%%% -*-BibTeX-*-
%%% ====================================================================
%%% BibTeX-file{
%%% author-1 = "Norbert Juffa",
%%% author-2 = "Nelson H. F. Beebe",
%%% version = "3.290",
%%% date = "27 November 2011",
%%% time = "10:10:30 MST",
%%% 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 = "33118 125465 575171 5515069",
%%% 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 3.290, 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 ( 21)
%%% 1845 ( 0) 1904 ( 0) 1963 ( 20)
%%% 1846 ( 0) 1905 ( 0) 1964 ( 27)
%%% 1847 ( 0) 1906 ( 0) 1965 ( 48)
%%% 1848 ( 0) 1907 ( 0) 1966 ( 30)
%%% 1849 ( 0) 1908 ( 0) 1967 ( 34)
%%% 1850 ( 0) 1909 ( 1) 1968 ( 26)
%%% 1851 ( 0) 1910 ( 1) 1969 ( 41)
%%% 1852 ( 0) 1911 ( 0) 1970 ( 46)
%%% 1853 ( 0) 1912 ( 0) 1971 ( 42)
%%% 1854 ( 0) 1913 ( 0) 1972 ( 45)
%%% 1855 ( 0) 1914 ( 0) 1973 ( 65)
%%% 1856 ( 0) 1915 ( 1) 1974 ( 35)
%%% 1857 ( 0) 1916 ( 0) 1975 ( 81)
%%% 1858 ( 0) 1917 ( 0) 1976 ( 43)
%%% 1859 ( 0) 1918 ( 0) 1977 ( 58)
%%% 1860 ( 0) 1919 ( 0) 1978 ( 93)
%%% 1861 ( 0) 1920 ( 0) 1979 ( 62)
%%% 1862 ( 0) 1921 ( 0) 1980 ( 94)
%%% 1863 ( 0) 1922 ( 0) 1981 ( 118)
%%% 1864 ( 0) 1923 ( 0) 1982 ( 74)
%%% 1865 ( 0) 1924 ( 1) 1983 ( 126)
%%% 1866 ( 0) 1925 ( 1) 1984 ( 91)
%%% 1867 ( 0) 1926 ( 0) 1985 ( 139)
%%% 1868 ( 0) 1927 ( 0) 1986 ( 93)
%%% 1869 ( 0) 1928 ( 0) 1987 ( 127)
%%% 1870 ( 0) 1929 ( 0) 1988 ( 143)
%%% 1871 ( 0) 1930 ( 2) 1989 ( 180)
%%% 1872 ( 0) 1931 ( 0) 1990 ( 141)
%%% 1873 ( 0) 1932 ( 1) 1991 ( 217)
%%% 1874 ( 0) 1933 ( 1) 1992 ( 171)
%%% 1875 ( 0) 1934 ( 1) 1993 ( 186)
%%% 1876 ( 0) 1935 ( 0) 1994 ( 175)
%%% 1877 ( 0) 1936 ( 2) 1995 ( 156)
%%% 1878 ( 0) 1937 ( 2) 1996 ( 166)
%%% 1879 ( 0) 1938 ( 4) 1997 ( 125)
%%% 1880 ( 0) 1939 ( 0) 1998 ( 121)
%%% 1881 ( 1) 1940 ( 3) 1999 ( 181)
%%% 1882 ( 0) 1941 ( 1) 2000 ( 138)
%%% 1883 ( 0) 1942 ( 2) 2001 ( 202)
%%% 1884 ( 0) 1943 ( 1) 2002 ( 148)
%%% 1885 ( 0) 1944 ( 1) 2003 ( 138)
%%% 1886 ( 0) 1945 ( 2) 2004 ( 163)
%%% 1887 ( 0) 1946 ( 5) 2005 ( 158)
%%% 1888 ( 0) 1947 ( 4) 2006 ( 110)
%%% 1889 ( 0) 1948 ( 4) 2007 ( 127)
%%% 1890 ( 0) 1949 ( 2) 2008 ( 58)
%%% 1891 ( 0) 1950 ( 3) 2009 ( 99)
%%% 1892 ( 0) 1951 ( 5) 2010 ( 64)
%%% 1893 ( 0) 1952 ( 4) 2011 ( 103)
%%% 1894 ( 0) 1953 ( 1)
%%% 1895 ( 0) 1954 ( 7)
%%% 19xx ( 2)
%%% 20xx ( 1)
%%%
%%% Article: 2439
%%% Book: 286
%%% InBook: 1
%%% InCollection: 54
%%% InProceedings: 1482
%%% Manual: 63
%%% MastersThesis: 143
%%% Misc: 136
%%% Periodical: 3
%%% PhdThesis: 69
%%% Proceedings: 351
%%% TechReport: 293
%%% Unpublished: 9
%%%
%%% Total entries: 5329
%%%
%%% 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-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-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"}
@String{j-IEE-PROC-COMPUT-DIGIT-TECH = "IEE Proceedings. Computers and Digital
Techniques"}
@String{j-IEE-PROC-E = "IEE proceedings, E: Computers and digital
techniques"}
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@String{j-IEEE-MICRO = "IEEE Micro"}
@String{j-IEEE-POT = "IEEE Potentials"}
@String{j-IEEE-J-SEL-AREAS-COMMUN = "IEEE Journal on Selected Areas in
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@String{j-IEEE-SIGNAL-PROCESS-LETT = "IEEE signal processing letters"}
@String{j-IEEE-SPECTRUM = "IEEE Spectrum"}
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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-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-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-IJSA = "The International Journal of Supercomputer
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@String{j-INFO-PROC-LETT = "Information Processing Letters"}
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@String{j-J-ACM = "Journal of the Association for Computing
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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"}
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@String{j-INFO-PROC-LETT = "Information Processing Letters"}
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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"}
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%%% ====================================================================
%%% Publishers and their addresses:
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Mathematics"}
@String{pub-SIAM:adr = "Philadelphia, PA, USA"}
@String{pub-SIEMENS = "Siemens Aktiengesellschaft"}
@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."}
@String{pub-SYNGRESS = "Syngress Publishing, Inc."}
@String{pub-SYNGRESS:adr = "Rockland, MA, USA"}
@String{pub-TEUBNER = "B. G. Teubner"}
@String{pub-TEUBNER:adr = "Stuttgart, Germany"}
@String{pub-TEWI = "te-wi"}
@String{pub-TEWI:adr = "M{\"u}nchen, Germany"}
@String{pub-USENIX = "USENIX"}
@String{pub-USENIX-EL-CERRITO:adr = "P.O. Box 7, El Cerrito 94530, CA,
USA"}
@String{pub-USENIX:adr = "San Francisco, CA, USA"}
@String{pub-VEB-VERLAG-TECHNIK = "VEB Verlag Technik"}
@String{pub-VEB-VERLAG-TECHNIK:adr = "Berlin, Germany"}
@String{pub-VIKING = "Viking"}
@String{pub-VIKING:adr = "New York, NY, USA"}
@String{pub-WCB = "William C. Brown Company Publishers"}
@String{pub-WCB:adr = "Dubuque, IA, USA"}
@String{pub-WEITEK = "Weitek Corporation"}
@String{pub-WEITEK:adr = "1060 E. Arques Ave., Sunnyvale, CA
94086-BRM-9759, USA"}
@String{pub-WESTERN-PERIODICALS = "Western Periodicals Co.,"}
@String{pub-WESTERN-PERIODICALS:adr = "North Hollywood, CA"}
@String{pub-WILEY = "Wiley"}
@String{pub-WILEY:adr = "New York, NY, USA"}
@String{pub-WILEY-INTERSCIENCE = "Wiley-In{\-}ter{\-}sci{\-}ence"}
@String{pub-WILEY-INTERSCIENCE:adr = "New York, NY, USA"}
@String{pub-WORLD-SCI = "World Scientific Publishing
Co. Pte. Ltd."}
@String{pub-WORLD-SCI:adr = "P. O. Box 128, Farrer Road,
Singapore 9128"}
%%% ====================================================================
%%% Series abbreviations:
@String{ser-LNCS = "Lecture Notes in Computer Science"}
@String{ser-LNM = "Lecture Notes in Mathematics"}
@String{ser-PROJECT-GUTENBERG = "Project Gutenberg"}
@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",
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",
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 = "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",
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",
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",
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 = "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",
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 = "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 = "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 = "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",
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 = "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",
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",
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 = "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",
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",
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",
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",
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://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",
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",
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",
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",
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",
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",
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 = "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",
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",
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",
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",
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",
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",
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 = "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",
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",
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",
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",
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 = "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",
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",
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",
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",
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",
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 = "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",
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",
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",
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",
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",
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",
MRclass = "65.0X",
MRnumber = "MR0041539 (12,861b)",
MRreviewer = "F. J. Murray",
bibdate = "Thu Nov 8 14:49:46 2007",
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",
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",
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/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",
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",
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",
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",
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/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",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "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/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/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",
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",
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 = "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",
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",
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",
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",
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/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/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 = "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/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",
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",
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",
