%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author-1 = "Norbert Juffa", %%% author-2 = "Nelson H. F. Beebe", %%% version = "3.323", %%% date = "21 April 2012", %%% time = "08:19:59 MDT", %%% filename = "fparith.bib", %%% address-1 = "2445 Mission College Blvd., %%% Santa Clara, CA 95054, %%% USA", %%% address-2 = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone-1 = "+1 408 727 1885", %%% telephone-2 = "+1 801 581 5254", %%% FAX-1 = "+1 408 727 1265", %%% FAX-2 = "+1 801 581 4148", %%% URL-2 = "http://www.math.utah.edu/~beebe", %%% checksum = "45834 137728 611580 6171097", %%% email-1 = "norbert at iit.com (Internet)", %%% email-2 = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "bibliography, BibTeX, floating-point %%% arithmetic", %%% license = "public domain", %%% supported = "yes", %%% docstring = "[From Norbert Juffa:] This is a bibliography %%% of material on floating-point arithmetic %%% that I came up with while doing research on %%% a floating-point package of his own. I %%% don't claim it to be anywhere near %%% complete. The material listed is only what %%% I myself possess. %%% %%% My main interest was in software based, %%% binary floating-point arithmetic on a %%% microprocessor, so you won't find much %%% material about the hardware used in %%% floating-point arithmetic (e.g., adders, %%% carry propagation schemes, higher radix %%% representation for multiplication and %%% division, etc.) in this list. There is also %%% not too much on non-binary floating-point %%% arithmetic. %%% %%% For most fields covered in this %%% bibliography, the important or historically %%% relevant articles should be included. There %%% is also some material on integer arithmetic %%% in this list as some of the methods used %%% with integer arithmetic contain interesting %%% ideas that may be useful in the realization %%% of a floating-point arithmetic package. %%% %%% Also, depending on the type of %%% microprocessor used, one may need to %%% implement integer multiplication and %%% division for use in the floating-point %%% package, so articles about this topic are %%% included as well. %%% %%% As I am German, there is a bit of material %%% in German in this bibliography. However, %%% English translations are provided for all %%% non-English titles. %%% %%% Thanks to the people who have helped me with %%% previous versions of this document by sending %%% me papers or additional references: Steven %%% Sommars (sesv at research.bell-labs.com), Jim %%% Kiernan (jmk at teak.cray.com), Warren %%% Ferguson (ferguson at seas.smu.edu), Nhuan %%% Doduc (ndoduc at framentec.fr), K. C. Ng %%% (kwok.ng at eng.sun.com). %%% %%% [From Nelson H. F. Beebe:] I took Norbert %%% Juffa's unmarked-up bibliography data, %%% converted it to BibTeX form, and then more %%% than doubled the size of the bibliography %%% by supplying additional entries on %%% floating-point arithmetic extracted from %%% my own extensive bibliography collections, %%% and from several online journal databases, %%% including the Compendex, OCLC, IEEE INSPEC, %%% MathSciNet, and UnCover databases. In August %%% 2010, access to an electronic copy of the %%% bibliography of Sterbenz's 1974 book allowed %%% further checks to make sure that all of his %%% references to early work are included here. %%% %%% The computation of sums of floating-point %%% numbers is a fundamental step in most %%% numerical computations. The special phrase %%% ``accurate floating-point summation'' appears %%% in the keywords values of publications that %%% address this important problem. %%% %%% The Web site %%% %%% http://www.acsel-lab.com/arithmetic/ %%% %%% archives papers from the IEEE conferences %%% on computer arithmetic (ARITH-1, ARITH-2, %%% ...). Keyword values for those papers %%% contain ARITH-n to more easily identify them. %%% %%% In \cite[p. 94]{Buchholz:1962:PCS}, S. G. %%% Campbell remarks: %%% %%% ``To avoid difficulties of limited range %%% and scaling in fixed-point arithmetic, %%% G. R. Stibitz in the early 1940's %%% proposed an automatic scaling procedure, %%% called {\emph floating-point arithmetic}, %%% which was incorporated in the Bell %%% Telephone Laboratories' Model V Relay %%% Computer. A similar procedure was %%% developed, apparently independently, for %%% the Harvard Mark II computer. Automatic %%% scaling was a controversial subject for %%% quite a few years. Many opposed it on the %%% basis that the programmer could not be %%% relieved of the responsibility of knowing %%% the size of his numbers and that %%% programmed scaling would give him better %%% control over significance. Nevertheless, %%% as early as 1950, users began to %%% incorporate automatic scaling on %%% fixed-point computers by means of %%% subroutines, first on the %%% plugboard-controlled CPC (Card Programmed %%% Calculator) and later on stored-program %%% machines. Then, after it had thus proved %%% its usefulness, floating-point arithmetic %%% was provided as a built-in feature, %%% starting with the IBM 704 and NORC %%% computers, and this gave an enormous %%% increase in speed over the %%% subroutines. Today floating-point %%% operation is available, at least as an %%% option, on all computers intended to be %%% used full- or part-time on substantial %%% scientific computing applications. In %%% view of the almost universal use of %%% floating-point arithmetic, it is %%% remarkable that there is very little %%% literature on the subject.'' %%% %%% We now know that Leonardo Torres y Quevedo %%% first suggested floating-point arithmetic on %%% paper in 1914 in Spain %%% \cite{TorresyQuevedo:1982:EAD}. Konrad Zuse %%% reinvented it independently in Germany in the %%% early 1936, and had it operational in the Z3, %%% an electromechanical computer, in 1941 %%% \cite{Zuse:1970:CML,Ceruzzi:1981:ECK, %%% Randell:1982:ODC,Schwarz:1981:EYC, %%% Zuse:1982:MAE,Zuse:1982:OCD,Zuse:1984:CML, %%% Zuse:1993:CML,Smiley:2010:MWI}. Zuse's work %%% remained unknown in the USA until about 1948. %%% F. L. Bauer's foreword to Zuse's %%% autobiography \cite{Zuse:1993:CML} suggests a %%% bust of Zuse engraved %%% %%% ``Creator of the first fully automated, %%% program-controlled and freely %%% programmable computer using binary %%% floating-point calculation. It was %%% operational in 1941.'' %%% %%% The experience with floating-point arithmetic %%% by George Stibitz on the Bell Labs Model V %%% General Purpose Relay Calculator (1945, but %%% floating-point arithmetic proposed in 1940 %%% Stibitz memo) \cite{Alt:1948:BTLa}, by %%% Howard Aiken on the Harvard Mark II (1947), %%% and by Gerald Alway and Jim Wilkinson on the %%% Pilot ACE in Britain (1946--1948) %%% \cite{Wilkinson:1975:PAA}, encouraged the %%% provision of floating-point arithmetic in the %%% American and British commercialization of %%% scientific computers in the 1950s. However, %%% Zuse's use of Infinity and Indefinite %%% predated by more than 15 years the Infinity %%% of the IBM 7030 Stretch (1956--1958, with %%% first customer delivery, to Los Alamos %%% Laboratory, in April 1961), and the Infinity %%% and Indefinite of the CDC 6400/6600/7600 %%% (1960--1963, with first customer delivery, to %%% Lawrence Livermore Laboratory, in September %%% 1964) %%% \cite{Thornton:1970:DCC,Thornton:1980:CP}. I %%% [NHFB] have so far been unable to find any %%% definitive published statement about whether %%% Zuse's ideas were known to, and inspired, the %%% CDC and IBM architects, or whether they %%% rediscovered them independently. %%% %%% It is our hope that this bibliography will %%% help to remedy the deficiency noted in the %%% last sentence of Campbell's remark, even %%% though the first edition of this bibliography %%% in 1994 appeared 32 years after the wonderful %%% book about IBM's Project Stretch, and it took %%% 48 years for that book to be included here. %%% %%% At version 3.323, the year coverage looked %%% like this: %%% %%% 1837 ( 1) 1896 ( 0) 1955 ( 7) %%% 1838 ( 0) 1897 ( 1) 1956 ( 8) %%% 1839 ( 0) 1898 ( 0) 1957 ( 11) %%% 1840 ( 0) 1899 ( 0) 1958 ( 16) %%% 1841 ( 0) 1900 ( 0) 1959 ( 23) %%% 1842 ( 0) 1901 ( 0) 1960 ( 19) %%% 1843 ( 0) 1902 ( 0) 1961 ( 27) %%% 1844 ( 0) 1903 ( 0) 1962 ( 26) %%% 1845 ( 0) 1904 ( 0) 1963 ( 23) %%% 1846 ( 0) 1905 ( 0) 1964 ( 31) %%% 1847 ( 0) 1906 ( 0) 1965 ( 53) %%% 1848 ( 0) 1907 ( 0) 1966 ( 32) %%% 1849 ( 0) 1908 ( 0) 1967 ( 40) %%% 1850 ( 0) 1909 ( 1) 1968 ( 31) %%% 1851 ( 0) 1910 ( 1) 1969 ( 46) %%% 1852 ( 0) 1911 ( 0) 1970 ( 53) %%% 1853 ( 0) 1912 ( 0) 1971 ( 51) %%% 1854 ( 0) 1913 ( 0) 1972 ( 53) %%% 1855 ( 0) 1914 ( 0) 1973 ( 75) %%% 1856 ( 0) 1915 ( 1) 1974 ( 45) %%% 1857 ( 0) 1916 ( 0) 1975 ( 93) %%% 1858 ( 0) 1917 ( 0) 1976 ( 50) %%% 1859 ( 0) 1918 ( 0) 1977 ( 69) %%% 1860 ( 0) 1919 ( 0) 1978 ( 97) %%% 1861 ( 0) 1920 ( 0) 1979 ( 67) %%% 1862 ( 0) 1921 ( 0) 1980 ( 102) %%% 1863 ( 0) 1922 ( 0) 1981 ( 119) %%% 1864 ( 0) 1923 ( 0) 1982 ( 78) %%% 1865 ( 0) 1924 ( 1) 1983 ( 141) %%% 1866 ( 0) 1925 ( 1) 1984 ( 98) %%% 1867 ( 0) 1926 ( 0) 1985 ( 146) %%% 1868 ( 0) 1927 ( 0) 1986 ( 96) %%% 1869 ( 0) 1928 ( 0) 1987 ( 134) %%% 1870 ( 0) 1929 ( 0) 1988 ( 150) %%% 1871 ( 0) 1930 ( 2) 1989 ( 186) %%% 1872 ( 0) 1931 ( 0) 1990 ( 145) %%% 