%%% -*-BibTeX-*-
%%% ====================================================================
%%% BibTeX-file{
%%% author-1 = "Norbert Juffa",
%%% author-2 = "Nelson H. F. Beebe",
%%% version = "3.323",
%%% date = "21 April 2012",
%%% time = "08:19:59 MDT",
%%% filename = "fparith.bib",
%%% address-1 = "2445 Mission College Blvd.,
%%% Santa Clara, CA 95054,
%%% USA",
%%% address-2 = "University of Utah
%%% Department of Mathematics, 110 LCB
%%% 155 S 1400 E RM 233
%%% Salt Lake City, UT 84112-0090
%%% USA",
%%% telephone-1 = "+1 408 727 1885",
%%% telephone-2 = "+1 801 581 5254",
%%% FAX-1 = "+1 408 727 1265",
%%% FAX-2 = "+1 801 581 4148",
%%% URL-2 = "http://www.math.utah.edu/~beebe",
%%% checksum = "45834 137728 611580 6171097",
%%% email-1 = "norbert at iit.com (Internet)",
%%% email-2 = "beebe at math.utah.edu, beebe at acm.org,
%%% beebe at computer.org (Internet)",
%%% codetable = "ISO/ASCII",
%%% keywords = "bibliography, BibTeX, floating-point
%%% arithmetic",
%%% license = "public domain",
%%% supported = "yes",
%%% docstring = "[From Norbert Juffa:] This is a bibliography
%%% of material on floating-point arithmetic
%%% that I came up with while doing research on
%%% a floating-point package of his own. I
%%% don't claim it to be anywhere near
%%% complete. The material listed is only what
%%% I myself possess.
%%%
%%% My main interest was in software based,
%%% binary floating-point arithmetic on a
%%% microprocessor, so you won't find much
%%% material about the hardware used in
%%% floating-point arithmetic (e.g., adders,
%%% carry propagation schemes, higher radix
%%% representation for multiplication and
%%% division, etc.) in this list. There is also
%%% not too much on non-binary floating-point
%%% arithmetic.
%%%
%%% For most fields covered in this
%%% bibliography, the important or historically
%%% relevant articles should be included. There
%%% is also some material on integer arithmetic
%%% in this list as some of the methods used
%%% with integer arithmetic contain interesting
%%% ideas that may be useful in the realization
%%% of a floating-point arithmetic package.
%%%
%%% Also, depending on the type of
%%% microprocessor used, one may need to
%%% implement integer multiplication and
%%% division for use in the floating-point
%%% package, so articles about this topic are
%%% included as well.
%%%
%%% As I am German, there is a bit of material
%%% in German in this bibliography. However,
%%% English translations are provided for all
%%% non-English titles.
%%%
%%% Thanks to the people who have helped me with
%%% previous versions of this document by sending
%%% me papers or additional references: Steven
%%% Sommars (sesv at research.bell-labs.com), Jim
%%% Kiernan (jmk at teak.cray.com), Warren
%%% Ferguson (ferguson at seas.smu.edu), Nhuan
%%% Doduc (ndoduc at framentec.fr), K. C. Ng
%%% (kwok.ng at eng.sun.com).
%%%
%%% [From Nelson H. F. Beebe:] I took Norbert
%%% Juffa's unmarked-up bibliography data,
%%% converted it to BibTeX form, and then more
%%% than doubled the size of the bibliography
%%% by supplying additional entries on
%%% floating-point arithmetic extracted from
%%% my own extensive bibliography collections,
%%% and from several online journal databases,
%%% including the Compendex, OCLC, IEEE INSPEC,
%%% MathSciNet, and UnCover databases. In August
%%% 2010, access to an electronic copy of the
%%% bibliography of Sterbenz's 1974 book allowed
%%% further checks to make sure that all of his
%%% references to early work are included here.
%%%
%%% The computation of sums of floating-point
%%% numbers is a fundamental step in most
%%% numerical computations. The special phrase
%%% ``accurate floating-point summation'' appears
%%% in the keywords values of publications that
%%% address this important problem.
%%%
%%% The Web site
%%%
%%% http://www.acsel-lab.com/arithmetic/
%%%
%%% archives papers from the IEEE conferences
%%% on computer arithmetic (ARITH-1, ARITH-2,
%%% ...). Keyword values for those papers
%%% contain ARITH-n to more easily identify them.
%%%
%%% In \cite[p. 94]{Buchholz:1962:PCS}, S. G.
%%% Campbell remarks:
%%%
%%% ``To avoid difficulties of limited range
%%% and scaling in fixed-point arithmetic,
%%% G. R. Stibitz in the early 1940's
%%% proposed an automatic scaling procedure,
%%% called {\emph floating-point arithmetic},
%%% which was incorporated in the Bell
%%% Telephone Laboratories' Model V Relay
%%% Computer. A similar procedure was
%%% developed, apparently independently, for
%%% the Harvard Mark II computer. Automatic
%%% scaling was a controversial subject for
%%% quite a few years. Many opposed it on the
%%% basis that the programmer could not be
%%% relieved of the responsibility of knowing
%%% the size of his numbers and that
%%% programmed scaling would give him better
%%% control over significance. Nevertheless,
%%% as early as 1950, users began to
%%% incorporate automatic scaling on
%%% fixed-point computers by means of
%%% subroutines, first on the
%%% plugboard-controlled CPC (Card Programmed
%%% Calculator) and later on stored-program
%%% machines. Then, after it had thus proved
%%% its usefulness, floating-point arithmetic
%%% was provided as a built-in feature,
%%% starting with the IBM 704 and NORC
%%% computers, and this gave an enormous
%%% increase in speed over the
%%% subroutines. Today floating-point
%%% operation is available, at least as an
%%% option, on all computers intended to be
%%% used full- or part-time on substantial
%%% scientific computing applications. In
%%% view of the almost universal use of
%%% floating-point arithmetic, it is
%%% remarkable that there is very little
%%% literature on the subject.''
%%%
%%% We now know that Leonardo Torres y Quevedo
%%% first suggested floating-point arithmetic on
%%% paper in 1914 in Spain
%%% \cite{TorresyQuevedo:1982:EAD}. Konrad Zuse
%%% reinvented it independently in Germany in the
%%% early 1936, and had it operational in the Z3,
%%% an electromechanical computer, in 1941
%%% \cite{Zuse:1970:CML,Ceruzzi:1981:ECK,
%%% Randell:1982:ODC,Schwarz:1981:EYC,
%%% Zuse:1982:MAE,Zuse:1982:OCD,Zuse:1984:CML,
%%% Zuse:1993:CML,Smiley:2010:MWI}. Zuse's work
%%% remained unknown in the USA until about 1948.
%%% F. L. Bauer's foreword to Zuse's
%%% autobiography \cite{Zuse:1993:CML} suggests a
%%% bust of Zuse engraved
%%%
%%% ``Creator of the first fully automated,
%%% program-controlled and freely
%%% programmable computer using binary
%%% floating-point calculation. It was
%%% operational in 1941.''
%%%
%%% The experience with floating-point arithmetic
%%% by George Stibitz on the Bell Labs Model V
%%% General Purpose Relay Calculator (1945, but
%%% floating-point arithmetic proposed in 1940
%%% Stibitz memo) \cite{Alt:1948:BTLa}, by
%%% Howard Aiken on the Harvard Mark II (1947),
%%% and by Gerald Alway and Jim Wilkinson on the
%%% Pilot ACE in Britain (1946--1948)
%%% \cite{Wilkinson:1975:PAA}, encouraged the
%%% provision of floating-point arithmetic in the
%%% American and British commercialization of
%%% scientific computers in the 1950s. However,
%%% Zuse's use of Infinity and Indefinite
%%% predated by more than 15 years the Infinity
%%% of the IBM 7030 Stretch (1956--1958, with
%%% first customer delivery, to Los Alamos
%%% Laboratory, in April 1961), and the Infinity
%%% and Indefinite of the CDC 6400/6600/7600
%%% (1960--1963, with first customer delivery, to
%%% Lawrence Livermore Laboratory, in September
%%% 1964)
%%% \cite{Thornton:1970:DCC,Thornton:1980:CP}. I
%%% [NHFB] have so far been unable to find any
%%% definitive published statement about whether
%%% Zuse's ideas were known to, and inspired, the
%%% CDC and IBM architects, or whether they
%%% rediscovered them independently.
%%%
%%% It is our hope that this bibliography will
%%% help to remedy the deficiency noted in the
%%% last sentence of Campbell's remark, even
%%% though the first edition of this bibliography
%%% in 1994 appeared 32 years after the wonderful
%%% book about IBM's Project Stretch, and it took
%%% 48 years for that book to be included here.
%%%
%%% At version 3.323, the year coverage looked
%%% like this:
%%%
%%% 1837 ( 1) 1896 ( 0) 1955 ( 7)
%%% 1838 ( 0) 1897 ( 1) 1956 ( 8)
%%% 1839 ( 0) 1898 ( 0) 1957 ( 11)
%%% 1840 ( 0) 1899 ( 0) 1958 ( 16)
%%% 1841 ( 0) 1900 ( 0) 1959 ( 23)
%%% 1842 ( 0) 1901 ( 0) 1960 ( 19)
%%% 1843 ( 0) 1902 ( 0) 1961 ( 27)
%%% 1844 ( 0) 1903 ( 0) 1962 ( 26)
%%% 1845 ( 0) 1904 ( 0) 1963 ( 23)
%%% 1846 ( 0) 1905 ( 0) 1964 ( 31)
%%% 1847 ( 0) 1906 ( 0) 1965 ( 53)
%%% 1848 ( 0) 1907 ( 0) 1966 ( 32)
%%% 1849 ( 0) 1908 ( 0) 1967 ( 40)
%%% 1850 ( 0) 1909 ( 1) 1968 ( 31)
%%% 1851 ( 0) 1910 ( 1) 1969 ( 46)
%%% 1852 ( 0) 1911 ( 0) 1970 ( 53)
%%% 1853 ( 0) 1912 ( 0) 1971 ( 51)
%%% 1854 ( 0) 1913 ( 0) 1972 ( 53)
%%% 1855 ( 0) 1914 ( 0) 1973 ( 75)
%%% 1856 ( 0) 1915 ( 1) 1974 ( 45)
%%% 1857 ( 0) 1916 ( 0) 1975 ( 93)
%%% 1858 ( 0) 1917 ( 0) 1976 ( 50)
%%% 1859 ( 0) 1918 ( 0) 1977 ( 69)
%%% 1860 ( 0) 1919 ( 0) 1978 ( 97)
%%% 1861 ( 0) 1920 ( 0) 1979 ( 67)
%%% 1862 ( 0) 1921 ( 0) 1980 ( 102)
%%% 1863 ( 0) 1922 ( 0) 1981 ( 119)
%%% 1864 ( 0) 1923 ( 0) 1982 ( 78)
%%% 1865 ( 0) 1924 ( 1) 1983 ( 141)
%%% 1866 ( 0) 1925 ( 1) 1984 ( 98)
%%% 1867 ( 0) 1926 ( 0) 1985 ( 146)
%%% 1868 ( 0) 1927 ( 0) 1986 ( 96)
%%% 1869 ( 0) 1928 ( 0) 1987 ( 134)
%%% 1870 ( 0) 1929 ( 0) 1988 ( 150)
%%% 1871 ( 0) 1930 ( 2) 1989 ( 186)
%%% 1872 ( 0) 1931 ( 0) 1990 ( 145)
%%% 1873 ( 0) 1932 ( 1) 1991 ( 218)
%%% 1874 ( 0) 1933 ( 1) 1992 ( 174)
%%% 1875 ( 0) 1934 ( 1) 1993 ( 188)
%%% 1876 ( 0) 1935 ( 0) 1994 ( 173)
%%% 1877 ( 0) 1936 ( 2) 1995 ( 157)
%%% 1878 ( 0) 1937 ( 2) 1996 ( 170)
%%% 1879 ( 0) 1938 ( 4) 1997 ( 128)
%%% 1880 ( 0) 1939 ( 0) 1998 ( 126)
%%% 1881 ( 1) 1940 ( 3) 1999 ( 182)
%%% 1882 ( 0) 1941 ( 1) 2000 ( 140)
%%% 1883 ( 0) 1942 ( 2) 2001 ( 204)
%%% 1884 ( 0) 1943 ( 1) 2002 ( 153)
%%% 1885 ( 0) 1944 ( 1) 2003 ( 143)
%%% 1886 ( 0) 1945 ( 2) 2004 ( 165)
%%% 1887 ( 0) 1946 ( 5) 2005 ( 162)
%%% 1888 ( 0) 1947 ( 4) 2006 ( 118)
%%% 1889 ( 0) 1948 ( 4) 2007 ( 128)
%%% 1890 ( 0) 1949 ( 2) 2008 ( 64)
%%% 1891 ( 0) 1950 ( 3) 2009 ( 104)
%%% 1892 ( 0) 1951 ( 5) 2010 ( 66)
%%% 1893 ( 0) 1952 ( 4) 2011 ( 121)
%%% 1894 ( 0) 1953 ( 1) 2012 ( 18)
%%% 1895 ( 0) 1954 ( 7)
%%% 19xx ( 2)
%%% 20xx ( 1)
%%%
%%% Article: 2713
%%% Book: 288
%%% InBook: 1
%%% InCollection: 55
%%% InProceedings: 1484
%%% Manual: 63
%%% MastersThesis: 143
%%% Misc: 137
%%% Periodical: 3
%%% PhdThesis: 69
%%% Proceedings: 353
%%% TechReport: 294
%%% Unpublished: 9
%%%
%%% Total entries: 5612
%%%
%%% This bibliography is sorted by year, and
%%% within each year, by author and title key,
%%% with ``bibsort -byyear''. Cross-referenced
%%% proceedings entries appear at the end,
%%% because of a restriction in the current
%%% BibTeX.
