%%% -*-BibTeX-*-
%%% ====================================================================
%%% BibTeX-file{
%%% author-1 = "Norbert Juffa",
%%% author-2 = "Nelson H. F. Beebe",
%%% version = "3.613",
%%% date = "24 October 2020",
%%% time = "08:36:19 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 = "45558 186731 856041 8613972",
%%% 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 3.613, the year coverage looked
%%% like this:
%%%
%%% 1726 ( 1) 1825 ( 0) 1924 ( 2)
%%% 1727 ( 0) 1826 ( 0) 1925 ( 1)
%%% 1728 ( 0) 1827 ( 0) 1926 ( 2)
%%% 1729 ( 0) 1828 ( 0) 1927 ( 1)
%%% 1732 ( 0) 1831 ( 0) 1930 ( 2)
%%% 1734 ( 0) 1833 ( 0) 1932 ( 1)
%%% 1735 ( 0) 1834 ( 0) 1933 ( 1)
%%% 1736 ( 0) 1835 ( 0) 1934 ( 1)
%%% 1738 ( 0) 1837 ( 1) 1936 ( 3)
%%% 1739 ( 0) 1838 ( 0) 1937 ( 3)
%%% 1740 ( 0) 1839 ( 0) 1938 ( 4)
%%% 1741 ( 0) 1840 ( 0) 1939 ( 2)
%%% 1742 ( 0) 1841 ( 0) 1940 ( 3)
%%% 1743 ( 0) 1842 ( 0) 1941 ( 1)
%%% 1744 ( 0) 1843 ( 0) 1942 ( 3)
%%% 1745 ( 0) 1844 ( 0) 1943 ( 2)
%%% 1746 ( 0) 1845 ( 0) 1944 ( 1)
%%% 1747 ( 0) 1846 ( 0) 1945 ( 2)
%%% 1748 ( 0) 1847 ( 0) 1946 ( 5)
%%% 1749 ( 0) 1848 ( 0) 1947 ( 10)
%%% 1750 ( 0) 1849 ( 0) 1948 ( 7)
%%% 1751 ( 0) 1850 ( 0) 1949 ( 3)
%%% 1752 ( 0) 1851 ( 0) 1950 ( 3)
%%% 1753 ( 0) 1852 ( 0) 1951 ( 8)
%%% 1754 ( 0) 1853 ( 0) 1952 ( 5)
%%% 1755 ( 0) 1854 ( 0) 1953 ( 3)
%%% 1756 ( 0) 1855 ( 0) 1954 ( 7)
%%% 1757 ( 0) 1856 ( 0) 1955 ( 8)
%%% 1758 ( 0) 1857 ( 0) 1956 ( 8)
%%% 1759 ( 0) 1858 ( 0) 1957 ( 17)
%%% 1760 ( 0) 1859 ( 0) 1958 ( 16)
%%% 1761 ( 0) 1860 ( 0) 1959 ( 26)
%%% 1762 ( 0) 1861 ( 0) 1960 ( 21)
%%% 1763 ( 0) 1862 ( 1) 1961 ( 30)
%%% 1764 ( 0) 1863 ( 0) 1962 ( 29)
%%% 1765 ( 0) 1864 ( 0) 1963 ( 25)
%%% 1766 ( 0) 1865 ( 0) 1964 ( 31)
%%% 1767 ( 0) 1866 ( 0) 1965 ( 57)
%%% 1768 ( 0) 1867 ( 0) 1966 ( 37)
%%% 1769 ( 0) 1868 ( 0) 1967 ( 44)
%%% 1770 ( 0) 1869 ( 0) 1968 ( 34)
%%% 1771 ( 0) 1870 ( 0) 1969 ( 53)
%%% 1772 ( 0) 1871 ( 0) 1970 ( 56)
%%% 1773 ( 0) 1872 ( 0) 1971 ( 59)
%%% 1774 ( 0) 1873 ( 0) 1972 ( 61)
%%% 1775 ( 0) 1874 ( 0) 1973 ( 78)
%%% 1776 ( 0) 1875 ( 1) 1974 ( 49)
%%% 1777 ( 0) 1876 ( 0) 1975 ( 99)
%%% 1778 ( 0) 1877 ( 0) 1976 ( 57)
%%% 1779 ( 0) 1878 ( 0) 1977 ( 76)
%%% 1780 ( 0) 1879 ( 1) 1978 ( 103)
%%% 1781 ( 0) 1880 ( 0) 1979 ( 74)
%%% 1782 ( 0) 1881 ( 1) 1980 ( 107)
%%% 1783 ( 0) 1882 ( 0) 1981 ( 121)
%%% 1784 ( 0) 1883 ( 0) 1982 ( 85)
%%% 1785 ( 0) 1884 ( 0) 1983 ( 148)
%%% 1786 ( 0) 1885 ( 0) 1984 ( 103)
%%% 1787 ( 0) 1886 ( 0) 1985 ( 150)
%%% 1788 ( 0) 1887 ( 0) 1986 ( 98)
%%% 1789 ( 0) 1888 ( 1) 1987 ( 140)
%%% 1790 ( 0) 1889 ( 0) 1988 ( 158)
%%% 1791 ( 0) 1890 ( 0) 1989 ( 190)
%%% 1792 ( 0) 1891 ( 0) 1990 ( 154)
%%% 1793 ( 0) 1892 ( 1) 1991 ( 231)
%%% 1794 ( 0) 1893 ( 2) 1992 ( 184)
%%% 1795 ( 0) 1894 ( 0) 1993 ( 200)
%%% 1796 ( 0) 1895 ( 0) 1994 ( 178)
%%% 1797 ( 0) 1896 ( 0) 1995 ( 161)
%%% 1798 ( 0) 1897 ( 1) 1996 ( 184)
%%% 1799 ( 0) 1898 ( 1) 1997 ( 135)
%%% 1800 ( 0) 1899 ( 0) 1998 ( 132)
%%% 1801 ( 0) 1900 ( 0) 1999 ( 195)
%%% 1802 ( 0) 1901 ( 0) 2000 ( 147)
%%% 1803 ( 0) 1902 ( 0) 2001 ( 209)
%%% 1804 ( 0) 1903 ( 0) 2002 ( 166)
%%% 1805 ( 0) 1904 ( 0) 2003 ( 152)
%%% 1806 ( 0) 1905 ( 0) 2004 ( 169)
%%% 1807 ( 0) 1906 ( 0) 2005 ( 178)
%%% 1808 ( 0) 1907 ( 0) 2006 ( 130)
%%% 1809 ( 0) 1908 ( 0) 2007 ( 151)
%%% 1810 ( 0) 1909 ( 1) 2008 ( 79)
%%% 1811 ( 0) 1910 ( 1) 2009 ( 117)
%%% 1812 ( 0) 1911 ( 0) 2010 ( 90)
%%% 1813 ( 0) 1912 ( 0) 2011 ( 139)
%%% 1814 ( 0) 1913 ( 0) 2012 ( 78)
%%% 1815 ( 0) 1914 ( 0) 2013 ( 86)
%%% 1816 ( 0) 1915 ( 1) 2014 ( 53)
%%% 1817 ( 0) 1916 ( 0) 2015 ( 106)
%%% 1818 ( 0) 1917 ( 0) 2016 ( 90)
%%% 1819 ( 0) 1918 ( 0) 2017 ( 122)
%%% 1820 ( 0) 1919 ( 0) 2018 ( 82)
%%% 1821 ( 0) 1920 ( 0) 2019 ( 142)
%%% 1822 ( 0) 1921 ( 0) 2020 ( 32)
%%% 19xx ( 2)
%%% 20xx ( 1)
%%%
%%% Article: 3409
%%% Book: 346
%%% InBook: 2
%%% InCollection: 66
%%% InProceedings: 1744
%%% Manual: 66
%%% MastersThesis: 147
%%% Misc: 217
%%% Periodical: 3
%%% PhdThesis: 78
%%% Proceedings: 382
%%% TechReport: 355
%%% Unpublished: 9
%%%
%%% Total entries: 6824
%%%
%%% 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 \booktitle \def \booktitle#1{{{\em #1}}} \fi" #
"\ifx \undefined \circled \def \circled #1{(#1)}\fi" #
"\ifx \undefined \mathbb \def \mathbb #1{{\bf #1}}\fi" #
"\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}}\fi" #
"\ifx \undefined \mathrm \def \mathrm #1{{\rm #1}}\fi" #
"\ifx \undefined \operatorname \def \operatorname #1{{\rm #1}}\fi" #
"\ifx \undefined \r \let \r = \ocirc \fi" #
"\ifx \undefined \reg \def \reg {\circled{R}}\fi" #
"\ifx \undefined \texttt \def \texttt #1{{\tt #1}}\fi" #
"\ifx \undefined \TM \def \TM {${}^{\sc TM}$} \fi" #
"\hyphenation{
Cor-dic
COR-DIC
Gleit-komma
Gleit-komma-zahl-en
Gleit-komma-pro-zess-or
Gleit-komma-for-mat
Mikro-rech-en-tech-nik
Mikro-rech-ner-sys-tem-en
Mikro-rech-ner
Mi-yo-shi
Quad-rat-wurz-eln
Semi-nu-mer-i-cal
Swartz-lan-der
}"
}
%%% ====================================================================
%%% 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-PRINCETON = "Princeton University"}
@String{inst-PRINCETON:adr = "Princeton, NJ, 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-ACM-J-EXP-ALGORITHMICS = "ACM Journal of Experimental Algorithmics"}
@String{j-ADA-LETT = "Ada Letters"}
@String{j-ADV-COMPUT-MATH = "Advances in Computational Mathematics"}
@String{j-ADV-SOFT-SCI-TECH = "Advances in software science and
technology"}
@String{j-ADV-THEORY-SIMUL = "Advanced Theory and Simulations"}
@String{j-ALGORITHMICA = "Algorithmica"}
@String{j-ALGORITHMS-BASEL = "Algorithms ({Basel})"}
@String{j-ALTA-FREQ = "Alta frequenza"}
@String{j-AM-J-MATH = "American Journal of Mathematics"}
@String{j-AM-SCI = "American Scientist"}
@String{j-AMER-J-PHYSICS = "American Journal of Physics"}
@String{j-AMER-MATH-MONTHLY = "American Mathematical Monthly"}
@String{j-AMER-STAT = "The American Statistician"}
@String{j-ANN-HIST-COMPUT = "Annals of the History of Computing"}
@String{j-ANN-MATH-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-APPL-MATH-LETT = "Applied Mathematics Letters"}
@String{j-APPL-NUM-MATH = "Applied Numerical Mathematics"}
@String{j-APPL-OPTICS = "Applied Optics"}
@String{j-APPL-STAT = "Applied Statistics"}
@String{j-ARCH-HIST-EXACT-SCI = "Archive for History of Exact Sciences"}
@String{j-ASTA-ADV-STAT-ANAL = "AStA. Advances in Statistical Analysis"}
@String{j-ASTRON-J = "Astronomical Journal"}
@String{j-AUSTRALIAN-COMP-J = "Australian Computer Journal"}
@String{j-AUTO-CTL-COMP-SCI = "Automatic Control and Computer Sciences"}
@String{j-AUTOMATION-REMOTE-CTL = "Automation and Remote Control"}
@String{j-BELL-LABS-RECORD = "Bell Laboratories Record"}
@String{j-BELL-SYST-TECH-J = "The Bell System Technical Journal"}
@String{j-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-CGF = "Com{\-}pu{\-}ter Graphics Forum"}
@String{j-COED = "CoED"}
@String{j-COLLEGE-MATH-J = "College Mathematics Journal"}
@String{j-COMBIN-PROBAB-COMPUT = "Combinatorics, Probability and Computing"}
@String{j-COMMUN-STAT-SIMUL-COMPUT = "Communications in Statistics: Simulation
and Computation"}
@String{j-COMMUN-STAT-THEORY-METH = "Communications in Statistics: Theory and
Methods"}
@String{j-COMP-ARCH-NEWS = "ACM SIGARCH Computer Architecture News"}
@String{j-COMP-DESIGN = "Computer Design"}
@String{j-COMP-EDU-J = "Computers in education journal"}
@String{j-COMP-GEOM = "Computational Geometry. Theory and
Applications"}
@String{j-COMP-GEOSCI = "Computers and Geosciences"}
@String{j-COMP-J = "The Computer Journal"}
@String{j-COMP-LANG-MAG = "Computer Language Magazine"}
@String{j-COMP-LANGS = "Computer Languages"}
@String{j-COMP-PHYS-COMM = "Computer Physics Communications"}
@String{j-COMP-SURV = "ACM Computing Surveys"}
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%%% ====================================================================
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%%% ====================================================================
%%% Series abbreviations:
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@String{ser-SIGPLAN = "ACM SIG{\-}PLAN Notices"}
%%% ====================================================================
%%% Bibliography entries, sorted by year, and within each year, by
%%% citation label, with ``bibsort -byyear''.
%%%
%%% 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.
%%%
%%% TO DO: Add entries for more of these US patents on floating-point
%%% arithmetic:
%%%
%%% http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&u=%2Fnetahtml%2FPTO%2Fsearch-adv.htm&r=0&p=1&f=S&l=50&Query=ttl%2F%28floating+and+point+and+arithmetic%29%0D%0A%0D%0A&d=PALL
%%% Searched on 17 October 2019 for "ttl/(floating and point and arithmetic)"
%%%
%%% 1 10,416,962 Decimal and binary floating point arithmetic calculations
%%% 2 10,318,241 Fixed-point and floating-point arithmetic operator circuits in specialized processing blocks
%%% 3 10,289,413 Hybrid analog-digital floating point number representation and arithmetic
%%% 4 10,216,480 Shift and divide operations using floating-point arithmetic
%%% 5 10,216,479 Apparatus and method for performing arithmetic operations to accumulate floating-point numbers
%%% 6 10,175,944 Mixed-precision floating-point arithmetic circuitry in specialized processing blocks
%%% 7 10,073,676 Reduced floating-point precision arithmetic circuitry
%%% 8 10,042,606 Fixed-point and floating-point arithmetic operator circuits in specialized processing blocks
%%% 9 9,904,514 Fused floating-point arithmetic circuitry
%%% 10 9,665,346 Performing arithmetic operations using both large and small floating point values
%%%
%%% 11 9,600,234 Floating-point arithmetic device, semiconductor device and information processing system
%%% 12 8,984,041 Performing arithmetic operations using both large and small floating point values
%%% 13 8,909,690 Performing arithmetic operations using both large and small floating point values
%%% 14 8,793,533 Method and device for performing failsafe hardware-independent floating-point arithmetic
%%% 15 8,694,567 Method and apparatus for arithmetic operation on a value represented in a floating-point format
%%% 16 8,615,542 Multi-function floating point arithmetic pipeline
%%% 17 8,166,092 Arithmetic device for performing division or square root operation of floating point number and arithmetic method therefor
%%% 18 8,117,426 System and apparatus for group floating-point arithmetic operations
%%% 19 7,949,696 Floating-point number arithmetic circuit for handling immediate values
%%% 20 7,730,287 Method and software for group floating-point arithmetic operations
%%%
%%% 21 7,530,061 Programmatic access to the widest mode floating-point arithmetic supported by a processor
%%% 22 7,392,274 Multi-function floating point arithmetic pipeline
%%% 23 7,188,133 Floating point number storage method and floating point arithmetic device
%%% 24 7,069,288 Floating point system with improved support of interval arithmetic
%%% 25 6,965,908 Multi-function floating point arithmetic pipeline
%%% 26 6,785,701 Apparatus and method of performing addition and rounding operation in parallel for floating-point arithmetic logical unit
%%% 27 6,748,587 Programmatic access to the widest mode floating-point arithmetic supported by a processor
%%% 28 6,571,264 Floating-point arithmetic device
%%% 29 6,388,672 Graphic translate engine, floating point arithmetic unit and floating point multiply-add calculation unit
%%% 30 6,314,442 Floating-point arithmetic unit which specifies a least significant bit to be incremented
%%%
%%% 31 6,205,461 Floating point arithmetic logic unit leading zero count using fast approximate rounding
%%% 32 6,199,089 Floating point arithmetic logic unit rounding using at least one least significant bit
%%% 33 6,185,593 Method and apparatus for parallel normalization and rounding technique for floating point arithmetic operations
%%% 34 6,175,847 Shifting for parallel normalization and rounding technique for floating point arithmetic operations
%%% 35 6,173,299 Method and apparatus for selecting an intermediate result for parallel normalization and rounding technique for floating point arithmetic operations
%%% 36 6,151,615 Method and apparatus for formatting an intermediate result for parallel normalization and rounding technique for floating point arithmetic operations
%%% 37 6,094,668 Floating point arithmetic unit including an efficient close data path
%%% 38 6,088,715 Close path selection unit for performing effective subtraction within a floating point arithmetic unit
%%% 39 6,085,212 Efficient method for performing close path subtraction in a floating point arithmetic unit
%%% 40 6,085,211 Logic circuit and floating-point arithmetic unit
%%%
%%% 41 6,085,208 Leading one prediction unit for normalizing close path subtraction results within a floating point arithmetic unit
%%% 42 6,078,939 Apparatus useful in floating point arithmetic
%%% 43 5,931,896 Floating point addition and subtraction arithmetic circuit performing preprocessing of addition or subtraction operation rapidly
%%% 44 5,931,895 Floating-point arithmetic processing apparatus
%%% 45 5,901,076 Ripple carry shifter in a floating point arithmetic unit of a microprocessor
%%% 46 5,831,884 Apparatus for performing arithmetic operation of floating point numbers capable of improving speed of operation by performing canceling prediction operation in parallel
%%% 47 5,771,183 Apparatus and method for computation of sticky bit in a multi-stage shifter used for floating point arithmetic
%%% 48 5,748,516 Floating point processing unit with forced arithmetic results
%%% 49 5,726,926 Shifter for shifting floating point number utilizing arithmetic operation of redundant binary number, and adder containing the same
%%% 50 5,677,861 Arithmetic apparatus for floating-point numbers
%%%
%%% 51 5,633,818 Method and apparatus for performing floating point arithmetic operation and rounding the result thereof
%%% 52 5,631,859 Floating point arithmetic unit having logic for quad precision arithmetic
%%% 53 5,568,412 Rounding-off method and apparatus of floating point arithmetic apparatus for addition/subtraction
%%% 54 5,550,768 Rounding normalizer for floating point arithmetic operations
%%% 55 5,515,308 Floating point arithmetic unit using modified Newton-Raphson technique for division and square root
%%% 56 5,434,809 Method and apparatus for performing floating point arithmetic operation and rounding the result thereof
%%% 57 5,432,727 Apparatus for computing a sticky bit for a floating point arithmetic unit
%%% 58 5,375,196 Rapid line drawing in computer graphics employing floating-point arithmetic
%%% 59 5,359,548 Floating-point arithmetic system having multiple-input addition and subtraction means
%%% 60 5,341,321 Floating point arithmetic unit using modified Newton-Raphson technique for division and square root
%%%
%%% 61 5,313,415 Method and apparatus for performing floatinga point arithmetic operation and rounding the result thereof
%%% 62 5,303,175 Floating point arithmetic unit
%%% 63 5,301,137 Circuit for fixed point or floating point arithmetic operations
%%% 64 5,241,493 Floating point arithmetic unit with size efficient pipelined multiply-add architecture
%%% 65 5,222,037 Floating-point processor for performing an arithmetic operation on fixed-point part data with high speed rounding of a result
%%% 66 5,212,662 Floating point arithmetic two cycle data flow
%%% 67 5,212,661 Apparatus for performing floating point arithmetic operation and rounding the result thereof
%%% 68 5,200,916 Mantissa processing circuit of floating point arithmetic apparatus for addition and subtraction
%%% 69 5,128,889 Floating-point arithmetic apparatus with compensation for mantissa truncation
%%% 70 5,121,351 Floating point arithmetic system
%%%
%%% 71 5,075,882 Normalizing circuit of floating-point arithmetic circuit for two input data
%%% 72 4,999,803 Floating point arithmetic system and method
%%% 73 4,999,802 Floating point arithmetic two cycle data flow
%%% 74 4,991,130 Normalization control system for floating point arithmetic operation
%%% 75 4,961,162 Multiprocessing system for performing floating point arithmetic operations
%%% 76 4,908,788 Shift control signal generation circuit for floating-point arithmetic operation
%%% 77 4,896,286 Floating-point arithmetic apparatus
%%% 78 4,872,132 Method and means for block floating point arithmetic
%%% 79 4,839,846 Apparatus for performing floating point arithmetic operations and rounding the result thereof
%%% 80 4,811,272 Apparatus and method for an extended arithmetic logic unit for expediting selected floating point operations
%%%
%%% 81 4,796,218 Arithmetic circuit capable of executing floating point operation and fixed point operation
%%% 82 4,796,217 Rounding unit for use in arithmetic processing of floating point data
%%% 83 4,780,842 Cellular processor apparatus capable of performing floating point arithmetic operations
%%% 84 4,758,972 Precision rounding in a floating point arithmetic unit
%%% 85 4,683,547 Special accumulate instruction for multiple floating point arithmetic units which use a putaway bus to enhance performance
%%% 86 4,649,508 Floating-point arithmetic operation system
%%% 87 4,620,292 Arithmetic logic unit for floating point data and/or fixed point data
%%% 88 4,562,553 Floating point arithmetic system and method with rounding anticipation
%%% 89 4,217,657 Floating point arithmetic control
%%% 90 4,161,784 Microprogrammable floating point arithmetic unit capable of performing arithmetic operations on long and short operands
%%%
%%% 91 4,130,879 Apparatus for performing floating point arithmetic operations using submultiple storage
%%% 92 3,829,673 FLOATING POINT ARITHMETIC UNIT ADAPTED FOR CONVERTING A COMPUTER TO FLOATING POINT ARITHMETIC
%%% 93 3,701,976 FLOATING POINT ARITHMETIC UNIT FOR A PARALLEL PROCESSING COMPUTER
%%% 94 3,193,669 708/505
%%% 95 3,037,701 708/495
%%% 96 2,965,297 708/503 708/504 708/671
@Article{Colson:1726:SAN,
author = "John {Colson, F.R.S.}",
title = "A Short Account of Negativo-Affirmative Arithmetick",
journal = j-PHILOS-TRANS-R-SOC-LOND,
volume = "34",
number = "392--398",
pages = "161--173",
month = "????",
year = "1726",
CODEN = "PTRSAV",
DOI = "https://doi.org/10.1098/rstl.1726.0032",
ISSN = "0370-2316",
bibdate = "Tue Jul 28 14:21:05 2015",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith22.gforge.inria.fr/slides/s2-ercegovac.pdf",
acknowledgement = ack-nhfb,
fjournal = "Philosophical transactions of the Royal Society of
London",
remark = "Early work on signed-digit arithmetic, reported by
Milo{\v{s}} Ercegovac in a talk at the ARITH'22
conference, Lyon, France, June 2015.",
}
@Unpublished{Babbage:1837:MPC,
author = "Charles Babbage",
title = "On the mathematical powers of the calculating engine",
month = dec,
year = "1837",
bibdate = "Wed Oct 13 11:09:59 2010",
bibsource = "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,
}
@Book{Nystrom:1862:PNS,
author = "John W. (John William) Nystrom",
title = "Project of a new system of arithmetic, weight, measure
and coins, proposed to be called the tonal system, with
sixteen to the base",
publisher = "J. B. Lippincott and Co.",
address = "Philadelphia, PA, USA",
pages = "106",
year = "1862",
LCCN = "QC96 .N95",
bibdate = "Sat Oct 29 10:28:27 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://unifoundry.com/tonal/;
https://catalog.hathitrust.org/Record/011602816;
https://lccn.loc.gov/04025433",
acknowledgement = ack-nhfb,
author-dates = "Johan Vilhelm Nystr{\"o}m (1824--1885)",
remark = "Thanks to Paul Hardy of Unifoundry in San Diego, CA,
USA, for information about Nystrom's promotion of
hexadecimal arithmetic, and for creating a Web site
about Nystrom's tonal system, as well as developing
Unicode-compatible fonts to represent the additional
digits needed by the system.",
subject = "Weights and measures; Numeration; base-16 arithmetic;
hexadecimal arithmetic",
}
@Article{Anonymous:1875:AOM,
author = "Anonymous",
title = "The Arithmetical Operations of Multiplication and
Division",
journal = j-SCI-AMER,
volume = "32",
number = "3",
pages = "41--42",
day = "16",
month = jan,
year = "1875",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican01161875-41",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Fri May 17 10:29:24 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/sciam1870.bib",
URL = "http://www.nature.com/scientificamerican/journal/v32/n3/pdf/scientificamerican01161875-41.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@Article{Anonymous:1879:TRA,
author = "Anonymous",
title = "Three Rules for Abbreviating Multiplication",
journal = j-SCI-AMER,
volume = "41",
number = "12",
pages = "184--184",
day = "20",
month = sep,
year = "1879",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican09201879-184",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Fri May 17 10:36:54 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/sciam1870.bib",
URL = "http://www.nature.com/scientificamerican/journal/v41/n12/pdf/scientificamerican09201879-184.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@Article{Newcomb:1881:NFU,
author = "Simon Newcomb",
title = "Note on the frequency of use of the different digits
in natural numbers",
journal = j-AM-J-MATH,
volume = "4",
number = "1/4",
pages = "39--40",
year = "1881",
CODEN = "AJMAAN",
ISSN = "0002-9327 (print), 1080-6377 (electronic)",
ISSN-L = "0002-9327",
bibdate = "Thu Feb 15 16:35:24 2007",
bibsource = "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,
fjournal = "American Journal of Mathematics",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From p. 40: ``The law of probability of the occurrence
of numbers is such that all mantissas of their
logarithms are equally probable.''",
}
@Article{Holman:1888:DPM,
author = "Silas W. Holman",
title = "Discussion of the precision of measurement",
journal = "Technol. Q.",
volume = "1",
number = "??",
pages = "194--207",
month = "????",
year = "1888",
bibdate = "Mon May 21 17:12:03 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite[ref. 14]{Carter:2013:ESF}.",
}
@Book{Holman:1892:DPM,
author = "Silas W. Holman",
title = "Discussion of the Precision of Measurements: With
Examples Taken Mainly From Physics And Electrical
Engineering",
publisher = "Ferris Brothers Printers",
address = "New York, NY, USA",
pages = "????",
year = "1892",
bibdate = "Mon May 21 17:14:39 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite[ref. 15]{Carter:2013:ESF}.",
}
@Article{Anonymous:1893:IDb,
author = "Anonymous",
title = "The Instantaneous Divider",
journal = j-SCI-AMER,
volume = "68",
number = "21",
pages = "325--325",
day = "27",
month = may,
year = "1893",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican05271893-325a",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Wed May 22 19:04:00 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/sciam1890.bib",
URL = "http://www.nature.com/scientificamerican/journal/v68/n21/pdf/scientificamerican05271893-325a.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@Article{Felt:1893:MA,
author = "Dorr E. Felt",
title = "Mechanical Arithmetic",
journal = j-SCI-AMER,
volume = "69",
number = "20",
pages = "309--310",
day = "11",
month = nov,
year = "1893",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican11111893-309b",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Wed May 22 19:04:25 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/sciam1890.bib",
URL = "http://www.nature.com/scientificamerican/journal/v69/n20/pdf/scientificamerican11111893-309b.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@Article{Aley:1897:DES,
author = "Robert J. Aley",
title = "A Device for Extracting the Square Root of Certain
Surd Quantities",
journal = j-AMER-MATH-MONTHLY,
volume = "4",
number = "8/9",
pages = "204--208",
month = aug # "\slash " # sep,
year = "1897",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:37:08 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
@Article{Anonymous:1898:OFA,
author = "Anonymous",
title = "Our Fingers as an Aid in Multiplication",
journal = j-SCI-AMER,
volume = "79",
number = "17",
pages = "265--266",
day = "22",
month = oct,
year = "1898",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican10221898-265",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Wed May 22 19:08:57 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/sciam1890.bib",
URL = "http://www.nature.com/scientificamerican/journal/v79/n17/pdf/scientificamerican10221898-265.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@Article{Ludgate:1909:PAM,
author = "P. E. Ludgate",
title = "On a proposed analytical machine",
journal = j-SCI-PROC-ROY-DUBLIN-SOC,
volume = "12",
number = "9",
pages = "77--91",
year = "1909",
CODEN = "SPRDAP",
ISSN = "0371-2303",
bibdate = "Wed Oct 13 11:14:08 2010",
bibsource = "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",
ISSN-L = "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,
fjournal = "Revue G{\'e}n{\'e}rale des Sciences Pures et
Appliqu{\'e}es",
language = "French",
}
@Article{Barrow:1924:QDD,
author = "D. F. Barrow",
title = "Questions and Discussions: Discussions: On Taking
Square Roots of Integers",
journal = j-AMER-MATH-MONTHLY,
volume = "31",
number = "10",
pages = "482--484",
month = dec,
year = "1924",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:37:29 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
@Article{Smith:1924:FPA,
author = "David Eugene Smith",
title = "The First Printed Arithmetic ({Treviso}, 1478)",
journal = j-ISIS,
volume = "6",
number = "3",
pages = "311--331",
month = "????",
year = "1924",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:57:26 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i211087;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/isis1920.bib",
URL = "http://www.jstor.org/stable/224315",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/page/journal/isis/about.html",
}
@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{Cajori:1926:BRB,
author = "Florian Cajori",
title = "Book Review: {{\booktitle{The History of Arithmetic}}
by Louis Charles Karpinski}",
journal = j-ISIS,
volume = "8",
number = "1",
pages = "231--232",
month = feb,
year = "1926",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:57:36 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i211094;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/isis1920.bib",
URL = "http://www.jstor.org/stable/223706",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/page/journal/isis/about.html",
}
@Article{Smith:1926:FGC,
author = "David Eugene Smith",
title = "The First Great Commercial Arithmetic",
journal = j-ISIS,
volume = "8",
number = "1",
pages = "41--49",
month = feb,
year = "1926",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:57:36 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i211094;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/isis1920.bib",
URL = "http://www.jstor.org/stable/223673",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/page/journal/isis/about.html",
}
@Article{Cajori:1927:EAP,
author = "Florian Cajori",
title = "The Earliest Arithmetic Published in {America}",
journal = j-ISIS,
volume = "9",
number = "3",
pages = "391--401",
month = dec,
year = "1927",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:57:45 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i214411;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/isis1920.bib",
URL = "http://www.jstor.org/stable/330806",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/page/journal/isis/about.html",
}
@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,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
@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,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
@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,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
@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,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
@Article{Calvert:1936:DDS,
author = "H. R. Calvert",
title = "Decimal Division of Scales before the Metric System",
journal = j-ISIS,
volume = "25",
number = "2",
pages = "433--436",
month = sep,
year = "1936",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:21:25 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i211115;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/isis1930.bib",
URL = "http://www.jstor.org/stable/225380",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/page/journal/isis/about.html",
}
@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,
language = "German",
}
@Article{Escott:1937:QDN,
author = "E. B. Escott",
title = "Questions, Discussions, and Notes: Rapid Method for
Extracting a Square Root",
journal = j-AMER-MATH-MONTHLY,
volume = "44",
number = "10",
pages = "644--646",
month = dec,
year = "1937",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:38:44 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
@Book{Millikan:1937:MMP,
author = "Robert A. Millikan and Duane E. Roller and Earnest C.