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/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",
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",
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",
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",
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/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/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",
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/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",
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",
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",
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/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",
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",
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",
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",
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",
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/",
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",
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",
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",
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/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",
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/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/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",
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",
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/",
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",
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",
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/",
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 = "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",
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/",
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/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/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/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",
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",
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",
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/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",
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/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/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/",
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/",
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://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",
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",
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://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",
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/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/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",
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",
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",
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;
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 = "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 = "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; 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",
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",
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",
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",
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",
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",
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",
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",
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",
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",
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",
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/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/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",
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",
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/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",
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",
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",
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",
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",
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/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",
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/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/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",
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",
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",
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",
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/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; 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",
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",
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 = "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",
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/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",
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 = "library.ox.ac.uk:210/ADVANCE",
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 = "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/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",
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{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",
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/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 = "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",
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",
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",
bibdate = "Thu Jul 14 09:11:51 MDT 2011",
bibsource = "http://www.computer.org/tc/;
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",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip",
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",
acknowledgement = ack-mfc # " and " # ack-nhfb,
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",
acknowledgement = ack-mfc # " and " # ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@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",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip",
acknowledgement = ack-nj,
}
@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 = "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",
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; 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",
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",
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",
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",
acknowledgement = ack-nj,
xxmonth = "(none)",
xxnumber = "(none)",
}
@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 = "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",
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",
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",
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",
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",
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{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/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",
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/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 = "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/",
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://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",
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",
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",
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 = "??",
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",
note = "Previously unpublished memorandum. Reprinted in
\cite[\S 5.1]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@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",
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",
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/",
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",
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/",
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",
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",
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/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",
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",
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",
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",
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 = "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",
}
@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 = "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",
acknowledgement = ack-nhfb,
}
@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 = "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 = "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",
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/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/",
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",
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",
acknowledgement = ack-nj,
}
@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",
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",
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/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",
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",
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",
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",
acknowledgement = ack-nhfb,
keywords = "ARI FLP",
}
@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",
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/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",
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/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",
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",
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",