%%%
%%% The checksum field above contains a CRC-16
%%% checksum as the first value, followed by the
%%% equivalent of the standard UNIX wc (word
%%% count) utility output of lines, words, and
%%% characters. This is produced by Robert
%%% Solovay's checksum utility.",
%%% }
%%% ====================================================================
%%% A delimited macro \toenglish ... \endtoenglish is NECESSARY here.
%%% The more conventional undelimited form \toenglish{...} has braces
%%% that prevent BibTeX's downcasing operation, and the alternate form
%%% {\toenglish{...}} is considered a `special character' by BibTeX,
%%% and all of {...} gets downcased. We avoid the name \english to
%%% prevent conflicts with language options in packages like Babel.
%%%
%%% To suppress output of English translations of non-English titles,
%%% use
%%% "\def \toenglish #1\endtoenglish{\unskip}"
%%% instead.
@Preamble{
"\def \toenglish #1\endtoenglish{[{\em English:} #1\unskip]} " #
"\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 \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
}"
}
%%% ====================================================================
%%% Acknowledgement abbreviations:
@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,
FAX: +1 801 581 4148,
e-mail: \path|beebe@math.utah.edu|,
\path|beebe@acm.org|,
\path|beebe@computer.org| (Internet),
URL: \path|http://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="}
%%% ====================================================================
%%% Institute abbreviations:
@String{inst-ANL = "Argonne National Laboratory"}
@String{inst-ANL:adr = "9700 South Cass Avenue, Argonne, IL
60439-4801, 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-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-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-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-UT-CS = "Department of Computer Science,
University of Tennessee, Knoxville"}
@String{inst-UT-CS:adr = "Knoxville, TN 37996, USA"}
%%% ====================================================================
%%% Journal abbreviations:
@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-ADA-LETT = "Ada Letters"}
@String{j-ADV-SOFT-SCI-TECH = "Advances in software science and
technology"}
@String{j-ALGORITHMICA = "Algorithmica"}
@String{j-AM-J-MATH = "American Journal of Mathematics"}
@String{j-AM-SCI = "American Scientist"}
@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-STAT = "Annals of Mathematical Statistics"}
@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-APP-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-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-BIT = "BIT (Nordisk tidskrift for
informationsbehandling)"}
@String{j-BIT-NUM-MATH = "BIT Numerical 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-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-COED = "CoED"}
@String{j-COMBIN-PROBAB-COMPUT = "Combinatorics, Probability and Computing"}
@String{j-COMM-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-GEOSCI = "Computers and Geosciences"}
@String{j-COMP-J = "The Computer Journal"}
@String{j-COMP-LANG-MAG = "Computer Language Magazine"}
@String{j-COMP-MATH-APPL = "Computers and Mathematics with
Applications"}
@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-ELECTR-ENG = "Computers and Electrical Engineering"}
@String{j-COMPUT-SCI-ENG = "Computing in Science and Engineering"}
@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-DESIGNS-CODES-CRYPTOGR = "Designs, Codes, and Cryptography"}
@String{j-DISCRETE-COMPUT-GEOM = "Discrete and Computational Geometry"}
@String{j-DOKL-AKAD-NAUK = "Doklady Akademii nauk SSSR"}
@String{j-EDN = "EDN"}
@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-ELECTRON-COMMUN-JPN = "Electronics and communications in Japan"}
@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-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-FUT-GEN-COMP-SYS = "Future Generation Computer Systems"}
@String{j-GAMM-MIT = "Mitteilungen der Gesellschaft f{\\\"u}r
Angewandte Mathematik und Mechanik"}
@String{j-HIGH-PERFORM-SYST = "High performance systems"}
@String{j-HEWLETT-PACKARD-J = "Hewlett--Packard 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"}
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@String{j-IEE-PROC-E = "IEE proceedings, E: Computers and digital
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@String{j-IEEE-ANN-HIST-COMPUT = "IEEE Annals of the History of Computing"}
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@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"}
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@String{j-IEEE-SIGNAL-PROCESS-LETT = "IEEE signal processing letters"}
@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,
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@String{j-IEEE-TRANS-APPL-SUPERCOND = "IEEE Transactions on Applied
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@String{j-IEEE-TRANS-AUDIO-ELECTROACOUST = "IEEE Transactions on Audio and
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@String{j-IEEE-TRANS-BIOMED-ENG = "IEEE Transactions on Biomedical
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@String{j-IEEE-TRANS-CIRCUITS-SYST-2 = "IEEE transactions on circuits and
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@String{j-IEEE-TRANS-CIRCUITS-SYST-VIDEO-TECH = "IEEE Transactions on Circuits
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@String{j-IEEE-TRANS-COMM = "IEEE Transactions on Communications"}
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@String{j-IEEE-TRANS-CONSUMER-ELECTRONICS = "IEEE Transactions on Consumer
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@String{j-IEEE-TRANS-CONTROL-SYST-TECHNOL = "IEEE Transactions on Control
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@String{j-IEEE-TRANS-IND-ELECTRON = "IEEE Transactions on Industrial
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@String{j-IEEE-TRANS-INF-THEORY = "IEEE Transactions on Information Theory"}
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@String{j-IEEE-TRANS-NUCL-SCI = "IEEE Transactions on Nuclear Science"}
@String{j-IEEE-TRANS-PAR-DIST-SYS = "IEEE Transactions on Parallel and
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@String{j-IEEE-TRANS-SOFTW-ENG = "IEEE Transactions on Software Engineering"}
@String{j-IEEE-TRANS-VIS-COMPUT-GRAPH = "IEEE Transactions on Visualization and
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@String{j-IEEE-TRANS-VLSI-SYST = "IEEE Transactions on Very Large Scale
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@String{j-IEEE-TSP = "IEEE Transactions on Signal Processing"}
@String{j-IFIP-TRANS-A = "IFIP Transactions. A. Computer Science and
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@String{j-IJSA = "The International Journal of Supercomputer
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@String{j-INT-J-MINI-MICROCOMPUTERS = "International Journal of Mini and
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@String{j-INT-J-PAR-EMER-DIST-SYS = "International Journal of Parallel, Emergent
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@String{j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER = "International Journal on
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@String{j-INTEGRATION-VLSI-J = "Integration, the VLSI journal"}
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@String{j-INTERVAL-COMP = "Interval Computations = Interval'nye
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@String{j-J-ACOUST-SOC-AM = "Journal of the Acoustical Society of
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@String{j-J-AM-STAT-ASSOC = "Journal of the American Statistical
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@String{j-J-APPL-PROBAB = "Journal of Applied Probability"}
@String{j-J-APPL-STAT = "Journal of Applied Statistics"}
@String{j-J-CHINESE-INST-ENG = "Journal of the Chinese Institute of Engineers
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@String{j-J-COMB-THEORY-A = "Journal of Combinatorial Theory (Series A)"}
@String{j-J-COMP-APPL-MATH = "Journal of Computational and Applied
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@String{j-J-FORTH-APPL-RES = "Journal of FORTH Application and Research"}
@String{j-J-FRANKLIN-INST = "Journal of the Franklin Institute"}
@String{j-J-INF-PROCESS = "Journal of Information Processing"}
@String{j-J-INFO-PROC-CYBERNETICS-EIK = "Journal of Information Processing and
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@String{j-INFO-PROC-LETT = "Information Processing Letters"}
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@String{j-J-INST-MATH-APPL = "Journal of the Institute of Mathematics and
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@String{j-J-KOREA-INFO-SCI-SOCIETY = "Journal of the Korea Information Science
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@String{j-KYBERNETIKA = "Kybernetika"}
@String{j-J-LOGIC-ALG-PROG = "Journal of Logic and Algebraic Programming"}
@String{j-MATHEMATICA-EDUC = "Mathematica in Education"}
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@String{j-J-PAR-DIST-COMP = "Journal of Parallel and Distributed
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@String{j-JAVAWORLD = "JavaWorld: IDG's magazine for the Java
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@String{j-JCLT = "The Journal of {C} Language Translation"}
@String{j-JETC = "ACM Journal on Emerging Technologies in
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@String{j-SCI-PROG = "Scientific Programming"}
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%%% ====================================================================
%%% Publishers and their addresses:
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Mathematics"}
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@String{pub-SIEMENS:adr = "Berlin and Munich, Germany"}
@String{pub-SPIE = "Society of Photo-optical
Instrumentation Engineers (SPIE)"}
@String{pub-SPIE:adr = "Bellingham, WA, USA"}
@String{pub-SPRINGER-WIEN = "Spring{\-}er"}
@String{pub-SPRINGER-WIEN:adr = "Wien / New York"}
@String{pub-SRNI = "Software Research Northwest, Inc."}
@String{pub-SRNI:adr = "17710 100th Avenue SW, Vashon Island, WA
98070, USA"}
@String{pub-SUN = "Sun Microsystems"}
@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."}
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@String{pub-SYNGRESS:adr = "Rockland, MA, USA"}
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Co. Pte. Ltd."}
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Singapore 9128"}
%%% ====================================================================
%%% Series abbreviations:
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@String{ser-SIGPLAN = "ACM SIG{\-}PLAN Notices"}
%%% ====================================================================
%%% Bibliography entries.
%%%
%%% NB: Some journals do not indicate a month for each issue, and a few
%%% have volumes, but no issue numbers, or issues without volumes. Such
%%% cases are identified by xxmonth, xxnumber, and xxvolume entries with a
%%% value of "(none)", so that searches can still be used to identify
%%% other entries where such information is still missing.
%%%
%%% ISBNs were introduced in 1972, so books published before that do not
%%% have ISBN entries, unless the publisher supplied one in a post-1971
%%% printing. A few books, and many conference proceedings, published
%%% since 1972, lack ISBNs; these are identified with xxISBN values of
%%% (none), again to facilitate searching for missing values.