Watson",
title = "Mechanics, Molecular Physics, Heat, and Sound",
publisher = pub-MIT,
address = pub-MIT:adr,
pages = "????",
year = "1937",
bibdate = "Mon May 21 17:16:04 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See Appendix: Significant Figures and Notations by
Powers of Ten.",
acknowledgement = ack-nhfb,
remark = "Cited in \cite[ref. 22]{Carter:2013:ESF}.",
}
@MastersThesis{Shannon:1937:SAR,
author = "Claude Elwood Shannon",
title = "A Symbolic Analysis of Relay and Switching Circuits",
type = "{Master of Science}",
school = "Department of Electrical Engineering, MIT",
address = "Cambridge, MA, USA",
pages = "72",
day = "10",
month = aug,
year = "1937",
bibdate = "Thu Nov 18 10:35:20 2010",
bibsource = "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 (print), 2326-9243 (electronic)",
ISSN-L = "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,
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
journal-URL = "http://www.jstor.org/journal/procamerphilsoci",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From \cite{Logan:1978:FDP}: ``Benford's paper was
published in 1938 in a journal of rather limited
circulation and not usually read by mathematicians. It
so happened that it was immediately followed in the
same issue by a physics paper which became of some
importance for secret nuclear work during World War II
[H. A. Bethe, M. E. Rose, and L. P. Smith, `The
Multiple Scattering of Electrons', Proc. Amer. Phil.
Soc. 78(4), 573--585 (1938)]. That is why Benford's
paper caught the attention of physicists in the early
1940's and was much discussed. This led to the notes in
Nature by Goudsmit and Furry [3] and Furry and Hurwitz
[4] containing an effort to explain Benford's law. We
considered it at that time merely a welcome diversion
and did not expect that over thirty papers would be
devoted to this subject in subsequent years.'' The 2006
bibliography \cite{Hurlimann:2006:BLB} cites 325
publications about Benford's Law.",
}
@PhdThesis{Couffignal:1938:AMA,
author = "L. Couffignal",
title = "Sur l'analyse m{\'e}canique. Application aux machines
{\`a} calculer et aux calculs de la m{\'e}canique
c{\'e}leste. ({French}) [{On} mechanical analysis.
Application to calculating machines and to calculation
in celestial mechanics]",
publisher = "Gauthier-Villars",
school = "Facult{\'e} des Sciences de Paris",
address = "Paris, France",
year = "1938",
bibdate = "Wed Oct 13 11:17:22 2010",
bibsource = "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 = j-TRANS-AMER-INST-ELEC-ENG,
volume = "57",
number = "??",
pages = "713--723",
month = dec,
year = "1938",
CODEN = "TAEEA5",
ISSN = "0096-3860",
bibdate = "Sat Nov 20 08:54:12 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www2.research.att.com/~njas/doc/shannonbio.html",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Institute of Electrical
Engineers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714",
remark = "This is Shannon's first published paper (his Master's
thesis). In 1940, it received the Alfred Noble Prize of
the combined engineering societies of the United
States, an award given each year to a person not over
thirty for a paper published in one of the journals of
the participating societies. H. H. Goldstine
\cite{Goldstine:1972:CPN} called this work ``one of the
most important master's theses ever written \ldots{} a
landmark in that it helped to change digital circuit
design from an art to a science.''",
}
@Article{Jager:1939:AAD,
author = "Robert Jager and Boyd C. Patterson",
title = "The Artificial Arithmetick in Decimals of {Robert
Jager} ({London}, 1651)",
journal = j-ISIS,
volume = "31",
number = "1",
pages = "25--31",
month = nov,
year = "1939",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:26:49 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302217;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/isis1930.bib",
URL = "http://www.jstor.org/stable/226014",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/page/journal/isis/about.html",
}
@Article{K:1939:BRBd,
author = "M. G. K.",
title = "Book Review: {{\booktitle{Duodecimal Arithmetic}}, by
George S. Terry}",
journal = j-J-R-STAT-SOC,
volume = "102",
number = "2",
pages = "299--300",
month = "????",
year = "1939",
DOI = "https://doi.org/10.2307/2980013",
bibdate = "Sat Jan 24 11:18:08 MST 2015",
bibsource = "http://www.jstor.org/stable/i349540;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jrss-a-1930.bib",
URL = "http://www.jstor.org/stable/2980013",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society",
}
@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.",
}
@Article{Lancaster:1942:MME,
author = "Otis E. Lancaster",
title = "Machine Method for the Extraction of Cube Root",
journal = j-J-AM-STAT-ASSOC,
volume = "37",
number = "217",
pages = "112--115",
month = mar,
year = "1942",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:24 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314096;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
URL = "http://www.jstor.org/stable/2279437",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@TechReport{Mauchly:1942:UHS,
author = "J. W. Mauchly",
title = "The use of high speed vacuum tube devices for
calculating",
type = "Privately circulated memorandum",
institution = "Moore School of Electrical Engineering, University of
Pennsylvania",
address = "Philadelphia, PA, USA",
month = aug,
year = "1942",
bibdate = "Wed Oct 13 11:52:54 2010",
bibsource = "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",
bibdate = "Sat Feb 8 10:28:55 2020",
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,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
@TechReport{Rademacher:1943:MTI,
author = "Hans Rademacher",
title = "Mathematical Topics of Interest in {PX}, Part Two:
Summary of Articles Dealing with Rounding off Errors",
type = "{PX} Report",
number = "14",
institution = "Moore School of Electrical Engineering, Office of the
Director Records, University of Pennsylvania",
address = "Philadelphia, PA, USA",
day = "30",
month = nov,
year = "1943",
bibdate = "Fri Jun 15 17:39:28 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited on page 34 of Haigh, Priestley, and Rope,
\booktitle{ENIAC in Action} (2016) (ISBN 0-262-03398-4)
as an annotated bibliography of rounding errors.",
}
@Article{Goudsmit:1944:SFN,
author = "S. A. Goudsmit and W. H. Furry",
title = "Significant Figures of Numbers in Statistical Tables",
journal = j-NATURE,
volume = "154",
number = "3921",
pages = "800--801",
day = "23",
month = dec,
year = "1944",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/154800a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Sun Sep 18 11:57:19 2011",
bibsource = "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,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Furry:1945:DND,
author = "W. H. Furry and Henry Hurwitz",
title = "Distribution of Numbers and Distribution of
Significant Figures",
journal = j-NATURE,
volume = "155",
number = "??",
pages = "52--53",
day = "13",
month = jan,
year = "1945",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/155052a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Sun Sep 18 11:51:37 2011",
bibsource = "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,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@TechReport{vonNeumann:1945:FDR,
author = "John von Neumann",
title = "First Draft of a Report on the {EDVAC}",
institution = "University of Pennsylvania",
day = "30",
month = jun,
year = "1945",
bibdate = "Mon Jun 06 19:17:03 2005",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib;
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 = j-ELECTR-ENG,
volume = "65",
number = "??",
pages = "384--391, 449--454, 522--528",
year = "1946",
CODEN = "ELENAC",
ISSN = "0095-9197",
bibdate = "Wed Oct 13 11:26:29 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Electrical Engineering (American Institute of
Electrical Engineers)",
}
@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,
fjournal = "Bell Laboratories Record",
}
@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,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@TechReport{Goldstine:1947:PCPa,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument. {Part 1}, Vol. 1",
type = "Technical report",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "??",
month = "????",
year = "1947",
bibdate = "Fri Nov 16 16:35:14 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Goldstine:1947:PCPb,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument. {Part 2}, Vol. 1",
type = "Technical report",
number = "1",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "69",
day = "1",
month = apr,
year = "1947",
MRnumber = "MR22443",
bibdate = "Wed Jun 01 17:41:33 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
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:1998:SA} cites pp. 142--151 of this report
as the first published treatment of double-precision
arithmetic on digital computers.",
acknowledgement = ack-nhfb,
}
@TechReport{Goldstine:1947:PCPc,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument. {Part 1}, Vol. 2",
type = "Technical report",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "??",
month = "????",
year = "1947",
bibdate = "Fri Nov 16 16:35:14 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Goldstine:1947:PCPd,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument. {Part 2}, Vol. 2",
type = "Technical report",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "??",
month = "????",
year = "1947",
bibdate = "Fri Nov 16 16:35:14 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Goldstine:1947:PCPe,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument. {Part 1}, Vol. 3",
type = "Technical report",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "??",
month = "????",
year = "1947",
bibdate = "Fri Nov 16 16:35:14 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Goldstine:1947:PCPf,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument. {Part 2}, Vol. 3",
type = "Technical report",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "??",
month = "????",
year = "1947",
bibdate = "Fri Nov 16 16:35:14 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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,
fjournal = "Bell Laboratories Record",
}
@InProceedings{Mauchly:1947:PPE,
author = "J. W. Mauchly",
booktitle = "{Proceedings of a Symposium on Large Scale Digital
Calculating Machinery, 7--10 January 1947}",
title = "Preparation of problems for {EDVAC}-type machines",
publisher = "Harvard University Press",
address = "Cambridge, MA, USA",
year = "1947",
bibdate = "Wed Oct 13 11:55:58 2010",
bibsource = "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{Richeson:1947:FAP,
author = "A. W. Richeson",
title = "The First Arithmetic Printed in {English}",
journal = j-ISIS,
volume = "37",
number = "1--2",
pages = "47--56",
month = may,
year = "1947",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:27:09 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302230;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/isis1940.bib",
URL = "http://www.jstor.org/stable/226161",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/page/journal/isis/about.html",
}
@Article{vonNeumann:1947:NIM,
author = "John von Neumann and Herman H. Goldstine",
title = "Numerical Inverting of Matrices of High Order",
journal = j-BULL-AMS,
volume = "53",
number = "11",
pages = "1021--1099",
month = nov,
year = "1947",
CODEN = "BAMOAD",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
MRclass = "65.0X",
MRnumber = "MR0024235 (9,471b)",
MRreviewer = "E. Bodewig",
bibdate = "Thu Nov 8 14:49:36 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Goldstine:1951:NIM} for Part II. Reprinted
in \cite[pp. 479--557]{Taub:1963:JNCa}.",
ZMnumber = "0031.31402",
acknowledgement = ack-nhfb # " and " # ack-jg,
fjournal = "Bulletin of the American Mathematical Society",
kwds = "nla, linear system, rounding error",
referred = "[Markov1999a].",
remark = "This may be the first journal publication about the
use of double-precision arithmetic on computers, used
for the accumulation of inner products and matrix
products. On pp.~1035--1038, the authors show that when
the sum of $m$ products of two $s$-digit numbers is
accumulated in precision $ 2 s $, with rounding to $s$
digits only after the final sum is complete, then the
rounding error is essentially one unit in the last
place, instead of $m$ times that value. Cited in
\cite{Sterbenz:1974:FPC}.",
}
@Article{Alt:1948:BTLa,
author = "Franz L. Alt",
title = "A {Bell Telephone Laboratories}' Computing
Machine---{I}",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "3",
number = "21",
pages = "1--13",
month = jan,
year = "1948",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "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,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Eckert:1948:EC,
author = "W. J. Eckert",
title = "Electrons and computation",
journal = j-SCI-MONTHLY,
volume = "67",
number = "5",
pages = "315--323",
month = nov,
year = "1948",
CODEN = "SCMOAA",
ISSN = "0096-3771",
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,
fjournal = "The Scientific Monthly",
}
@InProceedings{Rademacher:1948:AEP,
author = "Hans A. Rademacher",
title = "On the Accumulation of Errors in Processes of
Integration on High-Speed Calculating Machines",
crossref = "Anonymous:1948:PSL",
pages = "176--187",
year = "1948",
bibdate = "Mon Jun 18 11:03:56 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "From page 186, remark by John W. Mauchly: ``I just
wanted to remark that this paper is probably one of the
first to appear as a result of the interaction between
computing machines and mathematics. I think many of us
have been looking forward with certainty to the day
when the advent of computing machines would influence
the course of mathematics, and there are still many
directions in which we can look forward to further such
impacts. This reaction is not, of course, one way.
Mathematics should also influence the computing
machine.''",
}
@TechReport{Tukey:1948:NSR,
author = "John W. Tukey",
title = "A note on the square-root iteration",
type = "SRG Memorandum report",
number = "10",
institution = inst-PRINCETON,
address = inst-PRINCETON:adr,
pages = "18",
year = "1948",
bibdate = "Tue May 15 08:00:09 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Turing:1948:REM,
author = "A. M. Turing",
title = "Rounding-Off Errors in Matrix Processes",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "1",
pages = "287--308",
month = sep,
year = "1948",
CODEN = "QJMMAV",
ISSN = "0033-5614",
ISSN-L = "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",
ZMnumber = "0033.28501",
acknowledgement = ack-nhfb,
fjournal = "Quarterly Journal of Mechanics and Applied
Mathematics",
mynote = "The notes are not very good. They mainly correct
errors and fill in the gaps of derivations. Much better
would have been higher level comments from a numerical
analyst, e.g. on where Turing's ideas/predictions were
wrong.",
}
@Article{Williams:1948:EDC,
author = "F. C. Williams and T. Kilburn",
title = "Electronic digital computers",
journal = j-NATURE,
volume = "162",
number = "487",
pages = "??--??",
year = "1948",
CODEN = "NATUAS",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
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,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
}
@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 = "1",
pages = "57--62",
month = jan,
year = "1949",
CODEN = "JRNBAG",
DOI = "https://doi.org/10.6028/jres.042.005",
ISSN = "0091-0635 (print), 2376-5305 (electronic)",
ISSN-L = "0091-0635",
bibdate = "Fri Aug 20 09:32:34 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "With an appendix by Douglas R. Hartree.",
abstract = "An example of numerical integration is given that
shows very systematic effects in the less significant
digits. This lack of randomness gives rounding-off
errors that exceed the predicted standard deviation by
a factor of three. The example considered in this paper
shows that systematic rounding-off errors can occur in
numerical in integration, irrespective of the number of
digits kept in the contributions to the integral. In
the appendix this phenomenon is examined, and criteria
are set up to detect the cases in which it may arise to
a serious extent.",
acknowledgement = ack-nhfb,
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@TechReport{Tukey:1949:TRA,
author = "John W. Tukey and M. F. Freeman",
title = "Transformation related to the angular and the
square-root",
type = "SRG Memorandum report",
number = "24",
institution = inst-PRINCETON,
address = inst-PRINCETON:adr,
pages = "??",
year = "1949",
bibdate = "Tue May 15 08:00:09 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Stifler:1950:HSC,
editor = "W. W. {Stifler, Jr.}",
title = "High-speed computing devices",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xiii + 451",
year = "1950",
LCCN = "QA75 .E5",
bibdate = "Fri Aug 20 10:18:44 MDT 2010",
bibsource = "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",
ISSN-L = "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,
fjournal = "Quarterly Journal of Mechanics and Applied
Mathematics",
}
@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,
fjournal = "Proceedings of the Cambridge Philosophical Society.
