEH",
DOI = "https://doi.org/10.1006/jsco.1993.1030",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
MRclass = "65G10 (65Y05)",
MRnumber = "94j:65066",
MRreviewer = "De Ren Wang",
bibdate = "Sat May 10 15:54:09 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Arithmetic units based on a Residue Number System
(RNS) are fast and simple, and therefore attractive for
use in digital signal processing and symbolic
computation applications. However, RNS suffers from
overheads of converting numbers to and from residue
system. We present a new simple and uniform computation
formula for both conversion from RNS to binary and vice
versa. Two levels of parallelism for VLSI hardware
design of the proposed algorithm are introduced.",
acknowledgement = ack-nhfb,
classcodes = "C7310 (Mathematics); C7410D (Electronic engineering)",
corpsource = "Department of Computer Science, Regina University,
Sask., Canada",
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
keywords = "algorithm; binary number systems; circuit CAD;
computation; digital signal processing; parallel
implementations; parallelism; residue number systems;
symbol manipulation; symbolic; VLSI; VLSI hardware
design",
treatment = "A Application; P Practical",
}
@InProceedings{Zuras:1993:SML,
author = "D. Zuras",
title = "On Squaring and Multiplying Large Integers",
crossref = "Swartzlander:1993:SCA",
pages = "260--271",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Zuras.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Book{Zuse:1993:CML,
author = "Konrad Zuse",
title = "The Computer, My Life",
publisher = pub-SV,
address = pub-SV:adr,
pages = "245",
year = "1993",
ISBN = "3-540-56453-5 (Berlin), 0-387-56453-5 (New York)",
ISBN-13 = "978-3-540-56453-9 (Berlin), 978-0-387-56453-1 (New
York)",
LCCN = "TK7885.22.Z87 A3 1993",
bibdate = "Mon Nov 4 07:46:57 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "computer engineers --- Germany --- biography;
computers --- Germany --- history; Zuse, Konrad",
tableofcontents = "1: Ancestors and parents --- Early childhood
memories --- School days --- Metropolis --- Abitur / 1
\\
2: Studies (not without detours and byways) and general
studies --- First inventions --- The \emph{Akademische
Verein Motiv} --- Student life between science and
politics / 15 \\
3: The early years of the computer and a digression on
its prehistory --- Colleagues remember --- From
mechanics to electromechanics --- Schreyer's electronic
computing machine --- First outside contacts ---
Thoughts on the future / 33 \\
4: Outbreak of the war and first callup --- Structural
engineer in aircraft construction --- The Z2 and Z3 ---
Second callup --- \emph{Zuse Ingenieurb{\"u}ro und
Apparatebau, Berlin} --- The first process computer /
55 \\
5: Origins of the Z4 --- News from the United States
--- Attempt at a PhD dissertation --- Computing machine
for logic operations --- Final months of the war in
Berlin --- The evacuation --- Z4 completed in
G{\"o}ttingen --- Final war days in the Allg{\"a}u / 75
\\
6: End of the war --- Refugees in Hinterstein --- The
\emph{Plankalk{\"u}l} --- The computing universe ---
Automation and self-reproducing systems --- A
logarithmic computing machine --- Computer development
in Germany and the United States --- Move to Hopferau
near F{\"u}ssen --- The mill of the Patent Office / 95
\\
7: The \emph{Zuse-Ingenieurb{\"u}ro, Hopferau bei
F{\"u}ssen} --- First business partners: IBM and
Remington Rand --- The first pipelining design ---
Founding of ZUSE KG in Neukirchen --- The Z4 in the ETH
in Z{\"u}rich --- The computer in Europe: taking stock
--- Lost opportunities --- The first German contract:
the Z5 / 113 \\
8: The partners leave --- Computing machine for land
use zoning --- Electronics gains acceptance --- First
funds from the \emph{Deutsche Forschungsgemeinschaft}