1873 ( 0) 1932 ( 1) 1991 ( 218) %%% 1874 ( 0) 1933 ( 1) 1992 ( 174) %%% 1875 ( 0) 1934 ( 1) 1993 ( 188) %%% 1876 ( 0) 1935 ( 0) 1994 ( 173) %%% 1877 ( 0) 1936 ( 2) 1995 ( 157) %%% 1878 ( 0) 1937 ( 2) 1996 ( 170) %%% 1879 ( 0) 1938 ( 4) 1997 ( 128) %%% 1880 ( 0) 1939 ( 0) 1998 ( 126) %%% 1881 ( 1) 1940 ( 3) 1999 ( 182) %%% 1882 ( 0) 1941 ( 1) 2000 ( 140) %%% 1883 ( 0) 1942 ( 2) 2001 ( 204) %%% 1884 ( 0) 1943 ( 1) 2002 ( 153) %%% 1885 ( 0) 1944 ( 1) 2003 ( 143) %%% 1886 ( 0) 1945 ( 2) 2004 ( 165) %%% 1887 ( 0) 1946 ( 5) 2005 ( 162) %%% 1888 ( 0) 1947 ( 4) 2006 ( 118) %%% 1889 ( 0) 1948 ( 4) 2007 ( 128) %%% 1890 ( 0) 1949 ( 2) 2008 ( 64) %%% 1891 ( 0) 1950 ( 3) 2009 ( 104) %%% 1892 ( 0) 1951 ( 5) 2010 ( 66) %%% 1893 ( 0) 1952 ( 4) 2011 ( 121) %%% 1894 ( 0) 1953 ( 1) 2012 ( 18) %%% 1895 ( 0) 1954 ( 7) %%% 19xx ( 2) %%% 20xx ( 1) %%% %%% Article: 2713 %%% Book: 288 %%% InBook: 1 %%% InCollection: 55 %%% InProceedings: 1484 %%% Manual: 63 %%% MastersThesis: 143 %%% Misc: 137 %%% Periodical: 3 %%% PhdThesis: 69 %%% Proceedings: 353 %%% TechReport: 294 %%% Unpublished: 9 %%% %%% Total entries: 5612 %%% %%% This bibliography is sorted by year, and %%% within each year, by author and title key, %%% with ``bibsort -byyear''. Cross-referenced %%% proceedings entries appear at the end, %%% because of a restriction in the current %%% BibTeX. %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ==================================================================== %%% A delimited macro \toenglish ... \endtoenglish is NECESSARY here. %%% The more conventional undelimited form \toenglish{...} has braces %%% that prevent BibTeX's downcasing operation, and the alternate form %%% {\toenglish{...}} is considered a `special character' by BibTeX, %%% and all of {...} gets downcased. We avoid the name \english to %%% prevent conflicts with language options in packages like Babel. %%% %%% To suppress output of English translations of non-English titles, %%% use %%% "\def \toenglish #1\endtoenglish{\unskip}" %%% instead. @Preamble{ "\def \toenglish #1\endtoenglish{[{\em English:} #1\unskip]} " # "\ifx \undefined \circled \def \circled #1{(#1)}\fi" # "\ifx \undefined \mathbb \def \mathbb #1{{\bf #1}}\fi" # "\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}}\fi" # "\ifx \undefined \mathrm \def \mathrm #1{{\rm #1}}\fi" # "\ifx \undefined \operatorname \def \operatorname #1{{\rm #1}}\fi" # "\ifx \undefined \reg \def \reg {\circled{R}}\fi" # "\ifx \undefined \texttt \def \texttt #1{{\tt #1}}\fi" # "\ifx \undefined \TM \def \TM {${}^{\sc TM}$} \fi" # "\hyphenation{ Cor-dic COR-DIC Gleit-komma Gleit-komma-zahl-en Gleit-komma-pro-zess-or Gleit-komma-for-mat Mikro-rech-en-tech-nik Mikro-rech-ner-sys-tem-en Mikro-rech-ner Mi-yo-shi Quad-rat-wurz-eln Semi-nu-mer-i-cal Swartz-lan-der }" } %%% ==================================================================== %%% Acknowledgement abbreviations: @String{ack-jg = "Joe Grcar, email: \path=jfgrcar@lbl.gov="} @String{ack-jh = "John Harrison, email: \path=johnh@ichips.intel.com="} @String{ack-jr = "Jon Rokne, Department of Computer Science, The University of Calgary, 2500 University Drive N.W., Calgary, Alberta T2N 1N4, Canada"} @String{ack-kr = "Karin Remington, National Institute of Standards and Technology, Building 820, Room 365, Gaithersburg, MD 20899, USA, Tel: +1 301 975-5119, FAX: +1 301 990-4127, e-mail: \path|karin@cam.nist.gov|"} @String{ack-mfc = "Michael F. Cowlishaw, IBM UK (MP5), PO Box 31, Birmingham Road, Warwick, CV34 5JL, UK, e-mail: \path|mfc@uk.ibm.com|, URL: \path|http://www2.hursley.ibm.com/decimal|"} @String{ack-nhfb = "Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, FAX: +1 801 581 4148, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org| (Internet), URL: \path|http://www.math.utah.edu/~beebe/|"} @String{ack-nj = "Norbert Juffa, 2445 Mission College Blvd. Santa Clara, CA 95054 USA email: \path=norbert@iit.com="} @String{ack-pb = "Preston Briggs, Tera Computer Company, 2815 Eastlake East, Seattle, WA 98102, USA, Tel: +1 206 325-0800, e-mail: \path|preston@tera.com|"} @String{ack-rfb = "Ronald F. Boisvert, Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA, Tel: +1 301 975 3812, e-mail: \path=boisvert@cam.nist.gov="} @String{ack-sfo = "Stuart F. Oberman, e-mail: \path=stuart.oberman@amd.com="} %%% ==================================================================== %%% Institute abbreviations: @String{inst-ANL = "Argonne National Laboratory"} @String{inst-ANL:adr = "9700 South Cass Avenue, Argonne, IL 60439-4801, USA"} @String{inst-BERKELEY = "University of California"} @String{inst-BERKELEY:adr = "Berkeley, CA, USA"} @String{inst-BERKELEY-CPAM = "Center for Pure and Applied Mathematics, University of California"} @String{inst-BERKELEY-CPAM:adr = "Berkeley, CA, USA"} @String{inst-BERKELEY-CS = "Department of Computer Science, University of California"} @String{inst-BERKELEY-CS:adr = "Berkeley, CA, USA"} @String{inst-BERKELEY-EECS = "Department of Electrical Engineering and Computer Science, University of California, Berkeley"} @String{inst-BERKELEY-EECS:adr = "Berkeley, CA, USA"} @String{inst-CS-PURDUE = "Department of Computer Science, Purdue University"} @String{inst-CS-PURDUE:adr = "West Lafayette, IN 47907-2107, USA"} @String{inst-CSC = "Center for Scientific Computing, Department of Mathematics, University of Utah"} @String{inst-CSC:adr = "Salt Lake City, UT 84112, USA"} @String{inst-HP = "Hewlett--Packard Corporation"} @String{inst-HP:adr = "Palo Alto, CA, USA"} @String{inst-INST-ADV-STUDY = "Institute for Advanced Study"} @String{inst-INST-ADV-STUDY:adr = "Princeton, NJ, USA"} @String{inst-INTEL = "Intel Corporation"} @String{inst-INTEL:adr = "Santa Clara, CA, USA"} @String{inst-LASL = "Los Alamos Scientific Laboratory"} @String{inst-LASL:adr = "Los Alamos, NM, USA"} @String{inst-LORIA-INRIA-LORRAINE = "LORIA/INRIA Lorraine"} @String{inst-LORIA-INRIA-LORRAINE:adr = "B{\^a}timent A, Technop{\^o}le de Nancy-Brabois, 615 rue du jardin botanique, F-54602 Villers-l{\`e}s-Nancy Cedex, France"} @String{inst-NLRC = "NASA Langley Research Center"} @String{inst-NLRC:adr = "Hampton, VA, USA"} @String{inst-MATHWORKS = "The MathWorks, Inc."} @String{inst-MATHWORKS:adr = "3 Apple Hill Drive, Natick, MA 01760-2098, USA"} @String{inst-MRC-WISCONSIN = "Mathematics Research Center, University of Wisconsin, Madison"} @String{inst-MRC-WISCONSIN:adr = "Madison, WI, USA"} @String{inst-UT-CS = "Department of Computer Science, University of Tennessee, Knoxville"} @String{inst-UT-CS:adr = "Knoxville, TN 37996, USA"} %%% ==================================================================== %%% Journal abbreviations: @String{j-ACTA-INFO = "Acta Informatica"} @String{j-ACTA-NUMERICA = "Acta Numerica"} @String{j-ACM-COMM-COMP-ALGEBRA = "ACM Communications in Computer Algebra"} @String{j-ADA-LETT = "Ada Letters"} @String{j-ADV-SOFT-SCI-TECH = "Advances in software science and technology"} @String{j-ALGORITHMICA = "Algorithmica"} @String{j-AM-J-MATH = "American Journal of Mathematics"} @String{j-AM-SCI = "American Scientist"} @String{j-AMER-MATH-MONTHLY = "American Mathematical Monthly"} @String{j-AMER-STAT = "The American Statistician"} @String{j-ANN-HIST-COMPUT = "Annals of the History of Computing"} @String{j-ANN-MATH-STAT = "Annals of Mathematical Statistics"} @String{j-APL-QUOTE-QUAD = "ACM SIGAPL APL Quote Quad"} @String{j-APPL-ALGEBRA-ENG-COMMUN-COMPUT = "Applicable algebra in engineering, communication and computing"} @String{j-APPL-MATH-COMP = "Applied Mathematics and Computation"} @String{j-APP-MATH-LETT = "Applied Mathematics Letters"} @String{j-APPL-NUM-MATH = "Applied Numerical Mathematics"} @String{j-APPL-OPTICS = "Applied Optics"} @String{j-APPL-STAT = "Applied Statistics"} @String{j-ARCH-HIST-EXACT-SCI = "Archive for History of Exact Sciences"} @String{j-ASTRON-J = "Astronomical Journal"} @String{j-AUSTRALIAN-COMP-J = "Australian Computer Journal"} @String{j-AUTO-CTL-COMP-SCI = "Automatic Control and Computer Sciences"} @String{j-AUTOMATION-REMOTE-CTL = "Automation and Remote Control"} @String{j-BELL-LABS-RECORD = "Bell Laboratories Record"} @String{j-BELL-SYST-TECH-J = "The Bell System Technical Journal"} @String{j-BIT = "BIT (Nordisk tidskrift for informationsbehandling)"} @String{j-BIT-NUM-MATH = "BIT Numerical Mathematics"} @String{j-BRITISH-J-HIST-SCI = "British Journal for the History of Science"} @String{j-BULL-AMS = "Bulletin of the American Mathematical Society"} @String{j-BYTE = "Byte Magazine"} @String{j-C-R-ACAD-BULGARE-SCI = "Comptes rendus de l'Acad{\'e}mie bulgare des sciences"} @String{j-C-R-ACAD-SCI-PARIS-SER-I-MATH = "Comptes Rendus des S{\'e}ances de l'Acad{\'e}mie des Sciences. S{\'e}rie I. Math{\'e}matique"} @String{j-CACM = "Communications of the Association for Computing Machinery"} @String{j-CAD = "Computer Aided Design"} @String{j-CCCUJ = "C/C++ Users Journal"} @String{j-CCPE = "Concurrency and Computation: Prac\-tice and Experience"} @String{j-COED = "CoED"} @String{j-COMBIN-PROBAB-COMPUT = "Combinatorics, Probability and Computing"} @String{j-COMM-STAT-THEORY-METH = "Communications in Statistics. Theory and Methods"} @String{j-COMP-ARCH-NEWS = "ACM SIGARCH Computer Architecture News"} @String{j-COMP-DESIGN = "Computer Design"} @String{j-COMP-EDU-J = "Computers in education journal"} @String{j-COMP-GEOSCI = "Computers and Geosciences"} @String{j-COMP-J = "The Computer Journal"} @String{j-COMP-LANG-MAG = "Computer Language Magazine"} @String{j-COMP-MATH-APPL = "Computers and Mathematics with Applications"} @String{j-COMP-PHYS-COMM = "Computer Physics Communications"} @String{j-COMP-SURV = "ACM Computing Surveys"} @String{j-COMPUT-AIDED-ENG = "Computer-aided engineering: CAE"} @String{j-COMPUT-ELECTR-ENG = "Computers and Electrical Engineering"} @String{j-COMPUT-SCI-ENG = "Computing in Science and Engineering"} @String{j-COMPUTE = "Compute"} @String{j-COMPUTER = "Computer"} @String{j-COMPUTING = "Computing: Archiv fur informatik und numerik"} @String{j-COMPUTING-SUPPLEMENTUM = "Computing. Supplementum"} @String{j-CONG-NUM = "Congressus Numerantium"} @String{j-CONTEMP-PHYS = "Contemporary physics"} @String{j-CPE = "Concurrency: Prac\-tice and Experience"} @String{j-CRYPTOLOGIA = "Cryptologia"} @String{j-CT = "c't"} @String{j-CUJ = "C Users Journal"} @String{j-CYBER = "Cybernetics"} @String{j-DDJ = "Dr. Dobb's Journal of Software Tools"} @String{j-DEC-TECH-J = "Digital Technical Journal"} @String{j-DESIGNS-CODES-CRYPTOGR = "Designs, Codes, and Cryptography"} @String{j-DISCRETE-COMPUT-GEOM = "Discrete and Computational Geometry"} @String{j-DOKL-AKAD-NAUK = "Doklady Akademii nauk SSSR"} @String{j-EDN = "EDN"} @String{j-ELECT-COMM-JAPAN-3-FUND-ELECT-SCI = "Electronics and communications in Japan. Part 3, Fundamental electronic science"} @String{j-ELECT-LETTERS = "Electronics Letters"} @String{j-ELECT-NOTES-THEOR-COMP-SCI = "Electronic Notes in Theoretical Computer Science"} @String{j-ELECTRON-COMMUN-JPN = "Electronics and communications in Japan"} @String{j-ELECTRON-TRANS-NUMER-ANAL = "Electronic Transactions on Numerical Analysis"} @String{j-ELECTRONIC-DESIGN = "Electronic Design"} @String{j-ELECTRONIC-ENG-TIMES = "Electronic engineering times"} @String{j-ELECTRONICS = "Electronics"} @String{j-ELECTRONIK = "Elektronik"} @String{j-ELEK-RECHENANLAGEN = "Elektronische Rechenanlagen"} @String{j-ELEKTRONIKER = "Elektroniker (Switzerland)"} @String{j-EMBED-SYS-PROG = "Embedded Systems Programming"} @String{j-EURASIP-J-EMBED-SYS = "EURASIP Journal on Embedded Systems"} @String{j-FIB-QUART = "Fibonacci Quarterly"} @String{j-FORM-METHODS-SYST-DES = "Formal Methods in System Design"} @String{j-FORTH-DIMENSIONS = "Forth Dimensions"} @String{j-FORTRAN-FORUM = "ACM Fortran Forum"} @String{j-FUT-GEN-COMP-SYS = "Future Generation Computer Systems"} @String{j-GAMM-MIT = "Mitteilungen der Gesellschaft f{\\\"u}r Angewandte Mathematik und Mechanik"} @String{j-HIGH-PERFORM-SYST = "High performance systems"} @String{j-HEWLETT-PACKARD-J = "Hewlett--Packard Journal"} @String{j-IBM-JRD = "IBM Journal of Research and Development"} @String{j-IBM-SYS-J = "IBM Systems Journal"} @String{j-IBM-TDB = "IBM Technical Disclosure Bulletin"} @String{j-IEE-PROC-COMPUT-DIGIT-TECH = "IEE Proceedings. 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A. 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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", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Manuscript held by Museum of the History of Science, Oxford, UK. Reprinted in \cite[\S 2.1]{Randell:1982:ODC}.", acknowledgement = ack-nhfb, } @Article{Newcomb:1881:NFU, author = "Simon Newcomb", title = "Note on the frequency of use of the different digits in natural numbers", journal = j-AM-J-MATH, volume = "4", number = "1/4", pages = "39--40", year = "1881", CODEN = "AJMAAN", ISSN = "0002-9327 (print), 1080-6377 (electronic)", ISSN-L = "0002-9327", bibdate = "Thu Feb 15 16:35:24 2007", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "http://links.jstor.org/sici?sici=0002-9327%281881%294%3A1%2F4%3C39%3ANOTFOU%3E2.0.CO%3B2-K", abstract = "That the ten digits do not occur with equal frequency must be evident to any one making much use of logarithmic tables, and noticing how much faster the first pages wear out than the last ones. The first significant figure is oftener 1 than any other digit, and the frequency diminishes up to 9.", acknowledgement = ack-nhfb, keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", remark = "From p. 40: ``The law of probability of the occurrence of numbers is such that all mantissas of their logarithms are equally probable.''", } @Article{Aley:1897:DES, author = "Robert J. Aley", title = "A Device for Extracting the Square Root of Certain Surd Quantities", journal = j-AMER-MATH-MONTHLY, volume = "4", number = "8/9", pages = "204--208", month = aug # "\slash " # sep, year = "1897", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:37:08 MDT 1999", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database", acknowledgement = ack-nhfb, } @Article{Ludgate:1909:PAM, author = "P. E. Ludgate", title = "On a proposed analytical machine", journal = j-SCI-PROC-ROY-DUBLIN-SOC, volume = "12", number = "9", pages = "77--91", year = "1909", bibdate = "Wed Oct 13 11:14:08 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Reprinted in \cite[\S 2.4]{Randell:1982:ODC}.", acknowledgement = ack-nhfb, fjournal = "Scientific proceedings of the Royal Dublin Society", } @Article{Babbage:1910:BBA, author = "H. P. Babbage", title = "{Babbage}: {Babbage}'s analytical engine", journal = j-MONTHLY-NOT-ROY-ASTRON-SOC, volume = "70", number = "??", pages = "517--526, 645", year = "1910", CODEN = "MNRAA4", ISSN = "0035-8711", bibdate = "Wed Oct 13 11:12:08 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Reprinted in \cite[\S 2.3]{Randell:1982:ODC}.", acknowledgement = ack-nhfb, fjournal = "Monthly Notices of the Royal Astronomical Society", } @Article{TorresyQuevedo:1915:EAS, author = "L. {Torres y Quevedo}", title = "Essais sur l'automatique. Sa definition. {\'E}tendue th{\'e}orique de ses applications ({French}) [{Essays} on automation. {Its} definition. {Theoretical} extent of its applications]", journal = j-REV-GEN-SCI-PURES-APPL, volume = "??", number = "??", pages = "601--611", day = "15", month = nov, year = "1915", ISSN = "0370-7431", bibdate = "Wed Oct 13 11:15:08 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Reprinted in \cite[\S 2.5]{Randell:1982:ODC}. Translated by Mr. R. Basu.", acknowledgement = ack-nhfb, language = "French", } @Article{Barrow:1924:QDD, author = "D. F. Barrow", title = "Questions and Discussions: Discussions: On Taking Square Roots of Integers", journal = j-AMER-MATH-MONTHLY, volume = "31", number = "10", pages = "482--484", month = dec, year = "1924", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:37:29 MDT 1999", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database", acknowledgement = ack-nhfb, } @Book{Karpinski:1925:HA, author = "Louis Charles Karpinski", title = "The History of Arithmetic", publisher = "Rand McNally \& Company", address = "New York, NY, USA", pages = "xi + 200", year = "1925", bibdate = "Fri Nov 28 18:09:05 2003", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-mfc # " and " # ack-nhfb, } @Article{J:1930:RPRb, author = "R. A. J.", title = "Recent Publications: Reviews: {{\em Standard Table of Square Roots}}, by {L. M. Milne-Thomson}", journal = j-AMER-MATH-MONTHLY, volume = "37", number = "6", pages = "314--314", month = jun # "\slash " # jul, year = "1930", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:35:55 MDT 1999", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database", acknowledgement = ack-nhfb, } @Article{Laughlin:1930:LND, author = "Harry H. Laughlin", title = "Large-Number Division by Calculating Machine", journal = j-AMER-MATH-MONTHLY, volume = "37", number = "6", pages = "287--293", month = jun # "\slash " # jul, year = "1930", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:35:55 MDT 1999", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database", acknowledgement = ack-nhfb, } @Article{Garver:1932:QDNb, author = "Raymond Garver", title = "Questions, Discussions, and Notes: {A} Square Root Method and Continued Fractions", journal = j-AMER-MATH-MONTHLY, volume = "39", number = "9", pages = "533--535", month = nov, year = "1932", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:36:47 MDT 1999", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database", acknowledgement = ack-nhfb, } @Book{Couffignal:1933:MCL, author = "L. Couffignal", title = "Les machines {\`a} calculer, leurs principes, leur {\'e}volution. ({French}) [{Calculating} machines, their principles, their evolution]", publisher = "Gauthier-Villars", address = "Paris, France", year = "1933", bibdate = "Wed Oct 13 11:19:11 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Extracts reprinted in \cite[\S 3.2]{Randell:1982:ODC}. Translated by Mr. R. Basu.", acknowledgement = ack-nhfb, language = "French", } @Article{Kalbfell:1934:QDN, author = "D. C. Kalbfell", title = "Questions, Discussions and Notes: On a Method for Calculating Square Roots", journal = j-AMER-MATH-MONTHLY, volume = "41", number = "8", pages = "504--506", month = oct, year = "1934", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:37:31 MDT 1999", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database", acknowledgement = ack-nhfb, } @Article{Phillips:1936:BC, author = "E. W. Phillips", title = "Binary calculation", journal = j-J-INST-ACTUARIES, volume = "67", number = "??", pages = "187--221", year = "1936", ISSN = "0020-2681", bibdate = "Wed Oct 13 11:33:16 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Reprinted in \cite[\S 7.1]{Randell:1982:ODC}.", acknowledgement = ack-nhfb, fjournal = "Journal of the Institute of Actuaries", } @Misc{Zuse:1936:VSD, author = "K. Zuse", title = "{Verfahren zur selbstt{\"a}tigen Durchfuhrung von Rechnungen mit Hilfe von Rechenmaschinen}. ({German}) [{Procedure} for automatic execution of calculations by calculating machines]", howpublished = "German patent application Z23624.", day = "11", month = apr, year = "1936", bibdate = "Wed Oct 13 11:22:03 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Reprinted in \cite[\S 4.1]{Randell:1982:ODC}.", acknowledgement = ack-nhfb, } @Article{Escott:1937:QDN, author = "E. B. Escott", title = "Questions, Discussions, and Notes: Rapid Method for Extracting a Square Root", journal = j-AMER-MATH-MONTHLY, volume = "44", number = "10", pages = "644--646", month = dec, year = "1937", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:38:44 MDT 1999", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database", acknowledgement = ack-nhfb, } @MastersThesis{Shannon:1937:SAR, author = "Claude Elwood Shannon", title = "A Symbolic Analysis of Relay and Switching Circuits", type = "{Master of Science}", school = "Department of Electrical Engineering, MIT", address = "Cambridge, MA, USA", pages = "72", day = "10", month = aug, year = "1937", bibdate = "Thu Nov 18 10:35:20 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Not submitted until 1940", URL = "http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425.pdf", acknowledgement = ack-nhfb, author-dates = "April 30, 1916--February 24, 2001", remark = "Smiley \cite[p. 91]{Smiley:2010:MWI} claims: ``He [Shannon] also had the insight, like Atanasoff, that the binary arithmetic that relay switches represented would simplify information systems. His master's thesis, written when he as twenty-one and published when he was twenty-two, is considered to be one of the most important, if not the most important, master's thesis of the twentieth century.''\par Pages 59--61 of the thesis are a section called ``Electric Adder to the Base Two'', and pages 62--68, ``A Factor Table Machine'', describe a machine that will print a table of factors and primes of all the integers from 1 to 100,000,000. Shannon notes on page 68: ``As to the practicality of such a device, it might be said that J. P. Kulik spent 20 years in constructing a table of primes up to 100,000,000 and when finished it was found to contain so many errors that it was not worth publishing. The machine described here could probably be made to handle 5 numbers per second so that the table would require only about 2 months to construct.''", } @Article{Benford:1938:LAN, author = "Frank Benford", title = "The Law of Anomalous Numbers", journal = j-PROC-AMER-PHIL-SOC, volume = "78", number = "4", pages = "551--572", month = mar, year = "1938", CODEN = "PAPCAA", ISSN = "0003-049X", bibdate = "Thu Feb 15 16:28:28 2007", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "http://links.jstor.org/sici?sici=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-G", abstract = "It has been observed that the first pages of a table of common logarithms show more wear than do the last pages, indicating that more used numbers begin with the digit 1 than with the digit 9. A compilation of some 20,000 first digits taken from widely divergent sources shows that there is a logarithmic distribution of first digits when the numbers are composed of four or more digits. An analysis of the numbers from different sources shows that the numbers taken from unrelated subjects, such as a group of newspaper items, show a much better agreement with a logarithmic distribution than do numbers from mathematical tabulations or other formal data. There is here the peculiar fact that numbers that individually are without relationship are, when considered in large groups, in good agreement with a distribution law---hence the name ``Anomalous Numbers.''\par A further analysis of the data shows a strong tendency for bodies of numerical data to fall into geometric series. If the series is made up of numbers containing three or more digits the first digits form a logarithmic series. If the numbers contain only single digits the geometric relation still holds but the simple logarithmic relation no longer applies.\par An equation is given showing the frequencies of first digits in the different orders of numbers 1 to 10, 10 to 100, etc.\par The equation also gives the frequency of digits in the second, third + place of a multi-digit number, and it is shown that the same law applies to reciprocals.\par There are many instances showing that the geometric series, or the logarithmic law, has long been recognized as a common phenomenon in factual literature and in the ordinary affairs of life. The wire gauge and drill gauge of the mechanic, the magnitude scale of the astronomer and the sensory response curves of the psychologist are all particular examples of a relationship that seems to extend to all human affairs. The Law of Anomalous Numbers is thus a general probability law of widespread application.", acknowledgement = ack-nhfb, keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", remark = "From \cite{Logan:1978:FDP}: ``Benford's paper was published in 1938 in a journal of rather limited circulation and not usually read by mathematicians. It so happened that it was immediately followed in the same issue by a physics paper which became of some importance for secret nuclear work during World War II [H. A. Bethe, M. E. Rose, and L. P. Smith, `The Multiple Scattering of Electrons', Proc. Amer. Phil. Soc. 78(4), 573--585 (1938)]. That is why Benford's paper caught the attention of physicists in the early 1940's and was much discussed. This led to the notes in Nature by Goudsmit and Furry [3] and Furry and Hurwitz [4] containing an effort to explain Benford's law. We considered it at that time merely a welcome diversion and did not expect that over thirty papers would be devoted to this subject in subsequent years.'' The 2006 bibliography \cite{Hurlimann:2006:BLB} cites 325 publications about Benford's Law.", } @PhdThesis{Couffignal:1938:AMA, author = "L. Couffignal", title = "Sur l'analyse m{\'e}canique. Application aux machines {\`a} calculer et aux calculs de la m{\'e}canique c{\'e}leste. ({French}) [{On} mechanical analysis. Application to calculating machines and to calculation in celestial mechanics]", publisher = "Gauthier-Villars", school = "Facult{\'e} des Sciences de Paris", address = "Paris, France", year = "1938", bibdate = "Wed Oct 13 11:17:22 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Extracts reprinted in \cite[\S 2.7]{Randell:1982:ODC}. Translated by Mr. R. Basu.", acknowledgement = ack-nhfb, language = "French", } @Book{Hardy:1938:ITN, author = "G. H. (Godfrey Harold) Hardy and E. M. (Edward Maitland) Wright", title = "An Introduction to the Theory of Numbers", publisher = pub-OXFORD, address = pub-OXFORD:adr, pages = "xvi + 403", year = "1938", LCCN = "QA241 .H28", bibdate = "Fri Nov 30 06:49:15 2007", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nhfb, } @Article{Shannon:1938:SAR, author = "Claude E. Shannon", title = "A Symbolic Analysis of Relay and Switching Circuits", journal = "Transactions of the {AIEE}", volume = "57", number = "??", pages = "713--723", month = dec, year = "1938", bibdate = "Sat Nov 20 08:54:12 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www2.research.att.com/~njas/doc/shannonbio.html", acknowledgement = ack-nhfb, remark = "This is Shannon's first published paper (his Master's thesis). In 1940, it received the Alfred Noble Prize of the combined engineering societies of the United States, an award given each year to a person not over thirty for a paper published in one of the journals of the participating societies. H. H. Goldstine \cite{Goldstine:1972:CPN} called this work ``one of the most important master's theses ever written ... a landmark in that it helped to change digital circuit design from an art to a science.''", } @TechReport{Atanasoff:1940:CMS, author = "J. V. Atanasoff", title = "Computing machine for the solution of large systems of linear algebraic equations", type = "Unpublished memorandum", institution = "Iowa State College", address = "Ames, IA, USA", month = aug, year = "1940", bibdate = "Wed Oct 13 11:36:11 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Reprinted in \cite[\S 7.2]{Randell:1982:ODC}.", acknowledgement = ack-nhfb, } @Misc{Bush:1940:AM, author = "V. Bush", title = "Arithmetical Machine", howpublished = "Vannevar Bush Papers, Container 18, Folder: Caldwell, Samuel, 1939--1940", year = "1940", bibdate = "Wed Oct 13 11:37:32 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Reprinted in \cite[\S 7.3]{Randell:1982:ODC}. Copyright interest in the unpublished writings of Vannevar Bush has been dedicated to the public.", acknowledgement = ack-nhfb, } @TechReport{Stibitz:1940:C, author = "G. R. Stibitz", title = "Computer", type = "Unpublished memorandum", institution = "Bell Telephone Laboratories", address = "New York, NY, USA", year = "1940", bibdate = "Wed Oct 13 11:30:38 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Reprinted in \cite[\S 6.1]{Randell:1982:ODC}.", acknowledgement = ack-nhfb, } @MastersThesis{Berry:1941:DED, author = "Clifford Edward Berry", title = "Design of electrical data recording and reading mechanism", type = "{M.S.