Mathematical and physical sciences",
keywords = "accurate floating-point summation; floating-point
arithmetic; rounding errors",
remark = "Higham \cite{Higham:1993:AFP} comments ``In 1951 Gill
[8] noticed that the rounding error in the sum of two
numbers could be estimated by subtracting one of the
numbers from the sum, and he made use of this estimate
in a Runge--Kutta code in a program library for the
EDSAC computer.''",
}
@Article{Goldstine:1951:NIM,
author = "Herman H. Goldstine and John von Neumann",
title = "Numerical Inverting of Matrices of High Order. {II}",
journal = j-PROC-AM-MATH-SOC,
volume = "2",
pages = "188--202",
year = "1951",
CODEN = "PAMYAR",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "65.0X",
MRnumber = "MR0041539 (12,861b)",
MRreviewer = "F. J. Murray",
bibdate = "Thu Nov 8 14:49:46 2007",
bibsource = "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",
ZMnumber = "043.12301",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
}
@InProceedings{Rademacher:1951:AEP,
author = "Hans Rademacher",
booktitle = "Proceedings of a Symposium on Large-scale Digital
Calculating Machinery",
title = "On the accumulation of errors in processes of
integration on high-speed calculating machines",
publisher = pub-HARVARD,
address = pub-HARVARD:adr,
pages = "176--185",
year = "1951",
bibdate = "Mon Jun 18 06:50:41 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Shirley:1951:BNB,
author = "John W. Shirley",
title = "Binary Numeration before {Leibniz}",
journal = j-AMER-J-PHYSICS,
volume = "19",
number = "8",
pages = "452--454",
year = "1951",
CODEN = "AJPIAS",
DOI = "https://doi.org/10.1119/1.1933042",
ISSN = "0002-9505 (print), 1943-2909 (electronic)",
ISSN-L = "0002-9505",
bibdate = "Sat Feb 8 10:29:20 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://scitation.aip.org/content/aapt/journal/ajp/19/8/10.1119/1.1933042",
abstract = "Though it is frequently stated that binary numeration
was first formally proposed by Leibniz as an
illustration of his dualistic philosophy, the
mathematical papers of Thomas Hariot (1560--1621) show
clearly that Hariot not only experimented with number
systems, but also understood clearly the theory and
practice of binary numeration nearly a century before
Leibniz's time.",
acknowledgement = ack-nhfb,
fjournal = "American Journal of Physics",
journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp",
}
@Book{Wilkes:1951:PPE,
author = "Maurice V. Wilkes and David J. Wheeler and Stanley
Gill",
title = "The Preparation of Programs for an Electronic Digital
Computer",
publisher = pub-AW,
address = pub-AW:adr,
pages = "167",
year = "1951",
LCCN = "QA76.5 .W55 1951",
bibdate = "Mon Feb 10 09:42:47 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also second edition \cite{Wilkes:1957:PPE}, and
reprint \cite{Wilkes:1982:PPE}.",
acknowledgement = ack-nhfb,
tableofcontents = "Part I \\
Chapter 1. The Design of Programs for Electronic
Computing Machines / 1 \\
1-1 Introduction / 1 \\
1-2 Types of automatic computing machines / 2 \\
1-3 Description of the EDSAC / 3 \\
1-4 The EDSAC order code / 5 \\
1-5 Notes on the order code / 6 \\
1-6 The use of conditional orders / 7 \\
1-7 Modification of orders by the program / 8 \\
1-8 Multiaddress codes / 11 \\
1-9 Binary--decimal conversion / 12 \\
1-10 Checking facilities / 14 \\
Chapter 2. Input of Orders / 15 \\
2-1 Initial orders / 15 \\
2-2 Pseudo-orders / 17 \\
2-3 Examples / 17 \\
2-4 Control combinations / 17 \\
2-5 Starting the program / 18 \\
2-6 Use of code letters / 19 \\
2-7 Constants / 20 \\
2-8 Notation / 20 \\
Chapter 3. Subroutines and Parameters / 22 \\
3-1 Open subroutines / 22 \\
3-2 closed subroutines / 22 \\
3-3 preset parameters / 23 \\
3-4 program parameters / 23 \\
Chapter 4. Library Subroutines and their Use in
Constructing Programs / 25 \\
4-1 Library catalog / 25 \\
4-2 Input and output subroutines / 25 \\
4-3 Division subroutines / 27 \\
4-4 Trigonometrical and other functions / 27 \\
4-5 Quadrature / 27 \\
4-6 Assembly subroutines / 27 \\
4-7 Integration of differential equations / 32 \\
4-8 Processes, Interpretive subroutines / 34 \\
Chapter 5. Pitfalls / 38 \\
5-1 Proofreading of programs, points to be checked / 38
\\
5-2 Location of mistakes in a program / 39 \\
5-3 Counting operations / 41 \\
Chapter 6. Use of the EDSAC \& Its Associated Equipment
/ 42 \\
6-1 Tape Punching \& editing facilities / 42 \\
6-2 Storage of library subroutines / 43 \\
6-3 EDSAC organization / 43 \\
6-4 EDSAC controls / 43 \\
Chapter 7. Examples / 45 \\
7-1 Example 1. Calculation of $\exp(-\sin x)$ / 45 \\
7-2 Example 2. Calculation of $\pi$ by evaluation of
definite integral / 48 \\
7-3 Alternative method for Example 2 / 52 \\
7-4 Example 2, with extra print orders for checking /
53 \\
7-5 Application of checking subroutine C11 to Example 2
/ 54 \\
7-6 Example of integration of an ordinary differential
equation / 46 \\
7-7 Evaluation of a definite integral / 61 \\
7-8 Program to facilitate the solution of algebraic
equation / 66 \\
Part II. Specifications of Library Subroutines / 72 \\
A. Subroutines to carry out floating point arithmetic /
73 \\
B. Subroutines to carry out arithmetical operations on
complex numbers / 78 \\
C. Checking subroutines / 79 \\
D. Division subroutines / 82 \\
E. Exponential subroutines / 83 \\
F. General routines relating to functions / 84 \\
G. Subroutines for integration of ordinary differential
equations / 86 \\
J. Subroutines for calculating special functions
[Legendre polynomials] / 88 \\
K. Subroutines for the summation of power series / 88
\\
L. Subroutines for evaluating logarithms / 91 \\
M. Miscellaneous subroutines / 91 \\
P. Print subroutines / 92 \\
Q. Quadrature subroutines / 95 \\
R. Input subroutines / 96 \\
S. Subroutines for evaluation of fractional powers / 98
\\
T. Subroutines for calculating trigonometrical
functions / 99 \\
U. Subroutines for counting operations / 101 \\
V1. Multiplication of vector by symmetric matrix / 102
\\
V2. Addition and subtraction of $n$ dimensional vectors
/ 103 \\
Part III. Programs of Selected Library Subroutines /
104 \\
Appendix A. Keyboard perforator code, etc. / 158 \\
Appendix B. The initial orders / 159 \\
Appendix C. Control combinations / 161 \\
Appendix D. Interpretive subroutines: example of
packing of orders / 162 \\
Appendix E. Methods of counting in a simple cycle / 164
\\
Index",
}
@InProceedings{Andrews:1952:RBL,
author = "E. G. Andrews",
editor = "J. C. McPherson",
booktitle = "Proceedings of the AIEE-IRE '51: Papers and
discussions presented at the December 10--12, 1951,
joint AIEE-IRE computer conference, Philadelphia, PA:
Review of electronic digital computers",
title = "A review of the {Bell Laboratories}' digital computer
developments",
publisher = pub-ACM,
address = pub-ACM:adr,
bookpages = "vi + 114",
pages = "101--105",
year = "1952",
DOI = "https://doi.org/10.1145/1434770.1434787",
LCCN = "????",
bibdate = "Fri Dec 03 09:17:58 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Bell Laboratories Model 1--5 relay computers; complex
fixed-point decimal arithmetic; complex floating-point
decimal arithmetic",
}
@Article{Davis:1952:ARS,
author = "K. Davis and R. Biddulph and S. Balashek",
title = "Automatic Recognition of Spoken Digits",
journal = j-J-ACOUST-SOC-AM,
volume = "24",
number = "6",
pages = "637--642",
month = nov,
year = "1952",
CODEN = "JASMAN",
ISSN = "0001-4966",
ISSN-L = "0001-4966",
bibdate = "Fri Nov 28 16:38:51 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "Journal of the Acoustical Society of America",
}
@Article{Michaelson:1952:BA,
author = "R. L. Michaelson",
title = "Binary Arithmetic",
journal = j-INC-STAT,
volume = "3",
number = "1",
pages = "35--40",
month = feb,
year = "1952",
CODEN = "????",
DOI = "https://doi.org/10.2307/2986591",
ISSN = "1466-9404",
ISSN-L = "1466-9404",
bibdate = "Thu Jan 22 18:10:18 MST 2015",
bibsource = "http://www.jstor.org/stable/i349863;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jrss-d-1950.bib",
URL = "http://www.jstor.org/stable/2986591",
acknowledgement = ack-nhfb,
fjournal = "The Incorporated Statistician",
journal-URL = "http://www.jstor.org/journals/14669404.html",
}
@Article{Morrill:1952:SEM,
author = "C. D. Morrill and R. V. Baum",
title = "A Stabilized Electronic Multiplier",
journal = j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT,
volume = "EC-1",
number = "??",
pages = "52--59",
month = dec,
year = "1952",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Jul 15 15:20:53 2011",
bibsource = "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,
}
@Article{Brooker:1953:FOE,
author = "R. A. Brooker and D. J. Wheeler",
title = "Floating Operations on the {EDSAC} (in Automatic
Computing Machinery; Discussions)",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "7",
number = "41",
pages = "37--47",
month = jan,
year = "1953",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1953-0052901-3",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
abstract = "The difficulties which arise when programming
calculations for large automatic calculating machines
which have a fixed decimal point are discussed. This
leads to a consideration of the possibility of using
floating decimal arithmetic for certain kinds of
calculations. A method by which floating decimal
arithmetic can be carried out with any fixed
decimal-point machine is outlined and the scheme
adopted for use with the EDSAC is described in
detail.",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "floating-point decimal arithmetic",
remark-01 = "From page 38: ``The problem [of programmer-controlled
numeric scaling] does not arise with machines designed
to operate directly with numbers expressed in the
floating radix form. Numbers in this form are
represented by $a \cdot r^p$. The first machine of this
kind was the Bell Telephone Laboratories Relay Computer
Model V(1). This is a decimal machine (that is, $r =
10$) in which $1 > |a| > 0.1$, $19 > p > -19$ and $a$
is expressed to an accuracy of seven significant
figures. Since this was completed all important relay
machines have been equipped with similar facilities. No
electronic machine of this kind has yet been built but
we would remark that in our opinion an electronic
machine provided with a floating point arithmetical
unit would be a powerful computing instrument even if
it had a relatively slow store, a magnetic drum, for
example.''",
remark-02 = "From page 39: ``Two long and two short storage
locations are set aside to form a kind of `arithmetical
unit.' One long location holds the numerical part of a
number and one short location holds the exponent.
Together they form the {\em floating decimal
accumulator}. In a similar fashion the other long
location and the other short location form the {\em
floating decimal register}.''",
remark-03 = "From page 40: ``the floating decimal accumulator is
then `cleared' by replacing the number held in it by
zero, that is, by the special number $010^{-63}$.''",
remark-04 = "From page 40: `The use of two separate storage
locations for the floating decimal accumulator allows
the range and accuracy of numbers held therein to be
greater than those held in a single storage location
elsewhere. This enables products to be accumulated
without loss of accuracy due to intermediate
rounding-off errors.''",
remark-05 = "From the conclusion on page 46: ``From a direct
comparison it would seem that the floating 'orders,'
other than those used for reading and writing, are
about 60 times as slow as the machine orders and hence
that a programme using the interpretive subroutine
would be slower by the same factor. This is not
altogether true because in such a programme fewer
orders' are needed than would otherwise be necessary as
there are no scale factors to deal with and the
techniques for counting and for the modification of
orders' have been streamlined. Moreover, the time taken
by the C auxiliaries is about the same as that taken by
the corresponding subroutine in fixed decimal-point
working. These factors vary from problem to problem but
our experience has shown that the reduction in speed
varies from about 20 to 1 to about 4 to 1. The
reduction of the time taken to code a problem has to be
experienced to be believed!''",
}
@Book{IBM:1953:POT,
author = "{IBM Corporation}",
title = "Principles of Operation: Type 701 and Associated
Equipment",
publisher = pub-IBM,
address = pub-IBM:adr,
pages = "103",
year = "1953",
bibdate = "Wed Sep 14 23:17:49 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Samelson:1953:ORR,
author = "Klaus Samelson and Friedrich L. Bauer",
title = "{Optimale Rechengenauigkeit bei Rechenanlagen mit
gleitendem Komma}. ({German}) [{Optimal} calculation
accuracy for calculators with a floating point]",
journal = j-Z-ANGE-MATH-PHYS,
volume = "4",
number = "4",
pages = "312--316",
month = jul,
year = "1953",
CODEN = "ZAMPDB",
DOI = "https://doi.org/10.1007/bf02074638",
ISSN = "0044-2275 (print), 1420-9039 (electronic)",
ISSN-L = "0044-2275",
bibdate = "Sun Aug 16 18:04:35 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Digital automatic computing machines with floating
binary point are investigated with respect to their
accuracy. It is concluded that special devices can be
designed without difficulty, which guarantee the
highest accuracy obtainable with a fixed number of
digits. For binary computers, a modification of the
usual conversion routine is necessary, which is
discussed in detail.",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und Physik
= Journal of Applied Mathematics and Physics}",
journal-URL = "http://link.springer.com/journal/33",
keywords = "number base conversion",
language = "German",
}
@Article{Backus:1954:ISS,
author = "J. W. Backus",
title = "The {IBM 701 Speedcoding} System",
journal = j-J-ACM,
volume = "1",
number = "1",
pages = "4--6",
month = jan,
year = "1954",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Fri Nov 04 00:18:27 1994",
bibsource = "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,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Manual{Burroughs:1954:DH,
author = "{Burroughs Corporation.ElectroData}",
title = "Datatron handbooks",
organization = "The Division",
address = "Pasadena, CA, USA",
year = "1954",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "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,
fjournal = "Journal of the Society for Industrial and Applied
Mathematics",
}
@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 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Fri Nov 04 00:18:27 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "decimal floating-point arithmetic",
}
@Article{Clenshaw:1955:NSC,
author = "C. W. Clenshaw",
title = "A note on the summation of {Chebyshev} series",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "9",
number = "51",
pages = "118--120",
year = "1955",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1955-0071856-0",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRclass = "65.0X",
MRnumber = "0071856",
bibdate = "Thu Feb 08 16:17:25 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Hidden inside \cite{Brenner:1955:TNS}, but important
in its own right for commentary on the recursive
algorithm for summation of Chebyshev series, and a
brief analysis of its accuracy.",
}
@Article{Crockett:1955:GMM,
author = "J. B. Crockett and H. Chernoff",
title = "Gradient Methods of Maximization",
journal = j-PAC-J-MATH,
volume = "5",
number = "??",
pages = "33--50",
year = "1955",
CODEN = "PJMAAI",
ISSN = "0030-8730 (print), 1945-5844 (electronic)",
ISSN-L = "0030-8730",
bibdate = "Fri Aug 20 08:54:24 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Pacific Journal of Mathematics",
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 = j-ELECTRON-ENG,
volume = "27",
number = "??",
pages = "287--289",
month = jul,
year = "1955",
CODEN = "ELEGAP",
ISSN = "0013-4902",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Engineering",
}
@Article{Parsons:1955:SDC,
author = "Frances L. Parsons",
title = "A Simple Desk-Calculator Method for Checking Binary
Results of Digital Computer Arithmetic Operations",
journal = j-J-ACM,
volume = "2",
number = "3",
pages = "205--207",
month = jul,
year = "1955",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Wed Nov 09 01:00:34 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Book{Richards:1955:AOD,
author = "Richard Kohler Richards",
title = "Arithmetic Operations in Digital Computers",
publisher = "D. Van Nostrand",
address = "New York, NY, USA",
pages = "iv + 397",
year = "1955",
LCCN = "QA75 .R5 1955",
bibdate = "Fri Nov 28 18:46:37 2003",
bibsource = "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 = "https://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 = "https://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",
tableofcontents = "1. Introduction (significant figures, random
errors, error bounds, etc.) \\
2. Interpolation with divided differences \\
3. Lagrangian methods \\
4. Finite-difference interpolation \\
5. Operations with finite differences \\
6. Numerical solution of ordinary differential
equations \\
7. Least-squares polynomial approximation \\
8. Gaussian quadrature and related topics \\
9. Approximations of various types \\
10. Numerical solution of equations \\
Appendix: Justification of the Crout reduction",
}
@Article{Lilamand:1956:TDM,
author = "M. Lejet Lilamand",
title = "A Time-Division Multiplier",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-5",
number = "1",
pages = "26--34",
month = mar,
year = "1956",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1956.5219789",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 15:46:18 MDT 2011",
bibsource = "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 (print), 1557-735X (electronic)",
ISSN-L = "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,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "decimal floating-point arithmetic",
remark = "Early example of a decimal floating-point machine.",
}
@Article{Robertson:1956:NCD,
author = "J. E. Robertson",
title = "A new class of digital division methods",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-5",
number = "??",
pages = "65--73",
month = jun,
year = "1956",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Fri Nov 09 19:14:45 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@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 = "https://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,
fjournal = "IRE Transactions on Electronic Computers",
}
@Book{Alt:1957:EDC,
editor = "Franz L. Alt",
title = "Electronic Digital Computers: Their Use in Science and
Engineering",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "x + 335",
year = "1957",
bibdate = "Sun Jun 17 18:53:23 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Section 2.3 discusses number representation and
decimal versus binary arithmetic.",
tableofcontents = "
",
xxnote = "Check page count: incomplete view in Google books.
Price bibliography says 1958.",
}
@Article{Ercoli:1957:EDO,
author = "Paolo Ercoli and Roberto Vacca",
title = "Errors Due to Overflow in Arithmetic Operations
Particularly as Regards {FINAC} Electronic Computer",
journal = j-J-ACM,
volume = "4",
number = "4",
pages = "450--455",
month = oct,
year = "1957",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Thu Dec 08 09:28:48 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See letter \cite{Ercoli:1960:LEE}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "floating-point arithmetic; overflow",
}
@Article{Gini:1957:SFD,
author = "Corrado Gini",
title = "Sulla frequenza delle cifre iniziali dei numeri
osservati. ({Italian}) [{On} the frequency of initial
digits of observed numbers]",
journal = "Bull. Inst. Internat. Stat.",
volume = "35",
number = "??",
pages = "57--76",
year = "1957",
bibdate = "Sun Sep 18 11:54:25 2011",
bibsource = "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 = "https://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 = "https://doi.org/10.1109/TEC.1957.5221579",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 16:07:27 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221579",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@Article{Kogbetliantz:1957:CEN,
author = "E. G. Kogbetliantz",
title = "Computation of $ e^n $ for $ - \infty < n < + \infty $
Using an Electronic Computer",
journal = j-IBM-JRD,
volume = "1",
number = "2",
pages = "110--115",
month = apr,
year = "1957",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Sep 06 18:04:49 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Lehman:1957:HSD,
author = "M. Lehman",
title = "High-Speed Digital Multiplication",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-6",
number = "3",
pages = "204--205",
month = sep,
year = "1957",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1957.5222025",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 16:07:34 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222025",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@Article{Luke:1957:CLZ,
author = "Y. L. Luke",
title = "On the Computation of $ \log {Z} $ and $ \arctan {Z}
$",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "??",
pages = "16--18",
month = "????",
year = "1957",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@TechReport{Metze:1957:SPO,
author = "G. Metze",
title = "A Study of Parallel One's Complement Arithmetic Units
with Separate Carry or Borrow Storage",
type = "Report",
number = "81",
institution = "Digital Computer Laboratory, University of Illinois",
address = "Urbana, IL, USA",
pages = "77",
year = "1957",
bibdate = "Thu Nov 18 09:07:07 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Flores' book \cite[p. 485]{Flores:1963:LCA} cites this
report, and says that its conclusion is that the
disadvantages of one's complement arithmetic outweigh
the advantages.",
}
@Article{Murphy:1957:PIA,
author = "R. W. Murphy",
title = "A Positive-Integer Arithmetic for Data Processing",
journal = j-IBM-JRD,
volume = "1",
number = "2",
pages = "158--170",
month = apr,
year = "1957",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.12.0158",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "68.0X",
MRnumber = "18,939d",
bibdate = "Tue Sep 11 15:35:33 MDT 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
http://www.research.ibm.com/journal/",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392735;
http://www.research.ibm.com/journal/rd/012/ibmrd0102G.pdf",
abstract = "It is hypothesized that positive numbers suffice for
the expression of quantities in accounting. New
arithmetic operations are devised that yield
non-negative results in computation, and the
applicability of these operations to data processing is
studied. These operations permit a wide variety of
functions to be computed with fewer and less complex
steps and imply the feasibility of constructing less
complex data-processing machines.",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
reviewer = "C. C. Gotlieb",
}
@Article{Pawlak:1957:UEN,
author = "Z. Pawlak",
title = "Use of expansions with a negative basis in the
arithmometer of a digital computer",
journal = "Bull. Acad. Pol. Sci., Ser. Sci. Tech.",
volume = "5",
number = "??",
pages = "232--236",
month = "????",
year = "1957",
bibdate = "Thu Nov 06 05:56:32 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "negative base",
}
@TechReport{Taylor:1957:CCA,
author = "W. Bruce Taylor",
title = "{COIN} (Compile-Interpreter): an automatic
programming, fixed and floating-point library of
subroutines for the {ERA} 1103 computer",
institution = "Operations Research Office, Johns Hopkins University",
address = "Bethesda, MD, USA",
pages = "43",
year = "1957",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Staff paper / Johns Hopkins University, Operations
Research Office; ORO-SP-32 Staff paper (Johns Hopkins
University. Operations Research Office); ORO-SP-32.",
acknowledgement = ack-nhfb,
keywords = "Military art and science --- Data processing.;
Military research --- Data processing.",
remark = "Cover title. ``Operating under contract with the
Department of the Army.'' ``Project COMPLAB.''
``October 1957.'' ORO-SP-32",
}
@Article{Wadel:1957:NBN,
author = "L. B. Wadel",
title = "Negative base number systems",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-6",
number = "??",
pages = "123--??",
month = jun,
year = "1957",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Thu Nov 06 05:53:55 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
keywords = "negative base",
}
@Article{Walker:1957:EMA,
author = "R. M. Walker and D. E. Rosenheim and P. A. Lewis and
A. G. Anderson",
title = "An Experimental 50-Megacycle Arithmetic Unit",
journal = j-IBM-JRD,
volume = "1",
number = "3",
pages = "257--278",
month = jul,
year = "1957",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.13.0257",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Sep 11 15:35:35 MDT 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
http://www.research.ibm.com/journal/",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392687;
http://www.research.ibm.com/journal/rd/013/ibmrd0103H.pdf",
abstract = "An experimental 50-megacycle arithmetic unit has been
built which performs a repetitive multiplication
program and checks the results for errors. The unit
uses pulse circuitry which has been developed to
perform digital operations at a 50-megacycle
pulse-repetition rate. This paper describes the
arithmetic system and the circuits which perform the
required functions. These circuits include a full
binary adder, a phase-locked frequency divider which
provides a 3.125-megacycle secondary timing source, a
reshaping and retiming circuit using germanium diodes
and capacitive storage, a high-speed shift register, a
high-speed indicator register, and a binary word
generator.\par
Various novel features of a digital system operating at
these high speeds are described. These include the use
of coaxial delay lines for the distribution of signals
and as storage elements, and the use of secondary
emission tubes in amplifier and multivibrator
circuits.\par
In a 50-megacycle system the interdependence of the
space and time dimensions is marked, and although this
introduces problems which are not ordinarily
encountered in computing systems, it may be used
advantageously to provide features such as the
variable-phase clock system used in the arithmetic
unit.\par
The performance and reliability of the arithmetic unit
are discussed as well as the reliability of the
components and circuits which make up the system.
Although the techniques and circuitry discussed here
have been applied only to a relatively simple
arithmetic unit, it is felt that they could be useful
in a variety of high-speed computing and measurements
applications.",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Weibel:1957:EAM,
author = "Erich S. Weibel",
title = "An Electronic Analog Multiplier Using Carriers",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-6",
number = "1",
pages = "30--34",
month = mar,
year = "1957",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1957.5221558",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 16:07:23 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221558",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@Book{Wilkes:1957:PPE,
author = "Maurice V. Wilkes and David J. Wheeler and Stanley
Gill",
title = "The Preparation of Programs for an Electronic Digital
Computer",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Second",
pages = "xiv + 238",
year = "1957",
LCCN = "QA76.5 .W52 1957",
bibdate = "Mon Feb 10 09:42:47 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also first edition \cite{Wilkes:1951:PPE}.",
URL = "https://b-ok.org/book/3668116/b363ff",
acknowledgement = ack-nhfb,
remark-1 = "According to \cite{Anderson:2019:SAM}, this book
discusses the computation of integer population counts
on the Electronic Delay Storage Automatic Calculator
(EDSAC) computer using a recursive divide-and-conquer
algorithm. See also somewhat negative 1958 review by
Fernando J. Corbat{\'o}
\cite{https://doi.org/10.1063/1.3062687}.
Floating-point arithmetic is discussed on pages 60,
90--91, and 135--137.",
remark-2 = "From page 5: ``Each storage location in the EDSAC
holds 17 binary digits. In words representing numbers,
the binary point is regarded as being to the right of
the extreme left-hand digit; this digit (the most
significant digit) is used as a sign indicator and is
referred to as the sign digit. \ldots{} the capacity of
the accumulator is 70 digits; there is, therefore,
plenty of room to hold the full 33-digit product of two
17-digit numbers. \ldots{} A negative number $-x$
(where $O < x \leq 1$) is represented by a $1$ in the
sign-digit position, followed by the digits of $(1 -
x)$; for example, $1.1100\ldots{}$ represents $-(1 -
3/4 = -1/4$. \ldots{} Another way of explaining the
representation of negative numbers is to regard the
sign digit as an ordinary numerical digit, and to say
that $-x$ is stored as the number $(2 - x)$. Note in
particular that $1.0000\ldots{}$ represents $-1$.''