@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 = "http://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,
}
@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 = "http://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,
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{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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@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",
bibdate = "Wed Oct 13 11:14:08 2010",
bibsource = "http://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",
bibdate = "Wed Oct 13 11:12:08 2010",
bibsource = "http://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",
}
@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 = "http://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,
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 4.1]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@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 = "http://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",
bibdate = "Thu Feb 15 16:28:28 2007",
bibsource = "http://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,
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 = "http://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 = "http://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 = "Transactions of the {AIEE}",
volume = "57",
number = "??",
pages = "713--723",
month = dec,
year = "1938",
bibdate = "Sat Nov 20 08:54:12 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www2.research.att.com/~njas/doc/shannonbio.html",
acknowledgement = ack-nhfb,
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 ... a
landmark in that it helped to change digital circuit
design from an art to a science.''",
}
@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 = "http://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 = "http://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 = "http://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 = "http://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.",
}
@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 = "http://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",
bibsource = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.doi.org/10.1038/154800a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
bibdate = "Sun Sep 18 11:57:19 2011",
bibsource = "http://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,
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 = "??",
pages = "52--53",
day = "13",
month = jan,
year = "1945",
CODEN = "NATUAS",
DOI = "http://dx.doi.org/10.1038/155052a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
bibdate = "Sun Sep 18 11:51:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf",
acknowledgement = ack-nhfb,
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;
http://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 = "Electrical Engineering",
volume = "65",
number = "??",
pages = "384--391, 449--454, 522--528",
year = "1946",
bibdate = "Wed Oct 13 11:26:29 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@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",
bibdate = "Wed Oct 13 08:17:48 2004",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/arith.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Report to the U.S. Army Ordnance Department. Reprinted
in \cite[pp.~221--259]{Swartzlander:1976:CDD}, \cite[\S
8.3]{Randell:1982:ODC}, and
\cite[pp.~97--146]{Aspray:1987:PJN}",
acknowledgement = ack-nhfb,
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
note = "Reprinted in \cite[\S 7.7]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@TechReport{Goldstine:1947:PCP,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument",
type = "Technical report",
number = "1",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "69",
day = "1",
month = apr,
year = "1947",
bibdate = "Wed Jun 01 17:41:33 2005",
bibsource = "http://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:1997:SA} cites pp.~142--151 of this
report as the first published treatment of
double-precision arithmetic on digital computers.",
acknowledgement = ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.3]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@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 = "http://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{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",
MRclass = "65.0X",
MRnumber = "MR0024235 (9,471b)",
MRreviewer = "E. Bodewig",
bibdate = "Thu Nov 8 14:49:36 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Goldstine:1951:NIM} for Part II. Reprinted
in \cite[v.~5, pp.~479--557]{Taub:1961:JNC}.",
acknowledgement = ack-nhfb # " and " # ack-jg,
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 $2s$, 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}.",
ZMnumber = "0031.31402",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
note = "Reprinted in \cite[\S 6.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@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",
bibdate = "Wed Oct 13 11:27:40 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.3]{Randell:1982:ODC}.",
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",
MRclass = "65.0X",
MRnumber = "MR0028100 (10,405c)",
MRreviewer = "E. Bodewig",
bibdate = "Sat Nov 19 12:09:58 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/a/turing-alan-mathison.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://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",
acknowledgement = ack-nhfb,
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.",
ZMnumber = "0033.28501",
}
@Article{Williams:1948:EDC,
author = "F. C. Williams and T. Kilburn",
title = "Electronic digital computers",
journal = j-NATURE,
volume = "162",
number = "487",
pages = "??--??",
year = "1948",
CODEN = "NATUAS",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
bibdate = "Wed Oct 13 12:00:02 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@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 = "http://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 = "??",
pages = "57--62",
year = "1949",
CODEN = "JRNBAG",
ISSN = "0091-0635",
bibdate = "Fri Aug 20 09:32:34 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@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 = "http://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",
}
@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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.6]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@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",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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)",
MRclass = "65.0X",
MRnumber = "MR0041539 (12,861b)",
MRreviewer = "F. J. Murray",
bibdate = "Thu Nov 8 14:49:46 2007",
bibsource = "http://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",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
ZMnumber = "043.12301",
}
@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,
pages = "101--105",
year = "1952",
DOI = "http://dx.doi.org/10.1145/1434770.1434787",
LCCN = "????",
bibdate = "Fri Dec 03 09:17:58 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bookpages = "vi + 114",
keywords = "Bell Laboratories Model 1--5 relay computers; complex
fixed-point decimal arithmetic; complex floating-point
decimal arithmetic",
}
@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",
bibdate = "Fri Nov 28 16:38:51 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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 Confer ence. {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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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",
bibdate = "Fri Nov 04 00:18:27 1994",
bibsource = "http://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,
}
@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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@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",
bibdate = "Fri Nov 04 00:18:27 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@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",
bibdate = "Fri Aug 20 08:54:24 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://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;
http://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 = "Electronic Engineering",
volume = "27",
number = "??",
pages = "287--289",
month = jul,
year = "1955",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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",
bibdate = "Wed Nov 09 01:00:34 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Richards:1955:AOD,
author = "R. K. 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 = "http://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 = "http://dx.doi.org/10.1109/IRETELC.1955.5407911",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 15:10:39 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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 = "http://dx.doi.org/10.1109/TEC.1956.5219936",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 15:46:27 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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 = "http://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",
}
@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 = "http://dx.doi.org/10.1109/TEC.1956.5219789",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 15:46:18 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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",
bibdate = "Fri Nov 04 23:46:26 1994",
bibsource = "http://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,
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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 = "http://dx.doi.org/10.1109/TEC.1956.5219804",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 15:46:21 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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",
bibdate = "Thu Dec 08 09:28:48 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See letter \cite{Ercoli:1960:LEE}.",
acknowledgement = ack-nhfb,
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 = "http://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 = "http://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 = "http://dx.doi.org/10.1109/TEC.1957.5221576",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 16:07:27 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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 = "http://dx.doi.org/10.1109/TEC.1957.5221579",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 16:07:27 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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)",
bibdate = "Tue Sep 06 18:04:49 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://dx.doi.org/10.1109/TEC.1957.5222025",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 16:07:34 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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.",
}
@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 = "http://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{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 = "http://dx.doi.org/10.1109/TEC.1957.5221558",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 16:07:23 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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 = "http://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)",
bibdate = "Thu Sep 15 18:35:46 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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)",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
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",
bibdate = "Fri Nov 28 11:47:47 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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)",
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/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
xxmonth = "(none)",
xxnumber = "(none)",
}
@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)",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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)",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "????",
year = "1958",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1958.5222657",
ISSN = "0367-9950",
bibdate = "Wed Feb 14 19:23:38 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
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",
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@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 = "http://dx.doi.org/10.1109/TEC.1958.5222579",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:43 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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 = "http://dx.doi.org/10.1109/TEC.1958.5222094",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:43 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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)",
bibdate = "Mon Jan 22 07:22:12 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Sisson58;
http://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,
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",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@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)",
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/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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",
ISSN = "0004-5411",
MRclass = "68.00",
MRnumber = "MR0105833 (21 \#4568)",
MRreviewer = "H. H. Goldstine",
bibdate = "Fri Dec 08 13:06:24 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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",
ZMnumber = "0121.12102",
}
@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)",
bibdate = "Mon Jan 22 06:28:45 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Buchholz59;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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)",
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/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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,
year = "1959",
LCCN = "TJ213 .G72",
bibdate = "Fri Aug 20 08:41:16 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "Chapter 2.",
acknowledgement = ack-nhfb,
bookpages = "????",
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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)",
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/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "????",
year = "1959",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65.00",
MRnumber = "MR0099119 (20 \#5563)",
bibdate = "Tue Nov 22 09:08:17 MST 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
keywords = "numerical analysis",
ZMnumber = "0168.14002",
}
@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 = "http://dx.doi.org/10.1109/TEC.1959.5222757",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:44 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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 = "http://dx.doi.org/10.1109/TEC.1959.5219515",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:44 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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 = "http://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 = "http://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)",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://dx.doi.org/10.1109/TEC.1959.5222057",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:45 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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",
bibdate = "Tue Nov 1 09:33:26 1994",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
descriptors = "RVG",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@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 = "http://dx.doi.org/10.1109/TEC.1959.5219526",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:45 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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 = "http://dx.doi.org/10.1109/TEC.1959.5219529",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:45 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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)",
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/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See comments \cite{Traub:1960:CNM}.",
acknowledgement = ack-nhfb,
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)",
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/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://dx.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://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/",
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,
}
@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)",
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/",
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,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.doi.org/10.1109/TEC.1960.5219855",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:34:12 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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 = "http://dx.doi.org/10.1109/TEC.1960.5219830",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:34:11 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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)",
bibdate = "Fri Nov 25 18:19:29 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Ercoli:1957:EDO}.",
acknowledgement = ack-nhfb,
}
@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)",
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/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://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{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)",
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/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://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,
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)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@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)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@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)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nj # " and " # ack-nhfb,
}
@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)",
MRclass = "352.68.00",
MRnumber = "22\#8714",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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)",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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)",
MRclass = "65.00",
MRnumber = "22\#8639",
bibdate = "Fri Nov 25 18:19:26 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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)",
bibdate = "Fri Nov 25 18:19:29 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Sklansky:1960:CSA,
author = "J. Sklansky",
title = "Conditional Sum Addition Logic",
journal = "Trans. IRE",
volume = "EC-9",
number = "2",
pages = "226--230",
month = jun,
year = "1960",
bibdate = "Fri Nov 09 19:17:08 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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)",
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/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Sarafyan:1959:NMC}.",
acknowledgement = ack-nhfb,
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",
MRclass = "65.00 (68.00)",
MRnumber = "22\#6090",
bibdate = "Fri Dec 08 14:44:46 1995",
bibsource = "http://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,
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 = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
}
@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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://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,
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 = "http://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 = "http://dx.doi.org/10.1109/TEC.1961.5219227",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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 = "http://dx.doi.org/10.1109/TEC.1961.5219154",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:02 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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)",
bibdate = "Thu Sep 08 08:14:59 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Cox:1961:NMP,
author = "A. G. Cox and H. A. Luther",
title = "A Note on Multiple Precision Arithmetic",
journal = j-CACM,
volume = "4",
number = "8",
pages = "353",
month = aug,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Thu Sep 15 18:36:06 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://dx.doi.org/10.1109/TEC.1961.5219286",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:05 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
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 = "http://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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://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,
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 = "http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Garwick:1961:AFP,Amble:1961:AFP}.",
acknowledgement = ack-nhfb,
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 = "http://doi.acm.org/10.1145/800029.808563",
bibdate = "Thu Aug 07 19:04:58 2008",
bibsource = "http://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 = "http://dx.doi.org/10.1109/TEC.1961.5219198",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:03 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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)",
bibdate = "Tue Jan 09 07:10:22 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1960:INS}.",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.doi.org/10.1109/TEC.1961.5219240",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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 = "http://dx.doi.org/10.1109/TEC.1961.5219274",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite{Swartzlander:1976:CDD}.",
acknowledgement = ack-nhfb,
}
@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)",
MRclass = "65.99",
MRnumber = "23\#B555",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1960:INS}.",
acknowledgement = ack-nhfb,
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",
bibdate = "Thu Feb 15 15:07:57 2007",
bibsource = "http://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,
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 $d(uv) = u dv
+ v du$, 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 = "P. Rabinowitz",
title = "Multiple-Precision Division",
journal = j-CACM,
volume = "4",
number = "2",
pages = "98--98",
month = feb,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Thu Sep 08 00:29:25 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://dx.doi.org/10.1109/TEC.1961.5219186",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:03 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nj # " and " # ack-nhfb,
}
@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",
bibdate = "Sat Dec 09 14:01:44 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Book{Taub:1961:JNC,
editor = "A. H. Taub",
title = "{John von Neumann}: Collected Works",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "??? (vol. 1), 568 (vol. 2), 574 (vol. 3), 516 (vol.