--- Losing one's way (and possibly a lost opportunity)
--- The array processor --- Custom work for geodesics
--- The Graphomat Z64 --- Growth and crisis of ZUSE KG
--- The end / 133 \\
9: Free for science (again) --- Honors --- A look to
the future / 157 \\
Appendices \\
1: From Forms to Program Control / 185 \\
2: Construction of Devices / 190 \\
3: On Computer Architecture / 210 \\
4: On the Plan Calculus / 211 \\
5: Lecture on the Occasion of the Award of the Honorary
Doctorate by the Technical University of Berlin
(Extract) / 222 \\
6: The Computer Did Not Fall From Heaven / 225 \\
Notes / 229 \\
References / 231 \\
Name Index / 235 \\
Subject Index / 239 \\
Computer Index / 245",
}
@Article{Agarwal:1994:EFP,
author = "R. C. Agarwal and F. G. Gustavson and M. Zubair",
title = "Exploiting functional parallelism of {POWER2} to
design high-performance numerical algorithms",
journal = j-IBM-JRD,
volume = "38",
number = "5",
pages = "563--576",
month = sep,
year = "1994",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Mar 25 14:26:59 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.almaden.ibm.com/journal/rd38-5.html#eight",
abstract = "We describe the algorithms and architecture approach
to produce high-performance codes for numerically
intensive computations. In this approach, for a given
computation, we design algorithms so that they perform
optimally when run on a target machine --- in this
case, the new POWER2* machines from the RS\slash 6000
family of RISC processors. The algorithmic features
that we emphasize are functional parallelism,
cache/register blocking, algorithmic prefetching, loop
unrolling, and algorithmic restructuring. The
architectural features of the POWER2 machine that we
describe and that lead to high performance are multiple
functional units, high bandwidth between registers,
cache, and memory, a large number of fixed- and
floating-point registers, and a large cache and TLB
(translation lookaside buffer). The paper gives two
examples that illustrate how the algorithms and
architectural features interplay to produce
high-performance codes. They are BLAS (basic linear
algebra subroutines) and narrow-band matrix routines.
These routines are included in ESSL (Engineering and
Scientific Subroutine Library); an overview of ESSL is
also given in this paper.",
acknowledgement = ack-nhfb,
affiliation = "Res. Div., IBM Thomas J. Watson Res. Center, Yorktown
Heights, NY, USA",
classcodes = "C7310 (Mathematics computing); C5430 (Microcomputers);
C6140B (Machine-oriented languages); C6110P (Parallel
programming)",
classification = "C5430 (Microcomputers); C6110P (Parallel
programming); C6140B (Machine-oriented languages);
C7310 (Mathematics computing)",
corpsource = "Res. Div., IBM Thomas J. Watson Res. Center, Yorktown
Heights, NY, USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "algorithmic; Algorithmic prefetching; algorithmic
restructuring; Algorithmic restructuring; algorithms;
and Scientific Subroutine Library; basic linear
algebra; Basic linear algebra subroutines; BLAS;
cache/register blocking; Cache/register blocking;
computations; Engineering; Engineering and Scientific
Subroutine Library; ESSL; floating-point registers;
Floating-point registers; functional parallelism;
Functional parallelism; high-performance codes;
High-performance codes; high-performance numerical;
High-performance numerical algorithms; IBM computers;
loop unrolling; Loop unrolling; mathematics computing;
multiple functional units; Multiple functional units;
narrow-band matrix routines; Narrow-band matrix
routines; numerically intensive; Numerically intensive
computations; parallel algorithms; POWER2 workstations;
prefetching; processors; reduced instruction set
computing; RISC; RISC processors; RS/6000 family;