[Page 59 calls this a {\em True complements}
representation, distinguished from one's complement.]",
remark-3 = "From page 35: ``The EDSAC has a facility which enables
an even-numbered storage location and the following
odd-numbered storage to be used as a single storage
location holding 35 binary digits.'' [This suggests the
word size in 18, not 17 as page 5 suggests. The
Wikipedia article on the EDSAC reports: ``The EDSAC's
main memory consisted of 1024 locations, though only
512 locations were initially installed. Each contained
18 bits, but the topmost bit was always unavailable due
to timing problems, so only 17 bits were used.'']",
remark-4 = "From page 36: ``The multiplier register of the
arithmetical unit is of sufficient capacity to hold a
long number, and the accumulator is of sufficient
capacity to hold the complete (69) binary digit
[including the sign bit]) product of two long
numbers.''",
remark-5 = "From page 36: ``In some calculations, long numbers may
not provide sufficient precision. In such cases, the
programmer may make use of what is known as
double-length or double-precision working, in which two
long storage locations are used to hold the digits of a
single number.'' [this would be a quad-word number
holding 69 bits, including the sign bit.].",
remark-6 = "From page 60: ``\ldots{} two double-length numbers,
each stored in two locations, can be added and the
result put in two locations in the store, by means of
six orders''.",
remark-7 = "From page 90: ``Each number is expressed in the form
$a \cdot 10^p$, where $-10 \leq a \leq 10$ and $63 \leq
p < 63$ and is represented in the store by $a \cdot
2^{-11} + p \cdot 2^{-6}$.''",
remark-8 = "From page 91: ``Numbers are expressed in the form $a
\cdot 10^p$, where $a$ and $p$ are packed into a single
storage location. The number of digits defining $p$ may
be varied from 4 to 15 by means of a preset parameter,
so that a suitable value for the permissible range of
variation of numbers may be selected for a given
calculation.''",
remark-9 = "From page 91: ``Although the use of floating-point
operation can simplify the programmer's task by
relieving him of undue preoccupation with scaling, it
must not be thought that it solves all his
difficulties. In particular, the loss of significant
digits resulting from the subtraction of a number from
a nearly equal number can have serious consequences
unless proper precautions are taken.''",
tableofcontents = "CHAPTER 1. THE ELEMENTS OF PROGRAM DESIGN / 1 \\
1-1 Introduction / 1 \\
1-2 Types of automatic computing machine / 1 \\
1-3 The EDSAC / 3 \\
1-4 Store / 5 \\
1-5 Arithmetical unit / 5 \\
1-6 Form of numbers in the machine / 5 \\
1-7 Form of orders in the machine / 6 \\
1-8 Storage of orders / 6 \\
1-9 Written form of orders / 7 \\
1-10 Some simple examples / 7 \\
Exercises A / 9 \\
1-11 Jump orders / 9 \\
Exercises B / 11 \\
1-12 Repeated groups of orders / 11 \\
1-13 The use of the B-register / 15 \\
Exercises C / 18 \\
1-14 Equivalence between orders and numbers;
pseudo-orders / 18 \\
1-15 Use of the arithmetical unit for constructing or
modifying orders / 20 \\
1-16 The mix order / 23 \\
Exercises D / 24 \\
CHAPTER 2. SUBROUTINES / 25 \\
2-1 Introduction / 25 \\
2-2 Relative numbering of addresses / 25 \\
2-3 Internal and external forms of orders / 26 \\
2-4 Reading of orders from the input tape / 28 \\
2-5 Open and closed subroutines / 29 \\
2-6 Entering and leaving a closed subroutine / 29 \\
2-7 Closed B subroutines / 30 \\
2-8 Closed A subroutines / 31 \\
2-9 Use of library subroutines / 32 \\
Exercises E / 33 \\
2-10 Long numbers / 35 \\
2-11 Some further orders in the order code / 36 \\
2-12 Scale factors / 38 \\
2-13 Control combinations / 39 \\
Exercises F / 40 \\
2-14 Relative addresses in control combinations / 41
\\
2-15 Extension of the use of relative addresses / 41
\\
2-16 Setting of the constants to be added by terminal
code letters / 43 \\
2-17 Complete table of terminal code letters / 44 \\
2-18 Parameters / 45 \\
2-19 Preset parameters / 46 \\
2-20 Program parameters / 46 \\
2-21 Standard procedure for setting preset parameters /
46 \\
2-22 Interpretive subroutines / 47 \\
Exercises G / 49 \\
CHAPTER 3. PROGRAMMING FOR OTHER MACHINES / 51 \\
3-1 Introduction / 51 \\
3-2 Single-address codes / 52 \\
3-3 Multi-address codes / 53 \\
3-4 Multiplication and division / 56 \\
3-5 Source-destination codes / 57 \\
3-6 Representation of negative numbers / 59 \\
3-7 Miscellaneous facilities / 60 \\
3-8 Minimum-access coding / 61 \\
3-9 The evaluation of an order code / 63 \\
3-10 Use of an auxiliary store / 64 \\
CHAPTER 4. INPUT AND OUTPUT / 66 \\
4-1 Introduction / 66 \\
4-2 Input of numbers / 66 \\
4-3 Output of numbers / 67 \\
4-4 Input of orders / 69 \\
4-5 Recognition of the code letter S / 72 \\
4-6 Economy of input and output time / 72 \\
4-7 Some features of input systems used with other
machines / 73 \\
4-8 Punched tape / 73 \\
4-9 Punched cards / 75 \\
CHAPTER 5. THE LIBRARY OF SUBROUTINES / 80 \\
5-1 Introduction / 80 \\
5-2 Library catalog / 80 \\
5-3 Input subroutines / 81 \\
5-4 Output subroutines / 81 \\
5-5 Division subroutines / 82 \\
5-6 Trigonometric and other functions / 82 \\
5-7 The economization of a power series by the use of
Chebyshev polynomials / 83 \\
5-8 Quadrature / 86 \\
5-9 Integration of ordinary differential equations / 87
\\
5-10 Library subroutines Gl2 and G13: Runge--Kutta
processes / 88 \\
5-11 The independent variable / 88 \\
5-12 Definition of the Runge--Kutta--Gill process / 89
\\
5-13 Taylor-series method / 90 \\
5-14 Interpretive subroutines / 90 \\
5-15 Floating-point subroutines / 90 \\
CHAPTER 6. DIAGNOSIS OF ERRORS IN PROGRAM / 92 \\
6-1 Introduction / 92 \\
6-2 Proofreading of programs / 93 \\
6-3 Punching / 93 \\
6-4 Locating mistakes in a program- / 94 \\
6-5 Subroutines for checking programs / 96 \\
6-6 The development of a program / 97 \\
CHAPTER 7. EXAMPLES OF COMPLETE PROGRAMS FOR THE EDSAC
/ 99 \\
EXAMPLE 1 Calculation of $e^{-\sin x}$ / 99 \\
EXAMPLE 2 The evaluation of a definite integral / 102
\\
EXAMPLE 3 Integration of an ordinary differential
equation / 108 \\
EXAMPLE 4 Evaluation of a Fourier transform / 113 \\
EXAMPLE 5 Evaluation of a definite integral / 118 \\
CHAPTER 8. AUTOMATIC PROGRAMMING / 126 \\
8-1 Introduction / 126 \\
8-2 Conversion versus interpretation / 127 \\
8-3 Assembly of a program / 127 \\
8-4 Floating addresses / 129 \\
8-5 Formula recognition / 136 \\
Part Two: SPECIFICATIONS OF EDSAC LIBRARY SUBROUTINES /
139 \\
CATEGORY A. Subroutines to carry out floating-point
arithmetic / 140 \\
CATEGORY B. Subroutines to perform arithmetical
operations on complex numbers / 142 \\
CATEGORY C. Error-diagnosis subroutines / 144 \\
CATEGORY D. Division subroutines / 146 \\
CATEGORY E. Exponential subroutines / 148 \\
CATEGORY F. General subroutines relating to functions /
148 \\
CATEGORY G. Subroutines for the integration of
differential equations / 150 \\
CATEGORY L. Subroutines for evaluating logarithms / 153
\\
CATEGORY M. Miscellaneous subroutines / 154 \\
CATEGORY N. Operations on double-length numbers / 156
\\
CATEGORY P. Print subroutines / 158 \\
CATEGORY Q. Quadrature subroutines / 162 \\
CATEGORY R. Input subroutines / 164 \\
CATEGORY s. Subroutines for evaluating fractional
powers / 168 \\
CATEGORY T. Subroutines for calculating trigonometric
functions / 169 \\
CATEGORY Z. Post-mortem routines / 170 \\
PART THREE: PROGRAMS OF SELECTED EDSAC LIBRARY
SUBROUTINES / 173 \\
APPENDIX 1. Input and output codes of the EDSAC / 212
\\
APPENDIX 2. Order code and controls of the EDSAC / 214
\\
APPENDIX 3. The initial input routine of the EDSAC /
218 \\
APPENDIX 4. Control combinations / 221 \\
APPENDIX 5. Specimen solutions to programming exercises
/ 223 \\
BIBLIOGRAPHY / 233 \\
INDEX / 237",
}
@TechReport{Anonymous:1958:ARM,
author = "Anonymous",
title = "Analysis and research memorandum 294",
type = "{AR} Memo",
number = "294 (AD 207929)",
institution = "Massachusetts Institute of Technology, Naval
Supersonic Laboratory",
address = "Cambridge, MA, USA",
pages = "7",
day = "23",
month = oct,
year = "1958",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Error functions.; Floating-point arithmetic.",
}
@Article{Bemer:1958:MMS,
author = "Robert W. Bemer",
title = "A Machine Method for Square-Root Computation",
journal = j-CACM,
volume = "1",
number = "1",
pages = "6--7",
month = jan,
year = "1958",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 15 18:35:46 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Bemer:1958:SMC,
author = "R. W. Bemer",
title = "A Subroutine Method for Calculating Logarithms",
journal = j-CACM,
volume = "1",
number = "5",
pages = "5--7",
month = may,
year = "1958",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Couleur:1958:BBD,
author = "J. F. Couleur",
title = "{BIDEC} --- a Binary-to-Decimal or Decimal-to-Binary
Converter",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-7",
pages = "313--316",
year = "1958",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Fri Nov 28 16:28:12 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
keywords = "decimal floating-point arithmetic",
}
@Article{Delury:1958:CAN,
author = "Daniel B. Delury",
title = "Computation with Approximate Numbers",
journal = j-MATH-TEACH,
volume = "51",
pages = "521--530",
month = nov,
year = "1958",
ISSN = "0025-5769",
bibdate = "Fri Nov 28 11:47:47 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "The Mathematics Teacher",
}
@Article{Ershov:1958:PAO,
author = "Andrei P. Ershov",
title = "On Programming of Arithmetic Operations",
journal = j-CACM,
volume = "1",
number = "8",
pages = "3--6",
month = aug,
year = "1958",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:21 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Ershov58;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Ershov58",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Ershov58",
}
@Article{Gower:1958:NIM,
author = "J. C. Gower",
title = "A Note on an Iterative Method for Root Extraction",
journal = j-COMP-J,
volume = "1",
pages = "142--143",
year = "1958",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Thu Sep 15 18:36:55 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
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)",
ISSN-L = "0018-8646",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Kogbetliantz:1958:CANb,
author = "E. G. Kogbetliantz",
title = "Computation of Arcsin {$N$} for $ 0 < {N} < 1 $ Using
an Electronic Computer",
journal = j-IBM-JRD,
volume = "2",
number = "3",
pages = "218--222",
month = jul,
year = "1958",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Metropolis:1958:SDC,
author = "N. Metropolis and R. L. Ashenhurst",
title = "Significant Digit Computer Arithmetic",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-7",
number = "4",
pages = "265--267",
month = "????",
year = "1958",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1958.5222657",
ISSN = "0367-9950",
bibdate = "Wed Feb 14 19:23:38 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
abstract = "The usual floating point arithmetic makes error
analysis difficult. This paper describes an alternative
system which offers a means of analyzing floating point
calculations more effectively and which also possesses
certain advantages from an equipment standpoint.",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Robertson:1958:NCDa,
author = "J. E. Robertson",
title = "A new class of digital division methods",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-7",
number = "3",
pages = "88--92",
month = sep,
year = "1958",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@Article{Robertson:1958:NCDb,
author = "James E. Robertson",
title = "A New Class of Digital Division Methods",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-7",
number = "3",
pages = "218--222",
month = sep,
year = "1958",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1958.5222579",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:43 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222579",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@Article{Schmid:1958:TFQ,
author = "Hermann Schmid",
title = "A Transistorized Four-Quadrant Time-Division
Multiplier with an Accuracy of 0.1 Per Cent",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-7",
number = "1",
pages = "41--47",
month = mar,
year = "1958",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1958.5222094",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:43 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=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)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:22:12 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Sisson58;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "As more emphasis is placed on improving the accuracy
of data fed into automatic computing systems, more
emphasis will be placed on redundancy checking of
predictable fields within the input. Two systems (at
least) of checking a field of decimal digits have been
proposed. In both of these it is assumed that the field
to be checked is all numeric and that the redundancy
must be of only one digit.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
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",
ISSN-L = "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,
fjournal = "Quarterly Journal of Mechanics and Applied
Mathematics",
}
@Article{Wadey:1958:TSR,
author = "W. G. Wadey",
title = "Two Square-Root Approximations",
journal = j-CACM,
volume = "1",
number = "11",
pages = "13--14",
month = nov,
year = "1958",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Wadey58;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Wadey58",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Wadey58",
}
@Article{Ashenhurst:1959:UFP,
author = "Robert L. Ashenhurst and Nicholas Metropolis",
title = "Unnormalized Floating Point Arithmetic",
journal = j-J-ACM,
volume = "6",
number = "3",
pages = "415--428",
month = jul,
year = "1959",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/320986.320996",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "68.00",
MRnumber = "MR0105833 (21 \#4568)",
MRreviewer = "H. H. Goldstine",
bibdate = "Fri Dec 08 13:06:24 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jacm.bib",
ZMnumber = "0121.12102",
abstract = "Algorithms for floating point computer arithmetic are
described, in which fractional parts are not subject to
the usual normalization convention. These algorithms
give results in a form which furnishes some indication
of their degree of precision. An analysis of one-stage
error propagation is developed for each operation; a
suggested statistical model for long-run error
propagation is also set forth.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Buchholz:1959:FFC,
author = "Wilfried Buchholz",
title = "Fingers or Fists? (The Choice of Decimal or Binary
Representation)",
journal = j-CACM,
volume = "2",
number = "12",
pages = "3--11",
month = "????",
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:28:45 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Buchholz59;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "decimal floating-point arithmetic",
oldlabel = "Buchholz59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Buchholz59",
xxnote = "Check author first name: article has W. Buchholz; I
think it should be Werner, not Wilfried.",
}
@Article{Carr:1959:EAF,
author = "John W. {Carr III}",
title = "Error Analysis in Floating Point Arithmetic",
journal = j-CACM,
volume = "2",
number = "5",
pages = "10--15",
month = may,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:23 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Carr59a;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Carr59a",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Carr59a",
}
@InCollection{Carr:1959:PC,
author = "John W. {Carr III}",
editor = "Eugene M. Grabbe and Simon Ramo and Dean E.
Wooldridge",
booktitle = "Handbook of Automation, Computation, and Control",
title = "Programming and Coding",
publisher = pub-WILEY,
address = pub-WILEY:adr,
bookpages = "????",
year = "1959",
LCCN = "TJ213 .G72",
bibdate = "Fri Aug 20 08:41:16 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "Chapter 2.",
acknowledgement = ack-nhfb,
remark = "1958--1961: Volume 1. Control fundamentals. Volume 2.
Computers and data processing. Volume 3. Systems and
components. Cited in \cite{Sterbenz:1974:FPC}.",
subject = "automation; mathematics; computers; operations
research",
}
@Article{Daggett:1959:DBC,
author = "D. H. Daggett",
title = "Decimal-Binary Conversions in {CORDIC}",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "5",
pages = "335--339",
month = sep,
year = "1959",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Thu Sep 08 08:14:00 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IRE Transactions on Electronic Computers",
keywords = "decimal floating-point arithmetic",
}
@Article{Ercoli:1959:BAD,
author = "Paolo Ercoli and Roberto Vacca",
title = "Binary Arithmetic for Discretely Variable Word Length
in a Serial Computer",
journal = j-CACM,
volume = "2",
number = "4",
pages = "13--15",
month = apr,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#ErcoliV59;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "ErcoliV59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/ErcoliV59",
}
@Article{Forsythe:1959:RNR,
author = "George E. Forsythe",
title = "Reprint of a Note on Rounding-Off Errors",
journal = j-SIAM-REVIEW,
volume = "1",
number = "1",
pages = "66--67",
month = jan,
year = "1959",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1001011",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65.00",
MRnumber = "MR0099119 (20 \#5563)",
bibdate = "Thu Mar 27 09:04:24 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/1/1;
http://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
ZMnumber = "0168.14002",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
keywords = "numerical analysis; random rounding-off procedure",
onlinedate = "January 1959",
received = "7 February 1958",
remark = "From a footnote on the cover page: ``This note was
written in June 1950 at the National Bureau of
Standards, Los Angeles, and a few copies were
distributed in multilithed form by that organization as
an appendix to a reproduction of a well-known article
by Rademacher [1]. The note was abstracted in Math.
Reviews, Vol. 12 (1951), p. 208. Because he receives
frequent requests for copies of the note, which are
unavailable, the author has asked the editors to
reprint it in essentially its original form.''",
}
@Article{Garner:1959:RMS,
author = "Harvey L. Garner",
title = "A Ring Model for the Study of Multiplication for
Complement Codes",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "1",
pages = "25--30",
month = mar,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5222757",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:44 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222757",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@Article{Garner:1959:RNS,
author = "Harvey L. Garner",
title = "The Residue Number System",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "2",
pages = "140--147",
month = jun,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5219515",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:44 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=5219515",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@InProceedings{Gray:1959:NFP,
author = "H. L. Gray and C. Harrison",
booktitle = "Proceedings of the Eastern Joint Computer Conference,
Boston, MA, December 1--3, 1959",
title = "Normalized floating-point arithmetic with an index of
significance",
volume = "16",
publisher = pub-AFIPS,
address = pub-AFIPS:adr,
pages = "244--248",
year = "1959",
LCCN = "TK7885.A1 J6",
bibdate = "Tue Oct 09 09:43:31 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Henrici:1959:TES,
author = "Peter Henrici",
editor = "????",
booktitle = "Proceedings of the International Conference on
Information Processing, UNESCO",
title = "Theoretical and Experimental Studies on the
Accumulation of Error in the Numerical Solution of
Initial Value Problems for Systems of Ordinary
Differential Equations",
publisher = "????",
address = "????",
pages = "36--43",
year = "1959",
LCCN = "????",
bibdate = "Fri Aug 20 09:11:32 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Kogbetliantz:1959:CSC,
author = "E. G. Kogbetliantz",
title = "Computation of $ \sin {N} $, $ \cos {N} $, and {$M$
th} Root of {$N$} Using an Electronic Computer",
journal = j-IBM-JRD,
volume = "3",
number = "2",
pages = "147--152",
month = apr,
year = "1959",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Lucal:1959:AOD,
author = "Harold M. Lucal",
title = "Arithmetic Operations for Digital Computers Using a
Modified Reflected Binary Code",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "4",
pages = "449--458",
month = dec,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5222057",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:45 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222057",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@Article{Muller:1959:CMG,
author = "Mervin E. Muller",
title = "A Comparison of Methods for Generating Normal Deviates
on Digital Computers",
journal = j-J-ACM,
volume = "6",
number = "3",
pages = "376--383",
month = jul,
year = "1959",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Tue Nov 1 09:33:26 1994",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
descriptors = "RVG",
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Pawlak:1959:EDC,
author = "Z. Pawlak",
title = "An electronic digital computer based on the `$ - 2 $'
system",
journal = "Bull. Acad. Pol. Sci., Ser. Sci. Tech.",
volume = "7",
number = "??",
pages = "713--722",
month = "????",
year = "1959",
bibdate = "Thu Nov 06 05:58:31 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "negative base",
}
@Article{Pfeiffer:1959:FQM,
author = "Paul E. Pfeiffer",
title = "A Four-Quadrant Multiplier Using Triangular Waves,
Diodes, Resistors, and Operational Amplifiers",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "2",
pages = "222--227",
month = jun,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5219526",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:45 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219526",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@Article{Rothstein:1959:RBN,
author = "Jerome Rothstein",
title = "Residues of Binary Numbers Modulo Three",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "2",
pages = "229--229",
month = jun,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5219529",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:45 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=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)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:24 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sarafyan59;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See comments \cite{Traub:1960:CNM}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Sarafyan59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sarafyan59",
}
@Article{Sheridan:1959:ATC,
author = "Peter B. Sheridan",
title = "The Arithmetic Translator Compiler of the {IBM FORTRAN
Automatic Coding System}",
journal = j-CACM,
volume = "2",
number = "2",
pages = "9--21",
month = feb,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sheridan59;
http://ei.cs.vt.edu/~cs4304/bibliography.html;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Sheridan59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sheridan59",
}
@Article{Strachey:1959:TSR,
author = "C. Strachey",
title = "On taking the square root of a complex number",
journal = j-COMP-J,
volume = "2",
number = "2",
pages = "89--89",
month = jul,
year = "1959",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/2.2.89",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:55:11 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/020089.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/tiff/89.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Taranto:1959:BCF,
author = "Donald Taranto",
title = "Binary Conversion, with Fixed Decimal Precision, of a
Decimal Fraction",
journal = j-CACM,
volume = "2",
number = "7",
pages = "27--27",
month = jul,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:25:37 MST 2001",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Taranto59;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "decimal floating-point arithmetic",
oldlabel = "Taranto59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Taranto59",
}
@Article{Volder:1959:CTC,
author = "J. E. Volder",
title = "The {CORDIC} Trigonometric Computing Technique",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "5",
pages = "330--334",
month = sep,
year = "1959",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IRE Transactions on Electronic Computers",
}
@Article{Wensley:1959:CNA,
author = "J. H. Wensley",
title = "A Class of Non-Analytical Iterative Processes",
journal = j-COMP-J,
volume = "1",
number = "4",
pages = "163--167",
month = jan,
year = "1959",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:55:07 MDT 2000",
bibsource = "Compiler/semantics.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/010163.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/163.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/164.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/165.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/166.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/167.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Wilkinson:1959:EZIa,
author = "J. H. Wilkinson",
title = "The evaluation of the zeros of ill-conditioned
polynomials. {I}",
journal = j-NUM-MATH,
volume = "1",
pages = "150--166",
month = dec,
year = "1959",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01386381",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.00",
MRnumber = "MR0109435 (22 \#321)",
MRreviewer = "H. Rutishauser",
bibdate = "Mon Oct 18 01:28:20 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Wilkinson:1959:EZIb,
author = "J. H. Wilkinson",
title = "The evaluation of the zeros of ill-conditioned
polynomials. {II}",
journal = j-NUM-MATH,
volume = "1",
pages = "167--180",
month = dec,
year = "1959",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01386382",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.00",
MRnumber = "MR0109435 (22 \#321)",
MRreviewer = "H. Rutishauser",
bibdate = "Mon Oct 18 01:28:20 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@MastersThesis{Young:1959:SSM,
author = "John Mackay Young",
title = "A study of some methods of numerical integration using
floating point arithmetic",
type = "Thesis ({M.S. in Mathematics})",
school = "Texas A.\&M. College",
address = "College Station, TX, USA",
pages = "50",
year = "1959",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Bockstaele:1960:NFA,
author = "P. Bockstaele",
title = "Notes on the First Arithmetics Printed in {Dutch} and
{English}",
journal = j-ISIS,
volume = "51",
number = "3",
pages = "315--321",
month = sep,
year = "1960",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:28:03 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302265;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/isis1960.bib",
URL = "http://www.jstor.org/stable/226510",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/page/journal/isis/about.html",
}
@Article{Brown:1960:EDC,
author = "David T. Brown",
title = "Error Detecting and Correcting Binary Codes for
Arithmetic Operations",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-9",
number = "3",
pages = "333--337",
month = sep,
year = "1960",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1960.5219855",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:34:12 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219855",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@Article{Croy:1960:IAD,
author = "John E. Croy",
title = "Improved Arrangement of a Decimal Multiplier",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-9",
number = "2",
pages = "263--263",
month = jun,
year = "1960",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1960.5219830",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:34:11 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=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)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:29 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Ercoli:1957:EDO}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Gurzi:1960:HSM,
author = "Fred Gurzi",
title = "A High-Speed Multiplication Process for Digital
Computers",
journal = j-CACM,
volume = "3",
number = "4",
pages = "241--245",
month = apr,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:26 MST 2005",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Gurzi60;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Gurzi60",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Gurzi60",
}
@TechReport{Jensen:1960:CIF,
author = "B. A. Jensen",
title = "Coding instructions for floating point trigonometric,
inverse trigonometric hyperbolic and exponential
functions",
type = "Group report",
number = "30G-0009",
institution = "Massachusetts Institute of Technology, Lincoln
Laboratory",
address = "Lexington, MA, USA",
pages = "7",
year = "1960",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Trigonometrical functions --- Computer programs.",
remark = "Cover title. ``Millstone Hill Radar Station.'' ``1
November 1960.'' Air Force Contract",
}
@Article{Knuth:1960:INS,
author = "Donald E. Knuth",
title = "An Imaginary Number System",
journal = j-CACM,
volume = "3",
number = "4",
pages = "245--247",
month = apr,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.99",
MRnumber = "23\#B554",
MRreviewer = "C. B. Haselgrove",
bibdate = "Fri Nov 25 18:19:26 MST 2005",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Knuth60;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
note = "Errata, {\sl Commun\-i\-ca\-tions of the ACM\/ \bf 4}
(August 1961), 355 \cite{Knuth:1961:EIN}. See
\cite{Nadler:1961:DSR} for extension to division and
square root.",
abstract = "For centuries the decimal number system reigned
supreme, except, perhaps, among the Mayan Indians,
until the advent of digital computers brought the
binary and octal systems into the limelight. This paper
introduces another number system which may prove useful
for manipulating complex numbers on machines.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Knuth60",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Knuth60",
ZMreviewer = "C. B. Haselgrove",
}
@Article{Lowan:1960:PREa,
author = "Arnold N. Lowan",
title = "On the Propagation of Round-Off Errors in the
Numerical Integration of the Heat Equation",
journal = j-MATH-COMPUT,
volume = "14",
number = "70",
pages = "139--146",
month = apr,
year = "1960",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Lowan:1960:PREb,
author = "Arnold N. Lowan",
title = "On the Propagation of Round-Off Errors in the
Numerical Treatment of the Wave Equation",
journal = j-MATH-COMPUT,
volume = "14",
number = "71",
pages = "223--228",
month = jul,
year = "1960",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Pawlak:1960:ODC,
author = "Z. Pawlak",
title = "The organization of a digital computer based on the `$
- 2 $' system",
journal = "Bull. Acad. Pol. Sci., Ser. Tech. Sci.",
volume = "8",
number = "??",
pages = "253--258",
month = "????",
year = "1960",
bibdate = "Thu Nov 06 06:00:08 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "negative base",
}
@Article{Perlin:1960:HPC,
author = "I. E. Perlin and J. R. Garrett",
title = "High Precision Calculation of $ \operatorname {Arcsin}
x $, $ \operatorname {Arccos} x $, and $ \operatorname
{Arctan} x $ (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "14",
number = "71",
pages = "270--274",
month = jul,
year = "1960",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Perry:1960:CBF,
author = "C. Perry",
title = "Conversion between floating point representations",
journal = j-CACM,
volume = "3",
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "352.68.00",
MRnumber = "22\#8714",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Pope:1960:MPA,
author = "D. A. Pope and M. L. Stein",
title = "Multiple Precision Arithmetic",
journal = j-CACM,
volume = "3",
number = "12",
pages = "652--654",
month = dec,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@InCollection{Reitwiesner:1960:BA,
author = "G. W. Reitwiesner",
title = "Binary arithmetic",
crossref = "Alt:1960:AC",
pages = "231--308",
year = "1960",
bibdate = "Sat May 18 14:36:56 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Sarafyan:1960:DCS,
author = "Diran Sarafyan",
title = "Divisionless computation of square roots through
continued squaring",
journal = j-CACM,
volume = "3",
number = "5",
pages = "319--321",
month = may,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.00",
MRnumber = "22\#8639",
bibdate = "Fri Nov 25 18:19:26 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$\sqrt(x)$; elementary functions",
ZMreviewer = "M. Lotkin",
}
@Article{Silver:1960:LER,
author = "Roland Silver",
title = "Letter to the {Editor}: Rounding in Floating-Point
Arithmetic",
journal = j-CACM,
volume = "3",
number = "12",
pages = "A9--A9",
month = dec,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:29 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Sklansky:1960:CSA,
author = "J. Sklansky",
title = "Conditional Sum Addition Logic",
journal = j-TRANS-IRE,
volume = "EC-9",
number = "2",
pages = "226--230",
month = jun,
year = "1960",
bibdate = "Fri Nov 09 19:17:08 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the IRE",
}
@Article{Traub:1960:CNM,
author = "J. F. Traub",
title = "Comments on a recent paper [{``A New Method of
Computation of Square Roots Without Using
Division''}]",
journal = j-CACM,
volume = "3",
number = "2",
pages = "86--86",
month = feb,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:25 MST 2005",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Traub60;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Sarafyan:1959:NMC}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Traub60",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Traub60",
}
@Article{Wadey:1960:FA,
author = "W. G. Wadey",
title = "Floating-Point Arithmetics",
journal = j-J-ACM,
volume = "7",
number = "2",
pages = "129--139",
month = apr,
year = "1960",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "65.00 (68.00)",
MRnumber = "22\#6090",
bibdate = "Fri Dec 08 14:44:46 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Three types of floating-point arithmetics with error
control are discussed and compared with conventional
floating-point arithmetic. General multiplication and
division shift criteria are derived (for any base) for
Metropolis-style arithmetics. The limitations and most
suitable range of application for each arithmetic are
discussed.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
reviewer = "C. B. Haselgrove",
xxmonth = "none",
xxnumber = "none",
}
@Article{Wilkinson:1960:EAF,
author = "J. H. Wilkinson",
title = "Error Analysis of Floating-Point Computation",
journal = j-NUM-MATH,
volume = "2",
pages = "319--340",
month = dec,
year = "1960",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.00",
MRnumber = "MR0116477 (22 \#7264)",
MRreviewer = "C. B. Haselgrove",
bibdate = "Fri May 14 17:18:08 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Amble:1961:AFP,
author = "O. Amble and Jan V. Garwick",
title = "On the Accuracy of Floating Point Computers {[BIT {\bf
1}(2), 1961, pp. 87--88]}",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "3",
pages = "220--222",
month = sep,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01933434",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=3;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Garwick:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=3&spage=220",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
xxpages = "220--221??",
}
@TechReport{Anonymous:1961:MCM,
author = "Anonymous",
title = "Modern Computing Methods",
type = "Notes on Applied Science",
number = "16",
institution = "National Physical Laboratory",
address = "Her Majesty's Stationery Office, London",
year = "1961",
bibdate = "Fri Aug 20 10:05:25 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Avizienis:1961:SDN,
author = "Algirdas Avi{\v{z}}ienis",
title = "Signed-Digit Number Representations for Fast Parallel
Arithmetic",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "3",
pages = "389--400",
month = sep,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219227",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 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=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 = "https://doi.org/10.1109/TEC.1961.5219154",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:02 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=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{Cheney:1961:TNA,
author = "E. W. Cheney and H. L. Loeb",
title = "Two new algorithms for rational approximation",
journal = j-NUM-MATH,
volume = "3",
number = "1",
pages = "72--75",
month = dec,
year = "1961",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01386002",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 19:01:15 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Clarkson:1961:DMI,
author = "W. K. Clarkson",
title = "A Divisionless Method of Integer Conversion",
journal = j-CACM,
volume = "4",
number = "7",
pages = "315--316",
month = jul,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 08:14:59 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Cox:1961:NMP,
author = "Albert G. Cox and H. A. Luther",
title = "A Note on Multiple Precision Arithmetic",
journal = j-CACM,
volume = "4",
number = "8",
pages = "353--353",
month = aug,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/366678.366693",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Dec 03 14:07:44 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Since computers have means to detect overflow on
addition or subtraction, this can be used in a multiple
precision addition-subtraction subroutine to obviate a
sign analysis. Consider all integers in the computer to
be expressed ``radix t'', that is, in the form $ a =
a_0 + a_1 t + \cdots + a_n t^n $ where $ a_i $ are of
like sign and have magnitudes less than $t$. $t$ is a
positive integer determined by the word length of the
computer. Consider the expression $ c = a \pm b = (a_0
\pm b_0) + (a_1 \pm b_1)t + \cdots + (a_n \pm b_n)t^n$.