4), ??? (vol. 5), ??? (vol. 6)",
year = "1961--1963",
LCCN = "????",
bibdate = "Wed Jun 01 16:58:29 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Six volumes. Volume I: Logic, Theory of Sets and
Quantum Mechanics (1961); Volume II: Operators, Ergodic
Theory and Almost Periodic Functions in a Group (1961);
Volume III: Rings of Operators (1961); Volume IV:
Continuous Geometry and Other Topics (1962); Volume V:
Design of Computers, Theory of Automata and Numerical
Analysis (1963); Volume VI: Theory of Games,
Astrophysics, Hydrodynamics and Meteorology (1963).",
acknowledgement = ack-nhfb,
}
@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)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@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 = "http://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 = "http://dx.doi.org/10.1109/TEC.1961.5219271",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
http://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ibmjrd.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.",
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, 9s in a decimal machine). Sow 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 waling 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,
pages = "92--121",
year = "1962",
LCCN = "QA76.8.I2 I5",
bibdate = "Wed Feb 14 17:24:27 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
bookpages = "322",
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 = "http://dx.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;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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 = "http://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 = "http://dx.doi.org/10.1109/TEC.1962.5219366",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:50 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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)",
MRclass = "68.00",
MRnumber = "26\#4506",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://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,
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 = "http://dx.doi.org/10.1109/TEC.1962.5219349",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:49 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "The IBM 1620 normalized variable-precision arithmetic
provides up to 100 decimal digits with an exponent
range of $\pm99$.",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.doi.org/10.1109/TEC.1962.5219389",
ISSN = "0367-9950",
MRclass = "68.00",
MRnumber = "MR0150990 (27 \#976)",
MRreviewer = "N. H. Choksy",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@Article{Knuth:1962:EPC,
author = "D. E. Knuth",
title = "Evaluation of Polynomials By Computer",
journal = j-CACM,
volume = "5",
number = "12",
pages = "595--599",
month = dec,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Thu Sep 1 10:15:40 1994",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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)",
bibdate = "Fri Nov 28 18:16:30 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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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)",
bibdate = "Fri Nov 28 18:21:41 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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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",
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year = "1962",
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http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
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fjournal = "IRE Transactions on Electronic Computers",
}
@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)",
bibdate = "Thu Sep 1 10:15:31 1994",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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}
@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 = "http://dx.doi.org/10.1109/TEC.1962.5219460",
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219460",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@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",
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ISSN = "0367-9950",
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219391",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@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",
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DOI = "http://dx.doi.org/10.1109/TEC.1962.5219436",
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219436",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@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)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@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",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:40 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nj # " and " # ack-nhfb,
}
@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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://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,
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 = "http://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)",
bibdate = "Fri Nov 25 18:19:47 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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 = "http://dx.doi.org/10.1109/PGEC.1963.263644",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:42 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@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)",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Eve:1963:SAI,
author = "J. Eve",
title = "Starting approximation for the iterative calculation
of square roots",
journal = j-COMP-J,
volume = "6",
pages = "274--276",
year = "1963",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Thu Sep 15 18:37:30 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
xxmonth = "(none)",
xxnumber = "(none)",
}
@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;
http://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 = "http://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 = "http://dx.doi.org/10.1145/366274.366339",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:19:45 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://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,
}
@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 = "http://dx.doi.org/10.1109/PGEC.1963.263572",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:39 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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 = "http://dx.doi.org/10.1109/PGEC.1963.263479",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:40 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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 = "http://dx.doi.org/10.1109/PGEC.1963.263493",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:36 MDT 2011",
bibsource = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Wed Apr 29 18:26:14 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.doi.org/10.1109/PGEC.1963.263593;
http://dx.doi.org/10.1109/PGEC.1963.263592",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:44 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038037",
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",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
ZMnumber = "0124.07910",
}
@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 = "http://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",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/",
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,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "A. S. Householder",
}
@Book{Wilkinson:1963:REA,
author = "James H. Wilkinson",
title = "Rounding Errors in Algebraic Processes",
publisher = pub-PH,
address = pub-PH:adr,
pages = "vi + 161",
year = "1963",
LCCN = "QA76.5 .W53 1964",
bibdate = "Thu Sep 08 13:29:45 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Aiken:1964:PAC,
author = "H. H. Aiken",
title = "Proposed automatic calculating machine",
journal = j-IEEE-SPECTRUM,
volume = "1",
number = "??",
pages = "62--69",
month = aug,
year = "1964",
CODEN = "IEESAM",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Wed Oct 13 11:16:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
note = "Previously unpublished memorandum. Reprinted in
\cite[\S 5.1]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
remark = "This article does not appear in the IEEE Xplore
database, and that source lists only volume 1, number
1, for 1964. I found multiple references to this paper
as the August 1964 issue, so perhaps IEEE Xplore is
missing early journal issues??",
}
@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 = "http://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",
bibdate = "Thu Nov 03 22:33:52 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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)",
MRclass = "65.25",
MRnumber = "31\#865",
bibdate = "Mon Oct 24 09:33:02 MDT 2005",
bibsource = "http://portal.acm.org/;
http://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,
}
@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 = "http://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)",
bibdate = "Mon Oct 24 09:33:00 MDT 2005",
bibsource = "http://portal.acm.org/;
http://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,
}
@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 = "http://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 $\pm63$.",
}
@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 = "http://doi.acm.org/10.1145/355588.365122",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://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,
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 = "http://dx.doi.org/10.1109/PGEC.1964.263791",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:56:59 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
xxmonth = "(none)",
xxnumber = "(none)",
}
@MastersThesis{Goldschmidt:1964:ADC,
author = "R. E. Goldschmidt",
title = "Applications of division by convergence",
type = "Thesis ({M.S.})",
school = "Dept. of Electrical Engineering, Massachusetts
Institute of Technology",
address = "Cambridge, MA, USA",
pages = "44 (est.)",
month = jun,
year = "1964",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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 = "http://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,
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)",
MRclass = "68.00",
MRnumber = "30\#2706",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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 = "http://dx.doi.org/10.1109/PGEC.1964.263942",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:57:06 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.doi.org/10.1109/PGEC.1964.263919",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:57:00 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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 = "http://dx.doi.org/10.1109/PGEC.1964.263838",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:56:57 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@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 = "http://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 = "http://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 = "http://dx.doi.org/10.1109/PGEC.1964.263777;
http://dx.doi.org/10.1109/PGEC.1964.263776",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:56:58 MDT 2011",
bibsource = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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)",
bibdate = "Mon Oct 24 09:33:00 MDT 2005",
bibsource = "http://portal.acm.org/;
http://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,
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 = "http://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;
http://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 = "http://dx.doi.org/10.1109/PGEC.1964.263734",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:57:04 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib
http://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)",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://dx.doi.org/10.1109/PGEC.1964.263830",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:56:56 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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 = "J. M. Wolfe",
title = "Reducing Truncation Errors by Programming",
journal = j-CACM,
volume = "7",
number = "6",
pages = "355--356",
month = jun,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Thu Sep 08 00:17:16 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://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.",
acknowledgement = ack-jr,
fjournal = "The American Mathematical Monthly",
keywords = "error estimation; floating-point arithmetic",
ZMnumber = "0216.49602",
}
@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 = "http://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 = "http://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 = "http://dx.doi.org/10.1109/PGEC.1965.264145",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:33 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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)",
bibdate = "Thu Sep 8 08:20:53 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://dx.doi.org/10.1109/PGEC.1965.264080",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:41 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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 = "L. Dadda",
title = "Some Schemes for Parallel Multipliers",
journal = "Alta Frequenza",
volume = "34",
number = "??",
pages = "349--356",
month = mar,
year = "1965",
bibdate = "Fri Nov 09 10:47:42 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.doi.org/10.1109/PGEC.1965.264153",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:34 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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)",
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/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://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",
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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 = "http://dx.doi.org/10.1109/PGEC.1965.263975",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:23 MDT 2011",
bibsource = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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 = "http://dx.doi.org/10.1109/PGEC.1965.264031",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:40 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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:BRE,
author = "Preston C. Hammer",
title = "Book Review: {{\em 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",
bibdate = "Tue Mar 20 13:44:52 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0040-1706%28196502%297%3A1%3C82%3AEAHSCA%3E2.0.CO%3B2-9",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.doi.org/10.1109/PGEC.1965.264258",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:22 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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)",
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;
http://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",
}
@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)",
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nj # " and " # ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
http://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:FRR,
author = "W. Kahan",
title = "Further Remarks on Reducing Truncation Errors",
journal = j-CACM,
volume = "8",
number = "1",
pages = "40--40",
month = jan,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Thu Sep 08 00:18:17 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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}. Cited in
\cite{Sterbenz:1974:FPC}.",
}
@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",
bibdate = "Thu Nov 03 08:47:50 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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)",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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 = "http://doi.acm.org/10.1145/363791.363829",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
MRclass = "68.00",
MRnumber = "30\#2709",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip and
ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://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,
keywords = "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 = "http://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 = "http://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 = "http://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;
http://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)",
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/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See remarks \cite{Dodd:1965:RSB}.",
acknowledgement = ack-nhfb,
checked = "19940304",
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 = "http://dx.doi.org/10.1109/PGEC.1965.264010",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:39 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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 = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
ZMnumber = "0161.35502",
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See erratum \cite{Metropolis:1965:BAU}.",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
ZMnumber = "0128.36301",
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
}
@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)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://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",
acknowledgement = ack-nhfb,
ZMnumber = "0146.14607",
}
@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 = "http://dx.doi.org/10.1109/PGEC.1965.263963",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:22 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Moller:1965:QDP}.",
acknowledgement = ack-nj # " and " # ack-nhfb,
}
@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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01975722",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65.80",
MRnumber = "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;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://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,
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:FRR}. 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",
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 = "http://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,
bookpages = "????",
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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://dx.doi.org/10.1109/PGEC.1965.264250",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:22 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
bibdate = "Thu Nov 03 08:47:50 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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 = "http://dx.doi.org/10.1109/PGEC.1965.264051",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:20 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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)",
bibdate = "Sun Sep 18 22:55:00 1994",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
http://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",
keywords = "accurate floating-point summation",
sjb = "Refers to \cite{Wolfe:cacm:196,Wilhelm:1977:GMPb}.",
}
@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 = "http://dx.doi.org/10.1109/PGEC.1965.264066",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:21 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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)",
bibdate = "Wed Aug 31 14:02:19 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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",
ISSN = "0018-8670",
bibdate = "Thu Sep 15 18:42:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.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,
remark = "Page 34, containing a critical table, is missing from
the PDF file.",
xxmonth = "(none)",
}
@Article{Winograd:1965:TRP,
author = "S. 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",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Multi.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.doi.org/10.1109/PGEC.1966.264311",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 05:46:31 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/",
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,
}
@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 = "http://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",
bibdate = "Fri Nov 28 16:23:06 2003",
bibsource = "http://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,
}
@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://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_02/",
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,
}
@Article{Fike:1966:SAS,
author = "C. T. Fike",
title = "Starting Approximations for Square Root Calculation on
{IBM} System/360",
journal = j-CACM,
volume = "9",
number = "4",
pages = "297--299",
month = apr,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Probably November or December issue; missing from
amermathmonthly1960.bib.",
}
@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 = "http://dx.doi.org/10.1109/PGEC.1966.264566",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 05:46:38 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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{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 = "http://dx.doi.org/10.1109/PGEC.1966.264312",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 05:46:31 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
}
@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 = "http://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 = "http://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)",
bibdate = "Fri Nov 25 18:20:07 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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)",
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/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://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,
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 = "http://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 = "http://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 = "http://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;
http://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 = "http://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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "British Journal for the History of Science",
keywords = "history",
ZMnumber = "0143.24202",
}
@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",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:06 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://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,
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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-jr,
}
@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 = "http://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",
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
http://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,
}
@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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://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,
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 = "Proceedings of the IEEE",
volume = "54",
number = "12",
pages = "1920--1931",
month = dec,
year = "1966",
bibdate = "Fri Nov 09 19:37:52 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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)",
MRclass = "65.50",
MRnumber = "39\#2314",
bibdate = "Fri Nov 25 18:20:15 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://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,
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Anderson:1967:ISM,
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",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
bibdate = "Wed Sep 07 22:14:32 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://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 = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://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 = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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{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 = "http://dx.doi.org/10.1109/PGEC.1967.264580",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:02 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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: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",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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)",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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)",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
http://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/gvl.bib",
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",
ZMnumber = "0154.40401",
}
@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 = "http://dx.doi.org/10.1109/PGEC.1967.264752",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:06 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:15 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "$\abs(z)$; $\sqrt(z)$; elementary functions",
}
@Article{Goldberg:1967:BAN,
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",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 28 16:47:55 2003",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://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,
keywords = "decimal floating-point arithmetic",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/",
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,
}
@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;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://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",
}
@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)",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@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;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://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",
}
@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 = "http://dx.doi.org/10.1109/PGEC.1967.264810",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:01 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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 = "http://dx.doi.org/10.1109/PGEC.1967.264730",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:03 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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 = "D. W. Matula",
booktitle = "{Spring Joint Computer Conference}",
title = "Base Conversion Mappings",
publisher = pub-AFIPS,
address = pub-AFIPS:adr,
pages = "311--318",
year = "1967",
bibdate = "Wed Feb 14 19:18:24 2007",
bibsource = "http://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/;
http://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 = "http://dx.doi.org/10.1109/PGEC.1967.264781",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:05 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
ZMnumber = "0225.65059",
}
@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",
bibdate = "Tue Nov 1 09:43:17 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
keywords = "ir, nla, lud, iterative refinement",
}
@Article{Moursund:1967:OSV,
author = "D. 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",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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)",
bibdate = "Fri Nov 25 18:20:13 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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;
http://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",
}
@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 = "http://dx.doi.org/10.1109/PGEC.1967.264811",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:01 MDT 2011",
bibsource = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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 = "http://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)",
bibdate = "Fri Aug 26 10:27:10 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Polish translation of \cite{Wilkinson:1963:REA}",
acknowledgement = ack-nhfb,
}
@Article{Winograd:1967:TRP,
author = "S. 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",
ISSN = "0004-5411",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Multi.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Fri Nov 25 18:20:15 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://doi.acm.org/10.1145/363397.363565",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Thu Aug 07 17:25:16 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://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,
keywords = "cubical complexes; extremal; minimization; prime
implicants; switching function; ternary encoding",
}
@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;