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/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{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",
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",
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; 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",
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",
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",
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",
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",
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",
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",
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",
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",
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",
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}.",
}
@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",
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",
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",
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;
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/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",
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",
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",
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",
acknowledgement = ack-nj,
}
@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",
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 = "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{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",
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/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",
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",
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",
acknowledgement = ack-nhfb,
}
@Article{Brooker:1966:MFA,
author = "R. A. Brooker and J. S. Rohl and S. R. Clark",
title = "The main features of {Atlas Autocode}",
journal = j-COMP-J,
volume = "8",
number = "4",
pages = "303--310",
month = jan,
year = "1966",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:56:10 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/",
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",
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",
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://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",
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",
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",
acknowledgement = ack-nhfb,
remark = "Probably November or December issue; missing from
amermathmonthly1960.bib.",
}
@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/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",
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",
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",
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",
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",
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 = "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",
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",
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",
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 = "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",
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",
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",
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",
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 = "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",
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",
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",
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",
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/",
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",
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",
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",
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",
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",
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",
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",
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/",
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/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",
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",
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",
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/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{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",
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",
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",
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",
acknowledgement = ack-nhfb,
}
@Article{Howell:1967:MPA,
author = "K. M. Howell",
title = "Multiple precision arithmetic techniques",
journal = j-COMP-J,
volume = "9",
number = "4",
pages = "383--387",
month = feb,
year = "1967",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:56:19 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/",
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{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",
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",
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 = "JSTOR database",
acknowledgement = ack-nhfb,
}
@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",
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/; 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/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",
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",
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",
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",
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",
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/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 = "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",
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",
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",
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",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Apr 2 08:38:35 1998",
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",
acknowledgement = ack-nhfb,
}
@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",
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",
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",
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",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
ZMnumber = "0184.37503",
}
@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",
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",
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",
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",
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",
bibdate = "Fri Apr 21 07:26:39 2000",
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",
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",
acknowledgement = ack-nhfb,
classmath = "*65H05 (Single nonlinear equations (numerical
methods)) 65F05 (Direct methods for linear systems)",
ZMnumber = "0207.15804",
}
@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",
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",
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",
acknowledgement = ack-nj,
xxmonth = "(none)",
xxnumber = "(none)",
}
@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",
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/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",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 28 19:09:15 2003",
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",
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",
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",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
{Fortran} (Computer program language)",
remark = "Cited in \cite{Sterbenz:1974:FPC}, but given year
1969.",
}
@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 = "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",
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",
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",
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/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",
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",
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",
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",
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",
acknowledgement = ack-nhfb,
keywords = "Algorithms.; Arithmetic --- Foundations.; FLOP
(Computer program language).; Transformations
(Mathematics).",
}
@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",
acknowledgement = ack-nhfb,
}
@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/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",
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 = "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://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",
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",
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",
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",
acknowledgement = ack-nhfb,
keywords = "Computer storage devices.; Hybrid 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",
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",
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 = "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",
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/",
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",
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",
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",
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",
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",
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",
URL = "http://links.jstor.org/sici?sici=0025-5718%28196907%2923%3A107%3C679%3ASROI2T%3E2.0.CO%3B2-C",
acknowledgement = ack-nhfb,
}
@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; 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",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jun 24 20:44:42 2005",
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",
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",
bibdate = "Thu Feb 15 15:23:23 2007",
a