Here $ a_i \pm b_i$ may exceed the storage capacity of
one word or may have a sign different from $c$.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Croy:1961:RTM,
author = "John E. Croy",
title = "Rapid Technique of Manual or Machine Binary-to-Decimal
Integer Conversion Using Decimal Radix Arithmetic",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "4",
pages = "777--777",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219286",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:05 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219286",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@Article{Freiman:1961:SAC,
author = "C. V. Freiman",
title = "Statistical analysis of certain binary division
algorithms",
journal = j-IRE-PROC,
volume = "49",
number = "1",
pages = "91--103",
month = jan,
year = "1961",
bibdate = "Mon Sep 16 16:12:21 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IRE Proceedings",
xxnote = "Check author name: I have found this paper cited both
as Freiman and as Frieman?? Hennessy and Patterson
\cite{Hennessy:2002:CAQ} have Freiman.",
}
@TechReport{Garner:1961:RNS,
author = "H. L. Garner and R. F. Arnold and B. C. Benson and C.
G. Brockus and R. J. Gonzalez and D. P. Rozenberg",
title = "Residue number systems for computers",
type = "{ASD} Technical Report",
number = "61-483",
institution = "Electronic Technology Laboratory, The University of
Michigan",
address = "Ann Arbor, MI, USA",
month = oct,
year = "1961",
bibdate = "Thu Nov 18 09:27:06 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txt",
abstract = "The purpose of the research performed under this
contract was to investigate the feasibility of residue
number systems in their applications to digital
computers. The problems of such an application are the
ones of magnitude determination, sign determination,
overflow, scaling, and division. These problems are not
independent, but are found to be quite interrelated. A
theoretical treatment of residue number systems is
given which lays the foundation for a unified study of
the complete problem. Treatments of an organizational
nature are given which deal with multiplication,
division, and scaling. The matter of correlating the
theoretical and organizational studies to physical
realizations involving networks is treated also. The
question of whether the residue number system can be
successfully applied to general purpose computers is
still an open one. Their application to special purpose
machines is considered both feasible and practical.",
acknowledgement = ack-nhfb,
remark = "This report represents the results of research
performed by the group at The University of Michigan
under the direction of Professor H. L. Garner.
Concurrently, research on the same subject was being
conducted at Harvard University under the direction of
Professor Howard Aiken, and at the Lockheed Missile
System Division under the direction of Dr. Richard
Tanaka. There was a considerable exchange of
information among the above groups during the course of
the research effort. The efforts attained exhibit
little overlap, rather they are complementary. A
portion of this report was extracted from the doctoral
dissertation of D. P. Rozenberg. His work was supported
by this contract, and led to the Ph.D..",
}
@Article{Garwick:1961:AFP,
author = "Jan V. Garwick",
title = "The Accuracy of Floating Point Computers",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "2",
pages = "87--88",
month = jun,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01939221",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=2;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also comment and reply
\cite{Amble:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=2&spage=87",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
}
@Article{Garwick:1961:RAF,
author = "J. V. Garwick",
title = "Reply to {``On the Accuracy of Floating Point
Computers'' [BIT {\bf 1}(3), 1961, pp. 220--221]}",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "3",
pages = "222--222",
year = "1961",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon Nov 16 14:36:22 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Garwick:1961:AFP,Amble:1961:AFP}.",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
}
@InProceedings{Henderson:1961:RCE,
author = "D. S. Henderson",
booktitle = "{Proceedings of the 1961 16th ACM national meeting}",
title = "Residue class error checking codes",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "132.101--132.104",
year = "1961",
DOI = "https://doi.org/10.1145/800029.808563",
bibdate = "Thu Aug 07 19:04:58 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Error checking codes based on residues have the
advantage over parity-based codes of monitoring
arithmetic as well as transmission operations. Codes
may be devised to detect burst-type errors, to correct
single errors in a binary arithmetic operation, to
correct burst errors and finally to correct any
single-digit error in a decimal operation.",
acknowledgement = ack-nhfb,
keywords = "decimal arithmetic",
}
@Article{Kettel:1961:AAM,
author = "E. Kettel and W. Schneider",
title = "An Accurate Analog Multiplier and Divider",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "2",
pages = "269--272",
month = jun,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219198",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:03 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=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)",
ISSN-L = "0001-0782",
bibdate = "Tue Jan 09 07:10:22 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1960:INS}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Kovatch:1961:HEA,
author = "G. Kovatch and W. E. Meserve",
title = "The {Hall-Effect} Analog Multiplier",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "3",
pages = "512--515",
month = sep,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219240",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219240",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@Article{Lehman:1961:STH,
author = "M. Lehman and N. Burla",
title = "Skip Techniques for High-Speed Carry-Propagation in
Binary Arithmetic Units",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "4",
pages = "691--698",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219274",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 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=5219274",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@Article{MacSorley:1961:HSA,
author = "O. L. MacSorley",
title = "High-speed arithmetic in binary computers",
journal = j-IRE-PROC,
volume = "49",
number = "??",
pages = "67--91",
month = jan,
year = "1961",
bibdate = "Sat May 18 14:34:55 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite{Swartzlander:1976:CDD}.",
acknowledgement = ack-nhfb,
fjournal = "IRE Proceedings",
}
@Article{Nadler:1961:DSR,
author = "Morton Nadler",
title = "Division and square root in the quater-imaginary
number system",
journal = j-CACM,
volume = "4",
number = "4",
pages = "192--193",
month = apr,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.99",
MRnumber = "23\#B555",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1960:INS}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$\sqrt(x)$; elementary functions",
ZMreviewer = "C. B. Haselgrove",
}
@Article{Pinkham:1961:DFS,
author = "Roger S. Pinkham",
title = "On the Distribution of First Significant Digits",
journal = j-ANN-MATH-STAT,
volume = "32",
number = "4",
pages = "1223--1230",
month = dec,
year = "1961",
CODEN = "AASTAD",
ISSN = "0003-4851 (print), 2168-8990 (electronic)",
ISSN-L = "0003-4851",
bibdate = "Thu Feb 15 15:07:57 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0003-4851%28196112%2932%3A4%3C1223%3AOTDOFS%3E2.0.CO%3B2-T",
abstract = "It has been noticed by astute observers that well used
tables of logarithms are invariably dirtier at the
front than at the back. Upon reflection one is led to
inquire whether there are more physical constants with
low order first significant digits than high. Actual
counts by Benford [2] show that not only is this the
case but that it seems to be an empirical truth that
whenever one has a large body of physical data,
Farmer's Almanac, Census Reports, Chemical Rubber
Handbook, etc., the proportion of these data with first
significant digit $n$ or less is approximately $
\log_{10}(n + 1) $. Any reader formerly unaware of this
``peculiarity'' will find an actual sampling experiment
wondrously tantalizing. Thus, for example,
approximately $ 0.7 $ of the physical constants in the
Chemical Rubber Handbook begin with $4$ or less ($
\log_{10}(4 + 1) = 0.699 $) . This is to be contrasted
with the widespread intuitive evaluation $ 4 / 9 $
ths.",
acknowledgement = ack-nhfb,
fjournal = "Annals of Mathematical Statistics",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From p. 1223: ``\ldots{} the proportion of these data
with first significant digit $n$ or less is
approximately $ \log_{10}(n + 1) $.''\par
\ldots{} ``The only distribution for first significant
digits which is invariant under scale change of the
underlying distribution is $ \log_{10}(n + 1) $.
Contrary to suspicion this is a non-trivial
mathematical result, for the variable $n$ is
discrete.''.\par
From p. 1230: ``The foregoing results bear on questions
of round-off in computing machines. Since $ d(u v) = u
d v + v d u $, the error resulting from multiplying two
rounded numbers will be governed primarily by the first
significant digits of the two numbers being multiplied.
Now the distribution of first significant digits,
favoring as it does low order digits, tends to produce
less error than would be the case if first significant
digits were uniform as has sometimes been
assumed.''\par
Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Rabinowitz:1961:MPD,
author = "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)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 00:29:25 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Saltman:1961:RCT,
author = "Roy G. Saltman",
title = "Reducing Computing Time for Synchronous Binary
Division",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "2",
pages = "169--174",
month = jun,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219186",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:03 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219186",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@Article{Spielberg:1961:ECF,
author = "Kurt Spielberg",
title = "Efficient Continued Fraction Approximations To
Elementary Functions",
journal = j-MATH-COMPUT,
volume = "15",
number = "76",
pages = "409--417",
month = oct,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Spielberg:1961:RPS,
author = "K. Spielberg",
title = "Representation of Power Series in Terms of
Polynomials, Rational Approximations and Continued
Fractions",
journal = j-J-ACM,
volume = "8",
number = "4",
pages = "613--627",
month = oct,
year = "1961",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Sat Dec 09 14:01:44 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Thacher:1961:ISR,
author = "Henry C. {Thacher, Jr.}",
title = "Iterated Square Root Expansions for the Inverse Cosine
and Inverse Hyperbolic Cosine",
journal = j-MATH-COMPUT,
volume = "15",
number = "76",
pages = "399--403",
month = oct,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@TechReport{Weik:1961:TSD,
author = "Martin H. Weik",
title = "A Third Survey of Domestic Electronic Digital
Computing Systems",
type = "Report",
number = "1115",
institution = "Ballistic Research Laboratories",
address = "Aberdeen Proving Ground, MD, USA",
pages = "1131",
month = mar,
year = "1961",
bibdate = "Fri Nov 28 19:37:51 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Based on the results of a third survey, the
engineering and programming characteristics of two
hundred twenty-two different electronic digital
computing systems are given. The data are presented
from the point of view of application, numerical and
arithmetic characteristics, input, output and storage
systems, construction and checking features, power,
space, weight, and site preparation and personnel
requirements, production records, cost and rental
rates, sale and lease policy, reliability, operating
experience, and time availability, engineering
modifications and improvements and other related
topics. An analysis of the survey data, fifteen
comparative tables, a discussion of trends, a revised
bibliography, and a complete glossary of computer
engineering and programming terminology are included.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@Article{Wilson:1961:ARB,
author = "J. B. Wilson and R. S. Ledley",
title = "An Algorithm for Rapid Binary Division",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "4",
pages = "662--670",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219271",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 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=5219271",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@InProceedings{Ashenhurst:1962:MIA,
author = "R. L. Ashenhurst",
title = "The {Maniac III} Arithmetic System",
crossref = "AFIPS:1962:APS",
pages = "192--202",
year = "1962",
bibdate = "Wed Feb 14 17:14:21 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Buchholz:1962:PCS,
editor = "Werner Buchholz",
title = "Planning a computer system: {Project Stretch}",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xvii + 322",
year = "1962",
LCCN = "1876",
bibdate = "Fri Nov 19 10:02:31 MST 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
http://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
library.ox.ac.uk:210/ADVANCE",
note = "This important book is the primary description of the
influential IBM 7030 Stretch computer, written by its
architects.",
URL = "http://ed-thelen.org/comp-hist/IBM-7030-Planning-McJones.pdf",
acknowledgement = ack-nhfb,
remark = "The text of the book is in the public domain, with the
permission of the author in 2003.
See \cite{MacKenzie:1991:IAL} for a remark about the
noisy mode for floating-point arithmetic in the IBM
7030 Stretch. That mode is first mentioned on page 25
of this book, and described in detail on page 102,
which states:
``By definition of ordinary normalized FLP operations,
numbers are frequently extended on the right by
attaching zeros. During addition the n-digit operand
that is not preshifted is extended with n zeros, so as
to provide the extra positions to which the preshifted
operand can be added. Any operand or result that is
shifted left to be normalized requires a corresponding
number of zeros to be shifted in at the right. Both
sets of zeros tend to produce numbers smaller in
absolute value than they would have been if more digits
had been carried. In the noisy mode these numbers are
simply extended with 1's instead of zeros (1's in a
binary machine, 9's in a decimal machine). So all
numbers tend to be too large in absolute value. The
true value, if there had been no significance loss,
should lie between these two extremes. Hence, two runs,
one made without and one made with the noisy mode,
should show differences in result that indicate which
digits may have been affected by significance loss.
The principal weakness of the noisy-mode procedure is
that it requires two runs for the same problem. A much
less important weakness is that the loss of
significance cannot be guaranteed to show up --- it
merely has a very high probability of showing up ---
whereas built-in significance checks can be made
slightly pessimistic, so that actual significance loss
will not be greater than indicated. On the other hand,
little extra hardware and no extra storage are required
for the noisy-mode approach. Furthermore, significance
loss is relatively rare, so that running a problem
twice when Significance loss is suspected does not pose
a serious problem. What is serious is the possibility
of unsuspected significance loss.
In discussions of significance two points are often
overlooked. The first of these is trivial: the best way
of ensuring significant results is to use an adequate
number of fraction digits. The second is almost equally
mundane: for a given procedure, normalized FLP
arithmetic will ordinarily produce the greatest
precision possible for the number of fraction digits
used. Normalized FLP arithmetic has been criticized
with respect to significance loss, because such loss is
not indicated by the creation of leading zeros, as it
is with fixed-point arithmetic. In other words, the
contention is not that normalized FLP arithmetic is
more prone to significance loss than equivalent
fixed-point arithmetic, which would be untrue, but that
an equivalent indication of such loss is not provided.
Loss of significance, however, is also a serious
problem in fixed-point arithmetic; multiplication and
division do not handle it at all correctly by means of
leading zeros. (In particular, fixed-point
multiplication may lead to serious or even total
significance loss, which would not have occurred with
normalized FLP arithmetic: and although leading zeros
in addition and subtraction of fixed-point operands do
give correct significance indications, the use of other
operations and of built-in scaling loops frequently
destroys entirely the leading-zeros method of counting
significance.)''",
subject = "Computer architecture",
tableofcontents = "Foreword v \\
Preface vii \\
1. Project Stretch 1 \\
[by W. Buchholz] \\
2. Architectural Philosophy 5 \\
[by F. P. Brooks, Jr.] \\
2.1. The Two Objectives of Project Stretch 5 \\
2.2. Resources 6 \\
2.3. Guiding Principles 7 \\
2.4. Contemporary Trends in Computer Architecture 10
\\
2.5. Hindsight 15 \\
3. System Summary of IBM 7030 17 \\
[by W. Buchholz] \\
3.1. System Organization 17 \\
3.2. Memory Units 17 \\
3.3. Index Memory 19 \\
3.4. Special Registers 19 \\
3.5. Input and Output Facilities 19 \\
3.6. High-speed Disk Units 20 \\
3.7. Central Processing Unit 20 \\
3.8. Instruction Controls 21 \\
3.9. Index-arithmetic Unit 21 \\
3.10. Instruction Look-ahead 21 \\
3.11. Arithmetic Unit 22 \\
3.12. Instruction Set 24 \\
3.13. Data Arithmetic 24 \\
3.14. Radix-conversion Operations 27 \\
3.15. Connective Operations 27 \\
3.16. Index-arithmetic Operations 27 \\
3.17. Branching Operations 28 \\
3.18. Transmission Operations 28 \\
3.19. Input-Output Operations 29 \\
3.20. New Features 29 \\
3.21. Performance 32 \\
4. Natural Data Units 33 \\
[by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
\\
4.1. Lengths and Structures of Natural Data Units 33
\\
4.2. Procedures for Specifying Natural Data Units 36
\\
4.3. Data Hierarchies 39 \\
4.4. Classes of Operations 40 \\
5. Choosing a Number Base 42 \\
[by W. Buchholz] \\
5.1. Introduction 42 \\
5.2. Information Content 45 \\
5.3. Arithmetic Speed 49 \\
5.4. Numerical Data 50 \\
5.5. Nonnumerical Data 51 \\
5.6. Addresses 52 \\
5.7. Transformation 53 \\
5.8. Partitioning of Memory 54 \\
5.9. Program Interpretation 56 \\
5.10. Other Number Bases 58 \\
5.11. Conclusion 58 \\
6. Character Set 60 \\
[by R. W. Bemer and W. Buchholz] \\
6.1. Introduction 60 \\
6.2. Size of Set 62 \\
6.3. Subsets 62 \\
6.4. Expansion of Set 63 \\
6.5. Code 63 \\
6.6. Parity Bit 66 \\
6.7. Sequence 66 \\
6.8. Blank 67 \\
6.9. Decimal Digits 68 \\
6.10. Typewriter Keyboard 68 \\
6.11. Adjacency 69 \\
6.12. Uniqueness 69 \\
6.13. Signs 70 \\
6.14. Tape-recording Convention 71 \\
6.15. Card-punching Convention 71 \\
6.16. List of 7030 Character Set 72 \\
7. Variable-field-length Operation 75 \\
[by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
\\
7.1. Introduction 75 \\
7.2. Addressing of Variable-field-length Data 76 \\
7.3. Field Length 77 \\
7.4. Byte Size 78 \\
7.5. Universal Accumulator 79 \\
7.6. Accumulator Operand 79 \\
7.7. Binary and Decimal Arithmetic 80 \\
7.8. Integer Arithmetic 81 \\
7.9. Numerical Signs 82 \\
7.10. Indicators 84 \\
7.11. Arithmetical Operations 85 \\
7.12. Radix-conversion Operation 87 \\
7.13. Logical Connectives of Two Variables 87 \\
7.14. Connective Operations 89 \\
8. Floating-point Operation 92 \\
[by S. G. Campbell] \\
General Discussion \\
8.1. Problems of Fixed-point Arithmetic 92 \\
8.2. Floating-point Arithmetic 94 \\
8.3. Normalization 97 \\
8.4. Floating-point Singularities 98 \\
8.5. Range and Precision 99 \\
8.6. Round-off Error 100 \\
8.7. Significance Checks 101 \\
8.8. Forms of Floating-point Arithmetic 103 \\
8.9. Structure of Floating-point Data 104 \\
Floating-point Features of the 7030 \\
8.10. Floating-point Instruction Format 106 \\
8.11. Floating-point Data Formats 106 \\
8.12. Singular Floating-point Numbers 108 \\
8.13. Indicators 112 \\
8.14. Universal Accumulator 113 \\
8.15. Fraction Arithmetic 114 \\
8.16. Floating-point-arithmetic Operations 114 \\
8.17. Fixed-point Arithmetic Using Unnormalized \\
Floating-point Operations 118 \\
8.18. Special Functions and Forms of Arithmetic 119 \\
8.19. Multiple-precision Arithmetic 119 \\
8.20. General Remarks 121 \\
9. Instruction Formats 122 \\
[by W. Buchholz] \\
9.1. Introduction 122 \\
9.2. Earlier Instruction Languages 122 \\
9.3. Evolution of the Single-address Instruction 124
\\
9.4. Implied Addresses 125 \\
9.5. Basic 7030 Instruction Formats 126 \\
9.6. Instruction Efficiency 127 \\
9.7. The Simplicity of Complexity 131 \\
9.8. Relationship to Automatic Programming Languages
132 \\
10. Instruction Sequencing 133 \\
[by F. P. Brooks, Jr.] \\
10.1. Modes of Instruction Sequencing 133 \\
10.2. Instruction Counter 134 \\
10.3. Unconditional Branching 135 \\
10.4. Conditional Branching 136 \\
10.5. Program-interrupt System 136 \\
10.6. Components of the Program-interrupt System 137
\\
10.7. Examples of Program-interrupt Techniques 140 \\
10.8. Execute Instructions 146 \\
10.9. Execute Operations in the 7030 148 \\
11. Indexing 150 \\
[by G. P. Blaauw] \\
11.1. Introduction 150 \\
11.2. Indexing Functions 151 \\
11.3. Instruction Format for Indexing 155 \\
11.4. Incrementing 157 \\
11.5. Counting 159 \\
11.6. Advancing by One 161 \\
11.7. Progressive Indexing 161 \\
11.8. Data Transmission 162 \\
11.9. Data Ordering 163 \\
11.10. Refilling 165 \\
11.11. Indirect Addressing and Indirect Indexing 167
\\
11.12. Indexing Applications 169 \\
11.13. Record-handling Applications 172 \\
11.14. File Maintenance 175 \\
11.15. Subroutine Control 177 \\
11.16. Conclusion 178 \\
12. Input-Output Control 179 \\
[by W. Buchholz] \\
12.1. A Generalized Approach to Connecting \\
Input-Output and External Storage 179 \\
12.2. Input-Output Instructions 180 \\
12.3. Defining the Memory Area 181 \\
12.4. Writing and Reading 182 \\
12.5. Controlling and Locating 183 \\
12.6. An Alternative Approach 184 \\
12.7. Program Interruptions 184 \\
12.8. Buffering 180 \\
12.9. Interface 188 \\
12.10. Operator Control of Input-Output Units 190 \\
13. Multiprogramming 192 \\
[by E. F. Codd, E. S. Lowry, E. McDonough, and C. A.
Scalzi] \\
13.1. Introduction 192 \\
13.2. Multiprogramming Requirements 193 \\
13.3. 7030 Features that Assist Multiprogramming 195
\\
13.4. Programmed Logic 197 \\
13.5. Concluding Remarks 200 \\
13.6. References 201 \\
14. The Central Processing Unit 202 \\
[by E. Bloch] \\
14.1. Concurrent System Operation 202 \\
14.2. Concurrency within the Central Processing Unit
204 \\
14.3. Data Flow 204 \\
14.4. Arithmetic Unit 208 \\
14.5. Checking 216 \\
14.6. Component Count 216 \\
14.7. Performance 217 \\
14.8. Circuits 218 \\
14.9. Packaging 223 \\
15. The Look-ahead Unit 228 \\
[by R. S. Balance, J. Cocke, and H. G. Kolsky] \\
15.1. General Description 228 \\
15.2. Timing-simulation Program 230 \\
15.3. Description of the Look-ahead Unit 238 \\
15.4. Forwarding 240 \\
15.5. Counter Sequences 241 \\
15.6. Recovery after Interrupt 246 \\
15.7. A Look-back at the Look-ahead 247 \\
16. The Exchange 248 \\
[by W. Buchholz] \\
16.1. General Description 248 \\
16.2. Starting a WRITE or READ Operation 250 \\
16.3. Data Transfer during Writing 250 \\
16.4. Data Transfer during Reading 251 \\
16.5. Terminating a WRITE or READ Operation 252 \\
16.6. Multiple Operations 252 \\
16.7. CONTROL and LOCATE Operations 252 \\
16.8. Interrogating the Control Word 253 \\
16.9. Forced Termination 253 \\
17. A Nonarithmetical System Extension 254 \\
[by S. G. Campbell, P.S. Herwitz, and J. H. Pomerene]
\\
17.1. Nonarithmetical Processing 254 \\
17.2. The Set-up Mode 258 \\
17.3. Byte-sequence Formation 259 \\
17.4. Pattern Selection 260 \\
17.5. Transformation Facilities 261 \\
17.6. Statistical Aids 263 \\
17.7. The BYTE-BY-BYTE Instruction 263 \\
17.8. Monitoring for Special Conditions 264 \\
17.9. Instruction Set 265 \\
17.10. Collating Operations 266 \\
17.11. Table Look-up Operations 267 \\
17.12. Example 267 \\
Appendix A. Summary Data 273 \\
A.1. List of the Larger IBM Stored-program Computers
273 \\
A.2. Instruction Formats 275 \\
A.3. List of Registers and Special Addresses 276 \\
A.4. Summary of Operations and Modifiers 277 \\
A.5. Summary of Indicators 287 \\
Appendix B. Programming Examples 292 \\
Notation 292 \\
B.1. Polynomial Evaluation 295 \\
B.2. Cube-root Extraction 296 \\
B.3. Matrix Multiplication 298 \\
B.4. Conversion of Decimal Numbers to a \\
Floating-point Normalized Vector 299 \\
B.5. Editing a Typed Message 301 \\
B.6. Transposition of a Large Bit Matrix 303 \\
Index 305",
}
@InCollection{Campbell:1962:FPO,
author = "S. G. Campbell",
editor = "Werner Buchholz",
booktitle = "Planning a Computer System: {Project Stretch}",
title = "Floating-Point Operation",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
bookpages = "322",
pages = "92--121",
year = "1962",
LCCN = "QA76.8.I2 I5",
bibdate = "Wed Feb 14 17:24:27 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "IBM 7030 (Computer); IBM Stretch",
}
@Article{Cantor:1962:LEF,
author = "D. Cantor and G. Estrin and R. Turn",
title = "Logarithmic and Exponential Function Evaluation in a
Variable Structure Digital Computer",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "2",
pages = "155--164",
month = apr,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219348",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:49 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219348",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@TechReport{Descloux:1962:REF,
author = "J. Descloux",
title = "Remarks on errors in first order iterative processes
with floating-point computers",
institution = "University of Illinois Graduate College, Digital
Computer Laboratory",
address = "Urbana, IL, USA",
pages = "7",
year = "1962",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Report / University of Illinois, Digital Computer
Laboratory; no. 113 Report (University of Illinois
(Urbana-Champaign campus). Digital Computer
Laboratory); no. 113.",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers.; Numerical
calculations.",
remark = "Supported by: National Science Foundation under grant
G16489. ``March 22, 1962.''",
}
@Article{Fischler:1962:TRA,
author = "M. A. Fischler and E. A. Poe",
title = "Threshold Realization of Arithmetic Circuits",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "2",
pages = "287--288",
month = apr,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219366",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:50 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=5219366",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@Article{Grau:1962:FNR,
author = "A. A. Grau",
title = "On a floating-point number representation for use with
algorithmic languages",
journal = j-CACM,
volume = "5",
number = "3",
pages = "160--161",
month = mar,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00",
MRnumber = "26\#4506",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Algorithmic languages, such as ALGOL, make provision
for two types of numbers, real and integer, which are
usually implemented on the computer by means of
floating-point and fixed-point numbers respectively.