http://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 = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
ZMnumber = "0184.37503",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687268",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@Book{Hart:1968:CA,
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted 1978 with corrections.",
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 = "http://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 = "http://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 = "http://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",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
bibdate = "Fri Apr 21 07:26:39 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Matula:1968:IOC,
author = "D. W. Matula",
title = "In-and-Out Conversions",
journal = j-CACM,
volume = "11",
number = "1",
pages = "47--50",
month = jan,
year = "1968",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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 = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classmath = "*65H05 (Single nonlinear equations (numerical
methods)) 65F05 (Direct methods for linear systems)",
ZMnumber = "0207.15804",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687350",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687471",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://dx.doi.org/10.1109/PGEC.1967.264810;
http://dx.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 = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://dx.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 = "http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://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 = "http://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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687477",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://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,
}
@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 = "http://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 = "http://dx.doi.org/10.1109/T-C.1969.222658;
http://dx.doi.org/10.1109/PGEC.1967.264810",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 16:55:18 MDT 2011",
bibsource = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
keywords = "residue arithmetic; residue number system",
}
@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)",
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;
http://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",
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;
http://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;
http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671350",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671120",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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",
}
@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://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_01/",
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,
}
@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;
http://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",
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)",
MRclass = "65.35",
MRnumber = "MR0261775 (41 \#6388a)",
bibdate = "Thu Nov 8 14:50:15 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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)",
MRclass = "65.35",
MRnumber = "MR0261776 (41 \#6388b)",
MRreviewer = "J. Legras",
bibdate = "Thu Nov 8 14:50:18 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671344",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
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/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C4120 (Functional analysis)",
corpsource = "Argonne Nat. Lab., Argonne, IL, USA",
keywords = "$\sqrt(x)$; elementary functions; function evaluation;
iterative methods",
}
@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 = "http://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 = "Fri Mar 22 18:03:29 MST 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
price = "US\$19.75",
series = "The Art of Computer Programming",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See correction \cite{Liu:1970:CEA}.",
acknowledgement = ack-nhfb,
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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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;
http://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 = "http://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 = "http://doi.acm.org/10.1145/356540.356543",
ISSN = "0010-4892",
bibdate = "Mon Sep 19 18:18:44 1994",
bibsource = "http://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,
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)",
bibdate = "Tue Mar 20 13:34:21 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://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,
}
@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;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://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",
}
@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)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nj # " and " # ack-nhfb,
}
@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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
keywords = "decimal floating-point arithmetic",
}
@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 = "http://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}/{\tt 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)",
bibdate = "Thu Feb 15 15:23:23 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://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)",
bibdate = "Mon Mar 5 17:26:29 MST 2007",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@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",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Weinstein:1969:CRN}.",
acknowledgement = ack-nhfb,
}
@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",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See correction \cite{Weinstein:1969:CCR}.",
acknowledgement = ack-nhfb,
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",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
http://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 = "http://dx.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 = "http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://dx.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 = "http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://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",
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)",
MRclass = "65.15",
MRnumber = "MR0273773 (42 \#8649)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://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",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
ZMnumber = "0227.10044",
}
@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)",
MRclass = "62.70",
MRnumber = "MR0272129 (42 \#7010)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://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",
acknowledgement = ack-nhfb,
ZMnumber = "0208.19505",
}
@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 = "http://dx.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 = "http://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,
fjournal = "IEEE Transactions on Computers",
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;
http://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 = "http://dx.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 = "http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nhfb,
classmath = "*65G50 Roundoff error 65Y20 Complexity and performance
of numerical algorithms",
fjournal = "The American Mathematical Monthly",
ZMnumber = "0207.15401",
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://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",
bibdate = "Sun Nov 6 11:55:54 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671474",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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",
ISSN = "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.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol49/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 include.",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "The Bell System Technical Journal",
}
@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;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://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",
}
@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;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://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",
}
@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 = "http://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 = "http://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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Hornbuckle.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
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)",
MRclass = "65.35",
MRnumber = "MR0261777 (41 \#6389)",
MRreviewer = "J. Legras",
bibdate = "Thu Nov 8 14:50:19 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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)",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "http://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)",
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 = "http://doi.acm.org/10.1145/356580.356581",
ISSN = "0010-4892",
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;
http://www.math.utah.edu/pub/tex/bib/compsurv.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite{Aspray:1987:PJN}.",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671475",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://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,
fjournal = "IEEE Transactions on Computers",
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)",
MRclass = "65.25",
MRnumber = "44\#3468",
MRreviewer = "R. P. Brent",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "Compendex database;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip and
ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1970.bib;
http://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 Univ., NY, USA",
descriptors = "Simulation; statistics; numeric calculation;",
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",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Liu:1969:EAD}.",
acknowledgement = ack-nhfb,
}
@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;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://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",
}
@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 = "http://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,
Dept. 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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Programming (Mathematics)",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
keywords = "ARITH-1",
}
@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",
bibdate = "Tue Aug 28 06:12:04 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}
@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)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Nagoya Univ., Chikua ku, Japan",
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",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nj # " and " # ack-nhfb,
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671530",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://dx.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 = "http://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,
fjournal = "IEEE Transactions on Computers",
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;
http://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;
http://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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671456",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://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 = "181",
year = "1970",
LCCN = "TK7889.C6 T5 1970",
bibdate = "Wed Sep 14 22:45:51 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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 = "http://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,
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 = "http://dx.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 = "http://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,
fjournal = "IEEE Transactions on Computers",
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)",
bibdate = "Fri Aug 20 10:26:49 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://dx.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 = "http://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,
fjournal = "IEEE Transactions on Computers",
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)",
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;
http://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",
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 = "http://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 = "http://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.",
}
@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 = "http://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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://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,
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://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/",
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",
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 = "http://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 = "Honeywell Computer Journal",
volume = "5",
number = "3",
pages = "99--105",
month = "????",
year = "1971",
bibdate = "Thu Nov 25 09:37:15 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "The Gamma 60 decimal floating-point system provides 11
to 19 decimal digits with an exponent range of
$\pm40$.",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671914",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01931808",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Sat Nov 14 09:14:57 1998",
bibsource = "http://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,
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 = "http://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 $x(1\pm2^{-m})$
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671918",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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;
http://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 = "http://doi.acm.org/10.1145/1052614.1052616",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
bibdate = "Tue Apr 12 07:49:57 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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;
http://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",
year = "1971",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "68A55",
MRnumber = "45 8056",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb # " and " # ack-nj,
keywords = "accurate floating-point summation; balanced ternary",
xxmonth = "(none)",
}
@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)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@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 = "http://doi.acm.org/10.1145/1093425.1093426",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
bibdate = "Tue Jun 17 19:14:25 MDT 2008",
bibsource = "http://portal.acm.org/;
http://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,
issue = "18",
}
@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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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)",
bibdate = "Mon Aug 15 09:54:14 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "ACM Algorithm 414.",
acknowledgement = ack-nj,
}
@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://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/",
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,
}
@InProceedings{Kahan:1971:SEA,
author = "W. Kahan",
title = "A survey of error analysis",
crossref = "Freiman:1971:PIC",
pages = "1214--1239",
year = "1971",
bibdate = "Tue Aug 28 05:24:53 2001",
bibsource = "http://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}.",
}
@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",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See correction \cite{Kan:1973:CEA}.",
acknowledgement = ack-nhfb,
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{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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671863",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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;
http://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 = "http://dx.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 = "http://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,
}
@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 = "http://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",
keywords = "error estimation; errors; estimation theory; finite
set; floating point arithmetic; real functions;
simulation",
language = "German",
treatment = "T Theoretical or Mathematical",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671784",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671809",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Stanford Univ., CA, USA",
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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671767",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671667",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Norwegian",
}
@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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671854",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671808",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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;
http://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 = "http://dx.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;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
note = "Check pages??",
acknowledgement = ack-ec # " and " # ack-nhfb,
affiliation = "Univ., Konstanz, West Germany",
classification = "C5230",
description = "digital arithmetic",
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671770",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671917",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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;
http://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;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://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",
}
@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 = "http://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 = "http://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://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/",
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",
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009055",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.doi.org/10.1109/T-C.1972.223499;
http://dx.doi.org/10.1109/PGEC.1967.264810",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:48 MDT 2011",
bibsource = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
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)",
bibdate = "Fri May 12 09:41:08 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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)",
MRclass = "65D20",
MRnumber = "49 \#1738",
bibdate = "Tue Mar 25 14:26:59 MST 1997",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://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",
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009046",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672131",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672104",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672118",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://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 = "http://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)",
bibdate = "Mon Jan 22 06:46:23 MST 2001",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip and
ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib;
http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Gregory72;
http://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;",
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 = "http://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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@Article{Heising:1972:MM,
author = "W. Heising and M. O. Rabin and S. 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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009082",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009084",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@Article{Malcolm:1972:ARP,
author = "M. 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",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Thu Sep 1 10:14:16 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Gentleman:1974:MAR}.",
acknowledgement = ack-nj,
}
@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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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",
}
@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 = "http://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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009048",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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/;
http://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,
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",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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\'etique \`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 = "http://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",
keywords = "accurate floating-point summation; 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 = "http://dx.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;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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;
http://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;
http://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)",
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;
http://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",
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Numerical calculations.",
}
@Article{Samet:1972:CDS,
author = "P. A. Samet",
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",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Mon Jul 26 14:05:09 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/",
URL = "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",
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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672150",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://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,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://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)",
bibdate = "Fri Mar 30 11:34:37 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/amstat.bib;
http://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,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@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)",
bibdate = "Thu Sep 1 10:14:44 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Avizienis.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
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 = "http://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 = "http://dx.doi.org/10.1109/T-C.1973.223711;
http://dx.doi.org/10.1109/PGEC.1967.264810",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:18 MDT 2011",
bibsource = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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;
http://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 = "http://dx.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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Brent.pdf",
acknowledgement = ack-nj,
fjournal = "IEEE Transactions on Computers",
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672350",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Cody.pdf",
acknowledgement = ack-nj,
fjournal = "IEEE Transactions on Computers",
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)",
bibdate = "Tue Apr 12 07:49:59 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Univ. California, Los Alamos, NM, USA",
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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Du.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
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 = "http://dx.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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Ercegovac.pdf",
acknowledgement = ack-nj,
fjournal = "IEEE Transactions on Computers",
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, Dept. of Computer Science",
address = "Helsinki",
pages = "ii + 20",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://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",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Gelenbe.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
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://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/",
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",
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 = "http://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{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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Jacobsohn.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
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 = "http://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",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Kan:1971:EAD}.",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.doi.org/10.1109/TC.1973.5009117",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Kanani.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
keywords = "ARITH-2",
}
@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",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://doi.acm.org/10.1145/321765.321771",
ISSN = "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;
http://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,
reviewer = "V. V. Ivanov",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "In Polish.",
acknowledgement = ack-nhfb,
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 = "http://dx.doi.org/10.1109/T-C.1973.223674;
http://dx.doi.org/10.1109/PGEC.1967.264810",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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)",
MRclass = "68A20 (65G05)",
MRnumber = "51 2344",
MRreviewer = "I. Kaufmann",
bibdate = "Wed Aug 31 13:47:33 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://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",
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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",
bibdate = "Sat Jul 16 18:05:03 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://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 = "Dept. of Computer Science, Stanford University",
address = "Stanford, CA, USA",
pages = "ix + 129",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Marasa.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
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",
MRclass = "10A30 (02E10)",
MRnumber = "MR0321857 (48 \#222)",
MRreviewer = "R. L. Goodstein",
bibdate = "Thu Nov 8 14:50:22 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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",
ZMnumber = "0259.00001",
}
@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)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290B (Error analysis in numerical methods); C4110
(Error analysis in numerical methods)",
corpsource = "Univ. Kentucky, Lexington, KY, USA",
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009173",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
Theory/Matrix.bib",
note = "Cited in \cite{govl:89}.",
acknowledgement = ack-nhfb,
kwds = "na, polynomial, complexity",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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;
http://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)",
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;
http://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",
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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Robertson.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
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 = "http://dx.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 = "http://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,
fjournal = "IEEE Transactions on Computers",
keywords = "ARITH-2",
}
@MastersThesis{Rubinfield:1973:FM,
author = "Louis P. Rubinfield",
title = "A floating-point macromodule",
type = "Thesis ({M.S.})",
school = "Washington Univ., Dept. of Electrical Engineering",
address = "St. Louis, MO, USA",