} thesis", school = "Iowa State College", address = "Ames, IA, USA", pages = "32", year = "1941", bibdate = "Thu Nov 18 11:18:18 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nhfb, author-dates = "1918--1963", historical-note = "From http://www.lib.iastate.edu/arch/rgrp/5-2-1-1.html: ``John Vincent Atanasoff received his M.S. (1926) in Mathematics from Iowa State College (University) and received his Ph.D. (1930) in Theoretical Physics from the University of Wisconsin-Madison. He returned to Iowa State in 1930 as Assistant Professor in mathematics and physics and was promoted to Associate Professor (1936). Atanasoff began developing concepts for an electronic computing machine in 1937. It was shortly thereafter that he, along with graduate student Clifford Berry, started work on the world's first electronic digital computer. The computer would later be named the Atanasoff-Berry Computer (ABC). Work on the machine stopped at the start of World War II in 1941 and the ABC was never patented. Atanasoff and Berry were both called to support the war effort and left Iowa State. By the end of the decade, the ABC was removed from the basement of Physics Hall and dismantled. Atanasoff and the ABC were part of a major court case between Honeywell, Inc. and Sperry Rand Corporation which occurred 1967-1973. The case involved the ENIAC patent which covered basic ownership rights to the design of electronic digital computers. During the trial, the judge concluded that the invention of the ENIAC was derived from the work of John Vincent Atanasoff at Iowa State University. A replica of the Atanasoff-Berry Computer was completed and unveiled to the public in 1996. The ABC replica was constructed by a team of Iowa State scientists at the Ames Laboratory and was exhibited at museums throughout the country over the next several years.''", remark = "This thesis may be one of the earliest surviving records of the ABC computer built by John Atanasoff and Clifford Berry in the late 1930s. The one-of-a-kind ABC was destroyed in 1948, and most of its parts were lost. Also cited in ``Charles W. Bradley Collection on the ENIAC Trial, 1930--1966'', (found in http://discover.lib.umn.edu/): CWB as an attorney for the group retained by Honeywell in the Honeywell v. Sperry Rand ENIAC trial. The ABC had a 50-bit word.", } @TechReport{Mauchly:1942:UHS, author = "J. W. Mauchly", title = "The use of high speed vacuum tube devices for calculating", type = "Privately circulated memorandum", institution = "Moore School of Electrical Engineering, University of Pennsylvania", address = "Philadelphia, PA, USA", month = aug, year = "1942", bibdate = "Wed Oct 13 11:52:54 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Reprinted in \cite[\S 7.6]{Randell:1982:ODC}.", acknowledgement = ack-nhfb, } @TechReport{Rajchman:1942:REP, author = "J. A. Rajchman and G. A. Morton and A. W. Vance", title = "Report on Electronic Predictors for Anti-Aircraft Fire Control", institution = "Research Laboratories, R. C. A. Manufacturing Company, Inc.", address = "Camden, NJ, USA", month = apr, year = "1942", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Reprinted in \cite[\S 7.4]{Randell:1982:ODC}.", acknowledgement = ack-nhfb, } @Article{Crawford:1943:DNS, author = "W. S. H. Crawford", title = "Discussions and Notes: Square Roots from a Table of Cosines", journal = j-AMER-MATH-MONTHLY, volume = "50", number = "3", pages = "190--191", month = mar, year = "1943", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:36:57 MDT 1999", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database", acknowledgement = ack-nhfb, } @Article{Goudsmit:1944:SFN, author = "S. A. Goudsmit and W. H. Furry", title = "Significant Figures of Numbers in Statistical Tables", journal = j-NATURE, volume = "154", number = "3921", pages = "800--801", day = "23", month = dec, year = "1944", CODEN = "NATUAS", DOI = "http://dx.doi.org/10.1038/154800a0", ISSN = "0028-0836 (print), 1476-4687 (electronic)", bibdate = "Sun Sep 18 11:57:19 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf", abstract = "A rough qualitative explanation of this fact can easily be given. If we consider tables in which the entries become rarer the larger they are, we can draw the obvious conclusion that in any interval, say, between 10 and 99, or 10,000 and 99,999, there are more entries on the small side than on the large side.", acknowledgement = ack-nhfb, keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", } @Article{Furry:1945:DND, author = "W. H. Furry and Henry Hurwitz", title = "Distribution of Numbers and Distribution of Significant Figures", journal = j-NATURE, volume = "155", number = "??", pages = "52--53", day = "13", month = jan, year = "1945", CODEN = "NATUAS", DOI = "http://dx.doi.org/10.1038/155052a0", ISSN = "0028-0836 (print), 1476-4687 (electronic)", bibdate = "Sun Sep 18 11:51:37 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf", acknowledgement = ack-nhfb, keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", } @TechReport{vonNeumann:1945:FDR, author = "John von Neumann", title = "First Draft of a Report on the {EDVAC}", institution = "University of Pennsylvania", day = "30", month = jun, year = "1945", bibdate = "Mon Jun 06 19:17:03 2005", bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.", acknowledgement = ack-nhfb, remark = "This is the report that got von Neumann's name associated with the serial, stored-program, general purpose, digital architecture upon which 99.99\% of all computers today are based.", xxnote = "Report prepared for U.S. Army Ordinance Department under Contract W-670-ORD-4926. Reprinted in \cite[pp.~177--246]{Stern:1981:EUA}, \cite[pp.~399--413]{Randell:1982:ODC}, \cite{vonNeumann:1993:FDR}, and \cite{Laplante:1996:GPC}.", } @Article{Aiken:1946:ASC, author = "H. H. Aiken and G. M. Hopper", title = "The {Automatic Sequence Controlled Calculator}", journal = "Electrical Engineering", volume = "65", number = "??", pages = "384--391, 449--454, 522--528", year = "1946", bibdate = "Wed Oct 13 11:26:29 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Reprinted in \cite[\S 5.2]{Randell:1982:ODC}.", acknowledgement = ack-nhfb, } @TechReport{Burks:1946:PDL, author = "Arthur W. Burks and Herman H. Goldstine and John von Neumann", title = "Preliminary discussion of the logical design of an electronic computing instrument", institution = inst-INST-ADV-STUDY, address = inst-INST-ADV-STUDY:adr, pages = "42", day = "28", month = jun, year = "1946", bibdate = "Wed Oct 13 08:17:48 2004", bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.bib; ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib; ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/arith.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Report to the U.S. Army Ordnance Department. Reprinted in \cite[pp.~221--259]{Swartzlander:1976:CDD}, \cite[\S 8.3]{Randell:1982:ODC}, and \cite[pp.~97--146]{Aspray:1987:PJN}", acknowledgement = ack-nhfb, remark = "Discusses floating-point versus fixed-point computation, and concludes that floating-point is probably not justifiable. They wrote:\par ``There appear to be two major purposes in a `floating' decimal point system both of which arise from the fact that the number of digits in a word is a constant fixed by design considerations for each particular machine. The first of these purposes is to retain in a sum or product as many significant digits as possible and the second of these is to free the human operator from the burden of estimating and inserting into a problem `scale factors' --- multiplicative constants which serve to keep numbers within the limits of the machine.\par There is, of course, no denying the fact that human time is consumed in arranging for the introduction of suitable scale factors. We only argue that the time so consumed is a very small percentage of the total time we will spend in preparing an interesting problem for our machine. The first advantage of the floating point is, we feel, somewhat illusory. In order to have such a floating point, one must waste memory capacity which could otherwise be used for carrying more digits per word. It would therefore seem to us not at all clear whether the modest advantages of a floating binary point offset the loss of memory capacity and the increased complexity of the arithmetic and control circuits.''", } @Article{Cesareo:1946:RI, author = "O. Cesareo", title = "The Relay Interpolator", journal = j-BELL-LABS-RECORD, volume = "23", number = "??", pages = "457--460", year = "1946", CODEN = "BLRCAB", ISSN = "0005-8564", bibdate = "Wed Oct 13 11:31:47 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Reprinted in \cite[\S 6.2]{Randell:1982:ODC}.", acknowledgement = ack-nhfb, } @TechReport{Dreyer:1946:REM, author = "H.