The concepts real and integer, however, are taken from
mathematics, where the set of integers forms a proper
subset of the set of real numbers. In implementation a
real problem is posed by the fact that the set of
fixed-point numbers is not a proper subset of the set
of floating-point numbers; this problem becomes very
apparent in attempts to implement ALGOL 60.
Furthermore, the {\em one\/} mathematical operation of
addition is implemented in the machine by one of {\em
two\/} machine operations, fixed-point addition or
floating-point addition.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
reviewer = "R. L. Ashenhurst",
}
@Article{Guffin:1962:CSL,
author = "Ronald M. Guffin",
title = "A Computer for Solving Linear Simultaneous Equations
Using the Residue Number System",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "2",
pages = "164--173",
month = apr,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219349",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:49 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219349",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@Book{Hamming:1962:NMS,
author = "R. W. (Richard Wesley) Hamming",
title = "Numerical methods for scientists and engineers",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "411",
year = "1962",
LCCN = "QA297 .H28",
bibdate = "Fri Aug 20 09:12:08 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "International series in pure and applied mathematics",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
subject = "Numerical analysis; Electronic digital computers",
}
@Article{Jones:1962:FPF,
author = "F. B. Jones and A. W. Wymore",
title = "Floating Point Feature on the {IBM Type 1620}",
journal = j-IBM-TDB,
volume = "05-62",
pages = "43--46",
month = may,
year = "1962",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Fri Nov 28 11:26:02 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
keywords = "decimal floating-point arithmetic",
remark = "The IBM 1620 normalized variable-precision arithmetic
provides up to 100 decimal digits with an exponent
range of $ \pm 99 $.",
}
@Article{Karatsuba:1962:MMN,
author = "A. Karatsuba and Y. Ofman",
title = "Multiplication of multidigit numbers on automata",
journal = j-DOKL-AKAD-NAUK,
volume = "145",
number = "??",
pages = "293--294",
month = "????",
year = "1962",
CODEN = "DANKAS",
ISSN = "0002-3264",
bibdate = "Tue Jul 05 10:35:11 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Doklady Akademii nauk SSSR",
}
@Article{Keir:1962:DOD,
author = "Y. A. Keir and P. W. Cheney and M. Tannenbaum",
title = "Division and overflow detection in residue number
systems",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "4",
pages = "501--507",
month = aug,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219389",
ISSN = "0367-9950",
MRclass = "68.00",
MRnumber = "MR0150990 (27 \#976)",
MRreviewer = "N. H. Choksy",
bibdate = "Thu Jul 14 09:11:51 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219389",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@Article{Knuth:1962:EPC,
author = "Donald E. Knuth",
title = "Evaluation of polynomials by computer",
journal = j-CACM,
volume = "5",
number = "12",
pages = "595--599",
month = dec,
year = "1962",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355580.369074",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00 (12.00)",
MRnumber = "27 \#970",
bibdate = "Thu Dec 08 11:11:03 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
note = "See letter \cite{Knuth:1963:LEE}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
remark = "The author that Motzkin (1962) showed that Horner's
rule for polynomial evaluation may not be optimal, and
develops the idea further for arbitrary polynomials,
but also observes that the coefficients of the revised
polynomials may be difficult to find. He also asks
about, but does not answer, the question of error
analysis of the various methods.",
}
@Article{Lake:1962:LEH,
author = "G. T. Lake",
title = "Letter to the Editor: Hardware Conversion of Decimal
and Binary Numbers",
journal = j-CACM,
volume = "5",
number = "9",
pages = "468--469",
month = sep,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 28 18:16:30 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "decimal floating-point arithmetic",
}
@Article{Lynch:1962:WBD,
author = "W. C. Lynch",
title = "On a Wired-In Binary-to-Decimal Conversion Scheme",
journal = j-CACM,
volume = "5",
number = "3",
pages = "159--159",
month = mar,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 28 18:21:41 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "decimal floating-point arithmetic",
}
@Article{MacSorley:1962:RBA,
author = "O. L. MacSorley",
title = "Review: \booktitle{An Algorithm for Rapid Binary
Division}, by {J. B. Wilson and R. S. Ledley}",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "3",
pages = "420--420",
month = jun,
year = "1962",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Sat Jul 16 20:52:08 2011",
bibsource = "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{McGee:1962:BM,
author = "W. C. McGee",
title = "A Binary Multiplication",
journal = j-SIAM-REVIEW,
volume = "4",
number = "3",
pages = "256--256",
month = "????",
year = "1962",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1004066",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:04:54 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/4/3;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "July 1962",
}
@Article{Meggitt:1962:PDP,
author = "J. E. Meggitt",
title = "Pseudo Division and Pseudo Multiplication Processes",
journal = j-IBM-JRD,
volume = "6",
number = "2",
pages = "210--226",
month = apr,
year = "1962",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Metze:1962:CBD,
author = "Gernot Metze",
title = "A Class of Binary Divisions Yielding Minimally
Represented Quotients",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "6",
pages = "761--764",
month = dec,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219460",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:53 MDT 2011",
bibsource = "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=5219460",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@Article{Mitchell:1962:CMD,
author = "John N. Mitchell",
title = "Computer Multiplication and Division Using Binary
Logarithms",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "4",
pages = "512--517",
month = aug,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219391",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:51 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=5219391",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@Article{Rozier:1962:DBC,
author = "Charles P. Rozier",
title = "Decimal-to-Binary Conversion Using Octal Radix
Arithmetic",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "5",
pages = "708--709",
month = oct,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219436",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:52 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=5219436",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
@Article{Shanks:1962:CD,
author = "Daniel Shanks and John W. {Wrench, Jr.}",
title = "Calculation of $ \pi $ to 100,000 Decimals",
journal = j-MATH-COMPUT,
volume = "16",
number = "77",
pages = "76--99",
month = jan,
year = "1962",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Misc{Sierra:1962:FDP,
author = "Huberto M. Sierra",
title = "Floating Decimal Point Arithmetic Control Means for
Calculator",
howpublished = "US Patent 3,037,701",
day = "5",
month = jun,
year = "1962",
bibdate = "Sat Mar 24 05:59:45 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://patents.google.com/patent/US3037701A",
abstract = "The invention relates to digital computers and more
particularly to digital computers for making
calculations with numbers having a wide range of values
with a limited number of digit storing positions.",
acknowledgement = ack-nhfb,
remark = "US Patent filed 21 November 1956, granted to IBM on 5
June 1962, expired 5 June 1979 (17 years after grant).
This may be the earliest US patent on floating-point
arithmetic.",
}
@Article{Smith:1962:ACDa,
author = "Robert L. Smith",
title = "{Algorithm 116}: {Complex} Division",
journal = j-CACM,
volume = "5",
number = "8",
pages = "435--435",
month = aug,
year = "1962",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/368637.368661",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:40 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Spielberg:1962:PCF,
author = "Kurt Spielberg",
title = "Polynomial and Continued-Fraction Approximations for
Logarithmic Functions",
journal = j-MATH-COMPUT,
volume = "16",
number = "78",
pages = "205--217",
month = apr,
year = "1962",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Wynn:1962:AAP,
author = "P. Wynn",
title = "An Arsenal of {ALGOL} Procedures for Complex
Arithmetic",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "2",
number = "4",
pages = "232--255",
month = dec,
year = "1962",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01940171",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=2&issue=4;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=2&issue=4&spage=232",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@InCollection{Zuse:1962:ERE,
author = "K. Zuse",
editor = "W. Hoffman",
booktitle = "{Digitale Informationswandler}",
title = "{Entwicklungslinien einer Rechenger{\"a}te-Entwicklung
von der Mechanik zur Elektronik}. ({German}) [Lines of
development of computing equipment development from
mechanics to electronics]",
publisher = "Vieweg \& Sohn, GmbH",
address = "Braunschweig, West Germany",
pages = "508--532",
year = "1962",
bibdate = "Wed Oct 13 11:23:04 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 4.3]{Randell:1982:ODC}.
Translated by Mr. and Mrs. P. Jones.",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Bemer:1963:NRT,
author = "R. W. Bemer",
title = "A Note on Range Transformations for Square Root and
Logarithm",
journal = j-CACM,
volume = "6",
number = "6",
pages = "306--307",
month = jun,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:47 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$\log(x)$; $\sqrt(x)$; elementary functions",
}
@Article{Clenshaw:1963:ASF,
author = "C. W. Clenshaw and G. F. Miller and M. Woodger",
title = "Algorithms for Special Functions {I}",
journal = j-NUM-MATH,
volume = "4",
pages = "403--419",
year = "1963",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Sep 16 10:21:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
xxmonth = "(none)",
xxnumber = "(none)",
}
@Article{Daly:1963:HSA,
author = "W. G. Daly and J. F. Kruy",
title = "A High-Speed Arithmetic Unit Using Tunnel Diodes",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-12",
number = "5",
pages = "503--511",
month = oct,
year = "1963",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1963.263644",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:42 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037964",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Descloux:1963:NRE,
author = "J. Descloux",
title = "Note on the Round-Off Errors in Iterative Processes",
journal = j-MATH-COMPUT,
volume = "17",
number = "81",
pages = "18--27",
month = jan,
year = "1963",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Dietmeyer:1963:CPN,
author = "Donald L. Dietmeyer",
title = "Conversion from Positive to Negative and Imaginary
Radix",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-12",
number = "1",
pages = "20--22",
month = feb,
year = "1963",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1963.263391",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:36 MDT 2011",
bibsource = "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=4037765",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
keywords = "imaginary base; negative base",
}
@Article{Eisman:1963:PER,
author = "S. H. Eisman",
title = "Polynomial Evaluation Revisited",
journal = j-CACM,
volume = "6",
number = "7",
pages = "384--385",
month = jul,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Eve:1963:SAI,
author = "J. Eve",
title = "Starting approximation for the iterative calculation
of square roots",
journal = j-COMP-J,
volume = "6",
pages = "274--276",
year = "1963",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Thu Sep 15 18:37:30 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
xxmonth = "(none)",
xxnumber = "(none)",
}
@Book{Flores:1963:LCA,
author = "I. Flores",
title = "The Logic of Computer Arithmetic",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xii + 493",
year = "1963",
LCCN = "QA76.5 .F46",
bibdate = "Thu Sep 1 10:12:51 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Geier:1963:ACD,
author = "A. Geier and I. Sturz",
title = "The approximate calculation of a definite integral
with automatic choice of integration steps (intervals).
The program for the computer {$ {\rm MECIPTI} $} in a
floating point regime. ({Romanian})",
journal = "An. Univ. Timi{\c{s}}oara Ser. {\c{S}}ti. Mat.-Fiz.",
volume = "1",
pages = "133--139",
year = "1963",
MRclass = "68.00",
MRnumber = "30\#3588",
bibdate = "Fri Dec 08 13:52:47 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "R. N. Goss",
}
@Article{Goldstein:1963:SAD,
author = "Max Goldstein",
title = "Significance arithmetic on a digital computer",
journal = j-CACM,
volume = "6",
number = "3",
pages = "111--117",
month = mar,
year = "1963",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/366274.366339",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:45 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The 7090 at NYU has been modified to include a
``Significance Mode'' of operation which is intended to
facilitate the identification of significant bits in
the results of floating-point arithmetic operations.
The manner in which floating-point arithmetic is
handled in this mode is discussed. Several numerical
experiments using this mode are described and
comparisons are made with the ordinary ``normalized
mode.'' Examples include power series evaluation,
linear equations solution, determinant evaluation and
matrix inversion.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Knuth:1963:LEE,
author = "Donald E. Knuth",
title = "Letter to the {Editor}: {Evaluation} of polynomials by
computer",
journal = j-CACM,
volume = "6",
number = "2",
pages = "51--51",
month = feb,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
bibdate = "Tue Dec 26 16:31:38 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1962:EPC}.",
acknowledgement = ack-nhfb,
}
@Article{Krishnamurthy:1963:CMD,
author = "E. V. Krishnamurthy",
title = "On Computer Multiplication and Division Using Binary
Logarithms",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-12",
number = "3",
pages = "319--320",
month = jun,
year = "1963",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1963.263572",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:39 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=4037874",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Lehman:1963:MAB,
author = "M. Lehman",
title = "The Minimization of Assimilations in Binary
Carry-Storage Arithmetic Units",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-12",
number = "4",
pages = "409--410",
month = aug,
year = "1963",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1963.263479",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:40 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037921",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Lehmer:1963:RDO,
author = "D. H. Lehmer",
title = "{R63--17} Division and Overflow Detection in Residue
Number Systems",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-12",
number = "1",
pages = "36--37",
month = feb,
year = "1963",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1963.263493",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:36 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=4037786;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4037754",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
keywords = "residue arithmetic; residue number system",
}
@Article{Lindamood:1963:MCO,
author = "George E. Lindamood and George Shapiro",
title = "Magnitude Comparison and Overflow Detection in Modular
Arithmetic Computers",
journal = j-SIAM-REVIEW,
volume = "5",
number = "4",
pages = "342--350",
month = "????",
year = "1963",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1005095",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:05:07 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/5/4;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "October 1963",
}
@Article{Metropolis:1963:BOU,
author = "N. Metropolis and R. L. Ashenhurst",
title = "Basic Operations in an Unnormalized Arithmetic
System",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-12",
number = "6",
pages = "896--904",
month = dec,
year = "1963",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1963.263592;
https://doi.org/10.1109/PGEC.1963.263593",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:44 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038037",
ZMnumber = "0124.07910",
abstract = "A particular set of unnormalized arithmetic operations
termed ``basic'' are described, in the context of the
University of Chicago Maniac III Computer. Each basic
operation involves three operand words and generates
two result words, all in unnormalized floating point
format. The use of these operations in the
implementation of multi-precision arithmetic is
explained; in particular, it is demonstrated that
multiprecision division can be effected in a
nontentative manner with their aid.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Book{Mood:1963:ITS,
author = "Alexander McFarlane Mood and Franklin A. Graybill",
title = "Introduction to the theory of statistics",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
edition = "Second",
pages = "443",
year = "1963",
LCCN = "HA29 .M75 1963",
bibdate = "Fri Aug 20 10:02:03 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "McGraw-Hill series in probability and statistics",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
subject = "Mathematical statistics",
}
@Article{Stern:1963:CSR,
author = "T. E. Stern and R. M. Lerner",
title = "A circuit for the square root of the sum of the
squares",
journal = j-PROC-IEEE,
volume = "51",
number = "4",
pages = "593--596",
month = apr,
year = "1963",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "A piecewise-linear network can produce an output
proportional to the square root of the sum of the
squares of a set of input voltages, using resistors and
diodes alone. The required relationship between
voltages can be represented by a multi- \ldots{}",
}
@Article{Stroud:1963:MPF,
author = "A. H. Stroud and D. Secrest",
title = "A multiple-precision floating-point interpretive
program for the {Control Data} 1604",
journal = j-COMP-J,
volume = "6",
number = "1",
pages = "62--66",
month = apr,
year = "1963",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:55:45 MDT 2000",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/060062.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/62.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/63.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/64.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/65.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/66.tif",
acknowledgement = ack-nhfb # " and " # ack-nj,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Svoboda:1963:AD,
author = "A. Svoboda",
title = "An algorithm for division",
journal = j-INF-PROCESS-MACH,
volume = "9",
number = "??",
pages = "25--33",
month = "????",
year = "1963",
CODEN = "IPRMDD",
ISSN = "0373-885X",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "Information processing machines",
}
@InProceedings{Wilkinson:1963:PSA,
author = "J. H. Wilkinson",
title = "Plane rotations in floating-point arithmetic",
crossref = "Metropolis:1963:PFS",
pages = "185--198",
year = "1963",
MRclass = "65.35",
MRnumber = "28\#1744",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "A. S. Householder",
}
@Article{Aiken:1964:PAC,
author = "H. H. Aiken and A. G. Oettinger and T. C. Bartee",
title = "Proposed automatic calculating machine",
journal = j-IEEE-SPECTRUM,
volume = "1",
number = "8",
pages = "62--69",
month = aug,
year = "1964",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1964.6500770",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Tue Jan 14 11:14:17 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
note = "Previously unpublished memorandum written by Aiken and
dated by an unknown recipient as 4 November 1937.
Reprinted in \cite[\S 5.1]{Randell:1982:ODC}.",
abstract = "Here presented is the memorandum that 20 years ago
initiated a series of events whose revolutionary
implications are only beginning to manifest themselves
a description of the first large-scale general-purpose
automatic digital computer. Twenty years ago, on August
7, 1944, Mark I, the first large-scale general-purpose
automatic digital computer ever to be put in operation
was dedicated at Harvard University by James B. Conant,
then president of Harvard, and the late Thomas J.
Watson, founder of IBM.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
remark = "Pages 66--69 discuss computation of the elementary
functions with minimal intermediate storage: recipes
are given for integral and fractional power, log,
exponential, trigonometric, inverse trigonometric,
hyperbolic, and inverse hyperbolic. Mention is also
made of the probability integral, elliptic functions,
and Bessel functions, but the text says they will be
discussed later (meaning, in a future publication). The
methods involve recurrences and series summations, and
thus, can be regarded as precision independent.",
}
@Manual{Anonymous:1964:PPF,
author = "Anonymous",
title = "{PINT}: {Purdue} floating point interpretive system:
for the {RPC 4000 General Precision} electronic
computer",
organization = "General Precision, Inc.",
address = "West Lafayette, IN, USA",
pages = "45",
year = "1964",
bibdate = "Mon May 06 10:24:31 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.; Purdue
University School of Electrical Engineering; RPC 4000
(Computer)",
remark = "Program no. H1-02.0",
}
@Article{Ashenhurst:1964:FEU,
author = "R. L. Ashenhurst",
title = "Function Evaluation in Unnormalized Arithmetic",
journal = j-J-ACM,
volume = "11",
number = "2",
pages = "168--187",
month = apr,
year = "1964",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Thu Nov 03 22:33:52 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Baer:1964:MPA,
author = "Robert M. Baer and Martin G. Redlich",
title = "Multiple-precision arithmetic and the exact
calculation of the $ 3 - j $, $ 6 - j $ and $ 9 - j $
symbols",
journal = j-CACM,
volume = "7",
number = "11",
pages = "657--659",
month = nov,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.25",
MRnumber = "31\#865",
bibdate = "Mon Oct 24 09:33:02 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Described in this paper is a system of general-purpose
multiple-precision fixed-point routines and their use
in subroutines which calculate exactly the
quantum-mechanical 3-j, 6-j and 9-j symbols of large
arguments.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@MastersThesis{Bookhart:1964:SFP,
author = "Thomas Woodward Bookhart",
title = "A study of floating point arithmetic",
type = "Thesis ({M.S. in Math.})",
school = "Georgia Institute of Technology",
address = "Atlanta, GA, USA",
pages = "51",
year = "1964",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers.; Number theory.;
Numerical calculations --- Computer programs.",
}
@Article{Brooker:1964:PPS,
author = "R. A. Brooker",
title = "A programming package for some general modes of
arithmetic",
journal = j-CACM,
volume = "7",
number = "2",
pages = "119--127",
month = feb,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Oct 24 09:33:00 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An interpretive programming package is described for
computation with operands which may be real, complex,
single or double precision, or real multiple precision.
It also performs operations on matrices formed from
these elements. A simple language structure is used to
describe the computation.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Manual{Burroughs:1964:BBI,
author = "{Burroughs Corporation}",
title = "{Burroughs B5500} Information Processing Systems
Reference Manual",
organization = "Burroughs Corporation",
address = "Detroit, MI, USA",
year = "1964",
bibdate = "Wed Nov 22 21:15:11 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "The B5500 uses a decimal integer or fixed-point
coefficient of 21 or 22 digits, with an exponent range
of $ \pm 63 $.",
}
@Article{Cody:1964:DPS,
author = "W. J. {Cody, Jr.}",
title = "Double-Precision Square Root for the {CDC-3600}",
journal = j-CACM,
volume = "7",
number = "12",
pages = "715--718",
month = dec,
year = "1964",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355588.365122",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In January of 1960, the late Hans J. Maehly completed
a summary of approximations to the elementary functions
for the CDC-1604 computer. The approximations and
techniques suggested by Maehly are equally applicable
to the second large computer in the CDC line, the 3600.