pages = "vii + 111",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672264",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672265",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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",
ISSN-L = "0044-2267",
bibdate = "Mon Nov 14 16:35:28 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und
Mechanik}",
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",
bibdate = "Thu Sep 08 08:17:30 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://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",
}
@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;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://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",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672263",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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)",
bibdate = "Fri May 12 09:40:28 MDT 2006",
bibsource = "http://portal.acm.org/;
http://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,
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",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Spira.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
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 = "http://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 = "http://dx.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 = "http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672310",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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",
MRclass = "65H10",
MRnumber = "48 1457",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://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 = "http://dx.doi.org/10.1109/T-C.1973.223594;
http://dx.doi.org/10.1109/PGEC.1967.264810",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:11 MDT 2011",
bibsource = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://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 = "http://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",
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
keywords = "ARITH-2",
}
@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 = "http://dx.doi.org/10.1109/T-C.1974.223790;
http://dx.doi.org/10.1109/PGEC.1967.264810",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:29 MDT 2011",
bibsource = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672448",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.doi.org/10.1109/T-C.1974.224055;
http://dx.doi.org/10.1109/PGEC.1967.264810",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:35 MDT 2011",
bibsource = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
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{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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672573",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://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",
}
@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://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/",
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",
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://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/",
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",
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 = "http://doi.acm.org/10.1145/1206085.1206086",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
bibdate = "Tue Jun 17 18:47:00 MDT 2008",
bibsource = "http://portal.acm.org/;
http://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,
}
@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;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://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",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672659",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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{Dalhquist:1974:NM,
author = "Germund Dalhquist 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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Prentice-Hall Series in Automatic Computation",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
Theory/auto.diff.bib; Theory/Comp.Alg.1.bib",
acknowledgement = ack-nhfb,
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 = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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{}",
}
@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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@Article{Gentleman:1974:MAR,
author = "M. W. Gentleman and S. 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",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Sun May 02 09:19:10 1999",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Malcolm:1972:ARP}.",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
acknowledgement = ack-nhfb,
classification = "B0240 (Probability and statistics); C1140
(Probability and statistics)",
corpsource = "Dept. of Statistics, Univ. of Michigan, Ann Arbor, MI,
USA",
fjournal = "Journal of the American Statistical Association",
keywords = "Bose--Einstein allocation; distribution; random
processes; rank frequency form; statistics; Zipf's
law",
treatment = "T Theoretical or Mathematical",
ZMnumber = "Zbl 0301.60011",
}
@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, Dept. of Computer Science",
address = "Toronto, ON, Canada",
pages = "vi + 84",
year = "1974",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://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 = "http://dx.doi.org/10.1109/PGEC.1967.264810;
http://dx.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 = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "R. H. Bartels",
}
@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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01932946",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65G05",
MRnumber = "58 3381",
bibdate = "Fri Dec 08 13:05:19 1995",
bibsource = "http://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,
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 = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ZMnumber = "0311.65031",
}
@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 = "http://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 = "http://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",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-jr,
keywords = "accurate floating-point summation",
}
@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)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
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",
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://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;
http://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 = "http://dx.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 = "http://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,
fjournal = "IEEE Transactions on Computers",
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;
http://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.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",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672443",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://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)",
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;
http://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",
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",
MRclass = "65G05",
MRnumber = "49 8319",
bibdate = "Fri Dec 08 13:06:33 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4245313",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
fjournal = "Electronics Letters",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672702",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://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",
}
@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 = "http://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 = "http://dx.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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672709",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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",
bibdate = "Mon Mar 19 18:17:32 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://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 = "http://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 = "http://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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672900",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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)",
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;
http://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 $4n$
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",
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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@InProceedings{Ercegovac:1975:GME,
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 = "http://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 = "http://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 = "http://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 $3N = N +
2N$, 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 = "http://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 = "http://doi.acm.org/10.1145/355644.355647",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Fri Aug 26 23:44:16 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672710",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://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 = "http://dx.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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "Dept. of Math., Univ. of Miami, Coral Gables, FL,
USA",
classification = "921; C5230",
description = "digital arithmetic",
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 = "http://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",
}
@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 = "http://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://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/",
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 Univ., Dept. of Chem., Downsview, Ont., Canada",
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 = "http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
corpsource = "Dept. of Computer Sci., Univ. of Utah, Salt Lake City,
UT, USA",
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 = "http://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 = "http://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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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;
http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672761",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://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,
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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://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,
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 = "http://dx.doi.org/10.1007/BF01932690;
http://www.springerlink.com/openurl.asp?genre=article&id=doi: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 = "http://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,
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 = "http://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",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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{}",
}
@Book{Luke:1975:MFT,
author = "Y. 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",
ISBN-13 = "978-0-12-459950-5",
LCCN = "QA55 .M418",
bibdate = "Thu Sep 1 10:13:15 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672763",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672800",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://doi.acm.org/10.1145/355637.355639",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
MRclass = "65G05",
MRnumber = "53 #9622",
bibdate = "Fri Aug 26 23:44:16 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "James H. Wilkinson",
}
@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)",
bibdate = "Sat May 31 13:36:16 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/spe.bib",
acknowledgement = ack-nhfb,
}
@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)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Dept. of Computer Sci., Univ. of Kentucky, Lexington,
KY, USA",
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 = "http://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 = "http://dx.doi.org/10.1109/T-C.1975.224147;
http://dx.doi.org/10.1109/PGEC.1967.264810",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:58 MDT 2011",
bibsource = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://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 = "http://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 = "J. F. Reiser and Donald E. Knuth",
title = "Evading the drift in floating-point addition",
journal = j-INFO-PROC-LETT,
volume = "3",
pages = "84--87",
year = "1975",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Wed Aug 24 19:19:04 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Errata, p.\ 164.",
acknowledgement = ack-nj,
}
@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 = "http://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",
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672707",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://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 = "http://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 = "http://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)",
bibdate = "Mon Jan 22 07:22:40 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#Smith75a;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Chen:1975:SER}.",
acknowledgement = ack-nhfb,
classcodes = "C6130 (Data handling techniques)",
corpsource = "Univ. of California, Berkeley, CA, USA",
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{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)",
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;
http://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 = "Univ. of Calgary, Calgary, Alta., Canada",
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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://dx.doi.org/10.1109/T-C.1975.224172",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jun 24 18:41:13 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672933",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672780",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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 = "Dept. of Computer Science, Carnegie-Mellon
University",
address = "Pittsburgh, PA, USA",
pages = "16",
year = "1975",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classification = "B0250 (Combinatorial mathematics); C1160
(Combinatorial mathematics)",
corpsource = "Dept. of Math., Lehigh Univ., Bethlehem, PA, USA",
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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://doi.acm.org/10.1145/321941.321944",
ISSN = "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;
http://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 $O(M(n)log (n))$ 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",
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 = "http://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 = "http://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",
bibdate = "Thu Feb 15 16:29:51 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Combinatorial Theory. Series A",
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ZMnumber = "0319.65039",
}
@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 = "http://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,
}
@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 = "http://dx.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;
http://www.math.utah.edu/pub/tex/bib/archhistexactsci.bib;
http://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",
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Numerical calculations ---
Computer programs.",
}
@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 = "http://doi.acm.org/10.1145/321941.321948",
ISSN = "0004-5411",
bibdate = "Wed Jan 15 18:12:53 MST 1997",
bibsource = "Compendex database;
http://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",
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 = "http://dx.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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://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,
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674646",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009201",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674723",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://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 = "http://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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://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,
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 = "http://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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://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.
Special section on testing",
journal = j-IEEE-TRANS-SOFTW-ENG,
volume = "SE-2",
number = "3",
pages = "223--226",
year = "1976",
CODEN = "IESEDJ",
ISSN = "0098-5589 (print), 1939-3520 (electronic)",
MRclass = "68A05",
MRnumber = "55 1787",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "floating-point 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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
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 = "http://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 = "Dept. 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 = "http://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{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 = "http://doi.acm.org/10.1145/355681.355684",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Sat Aug 27 00:30:21 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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;
http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.6502.org/source/floats/wozfp1.txt",
acknowledgement = ack-nhfb,
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 = "http://dx.doi.org/10.1049/ree.1976.0057",
ISSN = "0033-7722",
bibdate = "Fri Dec 03 15:11:57 2010",
bibsource = "http://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)",
bibdate = "Tue Apr 12 07:50:03 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://portal.acm.org/;
http://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",
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
$\pm9999$. 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 = "http://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{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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674641",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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;
http://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 = "http://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)",
bibdate = "Mon Sep 12 08:07:55 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://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,
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674555",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674634",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674892",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674922",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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;
http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://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",
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,
fjournal = "IEEE Transactions on Computers",
ZMnumber = "0405.65056",
}
@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 = "http://dx.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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Transactions on Computers",
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 = "http://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",
MRclass = "68A05",
MRnumber = "58 3605",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "Costica Cazacu",
}
@Article{Collins:1977:APS,
author = "G. E. Collins and D. R. Musser",
title = "Analysis of the {Pope-Stein} Division Algorithm",
journal = j-INFO-PROC-LETT,
volume = "6",
number = "5",
pages = "151--155",
month = oct,
year = "1977",
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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)",
bibdate = "Fri Dec 08 13:06:08 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://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)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "B0290D (Functional analysis); B0290F (Interpolation
and function approximation); C4120 (Functional
analysis); C4130 (Interpolation and function
approximation); C7310 (Mathematics computing)",
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5420 (Mainframes and minicomputers); C7310
(Mathematics computing)",
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://dx.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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
URL = "http://www.jstor.org/stable/4025865",
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",
ZMnumber = "0358.01003",
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/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods); C6140D (High
level languages)",
corpsource = "George Washington Univ., Washington, DC, USA",
keywords = "complex numbers; data structure; data structures;
digital arithmetic; embedded; extended arithmetic;
procedure oriented languages; rotational numbers;
SNOBOL4",
treatment = "P Practical",
}
@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 = "http://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 = "Dept. of Computer Science, Southern Methodist
University",
address = "Dallas, TX, USA",
pages = "72",
year = "1977",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
reviewer = "N. N. Abdelmalek",
}
@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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://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,
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",
bibdate = "Thu Sep 1 10:14:44 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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., Univ. California,
Berkeley",
address = "Berkeley, CA, USA",
pages = "303",
month = feb,
year = "1977",
DOI = "http://wwwlib.umi.com/dissertations/fullcit/7731401",
bibdate = "Thu Jan 12 09:05:57 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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 = "http://doi.ieeecomputersociety.org/10.1109/PGEC.1967.264810",
ISSN = "0098-4094",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23467",
acknowledgement = ack-nhfb,
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 = "http://doi.ieeecomputersociety.org/10.1049/el:19770117",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://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{}",
}
@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 = "http://dx.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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674790",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674898",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674895",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Transactions on Computers",
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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674740",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@Book{Luke:1977:ACM,
author = "Y. 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 = "Thu Sep 1 10:13:16 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://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-COMP-MATH-APPL,
volume = "3",
number = "1",
pages = "77--81",
year = "1977",
CODEN = "CMAPDK",
ISSN = "0886-9561",
MRclass = "65G05 (10A30 65C10)",
MRnumber = "MR0458846 (56 \#17046)",
MRreviewer = "Artenio De Matteis",
bibdate = "Thu Nov 8 14:50:26 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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",
ZMnumber = "0371.60015",
}
@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;
http://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",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674819",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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",
bibdate = "Wed Oct 13 11:51:16 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.5]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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/;
http://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",
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://doi.ieeecomputersociety.org/10.1109/PGEC.1967.264810",
ISSN = "0018-9219",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=31255",
acknowledgement = ack-nhfb,
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 = "http://doi.ieeecomputersociety.org/10.1049/el:19770117",
ISSN = "0013-5194",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4249252",
acknowledgement = ack-nhfb,
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 = "http://dx.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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://doi.acm.org/10.1145/355719.355721",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Fri Sep 02 22:30:11 1994",
bibsource = "http://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,
}
@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",
MRclass = "65G05",
MRnumber = "55 1722",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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}\'ng 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 = "http://doi.acm.org/10.1145/355719.355723",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
MRclass = "65T05",
MRnumber = "55 #11658",
bibdate = "Sat Aug 27 22:12:55 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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)",
bibdate = "Sat May 31 13:36:16 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674814",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C4110 (Error analysis in numerical methods); C4140
(Linear algebra)",
corpsource = "Dept. of Computer Sci., Carnegie-Mellon Univ.,
Pittsburgh, PA, USA",
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 = "http://dx.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 = "http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://ieeexplore.ieee.org/;
http://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 = "http://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 = "http://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-COMP-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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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",
bibdate = "Thu Sep 1 10:14:44 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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",
bibdate = "Thu Sep 1 10:15:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://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 = "http://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 = "http://doi.ieeecomputersociety.org/10.1049/el:19770117",
ISSN = "0098-4094",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23475",
acknowledgement = ack-nhfb,
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 = "Dept. 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 = "http://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 = "http://dx.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 = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://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 = "http://doi.acm.org/10.1145/355769.355771",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
MRclass = "68A10",
MRnumber = "57 #18205",
bibdate = "Sat Aug 27 23:14:36 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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;
http://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",
bibdate = "Thu Sep 1 10:14:44 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://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",
}
@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 = "http://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 = "http://doi.acm.org/10.1145/355769.355776",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Mon Sep 05 22:49:15 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Brent:1979:RMF,Brent:1980:AIB}.",
acknowledgement = ack-nhfb,
}
@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 = "http://doi.acm.org/10.1145/355769.355775",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Sat Aug 27 23:13:25 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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)",