-J. Dreyer and A. Walther", title = "{Der Rechenautomat Ipm. Entwicklung Mathematischer Instrumente in Deutschland 1939 bis 1945}. ({German}) [{The} {Ipm} Calculator. {The} development of mathematical instruments in {Germany} 1939--1945]", type = "{Bericht}", number = "A3", institution = "Institut f{\"u}r Praktische Mathematik, Technische Hochschule", address = "Darmstadt, West Germany", day = "19", month = aug, year = "1946", bibdate = "Wed Oct 13 11:20:15 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Reprinted in \cite[\S 3.3]{Randell:1982:ODC}. Translated by Mr. and Mrs. P. Jones", acknowledgement = ack-nhfb, language = "German", } @Article{Goldstine:1946:ENI, author = "H. H. Goldstine and Adele Goldstine", title = "The {Electronic Numerical Integrator and Computer (ENIAC)}", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "2", number = "15", pages = "97--110", month = jul, year = "1946", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:44:19 MDT 1998", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database", note = "Reprinted in \cite[\S 7.7]{Randell:1982:ODC}.", acknowledgement = ack-nhfb, } @TechReport{Goldstine:1947:PCP, author = "Herman H. Goldstine and John von Neumann", title = "Planning and coding of problems for an electronic computing instrument", type = "Technical report", number = "1", institution = inst-INST-ADV-STUDY, address = inst-INST-ADV-STUDY:adr, pages = "69", day = "1", month = apr, year = "1947", bibdate = "Wed Jun 01 17:41:33 2005", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Report prepared for U.S. Army Ordnance Department under contract W-36-034-OKD-7481. Reprinted in \cite[80--151]{Taub:1963:JNCa}. Knuth \cite[p.~278]{Knuth:1997:SA} cites pp.~142--151 of this report as the first published treatment of double-precision arithmetic on digital computers.", acknowledgement = ack-nhfb, } @Article{Juley:1947:BC, author = "J. Juley", title = "The Ballistic Computer", journal = j-BELL-LABS-RECORD, volume = "24", number = "??", pages = "5--9", year = "1947", CODEN = "BLRCAB", ISSN = "0005-8564", bibdate = "Wed Oct 13 11:32:38 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Reprinted in \cite[\S 6.3]{Randell:1982:ODC}.", acknowledgement = ack-nhfb, } @InProceedings{Mauchly:1947:PPE, author = "J. W. Mauchly", booktitle = "{Proceedings of a Symposium on Large Scale Digital Calculating Machinery, 7--10 January 1947}", title = "Preparation of problems for {EDVAC}-type machines", publisher = "Harvard University Press", address = "Cambridge, MA, USA", year = "1947", bibdate = "Wed Oct 13 11:55:58 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Reprinted in {\em Annals of the Computation Laboratory of Harvard University}, {\bf 16}, 203--207 (1948). Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.", acknowledgement = ack-nhfb, } @Article{vonNeumann:1947:NIM, author = "John von Neumann and Herman H. Goldstine", title = "Numerical Inverting of Matrices of High Order", journal = j-BULL-AMS, volume = "53", number = "11", pages = "1021--1099", month = nov, year = "1947", CODEN = "BAMOAD", ISSN = "0002-9904", MRclass = "65.0X", MRnumber = "MR0024235 (9,471b)", MRreviewer = "E. Bodewig", bibdate = "Thu Nov 8 14:49:36 2007", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "See \cite{Goldstine:1951:NIM} for Part II. Reprinted in \cite[v.~5, pp.~479--557]{Taub:1961:JNC}.", acknowledgement = ack-nhfb # " and " # ack-jg, kwds = "nla, linear system, rounding error", referred = "[Markov1999a].", remark = "This may be the first journal publication about the use of double-precision arithmetic on computers, used for the accumulation of inner products and matrix products. On pp.~1035--1038, the authors show that when the sum of $m$ products of two $s$-digit numbers is accumulated in precision $2s$, with rounding to $s$ digits only after the final sum is complete, then the rounding error is essentially one unit in the last place, instead of $m$ times that value. Cited in \cite{Sterbenz:1974:FPC}.", ZMnumber = "0031.31402", } @Article{Alt:1948:BTLa, author = "Franz L. Alt", title = "A {Bell Telephone Laboratories}' Computing Machine---{I}", journal = j-MATH-TABLES-OTHER-AIDS-COMPUT, volume = "3", number = "21", pages = "1--13", month = jan, year = "1948", CODEN = "MTTCAS", ISSN = "0891-6837", bibdate = "Tue Oct 13 08:44:19 MDT 1998", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database", note = "Reprinted in \cite[\S 6.4]{Randell:1982:ODC}.", acknowledgement = ack-nhfb, } @Article{Eckert:1948:EC, author = "W. J. Eckert", title = "Electrons and computation", journal = j-SCI-MONTHLY, volume = "67", number = "5", pages = "315--323", month = nov, year = "1948", CODEN = "SCMOAA", ISSN = "0096-3771", bibdate = "Wed Oct 13 11:27:40 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Reprinted in \cite[\S 5.3]{Randell:1982:ODC}.", acknowledgement = ack-nhfb, } @Article{Turing:1948:REM, author = "A. M. Turing", title = "Rounding-Off Errors in Matrix Processes", journal = j-QUART-J-MECH-APPLIED-MATH, volume = "1", pages = "287--308", month = sep, year = "1948", CODEN = "QJMMAV", ISSN = "0033-5614", MRclass = "65.0X", MRnumber = "MR0028100 (10,405c)", MRreviewer = "E. Bodewig", bibdate = "Sat Nov 19 12:09:58 2005", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/a/turing-alan-mathison.bib; http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Reprinted in \cite{Turing:1992:PM} with summary and notes (including corrections)", URL = "http://turing.ecs.soton.ac.uk/browse.php/B/18", acknowledgement = ack-nhfb, mynote = "The notes are not very good. They mainly correct errors and fill in the gaps of derivations. Much better would have been higher level comments from a numerical analyst, e.g. on where Turing's ideas/predictions were wrong.", ZMnumber = "0033.28501", } @Article{Williams:1948:EDC, author = "F. C. Williams and T. Kilburn", title = "Electronic digital computers", journal = j-NATURE, volume = "162", number = "487", pages = "??--??", year = "1948", CODEN = "NATUAS", ISSN = "0028-0836 (print), 1476-4687 (electronic)", bibdate = "Wed Oct 13 12:00:02 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Reprinted in \cite[\S 8.4]{Randell:1982:ODC}.", acknowledgement = ack-nhfb, } @Article{Hartree:1949:NSR, author = "Douglas R. (Douglas Rayner) Hartree", title = "Note On Systematic Roundoff Errors in Numerical Integration", journal = "Journal of Research of the National Bureau of Standards", volume = "42", number = "??", pages = "62--??", month = "????", year = "1949", bibdate = "Wed Feb 14 19:07:37 2007", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nhfb, } @Article{Huskey:1949:PCP, author = "H. D. Huskey", title = "On the Precision of a Certain Procedure of Numerical Integration", journal = j-J-RES-NATL-BUR-STAND, volume = "42", number = "??", pages = "57--62", year = "1949", CODEN = "JRNBAG", ISSN = "0091-0635", bibdate = "Fri Aug 20 09:32:34 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nhfb, remark = "Cited in \cite{Sterbenz:1974:FPC}.", } @Book{Stifler:1950:HSC, editor = "W. W. {Stifler, Jr.}", title = "High-speed computing devices", publisher = pub-MCGRAW-HILL, address = pub-MCGRAW-HILL:adr, pages = "xiii + 451", year = "1950", LCCN = "QA75 .E5", bibdate = "Fri Aug 20 10:18:44 MDT 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, remark = "Supervised by Charles Brown Tompkins and C. H. Wakelin, Engineering Research Associates. The contents of this volume were first assembled in the form of a report to the Office of Naval Research, prepared under a provision of contract N6-ONR-240, Task 1. Cited in \cite{Sterbenz:1974:FPC}.", subject = "computers", } @InProceedings{Wilkes:1950:E, author = "M. V. Wilkes and W. Renwick", booktitle = "{Report of a Conference on High Speed Automatic Calculating Machines, 22--25 June 1949}", title = "The {EDSAC}", publisher = "University Mathematical Laboratory", address = "Cambridge, UK", pages = "9--11", month = jan, year = "1950", bibdate = "Wed Oct 13 12:00:41 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Reprinted in \cite[\S 8.5]{Randell:1982:ODC}.", acknowledgement = ack-nhfb, } @InProceedings{Worsley:1950:ED, author = "B. H. Worsley", booktitle = "Report of a Conference on High Speed Automatic Calculating Machines, {22--25 June 1949}", title = "The {EDSAC} demonstration", publisher = "University Mathematical Laboratory", address = "Cambridge, UK", pages = "12--16", month = jan, year = "1950", bibdate = "Wed Oct 13 11:39:09 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Reprinted in \cite[\S 8.6]{Randell:1982:ODC}.", acknowledgement = ack-nhfb, } @Article{Booth:1951:SBM, author = "A. D. Booth", title = "A signed binary multiplication technique", journal = j-QUART-J-MECH-APPLIED-MATH, volume = "4", number = "2", pages = "236--240", month = "????", year = "1951", CODEN = "QJMMAV", ISSN = "0033-5614", bibdate = "Thu Apr 2 08:38:35 1998", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-sfo # " and " # ack-nhfb, } @InCollection{Brown:1951:HRR, author = "G. W. Brown", title = "History of {RAND}'s random digits", crossref = "Householder:1951:MCM", pages = "31--32", year = "1951", bibdate = "Sun Sep 18 12:02:43 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "http://www.rand.org/pubs/papers/2008/P113.pdf", acknowledgement = ack-nhfb, } @Article{Gill:1951:PSS, author = "S. Gill", title = "A process for the step-by-step integration of differential equations in an automatic digital computing machine", journal = j-PROC-CAMBRIDGE-PHIL-SOC, volume = "47", pages = "96--108", year = "1951", CODEN = "PCPSA4", ISSN = "0008-1981", bibdate = "Tue Aug 28 05:54:12 2001", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nhfb, keywords = "accurate floating-point summation; floating-point arithmetic; rounding errors", remark = "Higham \cite{Higham:1993:AFP} comments ``In 1951 Gill [8] noticed that the rounding error in the sum of two numbers could be estimated by subtracting one of the numbers from the sum, and he made use of this estimate in a Runge--Kutta code in a program library for the EDSAC computer.''", } @Article{Goldstine:1951:NIM, author = "Herman H. Goldstine and John von Neumann", title = "Numerical Inverting of Matrices of High Order. {II}", journal = j-PROC-AM-MATH-SOC, volume = "2", pages = "188--202", year = "1951", CODEN = "PAMYAR", ISSN = "0002-9939 (print), 1088-6826 (electronic)", MRclass = "65.0X", MRnumber = "MR0041539 (12,861b)", MRreviewer = "F. J. Murray", bibdate = "Thu Nov 8 14:49:46 2007", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "See \cite{vonNeumann:1947:NIM} for Part I. Reprinted in \cite[Paper~15, pp.~558--572]{Taub:1963:JNCa}.", URL = "http://www.jstor.org/view/00029939/di970628/97p0185x/0", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", ZMnumber = "043.12301", } @InProceedings{Andrews:1952:RBL, author = "E. G. Andrews", editor = "J. C. McPherson", booktitle = "Proceedings of the AIEE-IRE '51: Papers and discussions presented at the December 10--12, 1951, joint AIEE-IRE computer conference, Philadelphia, PA: Review of electronic digital computers", title = "A review of the {Bell Laboratories}' digital computer developments", publisher = pub-ACM, address = pub-ACM:adr, pages = "101--105", year = "1952", DOI = "http://dx.doi.org/10.1145/1434770.1434787", LCCN = "????", bibdate = "Fri Dec 03 09:17:58 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nhfb, bookpages = "vi + 114", keywords = "Bell Laboratories Model 1--5 relay computers; complex fixed-point decimal arithmetic; complex floating-point decimal arithmetic", } @Article{Davis:1952:ARS, author = "K. Davis and R. Biddulph and S. Balashek", title = "Automatic Recognition of Spoken Digits", journal = j-J-ACOUST-SOC-AM, volume = "24", number = "6", pages = "637--642", month = nov, year = "1952", CODEN = "JASMAN", ISSN = "0001-4966", bibdate = "Fri Nov 28 16:38:51 2003", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-mfc # " and " # ack-nhfb, } @Article{Morrill:1952:SEM, author = "C. D. Morrill and R. V. Baum", title = "A Stabilized Electronic Multiplier", journal = j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT, volume = "EC-1", number = "??", pages = "52--59", month = dec, year = "1952", CODEN = "????", ISSN = "????", bibdate = "Fri Jul 15 15:20:53 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib", acknowledgement = ack-nhfb, fjournal = "Transactions of the I.R.E. Professional Group on Electronic Computers", } @InProceedings{Sheldon:1952:ICP, author = "J. W. Sheldon and L. Tatum", booktitle = "Review of Electronic Digital Computers. Joint {AIEE--IRE} Computer Confer ence. {10--12 December 1951}", title = "The {IBM} card-programmed electronic calculator", publisher = "American Institute of Electrical Engineers", address = "New York, NY, USA", pages = "30--36", year = "1952", bibdate = "Wed Oct 13 11:28:45 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "Reprinted in \cite[\S 5.4]{Randell:1982:ODC}.", acknowledgement = ack-nhfb, } @Book{IBM:1953:POT, author = "{IBM Corporation}", title = "Principles of Operation: Type 701 and Associated Equipment", publisher = pub-IBM, address = pub-IBM:adr, pages = "103", year = "1953", bibdate = "Wed Sep 14 23:17:49 1994", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nhfb, } @Article{Backus:1954:ISS, author = "J. W. Backus", title = "The {IBM 701 Speedcoding} System", journal = j-J-ACM, volume = "1", number = "1", pages = "4--6", month = jan, year = "1954", CODEN = "JACOAH", ISSN = "0004-5411", bibdate = "Fri Nov 04 00:18:27 1994", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "http://community.computerhistory.org/scc/projects/FORTRAN/paper/p4-backus.pdf", abstract = "The IBM 701 Speedcoding System is a set of instructions which causes the 701 to behave like a three-address floating point calculator. Let us call this the Speedcoding calculator. In addition to operating in floating point, this Speedcoding calculator has extremely convenient means for getting information into the machine and for printing results; it has an extensive set of operations to make the job of programming as easy as possible. Speedcoding also provides automatic address modification, flexible tracing, convenient use of auxiliary storage, and built-in checking.", acknowledgement = ack-nhfb, } @Manual{Burroughs:1954:DH, author = "{Burroughs Corporation. ElectroData}", title = "Datatron handbooks", organization = "The Division", address = "Pasadena, CA, USA", year = "1954", bibdate = "Sat Feb 24 15:01:45 MST 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "12 volumes in 1.", acknowledgement = ack-nhfb, keywords = "Datatron (Computer)", remark = "Datatron programming and coding manual --- Datatron operation manual --- Central computer handbook --- Paper tape system handbook --- Card converter Model 500 handbook --- Magnetic tape system handbook --- Cardatron system handbook --- Model 560 DATAFILE handbook --- Control console and consolette handbook --- Floating point control unit handbook --- External switching unit handbook --- Tape preparation unit handbook.", } @Article{Freeman:1954:TSA, author = "H. Freeman and E. Parsons", title = "Time-Sharing Analog Multiplier ({TSAM})", journal = j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT, volume = "EC-3", number = "1", pages = "11--17", month = mar, year = "1954", CODEN = "????", ISSN = "????", bibdate = "Fri Jul 15 15:20:53 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib", acknowledgement = ack-nhfb, fjournal = "Transactions of the I.R.E. Professional Group on Electronic Computers", remark = "Cited in US Patent 3,043,516 (10 July 1962): Time Summing Device for Division, Multiplication, Root Taking and Interpolation, by Harold W. Abbott and Vernon P. Mathis.", } @Article{Gorn:1954:AAC, author = "Saul Gorn", title = "The Automatic Analysis and Control of Computing Errors", journal = j-J-SIAM, volume = "2", number = "2", pages = "69--81", month = jun, year = "1954", CODEN = "JSIMAV", ISSN = "0368-4245 (print), 1095-712X (electronic)", bibdate = "Thu Oct 15 18:16:06 MDT 1998", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database", acknowledgement = ack-nhfb, } @Article{Kovach:1954:AMU, author = "L. D. Kovach and W. Comley", title = "An Analog Multiplier Using Thyrite", journal = j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT, volume = "EC-3", number = "2", pages = "42--45", month = jun, year = "1954", CODEN = "????", ISSN = "????", bibdate = "Sun Jul 17 09:57:13 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib", acknowledgement = ack-nhfb, fjournal = "Transactions of the I.R.E. Professional Group on Electronic Computers", } @Article{Mayer:1954:ODF, author = "M. A. Mayer and B. M. Gordon and R. N. Nicola", title = "An operational digital feedback divider", journal = j-IRE-TRANS-ELEC-COMPUT, volume = "EC-3", number = "1", pages = "17--20", month = mar, year = "1954", CODEN = "IRELAO", ISSN = "0367-9950", bibdate = "Sun Jul 17 09:52:58 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib", acknowledgement = ack-nhfb, fjournal = "IRE Transactions on Electronic Computers", } @Article{Moshman:1954:GPR, author = "Jack Moshman", title = "The Generation of Pseudo-Random Numbers on a Decimal Calculator", journal = j-J-ACM, volume = "1", number = "2", pages = "88--91", month = apr, year = "1954", CODEN = "JACOAH", ISSN = "0004-5411", bibdate = "Fri Nov 04 00:18:27 1994", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nhfb, keywords = "decimal floating-point arithmetic", } @Article{Crockett:1955:GMM, author = "J. B. Crockett and H. Chernoff", title = "Gradient Methods of Maximization", journal = j-PAC-J-MATH, volume = "5", number = "??", pages = "33--50", year = "1955", CODEN = "PJMAAI", ISSN = "0030-8730", bibdate = "Fri Aug 20 08:54:24 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nhfb, remark = "Cited in \cite{Sterbenz:1974:FPC}.", } @Book{Eckert:1955:FFS, author = "W. J. (Wallace John) Eckert and Rebecca Bradley Jones", title = "Faster, faster; a simple description of a giant electronic calculator and the problems it solves", publisher = pub-IBM, address = pub-IBM:adr, pages = "160", year = "1955", LCCN = "QA76 .E25", bibdate = "Fri Aug 20 08:57:56 MDT 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, author-dates = "1902--1971", remark = "Cited in \cite{Sterbenz:1974:FPC}.", subject = "Computers", xxaddress = pub-MCGRAW-HILL:adr, xxpublisher = pub-MCGRAW-HILL, } @Book{Hastings:1955:ADC, author = "Cecil B. {Hastings, Jr.