Unlike the 1604, however, the 3600 has built-in
double-precision floating-point arithmetic. The present
work, largely inspired by the successes of Maehly and
his associates, concerns the extension of one of
Maehly's ideas to a double-precision subroutine for the
3600.",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$sqrt(x)$; CDC 3600; elementary functions",
}
@Article{Cowgill:1964:LEB,
author = "D. Cowgill",
title = "Logic Equations for a Built-In Square Root Method",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "2",
pages = "156--157",
month = apr,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263791",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:56:59 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038119",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Eve:1964:EP,
author = "J. Eve",
title = "The Evaluation of Polynomials",
journal = j-NUM-MATH,
volume = "6",
pages = "17--21",
year = "1964",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Sep 16 10:21:47 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
xxmonth = "(none)",
xxnumber = "(none)",
}
@MastersThesis{Goldschmidt:1964:ADC,
author = "R. E. Goldschmidt",
title = "Applications of division by convergence",
type = "Thesis ({M.S.})",
school = "Dept. of Electrical Engineering, Massachusetts
Institute of Technology",
address = "Cambridge, MA, USA",
pages = "44 (est.)",
month = jun,
year = "1964",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@Article{Gram:1964:RZF,
author = "Christian Gram",
title = "On the Representation of Zero in Floating-Point
Arithmetic",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "4",
number = "3",
pages = "156--161",
month = sep,
year = "1964",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01956026",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "68.00",
MRnumber = "29\#5412",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=4&issue=3&spage=156",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Gregory:1964:FAN,
author = "Robert T. Gregory and James L. Raney",
title = "Floating-point arithmetic with $ 84 $-bit numbers",
journal = j-CACM,
volume = "7",
pages = "10--13",
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00",
MRnumber = "30\#2706",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Book{Henrici:1964:ENA,
author = "Peter Henrici",
title = "Elements of numerical analysis",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xv + 328",
year = "1964",
LCCN = "QA297 .H4",
bibdate = "Fri Aug 20 09:17:19 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Based on the author's lecture notes for a course
entitled {\em Numerical Mathematical Analysis\/} at the
University of California, Los Angeles. Cited in
\cite{Sterbenz:1974:FPC}.",
subject = "Numerical analysis",
}
@Article{Jacobsohn:1964:SFM,
author = "D. Jacobsohn",
title = "A Suggestion for a Fast Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "6",
pages = "754--754",
month = dec,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263942",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:57:06 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=4038318",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Book{Khinchin:1964:CF,
author = "Aleksandr Iakovlevich Khinchin",
title = "Continued fractions",
publisher = "P. Noordhoff",
address = "Groningen, The Netherlands",
pages = "101",
year = "1964",
LCCN = "QA295 .K513 1964a",
bibdate = "Fri Nov 30 06:55:53 MST 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "Translated by Peter Wynn",
URL = "http://www.loc.gov/catdir/description/dover032/97008056.html;
http://www.loc.gov/catdir/toc/dover031/97008056.html",
acknowledgement = ack-nhfb,
author-dates = "1894--1959",
}
@Article{Klokacev:1964:RNF,
author = "I. V. Kloka{\v{c}}ev",
title = "A refinement of the normalized floating point number
notation on digital computers. ({Russian})",
journal = "{\v{Z}}. Vy{\v{c}}isl. Mat. i Mat. Fiz.",
volume = "4",
pages = "192--194",
year = "1964",
MRclass = "68.00",
MRnumber = "28\#4694",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Kundu:1964:TMD,
author = "P. Kundu and S. Banerji",
title = "Transistorized Multiplier and Divider and Its
Applications",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "3",
pages = "288--295",
month = jun,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263919",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:57:00 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038157",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Lamson:1964:DAD,
author = "Roger C. Lamson",
title = "A Division Algorithm for a Digital Differential
Analyzer",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "1",
pages = "54--55",
month = feb,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263838",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:56:57 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=4038079",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Lynn:1964:REM,
author = "M. Stuart Lynn",
title = "On the Round-Off Error in the Method of Successive
Over-Relaxation",
journal = j-MATH-COMPUT,
volume = "18",
number = "85",
pages = "36--49",
month = jan,
year = "1964",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Maley:1964:MDC,
author = "Gerald A. Maley and Edward J. Skiko",
title = "Modern digital computers",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xiv + 216",
year = "1964",
LCCN = "QA76.5 .M192",
bibdate = "Thu Nov 18 10:04:00 MST 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "Prentice-Hall electrical engineering series",
acknowledgement = ack-nhfb,
keywords = "binary arithmetic",
subject = "Electronic digital computers",
}
@Book{McCracken:1964:NMF,
author = "Daniel D. McCracken and William S. Dorn",
title = "Numerical methods and {FORTRAN} programming, with
applications in engineering and science",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xii + 457",
year = "1964",
bibdate = "Sat Jan 27 13:40:57 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Numerical analysis --- Data processing.; {Fortran}
(Computer program language)",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Merrill:1964:IDC,
author = "Roy D. Merrill",
title = "Improving Digital Computer Performance Using Residue
Number Theory",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "2",
pages = "93--101",
month = apr,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263776;
https://doi.org/10.1109/PGEC.1964.263777",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:56:58 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038105;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4038099",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
keywords = "residue arithmetic; residue number system",
summary = "Residue arithmetic has the interesting characteristic
that in multiplication, addition and subtraction any
digit in the result is dependent only on its two
corresponding operand digits. Consequently, for these
operations, residue arithmetic is \ldots{}",
}
@Article{Miller:1964:ESD,
author = "R. H. Miller",
title = "An example in ``significant-digit'' arithmetic",
journal = j-CACM,
volume = "7",
number = "1",
pages = "21--21",
month = jan,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Oct 24 09:33:00 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Different methods of handling the summing process for
the geometric series are shown to give results
indicating widely differing significances when carried
out in a machine incorporating ``significant-digit''
arithmetic.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@MastersThesis{Moss:1964:RDC,
author = "George Joseph {Moss, Jr.}",
title = "Recording digital counter with floating point output
format",
type = "Thesis ({M.S.})",
school = "University of Maryland",
address = "College Park, MD, USA",
pages = "155",
year = "1964",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Rice:1964:AFV,
author = "John R. Rice",
title = "The Approximation of Functions",
volume = "1",
publisher = pub-AW,
address = pub-AW:adr,
pages = "various",
year = "1964",
LCCN = "QA221 .R5 V.1-2",
bibdate = "Fri Dec 08 13:02:52 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Santos:1964:BVB,
author = "J. Santos and H. Arango",
title = "Base $3$ vs Base $2$ Synchronous Arithmetic Units",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "5",
pages = "608--609",
month = oct,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263734",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:57:04 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=4038256",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Stein:1964:DCM,
author = "M. L. Stein",
title = "Divide-and-Correct Methods for Multiple Precision
Division",
journal = j-CACM,
volume = "7",
number = "8",
pages = "472--474",
month = aug,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@MastersThesis{Sweo:1964:SFP,
author = "David Ernest Sweo",
title = "A study of floating point arithmetic with the residue
number system",
type = "Thesis ({M.S.})",
school = "UCLA - Engineering",
address = "Los Angeles, CA, USA",
pages = "89",
year = "1964",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Congruences and residues.; Electronic digital
computers --- Programming.",
}
@Article{Wallace:1964:SFM,
author = "C. S. Wallace",
title = "A Suggestion for a Fast Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "1",
pages = "14--17",
month = feb,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263830",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:56:56 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=4038071",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Wolfe:1964:RTE,
author = "Jack M. Wolfe",
title = "Reducing Truncation Errors by Programming",
journal = j-CACM,
volume = "7",
number = "6",
pages = "355--356",
month = jun,
year = "1964",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/512274.512287",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:54 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In accumulating a sum such as in a numerical
integration with a large number of intervals, the sum
itself becomes much larger than the individual addends.
This may produce a less accurate sum as the number of
intervals is increased. Separate variables can be
established as accumulators to hold partial sums within
various distinct intervals. Thus, the extensive
successive truncations are eliminated.",
acknowledgement = ack-nhfb # " and " # ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "floating-point arithmetic; truncation errors",
remark = "This algorithm is a precursor of Kahan's compensated
summation algorithm \cite{Kahan:1965:PFR}; see \cite[p.
384]{Lange:2020:NDF} for a discussion.",
}
@Article{Ashenhurst:1965:EEC,
author = "R. L. Ashenhurst and N. Metropolis",
title = "Error Estimation in Computer Calculation",
journal = j-AMER-MATH-MONTHLY,
volume = "72",
number = "2 (Part 2)",
pages = "47--58",
year = "1965",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "65.80",
MRnumber = "MR0192671 (33 \#896)",
MRreviewer = "James H. Wilkinson",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in Department of Economics, Graduate School
of Business, University of Chicago, Center for
Mathematical Studies in Business and Economics, number
45.",
ZMnumber = "0216.49602",
acknowledgement = ack-jr,
fjournal = "The American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
keywords = "error estimation; floating-point arithmetic",
}
@InProceedings{Ashenhurst:1965:EIU,
author = "R. L. Ashenhurst",
editor = "L. B. Rall",
booktitle = "Error in digital computation",
title = "Experimental investigation of unnormalized
arithmetic",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "3--37",
year = "1965",
bibdate = "Thu Nov 8 14:49:59 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARI FLP",
}
@InProceedings{Ashenhurst:1965:TAE,
author = "R. L. Ashenhurst",
editor = "L. B. Rall",
booktitle = "Error in digital computation",
title = "Techniques for automatic error monitoring and
control",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "43--59",
year = "1965",
bibdate = "Tue Oct 9 09:42:56 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARI FLP",
}
@Article{Atrubin:1965:ODR,
author = "A. J. Atrubin",
title = "A One-Dimensional Real-Time Iterative Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "3",
pages = "394--399",
month = jun,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264145",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:33 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=4038457",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Blum:1965:EAP,
author = "B. I. Blum",
title = "An Extended Arithmetic Package",
journal = j-CACM,
volume = "8",
number = "5",
pages = "318--320",
month = may,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 8 08:20:53 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Combet:1965:CBT,
author = "M. Combet and H. {Van Zonneveld} and L. Verbeek",
title = "Computation of the Base Two Logarithm of Binary
Numbers",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "6",
pages = "863--867",
month = dec,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264080",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:41 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038605",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Dadda:1965:SSP,
author = "Luigi Dadda",
title = "Some Schemes for Parallel Multipliers",
journal = j-ALTA-FREQ,
volume = "34",
number = "??",
pages = "349--356",
month = mar,
year = "1965",
CODEN = "ALFRAJ",
ISSN = "0002-6557",
ISSN-L = "0002-6557",
bibdate = "Fri Nov 09 10:47:42 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[pages
118--225]{Swartzlander:1990:CAa}.",
URL = "http://en.wikipedia.org/wiki/Dadda_multiplier;
http://en.wikipedia.org/wiki/luigi_dadda",
acknowledgement = ack-nhfb,
author-dates = "29 April 1923--26 October 2012",
fjournal = "Alta frequenza",
remark = "According to an ARITH'21 conference attendee, this is
a recommended article for understanding the Wallace and
Dadda multipliers.",
}
@Article{Deiters:1965:ODD,
author = "Robert M. Deiters",
title = "Optimum Design of a Diode Squarer by Applying the
Criterion of Square Root of the Integral of Per Cent
Error Squared",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "3",
pages = "456--463",
month = jun,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264153",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:34 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038465",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Dodd:1965:RSB,
author = "George G. Dodd",
title = "Remarks on Simulation of {Boolean} Functions",
journal = j-CACM,
volume = "8",
number = "8",
pages = "517--517",
month = aug,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:01 MST 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Recently M. Morris Mano presented a method for
performing Boolean OR, AND and NOT operations by means
of arithmetic and conditional transfer operations in a
decimal computer lacking builtin logical
instructions.",
acknowledgement = ack-nhfb,
checked = "19940407",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "Boolean operations; decimal arithmetic",
sjb = "Commenting on \cite{Mano:1965:PSB}.",
}
@Article{Earle:1965:LCS,
author = "J. G. Earle",
title = "Latched Carry-Save Adder",
journal = j-IBM-TDB,
volume = "7",
number = "??",
pages = "909--910",
month = mar,
year = "1965",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Fri Nov 09 10:49:36 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
}
@InCollection{Garner:1965:NSA,
author = "H. L. Garner",
title = "Number systems and arithmetic",
crossref = "Alt:1965:AC",
volume = "6",
pages = "131--194",
year = "1965",
bibdate = "Sat May 18 14:18:19 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Garner:1965:RID,
author = "H. L. Garner",
title = "{R65-22} Improving Digital Computer Performance Using
Residue Number Theory",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
pages = "277--277",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.263975",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:23 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038430;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4038385",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
keywords = "residue arithmetic; residue number system",
}
@Article{Hammel:1965:RLC,
author = "D. Hammel",
title = "{R65-54} The Logic of Computer Arithmetic",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "4",
pages = "670--670",
month = aug,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264031",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:40 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038535",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Hammer:1965:BRBa,
author = "Preston C. Hammer",
title = "Book Review: {{\booktitle{Experimental Arithmetic,
High Speed Computing and Mathematics}} by N. C.
Metropolis; A. H. Taub; John Todd; C. B. Tompkins}",
journal = j-TECHNOMETRICS,
volume = "7",
number = "1",
pages = "82--82",
month = feb,
year = "1965",
CODEN = "TCMTA2",
DOI = "https://doi.org/10.2307/1266139",
ISSN = "0040-1706 (print), 1537-2723 (electronic)",
ISSN-L = "0040-1706",
bibdate = "Sat Jun 21 13:17:45 MDT 2014",
bibsource = "http://www.jstor.org/journals/00401706.html;
http://www.jstor.org/stable/i254241;
http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/technometrics1960.bib",
URL = "http://www.jstor.org/stable/1266139",
acknowledgement = ack-nhfb,
fjournal = "Technometrics",
journal-URL = "http://www.jstor.org/journals/00401706.html",
}
@Article{Hammer:1965:BRBb,
author = "Preston C. Hammer",
title = "Book Review: {{\booktitle{Experimental Arithmetic,
High Speed Computing and Mathematics}} by N. C.
Metropolis, A. H. Taub, John Todd, and C. B.
Tompkins}",
journal = j-TECHNOMETRICS,
volume = "7",
number = "1",
pages = "82--82",
month = feb,
year = "1965",
CODEN = "TCMTA2",
ISSN = "0040-1706 (print), 1537-2723 (electronic)",
ISSN-L = "0040-1706",
bibdate = "Tue Mar 20 13:44:52 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/technometrics1960.bib",
URL = "http://links.jstor.org/sici?sici=0040-1706%28196502%297%3A1%3C82%3AEAHSCA%3E2.0.CO%3B2-9",
acknowledgement = ack-nhfb,
fjournal = "Technometrics",
journal-URL = "http://www.jstor.org/journals/00401706.html",
}
@Article{Hamming:1965:NLB,
author = "R. W. Hamming and W. L. Mammel",
title = "A Note on the Location of the Binary Point in a
Computing Machine",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
pages = "260--261",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264258",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:22 MDT 2011",
bibsource = "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)",
ISSN-L = "0001-0782",
MRclass = "68.00",
MRnumber = "30\#2707",
bibdate = "Fri Dec 08 14:32:51 1995",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In a recent paper, Gregory and Raney described a
technique for double-precision floating-point
arithmetic. A similar technique can be developed for
triple-precision floating-point arithmetic and its is
the purpose of this note to describe this technique.
Only the multiplication and the division algorithms are
described, since the addition-subtraction algorithm can
be obtained by a trivial modification of the algorithm
in Gregory's and Raney's paper.",
acknowledgement = ack-nhfb,
checked = "19940404",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{James:1965:GSR,
author = "Wendy James and P. Jarratt",
title = "The Generation of Square Roots on a Computer with
Rapid Multiplication Compared with Division (in
{Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "19",
number = "91",
pages = "497--500",
month = jul,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InCollection{Kahan:1965:FPO,
author = "W. Kahan",
booktitle = "Programmer's Reference Manual",
title = "The Floating-Point Over\slash Underflow Trap Routine
{{\tt FPTRP}}",
publisher = "Institute of Computer Science, University of Toronto",
address = "Toronto, Ontario, Canada",
year = "1965",
LCCN = "????",
bibdate = "Wed Feb 14 19:11:11 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Section 4.1.",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Kahan:1965:PFR,
author = "W. Kahan",
title = "Pracniques: {Further} Remarks on Reducing Truncation
Errors",
journal = j-CACM,
volume = "8",
number = "1",
pages = "40--40",
month = jan,
year = "1965",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363707.363723",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 00:18:17 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "floating-point arithmetic; truncation errors",
remark = "Gives summation error estimate formula `s = fl(a + b);
error = (a - s) + b', also discovered independently by
\cite{Moller:1965:QDP}. Extends Gill's earlier
fixed-point result \cite{Gill:1951:PSS}. See
improvement \cite{Ozawa:1993:SAE}.",
}
@Article{Kanner:1965:NBC,
author = "Herbert Kanner",
title = "Number Base Conversion in Significant Digit
Arithmetic",
journal = j-J-ACM,
volume = "12",
number = "2",
pages = "242--246",
month = apr,
year = "1965",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Thu Nov 03 08:47:50 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{King:1965:LED,
author = "R. King",
title = "Letter to the {Editor}: On the Double-Precision Square
Root Routine",
journal = j-CACM,
volume = "8",
number = "4",
pages = "202",
month = apr,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$\sqrt(x)$; elementary functions; floating-point
arithmetic",
}
@Article{Krishnamurthy:1965:DCM,
author = "E. V. Krishnamurthy",
title = "On a Divide-and-Correct Method for Variable Precision
Division",
journal = j-CACM,
volume = "8",
number = "3",
pages = "179--181",
month = mar,
year = "1965",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363791.363829",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00",
MRnumber = "30\#2709",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Described in this paper is a divide-and-correct method
for variable precision division in digital computers.
Unlike the earlier methods of Stein and Pope, the
present method uses a suitably rounded form of the
normalized divisor for getting an estimate of the
quotient characters. This result is a correction of at
most plus or minus one to the estimate, to obtain the
exact quotient character. It is believed that this
method will be widely applicable for division
operations in variable word-length character-oriented
machines.",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "floating-point arithmetic",
}
@TechReport{Lederer:1965:FPP,
author = "E. Lederer",
title = "Floating-point-Pegasus, {FLPPEG}",
type = "{ISD-Bericht}",
number = "12",
institution = "ISD, Inst. f{\"u}r Statik u. Dynamik d. Luft- u.
Raumfahrtkonstruktionen, Universit{\"a}t Stuttgart",
address = "Stuttgart, Germany",
pages = "5",
year = "1965",
bibdate = "Thu May 09 09:05:51 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Lehman:1965:SAT,
author = "M. Lehman",
title = "Serial Arithmetic Techniques",
crossref = "AFIPS:1965:FJC",
pages = "715--725",
year = "1965",
bibdate = "Tue Jan 08 23:08:35 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Liddiard:1965:DPF,
author = "Lawrence Anthony Liddiard",
title = "Double precision floating point arithmetic",
type = "Thesis ({M.S.})",
school = "University of Minnesota",
address = "????",
pages = "various",
year = "1965",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Calculators.; Numerical calculations.",
}
@Book{Lyusternik:1965:HCE,
author = "L. A. Lyusternik and O. A. Chervonenkis and A. R.
Yanpolski",
title = "Handbook for Computing Elementary Functions",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "xiii + 251",
year = "1965",
LCCN = "QA221.L513",
bibdate = "Thu Sep 1 10:13:16 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Translated from the Russian by G. J. Tee. Translation
edited by K. L. Stewart.",
acknowledgement = ack-nj,
}
@Article{Mano:1965:PSB,
author = "M. Morris Mano",
title = "Pracniques: {Simulation} of {Boolean} functions in a
decimal computer",
journal = j-CACM,
volume = "8",
number = "1",
pages = "39--40",
month = jan,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:58 MST 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See remarks \cite{Dodd:1965:RSB}.",
acknowledgement = ack-nhfb,
checked = "19940304",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
sjb = "Describes how to perform Boolean operations by means
of arithmetic and conditional transfer operations on a
decimal computer lacking any built in logical
instructions. See also \cite{Dodd:cacm:65}.",
}
@Article{Martin:1965:SHS,
author = "A. R. Martin and A. B. Rosenstein",
title = "A Shiftrix for High-Speed Multiplication",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "4",
pages = "639--643",
month = aug,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264010",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:39 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038521",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@InProceedings{Metropolis:1965:AIE,
author = "N. Metropolis",
title = "Analysis of Inherent Errors in Matrix Decomposition
Using Unnormalized Arithmetic",
crossref = "Kalenich:1965:IPP",
volume = "2",
pages = "441--442",
year = "1965",
bibdate = "Wed Feb 14 19:21:38 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0161.35502",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Metropolis:1965:AUA,
author = "N. Metropolis",
title = "Algorithms in unnormalized arithmetic. {I}.
{Recurrence} relations",
journal = j-NUM-MATH,
volume = "7",
number = "2",
pages = "104--112",
month = apr,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "68.00",
MRnumber = "MR0178589 (31 \#2846)",
MRreviewer = "G. Dahlquist",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See erratum \cite{Metropolis:1965:BAU}.",
ZMnumber = "0128.36301",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Metropolis:1965:BAU,
author = "N. Metropolis",
title = "Berichtigung: {Algorithms} in unnormalized arithmetic.