software libraries; subroutines; translation lookaside
buffer; Translation lookaside buffer; workstations",
thesaurus = "IBM computers; Mathematics computing; Parallel
algorithms; Reduced instruction set computing; Software
libraries; Workstations",
treatment = "P Practical",
}
@Article{Anonymous:1994:C,
author = "Anonymous",
title = "Corrigenda",
journal = j-TOMS,
volume = "20",
number = "4",
pages = "553--553",
month = dec,
year = "1994",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Mar 14 16:17:03 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Hull:1994:ICE}",
acknowledgement = ack-rfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
xxURL = "Missing from ACM Digital Library",
}
@Article{Anonymous:1994:FPa,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "13",
number = "6",
pages = "65--??",
month = jun,
year = "1994",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Interactive Analysis Presentations.",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Article{Anonymous:1994:FPb,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "13",
number = "7",
pages = "85--??",
month = jul,
year = "1994",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Misplaced Value of CE.",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Article{Anonymous:1994:FPc,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "13",
number = "10",
pages = "122--??",
month = oct,
year = "1994",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Integration's Relational Dimension.",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Article{Anonymous:1994:SCSa,
author = "Anonymous",
title = "Single chip supercomputer: Vector processing is key to
high performance in floating point calculations",
journal = "New electronics",
volume = "27",
number = "4",
pages = "7--??",
day = "1",
month = apr,
year = "1994",
ISSN = "0047-9624",
bibdate = "Fri Aug 23 08:32:16 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
UnCover library database",
acknowledgement = ack-nhfb,
}
@Article{Anonymous:1994:SPF,
author = "Anonymous",
title = "Signal Path: Floating-point tactics",
journal = j-ELECTRONIC-ENG-TIMES,
volume = "??",
number = "807",
pages = "78--??",
month = jul,
year = "1994",
ISSN = "0192-1541",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronic engineering times",
}
@Book{Anonymous:1994:SRT,
author = "Anonymous",
title = "The Square Root of Two to 5 million digits",
volume = "129",
publisher = pub-PROJECT-GUTENBERG,
address = pub-PROJECT-GUTENBERG:adr,
year = "1994",
bibdate = "Sun Jan 24 10:00:27 MST 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-PROJECT-GUTENBERG,
URL = "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext94/2sqrt10a.zip",
acknowledgement = ack-nhfb # " and " # ack-st,
subject = "Mathematical constants.",
url-contents = "ZIP",
}
@Book{Apple:1994:IMP,
author = "{Apple Computers, Inc.}",
title = "Inside {Macintosh}: {PowerPC Numerics}",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xx + 300",
year = "1994",
ISBN = "0-201-40728-0",
ISBN-13 = "978-0-201-40728-0",
LCCN = "QA76.8.M3 I5622 1994",
bibdate = "Wed Sep 07 21:08:51 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$28.95",
acknowledgement = ack-nj,
}
@Article{Bajard:1994:BNH,
author = "J.-C. Bajard and S. Kla and Jean-Michel Muller",
title = "{BKM}: a New Hardware Algorithm for Complex Elementary
Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "8",
pages = "955--963",
month = aug,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.295857",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon May 20 06:16:49 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
remark = "Selected revised and extended papers from ARITH'11
\cite{Swartzlander:1993:SCA}.",
}
@Article{Bajard:1994:SOL,
author = "J.-C. Bajard and J. Duprat and S. Kla and J.-M.