bibdate = "Sat Jan 29 18:00:28 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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 = "http://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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675081",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://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,
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 = "http://doi.ieeecomputersociety.org/10.1049/el:19780260",
ISSN = "0013-5194",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://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,
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 = "http://doi.ieeecomputersociety.org/10.1049/el:19780088",
ISSN = "0013-5194",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://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,
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 = "http://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{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",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://doi.acm.org/10.1145/355780.355789",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Sat Aug 27 23:30:46 1994",
bibsource = "http://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",
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 = "http://doi.acm.org/10.1145/355780.355783",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Sat Aug 27 23:13:25 1994",
bibsource = "http://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,
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 = "http://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 = "http://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;
http://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 = "http://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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
keywords = "additive identity; compute through overflow (CTO);
computer arithmetic; models of computer arithmetic;
number systems; overflow behavior",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "McGraw-Hill series in computer organization and
architecture",
acknowledgement = ack-nhfb,
}
@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 = "http://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",
bibdate = "Thu Sep 01 12:14:34 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://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 = "http://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 = "http://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 = "http://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 = "http://dx.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 = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
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{}",
}
@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 = "http://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 = "http://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 = "http://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 = "http://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;
http://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; exponent over;
Floating point exponents; 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 = "http://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 = "http://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 = "http://dx.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 = "http://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,
fjournal = "IEEE Transactions on Computers",
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",
bibdate = "Fri Mar 30 11:20:35 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0003-049X(19780818)122%3A4%3C193%3ATFDP%3E2.0.CO%3B2-C",
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,
fjournal = "Proceedings of the American Philosophical Society",
}
@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 = "http://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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675186",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675187",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://dx.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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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{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 $n^{\hbox{\rm i{\`e}me}}$
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;
http://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",
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 = "http://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 = "http://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",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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)",
bibdate = "Fri Dec 08 13:08:43 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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 = "http://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;
http://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",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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 = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://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 $f = 3d + 2$\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 = "http://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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://doi.ieeecomputersociety.org/10.1049/el:19780088",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://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)",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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)",
bibdate = "Thu Dec 12 07:20:54 MST 1996",
bibsource = "Compendex database;
http://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",
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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 {PLA}s",
crossref = "IEEE:1978:PSC",
pages = "116--124",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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 = "Dept. of Computer Sci., Carnegie-Mellon Univ.,
Pittsburgh, PA, USA",
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;
http://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 = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675322",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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;
http://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, Univ. of Saarlandes,
Saarbrucken, West Germany",
classification = "723; C5230",
description = "digital arithmetic",
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)",
bibdate = "Thu Dec 12 07:20:54 MST 1996",
bibsource = "Compendex database;
http://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",
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 = "http://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 = "Dept. of Electrical Engineering and Computer
Sciences",
address = "Berkeley, CA, USA",
pages = "????",
year = "1979",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://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 = "http://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 = "http://doi.acm.org/10.1145/355853.355868",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Mon Sep 05 22:49:18 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Brent:1978:AMF,Brent:1980:AIB}.",
acknowledgement = ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Bustoz:1979:ITD,
author = "Joaqu\'in 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",
bibdate = "Wed Oct 26 23:35:40 1994",
bibsource = "http://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 mena
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,
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675239",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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)",
bibdate = "Tue Apr 12 07:50:07 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
http://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",
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",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
bibdate = "Tue Apr 12 07:50:07 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
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 = "http://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 = "http://ieeexplore.ieee.org/;
http://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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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",
keywords = "Benford's Law",
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)",
bibdate = "Mon Jan 22 06:37:26 MST 2001",
bibsource = "Compendex database;
http://dblp.uni-trier.de/db/journals/cacm/cacm22.html#EdgarL79;
http://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 = "Univ. of Oklahoma, Norman, OK, USA",
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 = "http://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)",
bibdate = "Tue Apr 12 07:50:07 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
http://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",
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 = "http://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 = "http://doi.acm.org/10.1145/355853.355871",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Tue Aug 30 00:28:06 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Fox:1978:AFP}.",
acknowledgement = ack-nhfb,
}
@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)",
bibdate = "Tue Apr 12 07:50:07 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
http://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",
keywords = "denormalized numbers; digital arithmetic; expense;
floating point",
treatment = "P Practical",
xxnumber = "si-2",
}
@TechReport{Ginsberg:1979:MFE,
author = "Myron Ginsberg",
title = "Monitoring floating-point error propagation in
scientific computation",
type = "Technical report",
number = "CSE 7910",
institution = "Dept. 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 = "http://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)",
bibdate = "Tue Apr 12 07:50:07 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Univ. of Tennessee, Knoxville, TN, USA",
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;
http://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 = "http://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 = "http://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 = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See note \cite{Heath:1986:NRD}.",
acknowledgement = ack-nhfb,
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See corrigendum \cite{Hehner:1980:CNR}.",
acknowledgement = ack-nhfb,
}
@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 = "http://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;
http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675350",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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)",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://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 = "http://doi.ieeecomputersociety.org/10.1049/el:19780088",
ISSN = "0096-3518",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26137",
acknowledgement = ack-nhfb,
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",
MRclass = "65G05",
MRnumber = "80i:65045",
bibdate = "Fri Dec 08 11:55:10 1995",
bibsource = "http://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,
}
@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",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
bibdate = "Tue Apr 12 07:50:07 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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 = "Univ. of California, Berkeley, CA, USA",
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 = "http://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 = "Dept. 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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
MRclass = "65G05 (68C25)",
MRnumber = "80d:65050",
MRreviewer = "C. W. Clenshaw",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nhfb,
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Math. Inst., Univ. Dortmund, Dortmund, West Germany",
keywords = "algorithm; approximation theory; polynomials",
treatment = "A Application; T Theoretical or Mathematical",
}
@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 = "http://doi.acm.org/10.1145/390009.804437",
ISSN = "0163-6006",
bibdate = "Thu Aug 07 19:13:11 2008",
bibsource = "http://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,
}
@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 = "http://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{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)",
bibdate = "Tue Apr 12 07:50:07 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
http://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",
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;
http://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;
http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675390",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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)",
bibdate = "Tue Apr 12 07:50:08 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
http://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",
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)",
bibdate = "Tue Apr 12 07:50:06 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Leibniz-Rechenzentrum, Munich, West Germany",
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",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See correction \cite{Rink:1980:CPS}.",
acknowledgement = ack-nhfb,
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{}",
}
@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 = "http://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 = "http://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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://dx.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 = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://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,
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "Frederick N. Fritsch",
}
@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;
http://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",
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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675502",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://doi.ieeecomputersociety.org/10.1109/TC.1979.1675263",
ISSN = "0096-3518",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26146",
acknowledgement = ack-nhfb,
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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://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,
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 = "Information and Control",
volume = "46",
number = "1",
pages = "16--25",
month = jul,
year = "1980",
DOI = "http://dx.doi.org/10.1016/S0019-9958(80)90471-4",
bibdate = "Thu Nov 18 09:54:38 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.sciencedirect.com/science/journal/00199958",
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,
}
@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 = "http://doi.acm.org/10.1145/355887.355889",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Mon Sep 05 22:49:19 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Brent:1978:AMF,Brent:1979:RMF}.",
acknowledgement = ack-nhfb,
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;
http://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 = "http://doi.acm.org/10.1145/355921.355924",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Thu Sep 1 10:15:05 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date); MathSciNet
database",
acknowledgement = ack-nhfb,
affiliation = "Sektion Math., Tech. Univ. Dresden, Dresden, East
Germany",
classification = "C4140",
description = "matrix algebra",
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 = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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;
http://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 = "Dept. 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 = "http://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)",
}
@Book{Cody:1980:SME,
author = "W. J. Cody and W. 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 = "Thu Sep 1 10:12:51 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
bibdate = "Sun May 02 09:17:48 1999",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://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,
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675631",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://doi.ieeecomputersociety.org/10.1109/TC.1979.1675263",
ISSN = "0096-3518",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26148",
acknowledgement = ack-nhfb,
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 = "http://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 = "http://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 = "http://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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@Article{Ginsberg:1980:MFE,
author = "Myron Ginsberg",
title = "Monitoring floating-point error propagation in
scientific computation",
journal = j-COMP-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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
xxnote = "Special Issue",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Book{Gregory:1980:ECW,
author = "Robert Todd Gregory",
title = "Error-free computation: why it is needed and methods
for doing it",
publisher = "R. E. Krieger",
address = "Huntington, NY, USA",
edition = "Original",
pages = "152",
year = "1980",
ISBN = "0-89874-240-4",
ISBN-13 = "978-0-89874-240-4",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Approximation theory --- Data processing.;
Floating-point arithmetic.",
}
@Book{Gregory:1980:EFC,
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date); MathSciNet
database",
acknowledgement = ack-nhfb,
affiliation = "Univ. Karlsruhe, Karlsruhe, West Germany",
classification = "C4240",
description = "computational complexity",
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 = "http://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;
http://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,
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://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,
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Hehner:1979:NRR}.",
acknowledgement = ack-nhfb,
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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;
http://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 = "http://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 = "http://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,
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 = "http://doi.ieeecomputersociety.org/10.1049/el:19800468",
ISSN = "0013-5194",
MRclass = "94A05",
MRnumber = "MR583226 (81h:94003)",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://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",
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",
bibdate = "Fri Nov 28 11:42:59 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675558",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675473",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "interval arithmetic",
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Macke:1980:DMF,
author = "Edward T. Macke",
title = "Design of a modular floating point arithmetic unit",
type = "Thesis ({M.S.})",
school = "Washington University, Dept. of Electrical
Engineering",
address = "St. Louis, MO, USA",
pages = "ix + 174",
year = "1980",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://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 = "http://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;
http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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)",
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nhfb,
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Fachbereich Math., Univ. of Siegen, Siegen, West
Germany",
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-COMP-MATH-APPL,
volume = "6",
number = "3",
pages = "297--299",
year = "1980",
CODEN = "CMAPDK",
DOI = "http://dx.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)",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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.",
fjournal = "Computers \& Mathematics with Applications. An
International Journal",
ZMnumber = "0458.65029",
}
@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)",
bibdate = "Tue Apr 12 07:50:08 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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;
http://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;
http://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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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 = "http://doitest.acm.org/10.1145/641845.641849",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
bibdate = "Sat Jun 24 12:02:21 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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;
http://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)",
bibdate = "Wed Oct 5 08:31:56 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
issue = "??",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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)",
bibdate = "Tue Apr 12 07:50:08 MDT 2005",
bibsource = "http://portal.acm.org/;
http://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",
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 = "http://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",
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",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Rink:1979:PSR}.",
acknowledgement = ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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 = "http://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 = "http://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{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)",
bibdate = "Wed Nov 24 10:59:34 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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",
}
@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 = "http://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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675584",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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;
http://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.",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675482",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.doi.org/10.1109/MAHC.1980.10044",
ISSN = "0164-1239",
bibdate = "Fri Nov 1 15:29:17 MST 2002",
bibsource = "http://www.computer.org/annals/an1980/;
http://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,
}
@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 = "http://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 = "http://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 = "http://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;
http://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)",
bibdate = "Thu Sep 8 08:20:53 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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;
http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675537",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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-COMP-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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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)",
bibdate = "Mon Jan 24 21:36:17 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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 = "http://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",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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;
http://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",
genterm = "LANGUAGES; RELIABILITY; THEORY; VERIFICATION",
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 = "http://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 = "http://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 = "http://doi.acm.org/10.1145/355972.355975",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Mon Aug 29 23:03:20 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://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 = "http://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 = "http://www.computer.org/annals/an1981/;
http://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,
}
@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 = "http://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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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 = "http://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 = "http://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--69",
month = mar,
year = "1981",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
bibdate = "Sun May 2 09:17:22 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
acknowledgement = ack-nj,
}
@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 = "http://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",
month = mar,
year = "1981",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
bibdate = "Sun May 02 09:18:24 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See
\cite{Coonen:1980:IGP,IEEE:1985:AIS,IEEE:1985:ASI}.",
acknowledgement = ack-nj,
}
@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",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
bibdate = "Sun May 02 09:18:30 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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;
http://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,
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://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",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
bibdate = "Sun May 02 09:19:18 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
acknowledgement = ack-nj,
}
@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 = "http://doi.ieeecomputersociety.org/10.1049/el:19800468",
ISSN = "0098-4094",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23509",
acknowledgement = ack-nhfb,
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 = "http://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 = "http://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 = "http://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 = "http://doi.ieeecomputersociety.org/10.1049/el:19800468",
ISSN = "0018-9219",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://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,
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 = "http://doi.ieeecomputersociety.org/10.1049/el:19800468",
ISSN = "0018-9219",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://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,
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 = "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://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)",
bibdate = "Fri Nov 09 19:01:34 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://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,
keywords = "floating-point arithmetic; variable-precision
arithmetic",
}
@Misc{Kitajima:1981:MS,
author = "Osamu Kitajima",
title = "Masterless samurai",
publisher = "Headfirst",
address = "Los Angeles, CA, USA",
year = "1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "1 sound disc",
acknowledgement = ack-nhfb,
keywords = "New Age music.; Popular music --- 1981-1990.",
remark = "Golden mean --- Wild monk --- Sei-- essence --- Where
is the real Japan? --- Masterless samurai --- Breath of
night --- Edo townsfolk - - Floating garden ---
Koshaku-- to the point --- Whoga-- grace. HF-9706;
Headfirst",
}
@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;
http://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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://doi.ieeecomputersociety.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 = "http://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,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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)",
bibdate = "Tue Mar 25 14:26:59 MST 1997",
bibsource = "http://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",
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)",
bibdate = "Tue Apr 12 07:50:09 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://doi.acm.org/10.1145/355958.355960",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
MRclass = "68B99 (65G99 68C05)",
MRnumber = "82h:68041",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://doi.acm.org/10.1145/355958.355960",
acknowledgement = ack-nhfb,
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)",
bibdate = "Fri Nov 09 19:04:04 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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)",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