} and Jeanne T. Hayward and James P. {Wong, Jr.}", title = "Approximations for Digital Computers", publisher = pub-PRINCETON, address = pub-PRINCETON:adr, pages = "viii + 201", year = "1955", LCCN = "QA76 .H33", bibdate = "Mon Sep 30 14:51:50 1996", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nj, } @Article{Lenaerts:1955:ASR, author = "E. H. Lenaerts", title = "Automatic Square Rooting", journal = "Electronic Engineering", volume = "27", number = "??", pages = "287--289", month = jul, year = "1955", bibdate = "Thu Sep 1 10:15:41 1994", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nj, } @Article{Parsons:1955:SDC, author = "Frances L. Parsons", title = "A Simple Desk-Calculator Method for Checking Binary Results of Digital Computer Arithmetic Operations", journal = j-J-ACM, volume = "2", number = "3", pages = "205--207", month = jul, year = "1955", CODEN = "JACOAH", ISSN = "0004-5411", bibdate = "Wed Nov 09 01:00:34 1994", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nhfb, } @Book{Richards:1955:AOD, author = "R. K. Richards", title = "Arithmetic Operations in Digital Computers", publisher = "D. Van Nostrand", address = "New York, NY, USA", pages = "iv + 397", year = "1955", LCCN = "QA75 .R5 1955", bibdate = "Fri Nov 28 18:46:37 2003", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nhfb, } @Article{Robertson:1955:TCM, author = "J. E. Robertson", title = "Two's Complement Multiplication in Binary Parallel Digital Computers", journal = j-IRE-TRANS-ELEC-COMPUT, volume = "EC-4", number = "3", pages = "118--119", month = sep, year = "1955", CODEN = "IRELAO", DOI = "http://dx.doi.org/10.1109/IRETELC.1955.5407911", ISSN = "0367-9950", bibdate = "Thu Jun 30 15:10:39 MDT 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5407911", acknowledgement = ack-nhfb, fjournal = "IRE Transactions on Electronic Computers", } @Article{Estrin:1956:NHS, author = "G. Estrin and B. Gilchrist and J. H. Pomerene", title = "A Note on High-Speed Digital Multiplication", journal = j-IRE-TRANS-ELEC-COMPUT, volume = "EC-5", number = "3", pages = "140--140", month = sep, year = "1956", CODEN = "IRELAO", DOI = "http://dx.doi.org/10.1109/TEC.1956.5219936", ISSN = "0367-9950", bibdate = "Thu Jun 30 15:46:27 MDT 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219936", acknowledgement = ack-nhfb, fjournal = "IRE Transactions on Electronic Computers", } @Book{Hildebrand:1956:INA, author = "Francis Begnaud Hildebrand", title = "Introduction to numerical analysis", publisher = pub-MCGRAW-HILL, address = pub-MCGRAW-HILL:adr, pages = "511", year = "1956", LCCN = "QA300 .H5", bibdate = "Fri Aug 20 09:19:58 MDT 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager", series = "International series in pure and applied mathematics", acknowledgement = ack-nhfb, remark = "See also second edition \cite{Hildebrand:1974:INA,Hildebrand:1987:INA}.", subject = "Numerical analysis", } @Article{Lilamand:1956:TDM, author = "M. Lejet Lilamand", title = "A Time-Division Multiplier", journal = j-IRE-TRANS-ELEC-COMPUT, volume = "EC-5", number = "1", pages = "26--34", month = mar, year = "1956", CODEN = "IRELAO", DOI = "http://dx.doi.org/10.1109/TEC.1956.5219789", ISSN = "0367-9950", bibdate = "Thu Jun 30 15:46:18 MDT 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219789", acknowledgement = ack-nhfb, fjournal = "IRE Transactions on Electronic Computers", } @Article{Perkins:1956:EPC, author = "Robert Perkins", title = "{EASIAC}, {A} Pseudo-Computer", journal = j-J-ACM, volume = "3", number = "2", pages = "65--72", month = apr, year = "1956", CODEN = "JACOAH", ISSN = "0004-5411", bibdate = "Fri Nov 04 23:46:26 1994", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", abstract = "One of the primary functions of the MIDAC installation at the University of Michigan is the instruction of beginners in the various aspects of digital machine use including programming and coding. \ldots{} In conducting these courses it was soon found to be extremely difficult, in five or six instruction periods, to bring a complete newcomer up to the point where he can code and check out on MIDAC anything more than a rather trivial routine. As might be expected the difficulty centers around problems of scaling, instruction modification and binary representation. \ldots{} To alleviate these problems it was decided that a new computer was needed: one designed to make programming easier. At the cost of some of MIDAC's speed and capacity plus two or three man-months of programming time EASIAC, the EASy Instruction Automatic Computer, was realized as a translation-interpretation program in MIDAC.", acknowledgement = ack-nhfb, keywords = "decimal floating-point arithmetic", remark = "Early example of a decimal floating-point machine.", } @Article{Robertson:1956:NCD, author = "J. E. Robertson", title = "A new class of digital division methods", journal = j-IRE-TRANS-ELEC-COMPUT, volume = "EC-5", number = "??", pages = "65--73", month = jun, year = "1956", CODEN = "IRELAO", ISSN = "0367-9950", bibdate = "Fri Nov 09 19:14:45 2007", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nhfb, } @Article{Stegun:1956:PC, author = "Irene A. Stegun and Milton Abramowitz", title = "Pitfalls in computation", journal = "Journal of the Society for Industrial and Applied Mathematics", volume = "4", pages = "207--219", year = "1956", bibdate = "Tue Aug 28 06:16:28 2001", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nhfb, remark = "Cited in \cite{Sterbenz:1974:FPC}.", } @Article{Sydnor:1956:AMS, author = "R. L. Sydnor and T. R. O'Meara and J. Strathman", title = "Analog Multipliers and Squarers Using a Multigrid Modulator", journal = j-IRE-TRANS-ELEC-COMPUT, volume = "EC-5", number = "2", pages = "82--85", month = jun, year = "1956", CODEN = "IRELAO", DOI = "http://dx.doi.org/10.1109/TEC.1956.5219804", ISSN = "0367-9950", bibdate = "Thu Jun 30 15:46:21 MDT 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219804", acknowledgement = ack-nhfb, fjournal = "IRE Transactions on Electronic Computers", } @Article{Weinberger:1956:OMA, author = "A. Weinberger and J. L. Smith", title = "A One-Microsecond Adder Using One-Megacycle Circuitry", journal = j-IRE-TRANS-ELEC-COMPUT, volume = "EC-5", number = "??", pages = "65--73", month = jun, year = "1956", CODEN = "IRELAO", ISSN = "0367-9950", bibdate = "Fri Nov 09 19:38:57 2007", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nhfb, } @Article{Ercoli:1957:EDO, author = "Paolo Ercoli and Roberto Vacca", title = "Errors Due to Overflow in Arithmetic Operations Particularly as Regards {FINAC} Electronic Computer", journal = j-J-ACM, volume = "4", number = "4", pages = "450--455", month = oct, year = "1957", CODEN = "JACOAH", ISSN = "0004-5411", bibdate = "Thu Dec 08 09:28:48 2005", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "See letter \cite{Ercoli:1960:LEE}.", acknowledgement = ack-nhfb, keywords = "floating-point arithmetic; overflow", } @Article{Gini:1957:SFD, author = "Corrado Gini", title = "Sulla frequenza delle cifre iniziali dei numeri osservati. (Italian) [{On} the frequency of initial digits of observed numbers]", journal = "Bull. Inst. Internat. Stat.", volume = "35", number = "??", pages = "57--76", year = "1957", bibdate = "Sun Sep 18 11:54:25 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "29th session, 2nd delivery, Rio de Janerio.", URL = "", acknowledgement = ack-nhfb, keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", language = "Italian", } @Article{Herzel:1957:SDD, author = "Amato Herzel", title = "Sulla distribuzione della cifre iniziali dei numeri statistici. ({Italian}) [{On} the frequency of initial digits of statistical numbers]", journal = "Atti dell XV e XVII Riunione, Societa Italiana di Statistica", volume = "??", number = "??", pages = "??--??", year = "1957", bibdate = "Sun Sep 18 12:00:07 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", language = "Italian", } @Article{Howe:1957:TRA, author = "R. M. Howe and E. G. Gilbert", title = "Trigonometric Resolution in Analog Computers by Means of Multiplier Elements", journal = j-IRE-TRANS-ELEC-COMPUT, volume = "EC-6", number = "2", pages = "86--92", month = jun, year = "1957", CODEN = "IRELAO", DOI = "http://dx.doi.org/10.1109/TEC.1957.5221576", ISSN = "0367-9950", bibdate = "Thu Jun 30 16:07:27 MDT 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221576", acknowledgement = ack-nhfb, fjournal = "IRE Transactions on Electronic Computers", } @Article{Kalbfell:1957:EAM, author = "David C. Kalbfell", title = "An Electronic Analog Multiplier", journal = j-IRE-TRANS-ELEC-COMPUT, volume = "EC-6", number = "2", pages = "100--103", month = jun, year = "1957", CODEN = "IRELAO", DOI = "http://dx.doi.org/10.1109/TEC.1957.5221579", ISSN = "0367-9950", bibdate = "Thu Jun 30 16:07:27 MDT 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221579", acknowledgement = ack-nhfb, fjournal = "IRE Transactions on Electronic Computers", } @Article{Kogbetliantz:1957:CEN, author = "E. G. Kogbetliantz", title = "Computation of $e^n$ for $-\infty