Muller",
title = "Some Operators for On-Line Radix-2 Computations",
journal = j-J-PAR-DIST-COMP,
volume = "22",
number = "2",
pages = "336--345",
month = aug,
year = "1994",
CODEN = "JPDCER",
DOI = "https://doi.org/10.1006/jpdc.1994.1093",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Thu Mar 9 09:18:55 MST 2000",
bibsource = "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.idealibrary.com/links/doi/10.1006/jpdc.1994.1093/production;
http://www.idealibrary.com/links/doi/10.1006/jpdc.1994.1093/production/pdf",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
corpsource = "Lab. LIP, Ecole Normale Superieure de Lyon, France",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "bit-level representation; Borrow-Save; delay; digital
arithmetic; online radix-2 computations; operators;
optimal online; radix-2 digits; representation",
treatment = "P Practical",
}
@Article{Barsi:1994:TOM,
author = "Ferruccio Barsi and M. Cristina Pinotti",
title = "Time optimal mixed radix conversion for residue number
applications",
journal = j-COMP-J,
volume = "37",
number = "10",
pages = "907--916",
month = "????",
year = "1994",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Wed Jul 21 09:54:19 MDT 1999",
bibsource = "http://www3.oup.co.uk/computer_journal/Volume_37/Issue_10/Vol37_10.index.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/Volume_37/Issue_10/Vol37_10.body.html#AbstractBarsi",
acknowledgement = ack-nhfb,
affiliation = "Dipartimento di Matematica, Perugia University,
Italy",
author-1-adr = "Dipartimento at Matematica, Universita di Perugia, Via
Vanvitelli, 061OO Perugia, Italy",
author-2-adr = "Istituto di Elaborazione dell'Informazione del CNR,
Via S. Maria 46, 56100 Pisa, Italy",
classcodes = "B2570 (Semiconductor integrated circuits); C5230
(Digital arithmetic methods); C6130 (Data handling
techniques); C4240C (Computational complexity)",
classification = "B2570 (Semiconductor integrated circuits); C4240C
(Computational complexity); C5230 (Digital arithmetic
methods); C6130 (Data handling techniques)",
corpsource = "Dipartimento di Matematica, Perugia University,
Italy",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "applications; asymptotic conversion time; Chinese
Remainder Theorem; computational complexity;
constructive VLSI design; Constructive VLSI design;
conventional logic; Conventional logic; logic
circuitry; Logic circuitry; lookup; lookup table
implementations; Lookup table implementations; mixed
radix; Mixed radix notation; notation; practical ECL
IC; Practical ECL IC; residue integer conversion;
Residue integer conversion; residue number; Residue
number applications; residue number systems;
residue-to-weighted system; Residue-to-weighted system
asymptotic conversion time; table; time optimal mixed
radix conversion; Time optimal mixed radix conversion;
VLSI",
thesaurus = "Computational complexity; Residue number systems;
Table lookup; VLSI",
treatment = "P Practical",
}
@Article{Bartolucci:1994:REC,
author = "M. Bartolucci and G. R. Sechi",
title = "Rounding error in the computation of opposite sign
floating point number parametric addition: a case
study",
journal = j-MICROPROC-MICROPROG,
volume = "40",
number = "10-12",
pages = "833--839",
month = dec,
year = "1994",
CODEN = "MMICDT",
ISSN = "0165-6074 (print), 1878-7061 (electronic)",
ISSN-L = "0165-6074",
bibdate = "Thu Dec 14 15:33:45 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "20th Annual Euromicro Conference. System Architecture
and Integration.",
abstract = "Presents a study about rounding errors arising in the
addition of opposite-sign floating-point operands. The
algebraic study of the adder functionalities provides
the possibility of modifying the hardware in order to
measure the rounding error effect in terms of error
size and incoming rate.",
acknowledgement = ack-nhfb,
affiliation = "Istituto di Fisica Cosmica e Tecnologie Relative, CNR,
Milano, Italy",
classification = "C1110 (Algebra); C5230 (Digital arithmetic
methods)",
confdate = "Sept. 1994",
conflocation = "Liverpool, UK",
fjournal = "Microprocessing and Microprogramming",
keywords = "Adder functionalities; Algebraic properties; Case
study; Computational units; Error size; Errors