Parallel/Multi.bib",
acknowledgement = ack-nhfb,
}
@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);
http://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",
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "Univ of Ariz, Tucson, USA",
classification = "723",
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",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://ieeexplore.ieee.org/;
http://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,
}
@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 = "http://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 = "http://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 = "http://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)",
bibdate = "Sat Jan 29 17:56:34 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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;
http://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;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://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",
}
@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 = "http://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 = "http://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 = "http://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 = "http://doi.ieeecomputersociety.org/10.1049/el:19800468",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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",
}
@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;
http://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",
ISSN = "0164-1239",
bibdate = "Fri Nov 1 15:29:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://www.computer.org/annals/an1981/;
http://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,
catcode = "K; K.2; K.2; K.2",
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",
reviewer = "D. Ross",
subject = "K. Computing Milieux; K.2 HISTORY OF COMPUTING",
}
@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 = "http://doi.acm.org/10.1145/355934.355940",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
MRclass = "65D20 (65G05)",
MRnumber = "83a:65017",
bibdate = "Mon Aug 29 22:02:12 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://doi.acm.org/10.1145/355934.355940",
acknowledgement = ack-nhfb,
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "English translation of \cite{Spaniol:1976:AR}.",
acknowledgement = ack-nhfb,
}
@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)",
bibdate = "Thu Sep 1 10:14:17 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://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;",
}
@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",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
bibdate = "Sun May 2 09:21:54 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
acknowledgement = ack-nj,
}
@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 = "http://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",
MRclass = "65G05 (65F10)",
MRnumber = "84j:65039",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://doi.ieeecomputersociety.org/10.1109/CDC.1981.269326",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://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 = "http://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",
}
@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",
ISSN = "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);
http://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",
genterm = "DESIGN",
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 = "http://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",
}
@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 = "http://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 = "http://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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://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",
}
@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 = "http://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 = "http://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 = "http://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 = "http://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;
http://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;
http://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 = "http://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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675869",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = may,
year = "1982",
CODEN = "IEMIDZ",
DOI = "http://dx.doi.org/10.1109/MM.1982.290970",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = nov,
year = "1982",
CODEN = "IEMIDZ",
DOI = "http://dx.doi.org/10.1109/MM.1982.291010",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
bibdate = "Thu Dec 14 06:08:58 MST 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
Science Citation Index database (1980--2000)",
acknowledgement = ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Arnold:1982:EPS,
author = "Mark G. 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 = "http://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 = "http://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 = "http://doi.ieeecomputersociety.org/10.1049/el:19820632",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://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",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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{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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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",
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{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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://dx.doi.org/10.1007/3-540-11603-6_1",
bibdate = "Fri Sep 23 23:12:32 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://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);
http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://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 = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://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 = "http://dx.doi.org/10.1007/3-540-11603-6_1",
bibdate = "Sat Sep 24 01:18:12 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C6140D (High level languages)",
corpsource = "Dept. of Computer Sci., Univ. of California, Berkeley,
CA, USA",
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 = "http://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 = "http://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 = "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);
http://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",
}
@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)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://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",
genterm = "algorithms",
guideno = "09324",
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)",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://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",
genterm = "algorithms",
guideno = "09325",
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 = "http://doi.acm.org/10.1145/357162.357168",
ISSN = "0164-0925 (print), 1558-4593 (electronic)",
bibdate = "Thu Nov 8 14:50:28 2007",
bibsource = "Compiler/bevan.bib;
http://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",
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 = "http://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 = "http://doi.acm.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;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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;
http://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",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675945",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://doi.ieeecomputersociety.org/10.1049/el:19820632",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://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 = "http://doi.ieeecomputersociety.org/10.1049/el:19820632",
ISSN = "0013-5194",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4246948",
acknowledgement = ack-nhfb,
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);
http://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 = "http://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 = "http://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",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://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",
genterm = "DESIGN; LANGUAGES",
guideno = "08785",
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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-COMP-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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
xxmonth = "(none)",
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675887",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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;
http://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 = "http://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",
pages = "343--356",
month = aug,
year = "1982",
bibdate = "Wed Oct 13 21:52:01 2010",
bibsource = "http://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,
bookpages = "xiv + 606",
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 = "http://doi.ieeecomputersociety.org/10.1049/el:19820632",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Rump:1982:CR,
author = "S. 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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/",
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 = "Dept. of Computer Sci., Monash Univ., Clayton, Vic.,
Australia",
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;
http://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 = "http://doi.acm.org/10.1145/356004.356007",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://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",
genterm = "ALGORITHMS; PERFORMANCE",
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;
http://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;
http://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)",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
keywords = "algorithms",
subject = "G Mathematics of Computing, MISCELLANEOUS \\ J.2
Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Chemistry",
}
@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, Dept. of Electrical
Engineering and Computer Sciences",
address = "Berkeley, CA, USA",
pages = "various",
year = "1982",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676000",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676085",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://doi.ieeecomputersociety.org/10.1109/CDC.1981.269326",
ISSN = "0018-9286",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://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,
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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676036",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = nov,
year = "1982",
CODEN = "IEMIDZ",
DOI = "http://dx.doi.org/10.1109/MM.1982.290929",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
bibdate = "Thu Dec 14 06:08:58 MST 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
Science Citation Index database (1980--2000)",
acknowledgement = ack-nhfb,
}
@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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@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",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
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 = "http://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.",
}
@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 = "http://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. Dept. of Engineering",
address = "Boston, MA, USA",
pages = "iii + 102",
year = "1982",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://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 = "http://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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676232",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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{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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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)",
bibdate = "Mon Jan 22 06:22:06 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm26.html#AsaiC83;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer architecture.; Floating-point arithmetic.;
Microprogramming.; VAX-11 (Computer) --- Programming.",
}
@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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676312",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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;
http://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 = "http://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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676273",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://ieeexplore.ieee.org/;
http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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)",
bibdate = "Mon Jan 22 06:31:47 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm26.html#CloutierF83;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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 = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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)",
bibdate = "Tue Apr 12 07:50:11 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Dadda:1983:SSF,
author = "L. 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 = "http://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,
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 = "http://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 = "http://dx.doi.org/10.1109/TIM.1983.4315069",
ISSN = "0018-9456",
bibdate = "Tue Jan 08 22:43:51 2008",
bibsource = "http://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",
}
@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",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:28:04 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/0010465583900048",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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)",
bibdate = "Tue Mar 25 14:26:59 MST 1997",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Moler:1983:RSR} and generalization
\cite{Jamieson:1989:RCI}.",
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",
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676261",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676341",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676227",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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;
http://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 = "http://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 = "http://dx.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 = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
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 = dec,
year = "1983",
CODEN = "IEMIDZ",
DOI = "http://dx.doi.org/10.1109/MM.1983.291185",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
bibdate = "Thu Dec 14 06:08:58 MST 2000",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://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",
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://dx.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 = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://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; 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;
http://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 = "http://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",
pages = "12--26",
year = "1983",
bibdate = "Fri May 03 12:02:15 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/MathSand.pdf",
acknowledgement = ack-nhfb,
bookpages = "vi + 344",
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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676241",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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;
http://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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://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,
}
@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 = "http://dx.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);
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
catcode = "G.1.0",
CRclass = "G.1.0 General; G.1.0 Error analysis",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis",
fjournal = "IEEE Transactions on Computers",
genterm = "ALGORITHMS; PERFORMANCE",
guideno = "06575",
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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://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 = "http://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{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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "English translation in \cite{Mikov:1983:PAFb}.",
acknowledgement = ack-nhfb,
}
@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",
year = "1983",
CODEN = "CYBNAW",
ISSN = "0011-4235",
MRclass = "60K99 (65G05)",
MRnumber = "85h:60154",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Translated from \cite{Mikov:1983:PAFa}.",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.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 = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://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)",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Dubrulle:1983:CNM} and generalization
\cite{Jamieson:1989:RCI}.",
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 = "Dept. of Computer Sci., Univ. of New Mexico,
Albuquerque, NM, USA",
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",
}
@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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676150",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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",
bibdate = "Fri Dec 08 13:05:28 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676244",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676246",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://doi.acm.org/10.1145/1057605.1057606",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://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,
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 = "http://doi.acm.org/10.1145/1057600.1057602",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://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,
keywords = "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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676203",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/",
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",
keywords = "binary; computer; fixed-point number; integer;
iterative methods; PASCAL; Pascal implementation;
square root; subroutines; successive subtraction",
treatment = "P Practical",
}
@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 = "http://dx.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 = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
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 = "http://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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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);
http://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;
http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://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 = "http://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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://doi.ieeecomputersociety.org/10.1049/el:19820632",
ISSN = "0098-4094",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23540",
acknowledgement = ack-nhfb,
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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676263",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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 = "http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676282",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://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 = "http://dx.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);
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
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",
fjournal = "IEEE Transactions on Computers",
guideno = "06565",
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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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",
}
@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;
http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://doi.ieeecomputersociety.org/10.1109/TC.1984.1676355",
ISSN = "0098-4094",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23552",
acknowledgement = ack-nhfb,
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);
http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://ieeexplore.ieee.org/;
http://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 = "http://doi.acm.org/10.1145/2701.356101",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
bibdate = "Sun Sep 04 20:32:29 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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 = "Dept. of Appl. Maths., Twente Univ. of Technol.,
Enschede, Netherlands",
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;
http://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-REV,
volume = "26",
number = "3",
pages = "351--366",
month = jul,
year = "1984",
bibdate = "Thu Sep 1 10:15:30 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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;
http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://ieeexplore.ieee.org/;
http://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) 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;
http://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 = "http://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 = "http://dx.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.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.tandf.co.uk/journals/routledge/02664763.html",
acknowledgement = ack-nhfb,
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",
ISSN = "0004-5411",
MRclass = "65G05",
MRnumber = "819 141",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "rounding error, computer arithmetic",
}
@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 = aug,
year = "1984",
CODEN = "IEMIDZ",
DOI = "http://dx.doi.org/10.1109/MM.1984.291224",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
bibdate = "Thu Nov 8 14:50:28 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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;
http://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 = "http://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",
}
@TechReport{Corporation:1984:ISR,
author = "{IBM Corporation}",
title = "{IBM System\slash 370 RPQ}. High Accuracy Arithmetic",
type = "Technical report",
number = "SA 22-7093-0",
institution = pub-IBM,
address = pub-IBM:adr,
year = "1984",
bibdate = "Wed Oct 04 09:39:49 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "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.",
}
@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;
http://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",
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 $\pm10^9$.
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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
corpsource = "Div. of Comput. Sci., California Univ., Berkeley, CA,
USA",
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",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:58 MST 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.sciencedirect.com/science/journal/00104655",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584829811",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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;
http://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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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.",
}
@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 = "http://dx.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 = "http://ieeexplore.ieee.org/;
http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://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,
fjournal = "IEEE Transactions on Computers",
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 May 18 14:24:11 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "McGraw-Hill series in computer organization and
architecture",
acknowledgement = ack-nhfb,
}
@Book{Hamacher:1984:COE,
author = "V. C. Hamacher and Zvonko G. Vranesic and Safwat G.
Zaky",
title = "Computer organization",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
edition = "Second",
pages = "590",
year = "1984",
ISBN = "0-07-025683-7",
ISBN-13 = "978-0-07-025683-5",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://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",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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 = "http://doi.acm.org/10.1145/356068.356076",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
MRclass = "65G05 (65G10)",
MRnumber = "86e:65063",
bibdate = "Sun Sep 04 20:02:26 1994",
bibsource = "http://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,
}
@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 = "http://dx.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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://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",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
http://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",
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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009346",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://ieeexplore.ieee.org/;
http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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;
http://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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://dx.doi.org/10.1109/JSSC.1984.1052151",
ISSN = "0018-9200",
bibdate = "Thu Jul 07 10:57:50 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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)",
MRclass = "65G99 (03B70 03C70 68Q40)",
MRnumber = "85k:65040",
MRreviewer = "R. P. Brent",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Dept. of Math., Pennsylvania State Univ., University
Park, PA, USA",
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 = "http://doi.ieeecomputersociety.org/10.1109/TC.1984.1676355",
ISSN = "0098-4094",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23556",
acknowledgement = ack-nhfb,
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Murray:1984:SFA,
author = "J. T. Murray",
title = "Sin/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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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 = "http://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{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 = "http://doi.ieeecomputersociety.org/10.1109/TC.1984.1676355",
ISSN = "0018-9286",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://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,
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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",
LCCN = "QA 76.5 B98",
bibdate = "Thu Nov 8 14:50:29 2007",
bibsource = "/usr/local/src/bib/bibliography/Ai/log.prog.85.bib;
http://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,
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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@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;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@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 = "http://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;
http://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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676480",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009343",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://dx.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 = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009311",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
}
@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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://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,
}
@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 = "http://ieeexplore.ieee.org/;
http://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 = "http://doi.ieeecomputersociety.org/10.1109/TC.1983.1676240",
ISSN = "0098-4094",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23555",
acknowledgement = ack-