detection; Errors elimination; Floating-point operands;
Hardware modification; High-speed floating point
operators; Incoming rate; Opposite-sign floating-point
number parametric addition; Real time applications;
Rounding error",
pubcountry = "Netherlands",
thesaurus = "Algebra; Error detection; Floating point arithmetic;
Roundoff errors",
}
@Article{Bauer:1994:MDS,
author = "F. L. Bauer",
title = "Multiplication and dual system",
journal = j-INFORMATIK-SPEKTRUM,
volume = "17",
number = "4",
pages = "245--250",
month = aug,
year = "1994",
CODEN = "INSKDW",
ISSN = "0170-6012 (print), 1432-122X (electronic)",
ISSN-L = "0170-6012",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A history of methods of multiplication is introduced
with a table showing the assignments of Greek and
Hebrew letters to the units, tens and hundreds up to
900, with no zero. The ancient Egyptian method using
decimal-to-binary conversion with addition of
successive even multiples of the multiplicand is
explained. Napier's (1617) method of `numeri locales'
is described with the aid of a multiplication table for
algebraic symbols each representing a different power
of 2. The application of these principles in electronic
computing circuits is discussed with reference to
Braun's (1963) full-adder correction circuit and
Wallace's (1964) cascaded half-adders. Progress from
the 8*8 field multiplier chips of 1971 to the
floating-point 1.2 mu m CMOS 56*56 RISC multiplier of
1989 is summarised.",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
fjournal = "Informatik Spektrum",
journal-URL = "http://link.springer.com/journal/287",
keywords = "Algebraic symbols; Cascaded half-adders; decimal
floating-point arithmetic; Decimal-to-binary
conversion; Egyptian method; Electronic computing
circuits; Floating-point; Full-adder correction
circuit; Multiplication; Multiplier chips; Numeri
locales; RISC",
language = "German",
pubcountry = "Germany",
thesaurus = "Digital arithmetic; History; Multiplying circuits",
}
@PhdThesis{Bewick:1994:FMA,
author = "Gary Bewick",
title = "Fast Multiplication: Algorithms and Implementations",
type = "{Ph.D.} thesis",
school = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
pages = "170",
month = feb,
year = "1994",
bibdate = "Mon Dec 24 09:59:22 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Also issued as report CSL-TR-94-617",
acknowledgement = ack-nhfb,
}
@Article{BrinchHansen:1994:MLD,
author = "Per {Brinch Hansen}",
title = "Multiple-length Division Revisited: a Tour of the
Minefield",
journal = j-SPE,
volume = "24",
number = "6",
pages = "579--601",
month = jun,
year = "1994",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.4380240605",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Fri Nov 28 17:07:54 2003",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/bibnet/authors/h/hansen-per-brinch.bib;
https://www.math.utah.edu/pub/tex/bib/cryptography1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/litprog.bib;
https://www.math.utah.edu/pub/tex/bib/spe.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "This paper derives an algorithm for division of long
integers, and implements it as a literate program,
although without identifier cross-references. See also
related work on division
\cite{BrinchHansen:1995:LDA,Regener:1984:MID} .",
URL = "http://brinch-hansen.net/papers/1994b.pdf",
abstract = "Long division of natural numbers plays a crucial role
in Cobol arithmetic, cryptography, and primality
testing. Only a handful of textbooks discuss the theory
and practice of long division, and none of them do it
satisfactorily. This tutorial attempts to fill this
surprising gap in the literature on computer
algorithms. We illustrate the subtleties of long
division by examples, define the problem concisely,
summarize the theory, and develop a complete Pascal
algorithm using a consistent terminology.",
acknowledgement = ack-nj # " and " # ack-mfc # " and " # ack-nhfb,
ajournal = "Softw. Pract. Exp.",
fjournal = "Software --- Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
keywords = "algorithms; multiple-length integer division",
onlinedate = "30 Oct 2006",
}
@InProceedings{Brosgol:1994:ISD,
author = "Benjamin M. Brosgol and Robert I. Eachus and David E.
Emery",
title = "Information Systems Development in {Ada}",
crossref = "ACM:1994:AAW",
pages = "2--16",
year = "1994",
bibdate = "Fri Nov 28 16:05:55 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper we survey how to use Ada (both Ada 83
and Ada 9X) for IS applications, with a focus on two
principal issues: Specification of the information
architecture of an IS application, and Programming
techniques relevant to financial and related
applications.\par
We cover both the language features and the
supplemental packages for IS development. Special
attention will be paid to the Ada Decimal-Associated
Reusabilia (`ADAR') components for Ada 83 and
transitioning to Ada 9X.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@MastersThesis{Bull:1994:SFF,
author = "Nathan Lee Bull",
title = "A study of frequency-sampling filters realized on
floating-point digital signal processors",
type = "Thesis ({M.S.})",
school = "University of Tennessee, Knoxville",
address = "Knoxville, TN, USA",
pages = "vii + 56",
year = "1994",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Digital filters (Mathematics)",
}
@Article{Carr:1994:IRM,
author = "S. Carr and K. Kennedy",
title = "Improving the Ratio of Memory Operations in
Floating-Point Operations in Loops",
journal = j-TOPLAS,
volume = "16",
number = "6",
pages = "1768--1810",
month = nov,
year = "1994",
CODEN = "ATPSDT",
ISSN = "0164-0925 (print), 1558-4593 (electronic)",
ISSN-L = "0164-0925",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Over the past decade, microprocessor design strategies
have focused on increasing the computational power on a
single chip. Because computations often require more
data from cache per floating-point operation than a
machine can deliver and because operations are
pipelined, idle computational cycles are common when
scientific applications are executed. To overcome these
bottlenecks, programmers have learned to use a coding
style that ensures a better balance between memory
references and floating-point operations. In our view,
this is a step in the wrong direction because it makes
programs more machine-specific. A programmer should not
be required to write a new program version for each new
machine; instead, the task of specializing a program to
a target machine should be left to the compiler. But is
our view practical? Can a sophisticated optimizing
compiler obviate the need for the myriad of programming
tricks that have found their way into practice to
improve the performance of the memory hierarchy? In
this paper we attempt to answer that question. To do
so, we develop and evaluate techniques that
automatically restructure program loops to achieve high
performance on specific target architectures. These
methods attempt to balance computation and memory
accesses and seek to eliminate or reduce pipeline
interlock. To do this, they estimate statically the
balance between memory operations and floating-point
operations for each loop in a particular program and
use these estimates to determine whether to apply
various loop transformations. Experiments with our
automatic techniques show that integer-factor speedups
are possible on kernels. Additionally, the estimate of
the balance between memory operations and computation,
and the application of the estimate are very
accurate-experiments reveal little difference between
the balance achieved by our automatic system and that
possible by hand optimization.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Michigan Technol.
University, Houghton, MI, USA",
classification = "C5230 (Digital arithmetic methods); C6120 (File
organisation); C6150C (Compilers, interpreters and
other processors)",
fjournal = "ACM Transactions on Programming Languages and
Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J783",
keywords = "Bottlenecks; Floating-point operations; Integer-factor
speedups; Memory operations; Memory references;
Microprocessor design strategies; Pipeline interlock;
Program loops; Sophisticated optimizing compiler",
thesaurus = "Floating point arithmetic; Optimising compilers;
Pipeline processing; Program control structures;
Storage management",
}
@MastersThesis{Chandramouli:1994:DSP,
author = "V. Chandramouli",
title = "Design of a self-timed, pipelined, floating point
multiplier in gallium arsenide",
type = "Thesis ({M.S.})",
school = "Department of Computer Science, University of Utah",
address = "Salt Lake City, UT, USA",
pages = "xiii + 121",
year = "1994",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer architecture.; Gallium arsenide
semiconductors.",
}
@InProceedings{Chen:1994:EDU,
author = "Sau-Gee Chen and Chieh-Chih Li",
booktitle = "Proceedings of {TENCON '94}. {IEEE} Region 10's Ninth
Annual International Conference. Theme: `Frontiers of
Computer Technology'",
title = "Efficient designs of unified $2$'s complement division
and square root algorithm and architecture",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "943--947",
year = "1994",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Efficient unified 2's complement division and square
root algorithm, and their architectures are proposed in
this work. The designs are high speed, small area and
high compatibility. The architectures provide bit level
pipelined operation, as well \ldots{}",
}
@Article{Chesneaux:1994:ERS,
author = "J.-M. Chesneaux",
title = "The equality relations in scientific computing",
journal = j-NUMER-ALGORITHMS,
volume = "7",
number = "2-4",
pages = "129--143",
month = jul,
year = "1994",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The equality relation (more generally, the ordering
relations) in floating point arithmetic is the exact
translation of the mathematical equality relation.
Because of the pr