{I}. {Recurrence} relations",
journal = j-NUM-MATH,
volume = "7",
number = "4",
pages = "354",
month = aug,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "Contributed Item",
MRnumber = "MR1553943",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Metropolis:1965:RCU,
author = "N. Metropolis and R. L. Ashenhurst",
title = "Radix Conversion in an Unnormalized Arithmetic
System",
journal = j-MATH-COMPUT,
volume = "19",
number = "91",
pages = "435--441",
month = jul,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
URL = "http://links.jstor.org/sici?sici=0025-5718%28196507%2919%3A91%3C435%3ARCIAUA%3E2.0.CO%3B2-D",
ZMnumber = "0146.14607",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Metze:1965:MSR,
author = "Gernot Metze",
title = "Minimal Square Rooting",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
pages = "181--185",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.263963",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:22 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038397",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Miller:1965:ASF,
author = "G. F. Miller",
title = "Algorithms for Special Functions {II}",
journal = j-NUM-MATH,
volume = "7",
pages = "194--196",
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Sep 16 10:22:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
xxmonth = "(none)",
xxnumber = "(none)",
}
@Article{Moller:1965:NQD,
author = "Ole M{\o}ller",
title = "Note on Quasi Double-Precision",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "5",
number = "4",
pages = "251--255",
year = "1965",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Sat Nov 14 09:14:57 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Moller:1965:QDP}.",
acknowledgement = ack-nj # " and " # ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Moller:1965:QDP,
author = "Ole M{\o}ller",
title = "Quasi Double-Precision in Floating Point Addition",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "5",
number = "1",
pages = "37--50",
month = mar,
year = "1965",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01975722",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65.80",
MRnumber = "MR0181130 (31 \#5359)",
bibdate = "Wed Jan 4 18:52:08 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=5&issue=1;
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,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "accurate floating-point summation; floating-point
arithmetic; rounding errors",
remark = "Gives summation error estimate formula `s = fl(a + b);
error = (a - s) + b', also discovered independently by
\cite{Kahan:1965:PFR}. Extends Gill's earlier
fixed-point result \cite{Gill:1951:PSS}.",
}
@InCollection{Moore:1965:AACa,
author = "Ramon E. Moore",
title = "The automatic analysis and control of error in digital
computing based on the use of interval numbers",
crossref = "Rall:1965:EDCa",
chapter = "2",
bookpages = "????",
pages = "61--130",
year = "1965",
MRclass = "65.61 (65.80)",
MRnumber = "MR0176614 (31 \#886)",
MRreviewer = "T. E. Hull",
bibdate = "Thu Jun 20 10:51:40 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://interval.louisiana.edu/Moores_early_papers/Moore_in_Rall_V1.pdf",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@InCollection{Moore:1965:AACb,
author = "Ramon E. Moore",
title = "Automatic local coordinate transformations to reduce
the growth of error bounds in interval computation of
solutions of ordinary differential equations",
crossref = "Rall:1965:EDCb",
chapter = "2",
pages = "103--140",
year = "1965",
MRclass = "65.80 (65.60)",
MRnumber = "MR0185839 (32 \#3299)",
MRreviewer = "T. E. Hull",
bibdate = "Thu Jun 20 10:51:40 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://interval.louisiana.edu/Moores_early_papers/Moore_in_Rall_V2.pdf",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Morrison:1965:MCC,
author = "D. R. Morrison",
title = "A Method for Computing Certain Inverse Functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "10",
number = "??",
pages = "202--208",
month = "????",
year = "1965",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Nathan:1965:CM,
author = "Amos Nathan",
title = "The Cascade Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
pages = "243--247",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264250",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:22 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038406",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Penney:1965:BSC,
author = "Walter Penney",
title = "A ``Binary'' System for Complex Numbers",
journal = j-J-ACM,
volume = "12",
number = "2",
pages = "247--248",
month = apr,
year = "1965",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Thu Nov 03 08:47:50 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Book{Ralston:1965:FCN,
author = "Anthony Ralston",
title = "A first course in numerical analysis",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xix + 578",
year = "1965",
LCCN = "QA297 .R3",
bibdate = "Fri Aug 20 10:13:32 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "International series in pure and applied mathematics",
acknowledgement = ack-nhfb,
remark = "See also second edition
\cite{Ralston:1978:FCN,Ralston:2001:FCN}. Cited in
\cite{Sterbenz:1974:FPC}.",
subject = "Numerical analysis",
}
@Article{Riordan:1965:UAT,
author = "R. H. S. Riordan and R. R. A. Morton",
title = "The Use of Analog Techniques in Binary Arithmetic
Units",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "1",
pages = "29--35",
month = feb,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264051",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:20 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=4038346",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Ross:1965:RTE,
author = "D. R. Ross",
title = "Reducing Truncation Errors Using Cascading
Accumulators",
journal = j-CACM,
volume = "8",
number = "1",
pages = "32--33",
month = jan,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sun Sep 18 22:55:00 1994",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "When accumulating a large number of quantities as in
numerical integration, the sum itself may become much
larger than the individual addends. This results in
truncation error. Much of this error can be eliminated
using cascading accumulators as noted in a recent
article by Wolfe. A simpler and slightly more flexible
algorithm is presented which deals also with the case
of negative addends.",
acknowledgement = ack-nhfb,
checked = "19940304",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "accurate floating-point summation",
sjb = "Refers to \cite{Wolfe:cacm:196,Wilhelm:1977:GMPb}.",
}
@Article{Schreiber:1965:BRB,
author = "Alvin L. Schreiber",
title = "Book Review: {{\booktitle{A Binary Multiplication}}
(W. C. McGee)}",
journal = j-SIAM-REVIEW,
volume = "7",
number = "1",
pages = "134--136",
month = "????",
year = "1965",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1007016",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:05:20 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/7/1;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1965",
}
@Article{Smith:1965:ASO,
author = "Francis J. Smith",
title = "An Algorithm for Summing Orthogonal Polynomial Series
and their Derivatives with Applications to
Curve-Fitting and Interpolation",
journal = j-MATH-COMPUT,
volume = "19",
number = "89",
pages = "33--36",
month = apr,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Specker:1965:CAL,
author = "W. H. Specker",
title = "A Class of Algorithms for $ \ln x $, $ \exp x $, $
\sin x $, $ \cos x $, $ \tan^{-1} x $, and $ \cot^{-1}
x $",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "1",
pages = "85--86",
month = feb,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264066",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:21 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038361",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Swarztrauber:1965:LED,
author = "P. N. Swarztrauber",
title = "Letter to the {Editor}: On the Double-Precision Square
Root Routine",
journal = j-CACM,
volume = "8",
number = "4",
pages = "202",
month = apr,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Aug 31 14:02:19 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$\sqrt(x)$; elementary functions; floating-point
arithmetic",
}
@Article{Sweeney:1965:AFP,
author = "D. W. Sweeney",
title = "An analysis of floating-point addition",
journal = j-IBM-SYS-J,
volume = "4",
number = "1",
pages = "31--42",
year = "1965",
CODEN = "IBMSA7",
ISSN = "0018-8670",
bibdate = "Thu Sep 15 18:42:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in
\cite[pp.~317--328]{Swartzlander:1990:CAa}.",
URL = "http://www.research.ibm.com/journal/sj/041/ibmsjIVRID.pdf",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
fjournal = "IBM Systems Journal",
remark = "Page 34, containing a critical table, is missing from
the PDF file.",
xxmonth = "(none)",
}
@Article{Winograd:1965:TRP,
author = "Shmuel Winograd",
title = "On the Time Required to Perform Addition",
journal = j-J-ACM,
volume = "12",
number = "2",
pages = "277--285",
month = apr,
year = "1965",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Multi.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Arango:1966:FCP,
author = "H. Arango and J. Santos",
title = "A Fast Carry-Propagation Circuit for Base $3$ Signed
Non redundant Arithmetic",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-15",
number = "2",
pages = "254--255",
month = apr,
year = "1966",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1966.264311",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 05:46:31 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038725",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Brooker:1966:MFA,
author = "R. A. Brooker and J. S. Rohl and S. R. Clark",
title = "The main features of {Atlas Autocode}",
journal = j-COMP-J,
volume = "8",
number = "4",
pages = "303--310",
month = jan,
year = "1966",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:56:10 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/",
note = "See comment \cite{Clark:1966:CMP}.",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/080303.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/303.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/304.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/305.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/306.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/307.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/308.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/309.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/310.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@MastersThesis{Chang:1966:DHR,
author = "Henry Kwan-cheung Chang",
title = "Design of a high rate floating point digital
accumulator",
type = "Thesis ({M.S. in Engineering})",
school = "University of California, Davis",
address = "Davis, CA, USA",
pages = "60",
year = "1966",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Dissertations, Academic --- California ---
Engineering.",
}
@Article{Chartres:1966:ACP,
author = "Bruce A. Chartres",
title = "Automatic Controlled Precision Calculations",
journal = j-J-ACM,
volume = "13",
number = "3",
pages = "386--403",
month = jul,
year = "1966",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Fri Nov 28 16:23:06 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Recent developments in computer design and error
analysis have made feasible the use of variable
precision arithmetic and the preparation of programs
that automatically determine their own precision
requirements. Such programs enable the user to specify
the accuracy he wants, and yield answers guaranteed to
lie within the bounds prescribed. A class of such
programs, called ``contracting error programs'', is
defined in which the precision is determined by
prescribing error bounds on the data. A variant of
interval arithmetic is defined which enables a limited
class of algorithms to be programmed as contracting
error programs. A contracting error program for the
solution of simultaneous linear equations is described,
demonstrating the application of the idea to a wider
class of problems.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Clark:1966:CMP,
author = "S. R. Clark and W. F. Lunnon",
title = "Correspondence: Multiple precision arithmetic (real
and complex)",
journal = j-COMP-J,
volume = "9",
number = "2",
pages = "174--174",
month = aug,
year = "1966",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:56:14 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_02/",
note = "See \cite{Brooker:1966:MFA}.",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_02/tiff/174.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Clark:1966:MPA,
author = "S. R. Clark and W. F. Lunnon",
title = "Multiple precision arithmetic in {Atlas Autocode}",
journal = j-COMP-J,
volume = "9",
number = "2",
pages = "174--174",
month = aug,
year = "1966",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/9.2.174",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:36 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/9/2.toc;
http://www.math.utah.edu/pub/tex/bib/compj1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/9/2/174.full.pdf+html",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Fike:1966:SAS,
author = "C. T. Fike",
title = "Starting Approximations for Square Root Calculation on
{IBM} System/360",
journal = j-CACM,
volume = "9",
number = "4",
pages = "297--299",
month = apr,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$\sqrt(x)$; elementary functions; IBM S/360",
}
@Article{Filippi:1966:BEE,
author = "S. Filippi",
title = "{Die Berechnung einiger elementarer transzendenter
Funktionen mit Hilfe des Richardson-Algorithmus}
\toenglish {The Computation of Some Elementary
Transcendental Functions by Means of the Richardson
Algorithm} \endtoenglish",
journal = j-COMPUTING,
volume = "1",
number = "??",
pages = "127--132",
month = "????",
year = "1966",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Flehinger:1966:PRI,
author = "B. J. Flehinger",
title = "On the Probability that a Random Integer Has Initial
Digit `{A}'",
journal = j-AMER-MATH-MONTHLY,
volume = "73",
number = "??",
pages = "1056--1061",
year = "1966",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Wed Feb 14 18:53:58 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
remark = "Probably November or December issue; missing from
amermathmonthly1960.bib.",
}
@Article{Garner:1966:ECA,
author = "Harvey L. Garner",
title = "Error Codes for Arithmetic Operations",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-15",
number = "5",
pages = "763--770",
month = oct,
year = "1966",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1966.264566",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 05:46:38 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=4038884",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Grau:1966:BRB,
author = "A. A. Grau",
title = "Book Review: {{\booktitle{Rounding Errors in Algebraic
Processes}} (J. H. Wilkinson)}",
journal = j-SIAM-REVIEW,
volume = "8",
number = "3",
pages = "397--398",
month = "????",
year = "1966",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1008087",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:05:37 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/8/3;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "July 1966",
}
@Article{Gregory:1966:DAU,
author = "Robert T. Gregory",
title = "On the Design of the Arithmetic Unit of a
Fixed-Word-Length Computer from the Standpoint of
Computational Accuracy",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-15",
number = "2",
pages = "255--257",
month = apr,
year = "1966",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1966.264312",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 05:46:31 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038726",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@InProceedings{Harding:1966:ISF,
author = "L. J. {Harding, Jr.}",
editor = "????",
booktitle = "SHARE XXVII, Toronto, Canada, August 1966",
title = "Idiosyncracies of {System\slash 360} Floating-Point",
publisher = "????",
address = "????",
pages = "??--??",
year = "1966",
LCCN = "????",
bibdate = "Wed Feb 14 19:04:14 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{Harding:1966:MSF,
author = "L. J. {Harding, Jr.}",
title = "Modifications of {System\slash 360} Floating-Point",
number = "SSD 157, C4470",
howpublished = "SHARE Secretarial Distribution",
pages = "11--27",
month = "????",
year = "1966",
bibdate = "Wed Feb 14 19:05:45 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Henrici:1966:TPM,
author = "Peter Henrici",
title = "Test of probabilistic models for the propagation of
roundoff errors",
journal = j-CACM,
volume = "9",
number = "6",
pages = "409--410",
month = jun,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:07 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Hull:1966:TPM,
author = "T. E. Hull and J. R. Swenson",
title = "Tests of Probabilistic Models for Propagation of
Roundoff Errors",
journal = j-CACM,
volume = "9",
number = "2",
pages = "108--113",
month = feb,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.80",
MRnumber = "32\#3297",
bibdate = "Fri Nov 25 18:20:04 MST 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/gvl.bib;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In any prolonged computation it is generally assumed
that the accumulated effect of roundoff errors is in
some sense statistical. The purpose of this paper is to
give precise descriptions of certain probabilistic
models for roundoff error, and then to describe a
series of experiments for testing the validity of these
models. It is concluded that the models are in general
very good. Discrepancies are both rare and mild. The
test techniques can also be used to experiment with
various types of special arithmetic.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "decimal floating-point arithmetic; rounding errors",
}
@Manual{IBM:1966:ISM,
key = "IBM",
title = "{IBM System\slash 360 Model 91}: Functional
Characteristics",
publisher = pub-IBM,
address = pub-IBM:adr,
year = "1966",
bibdate = "Fri Aug 20 09:34:43 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "File No. S360-01, Form A22-6907-2.",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Book{Isaacson:1966:ANM,
author = "Eugene Isaacson and Herbert Bishop Keller",
title = "Analysis of numerical methods",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xv + 541",
year = "1966",
LCCN = "QA297 .I8",
bibdate = "Fri Aug 20 09:37:14 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}. Reprinted in
\cite{Isaacson:1994:ANM}.",
subject = "Numerical analysis",
}
@Misc{Kahan:1966:ISS,
author = "W. Kahan",
title = "{7094 II} System Support for Numerical Analysis",
howpublished = "SHARE Secretary Distribution 159, C4537",
pages = "1--54",
year = "1966",
bibdate = "Wed Nov 07 08:39:33 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@InCollection{Kogbetliantz:1966:GEF,
author = "E. G. Kogbetliantz",
title = "Generation of Elementary Functions",
crossref = "Ralston:1966:MMD",
pages = "7--35",
year = "1966",
bibdate = "Sat Dec 09 14:09:27 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Kuki:1966:EGS,
author = "H. Kuki and E. Hanson and J. J. Ortega and J. C.
Butcher and P. G. Anderson",
title = "Evaluation Guidelines {SHARE Numerical Analysis
Project (N.A.P.)}",
journal = "{SHARE Secretary Distribution}",
volume = "SSD 150, part II",
number = "C4304",
pages = "1--42",
year = "1966",
bibdate = "Fri Aug 20 09:45:16 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Lam:1966:COG,
author = "Lay-yong Lam",
title = "On the {Chinese} origin of the {Galley} method of
arithmetical division",
journal = j-BRITISH-J-HIST-SCI,
volume = "3",
number = "part 1, 9",
pages = "66--69",
year = "1966",
CODEN = "BJHSAT",
DOI = "https://doi.org/10.1017/S0007087400000200",
ISSN = "0007-0874 (print), 1474-001X (electronic)",
ISSN-L = "0007-0874",
MRclass = "01.10",
MRnumber = "0204243 (34 \#4087)",
MRreviewer = "I. N. Veselovski{\u\i}",
bibdate = "Wed Sep 22 18:01:23 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
ZMnumber = "0143.24202",
acknowledgement = ack-nhfb,
fjournal = "British Journal for the History of Science",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BJH",
keywords = "history",
}
@Article{Mancino:1966:MPF,
author = "O. G. Mancino",
title = "Multiple precision floating-point conversion from
decimal-to-binary and vice versa",
journal = j-CACM,
volume = "9",
number = "5",
pages = "347--348",
month = may,
year = "1966",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355592.365635",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:06 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Decimal-to-binary and binary-to-decimal floating-point
conversion is often performed by using a table of the
powers $ 10^i $ ($i$ a positive integer) for converting
from base $ 10$ to base $2$, and by using a table of
the coefficients of a polynomial approximation of $
10^x (0 \leq x < 1)$ for converting from base $2$ to
base $ 10$. These tables occupy a large storage region
in the case of a nonsingle precision conversion. This
paper shows that a single small table suffices for a
floating-point conversion from decimal to binary, and
vice versa, in any useful precision.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "floating-point arithmetic; Multiple precision
arithmetic; number base conversion",
}
@Unpublished{Mazor:1966:FSI,
author = "Stan Mazor",
title = "{Fairchild Symbol II} Decimal Floating Point Unit",
year = "1966",
bibdate = "Wed Nov 22 21:18:53 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Cited in \cite[p. 106]{Cowlishaw:2003:DFP}.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Book{Moore:1966:IA,
author = "Ramon E. Moore",
title = "Interval analysis",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xi + 145",
year = "1966",
LCCN = "QA297 .M63",
bibdate = "Sat Feb 14 08:15:54 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Nickel:1966:NFA,
author = "K. Nickel",
title = "{{\"U}ber die Notwendigkeit einer Fehlerschranken-
Arithmetik f{\"u}r Rechenautomaten}",
journal = j-NUM-MATH,
volume = "9",
pages = "69--79",
year = "1966",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-jr,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Book{Parker:1966:SNS,
author = "Francis D. Parker",
title = "The structure of number systems",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xi + 137",
year = "1966",
LCCN = "QA241 .P3; QA241 .P239",
bibdate = "Fri Nov 9 19:10:47 MST 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
series = "Teachers' mathematics reference series",
acknowledgement = ack-nhfb,
subject = "Number theory",
}
@Book{Richards:1966:EDS,
author = "R. K. (Richard Kohler) Richards",
title = "Electronic Digital Systems",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "ix + 637",
year = "1966",
LCCN = "TK7888.3 .R52",
bibdate = "Mon Oct 24 05:33:53 MDT 2016",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1921--",
remark = "According to \cite[pp. 168--170]{Smiley:2010:MWI},
this was the first book to draw attention to the
pre-World War II work by John Atanasoff (1903--1995)
and Clifford Berry (1918--1963) at Iowa State College
of Agricultural and Mechanic Arts (renamed on 4 July
1959 to Iowa State University of Science and
Technology), and to name their computer the ABC.
Richards is quoted with ``The ancestry of all
electronic digital systems appears to be traceable to a
computer which will be called the Atanasoff--Berry
Computer.'' The book provided important evidence in the
priority dispute and courtroom battles over who
invented the computer (Atanasoff and Berry versus
Mauchly and Eckert). Berry died in unresolved
circumstances: suicide or murder?",
subject = "Electronic digital computers",
tableofcontents = "1: History and Introduction / 1 \\
2: Theory of Digital Systems / 50 \\
3: The Stored-Program Concept / 109 \\
4: Automatic Programming / 293 \\
5: Digital Data Transmission / 362 \\
6: Combined Analog and Digital Techniques / 451 \\
7: Telephone and Message Switching Systems / 481 \\
8: The Relationship between Thinking and Digital
Systems / 519 \\
9: Miscellaneous Digital Systems / 541 \\
10: Digital System Reliability / 571 \\
11: The Automatic Design of Digital Systems / 610 \\
Index / 631",
}
@Article{Saidan:1966:EEA,
author = "A. S. Saidan",
title = "The Earliest Extant {Arabic} Arithmetic:
{{\booktitle{Kitab al-Fusul fi al Hisab al-Hindi}}} of
{Abu al-Hasan, Ahmad ibn Ibrahim al-Uqlidisi}",
journal = j-ISIS,
volume = "57",
number = "4",
pages = "475--490",
month = "Winter",
year = "1966",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:22:16 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i211145;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/isis1960.bib",
URL = "http://www.jstor.org/stable/228518",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/page/journal/isis/about.html",
}
@Article{Smith:1966:CP,
author = "John Smith",
title = "The Challenge of {Pi}",
journal = j-IEEE-SPECTRUM,
volume = "3",
number = "10",
pages = "5--5",
month = oct,
year = "1966",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1966.5217340",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Wed Jan 15 08:45:04 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib;
http://www.math.utah.edu/pub/tex/bib/pi.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "Computer errors; Digital arithmetic; Educational
institutions; Hardware; Physics computing; Power
engineering computing; Programming profession;
Registers; Testing; Upper bound",
remark = "Report of a computation of $ \pi $ to 17,935 places
using base-1,000,000 arithmetic. A footnote reports
``The AIL result to 17,940 places was identical with
the reference to 17,935 places. Reference: D. Shanks
and J. W. Wrench, Jr., `Calculation of Pi to 100,000
Decimals', Mathematics of Computation, January 1962,
Vol. 16, No. 77, pp. 67--99.''",
}
@Article{Spielberg:1966:CEU,
author = "K. Spielberg",
title = "Computation of $ e^x $ with the use of large tables",
journal = j-IBM-SYS-J,
volume = "5",
number = "2",
pages = "102--114",
year = "1966",
CODEN = "IBMSA7",
ISSN = "0018-8670",
bibdate = "Thu Sep 15 18:43:03 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Systems Journal",
xxmonth = "(none)",
}
@Article{Tienari:1966:SPM,
author = "M. Tienari and V. Suokonautio",
title = "A Set of Procedures Making Real Arithmetic of
Unlimited Accuracy Possible Within {Algol 60}",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "6",
number = "4",
pages = "332--338",
month = jul,
year = "1966",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01966093",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon Sep 12 08:07:38 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=6&issue=4&spage=332",
acknowledgement = ack-nj,
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{vanWijngaarden:1966:NAI,
author = "A. {van Wijngaarden}",
title = "Numerical Analysis as an Independent Science",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "6",
number = "1",
pages = "66--81",
month = mar,
year = "1966",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01939551",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:09 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=6&issue=1;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=6&issue=1&spage=66",
abstract = "The paper describes how a number of well-known
mathematical concepts ought to be modified in order to
make sense within the scope of numerical analysis. It
is also shown how obvious difficulties can be overcome
in a logical way. All algorithms suggested are given as
ALGOL procedures.",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Watson:1966:SCC,
author = "R. W. Watson and C. W. Hastings",
title = "Self-Checked Computation using Residue Arithmetic",
journal = j-PROC-IEEE,
volume = "54",
number = "12",
pages = "1920--1931",
month = dec,
year = "1966",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Fri Nov 09 19:37:52 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}
@Article{Whitney:1966:PCR,
author = "D. E. Whitney",
title = "Propagation and control of roundoff error in the
matrix exponential method",
journal = j-PROC-IEEE,
volume = "54",
number = "10",
pages = "1483--1484",
month = oct,
year = "1966",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}
@TechReport{Wiegel:1966:MBA,
author = "R. E. Wiegel",
title = "Methods of Binary Addition",
type = "Technical report",
number = "195",
institution = "Department of Computer Science, University of
Illinois",
address = "Urbana, IL, USA",
month = feb,
year = "1966",
bibdate = "Fri Nov 09 19:40:18 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Adams:1967:SCP,
author = "Duane A. Adams",
title = "A stopping criterion for polynomial root finding",
journal = j-CACM,
volume = "10",
number = "10",
pages = "655--658",
month = oct,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.50",
MRnumber = "39\#2314",
bibdate = "Fri Nov 25 18:20:15 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "When searching for the root of a polynomial, it is
generally difficult to know just when to accept a
number as an adequate approximation to the root. In
this paper an algorithm is presented which allows one
to terminate the iteration process on the basis of
calculated bounds for the roundoff error which occurs
in evaluating the polynomial. This stopping criterion
has been tested on numerous examples and has been found
to serve as a satisfactory means for accepting a
complex number as a zero of a real polynomial.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Anderson:1967:ISMb,
author = "S. F. Anderson and J. G. Earle and R. E. Goldschmidt
and D. M. Powers",
title = "The {IBM System\slash 360 Model 91}: Floating-point
execution unit",
journal = j-IBM-JRD,
volume = "11",
number = "1",
pages = "34--53",
month = jan,
year = "1967",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.111.0034",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Sep 11 15:36:09 MDT 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
http://www.research.ibm.com/journal/",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392016",
abstract = "The principal requirement for the Model 91
floating-point execution unit was that it be designed
to support the instruction-issuing rate of the
processor. The chosen solution was to develop separate,
instruction-oriented algorithms for the add, multiply,
and divide functions. Linked together by the
floating-point instruction unit, the multiple execution
units provide concurrent instruction execution at the
burst rate of one instruction per cycle.",
acknowledgement = ack-nhfb # "\slash " # ack-nj,
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@TechReport{Clark:1967:PSF,
author = "N. A. Clark and W. J. Cody and K. E. Hillstrom and E.
A. Thieleker",
title = "Performance Statistics of the {FORTRAN IV (H)} Library
for the {IBM System\slash 360}",
type = "Technical Report",
number = "ANL-7231",
institution = inst-ANL,
address = inst-ANL:adr,
year = "1967",
bibdate = "Fri Aug 20 08:47:24 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in SHARE Secretary Distribution, SDD 169,
C4473, pp. 12 46.",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Cody:1967:CFI,
author = "W. J. Cody",
title = "Critique of the {FORTRAN IV (H)} Library for the {IBM
System\slash 360}",
journal = "{SHARE Secretary Distribution}",
volume = "SSD 169",
number = "C4473",
pages = "4--11",
year = "1967",
bibdate = "Fri Aug 20 08:52:04 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@InProceedings{Cody:1967:IMD,
author = "W. J. Cody",
title = "The influence of machine design on numerical
algorithms",
crossref = "AFIPS:1967:ACP",
pages = "305--309",
year = "1967",
bibdate = "Sat Sep 24 00:18:32 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Crisansan-Zverca:1967:PED,
author = "Mariana Cri{\c{s}}an-Zverca",
title = "Pseudo-operations of an electronic digital machine
with floating point. ({Romanian})",
journal = j-STUD-CERCET-MAT,
volume = "19",
pages = "1413--1424",
year = "1967",
ISSN = "0039-4068, 0567-6401",
MRclass = "68.00",
MRnumber = "40\#3753",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Studii {\c{s}}i cercet{\u{a}}ri Matematice",
}
@Article{Curry:1967:ART,
author = "E. Curry",
title = "The analysis of round-off and truncation errors in a
hybrid control system",
journal = j-IEEE-TRANS-AUTOMAT-CONTR,
volume = "12",
number = "5",
pages = "601--604",
month = oct,
year = "1967",
CODEN = "IETAA9",
ISSN = "0018-9286",
ISSN-L = "0018-9286",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Automatic Control",
summary = "The round-off and truncation errors of a
digital-analog (hybrid) servo system are studied in
terms of the least upper bound and second moment, or
variance. The study was applied to the azimuth function
of a guided missile launcher system and a \ldots{}",
}
@Article{DeRegt:1967:NRA,
author = "M. P. DeRegt",
title = "Negative radix arithmetic",
journal = "Computer Design",
volume = "6",
number = "??",
pages = "52--63",
month = may,
year = "1967",
bibdate = "Thu Nov 06 06:07:24 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "negative base",
}
@Article{Ferrari:1967:DMU,
author = "Domenico Ferrari",
title = "A Division Method Using a Parallel Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-16",
number = "2",
pages = "224--226",
month = apr,
year = "1967",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1967.264580",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:02 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
note = "See correction \cite{Ferrari:1969:CDM}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039036",
abstract = "The use of a parallel multiplier for performing
high-speed binary division requires that an algorithm
be devised that obtains the quotient by means of
multiplications and additions. Furthermore, its
hardware implementation must be as simple and as fast
as possible. A suitable algorithm, which applies to a
first approximation to the reciprocal of the divisor,
has already been proposed [1]. A similar algorithm is
presented in this paper. The comparison between the two
methods for equal numbers of multiplications shows that
the latter is more accurate. Conversely, a given
accuracy can often be obtained with a higher speed. The
generation of a piecewise-linear initial approximation
is also discussed.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Fike:1967:MEP,
author = "C. T. Fike",
title = "Methods of Evaluating Polynomial Approximations in
Function Evaluation Routines",
journal = j-CACM,
volume = "10",
number = "3",
pages = "175--178",
month = mar,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
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,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Fike:1967:RAO,
author = "C. T. Fike",
title = "A Rational Approximation Optimal by {Moursund}'s
Criterion (letter to the editor)",
journal = j-CACM,
volume = "10",
number = "11",
pages = "683--684",
month = nov,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Filho:1967:AGF,
author = "A. M. S. Filho and G. Schwachheim",
title = "Algorithm 309: Gamma Function with Arbitrary
Precision",
journal = j-CACM,
volume = "10",
number = "8",
pages = "511--512",
month = aug,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Book{Forsythe:1967:CSL,
author = "George E. Forsythe and Cleve B. Moler",
title = "Computer Solution of Linear Algebraic Systems",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xi + 148",
year = "1967",
LCCN = "QA297 .F57 1967",
MRclass = "65.35",
MRnumber = "MR0219223 (36 \#2306)",
MRreviewer = "N. Gastinel",
bibdate = "Tue May 25 08:52:32 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
http://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/gvl.bib",
ZMnumber = "0154.40401",
acknowledgement = ack-nhfb,
keywords = "numerical analysis; software",
remark = "Translated to Russian (1969), Japanese (1969), and
German (1971). Cited in \cite{Sterbenz:1974:FPC}.",
subject = "numerical analysis; data processing; matrices",
tableofcontents = "Reader's background and purpose of book \\
Vector and matrix norms \\
Diagonal form of a matrix under orthogonal equivalence
\\
Proof of diagonal-form theorem \\
Types of computational problems in linear algebra \\
Types of matrices encountered impractical problems \\
Sources of computational problems of linear algebra \\
Condition of a linear system \\
Gaussian elimination and LU decomposition \\
Need for interchanging rows \\
Scaling equations and unknowns \\
The Crout and Doolittle variants \\
Iterative improvement \\
Computing the determinant \\
Nearly singular matrices \\
Algol 60 program \\
Fortran, extended Algol, and PL/1 programs \\
Matrix inversion \\
An example: Hilbert matrices \\
Floating-point round-off analysis \\
Rounding error in Gaussian elimination \\
Convergence of iterative improvement \\
Positive definite matrices; band matrices \\
Iterative methods for solving linear systems \\
Nonlinear systems of equations",
}
@Article{Freeman:1967:CMS,
author = "Herbert Freeman",
title = "Calculation of Mean Shift for a Binary Multiplier
Using $2$, $3$, or $4$ Bits at a Time",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-16",
number = "6",
pages = "864--866",
month = dec,
year = "1967",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1967.264752",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:06 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039205",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Freiman:1967:CDU,
author = "C. V. Freiman and others",
title = "Composite Division Unit",
journal = j-IBM-TDB,
volume = "9",
number = "8",
pages = "994--995",
month = jan,
year = "1967",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Tue Jan 08 22:40:53 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Article{Friedland:1967:AAV,
author = "Paul Friedland",
title = "{Algorithm 312}: {Absolute} Value and Square Root of a
Complex Number",
journal = j-CACM,
volume = "10",
number = "10",
pages = "665--665",
month = oct,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363717.363780",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:15 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$\abs(z)$; $\sqrt(z)$; elementary functions",
}
@Article{Goldberg:1967:BED,
author = "I. Bennett Goldberg",
title = "$ 27 $ Bits Are Not Enough For $8$-Digit Accuracy",
journal = j-CACM,
volume = "10",
number = "2",
pages = "105--106",
month = feb,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363067.363112",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:11 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "From the inequality $ 10^8 < 2^{27} $, we are likely
to conclude that we can represent 8-digit decimal
floating-point numbers accurately by 27-bit [binary]
floating-point numbers. However, we need 28 significant
bits to represent some 8-digit numbers accurately. In
general, we can show that if $ 10^p < 2^{q - 1} $, then
$q$ significant bits are always enough for $p$-digit
decimal accuracy. Finally, we can define a compact
27-bit floating-point representation that will give 28
significant bits, for numbers of practical
importance.",
acknowledgement = ack-nj # " and " # ack-mfc # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "decimal floating-point arithmetic",
received = "August 1966 (revised October 1966)",
}
@Book{Gschwind:1967:DDC,
author = "H. W. Gschwind",
title = "Design of Digital Computers: An Introduction",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 530",
year = "1967",
LCCN = "TK7888.3 .G72",
bibdate = "Fri Nov 09 18:56:39 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{Hertz:1967:CHF,
author = "Theodore M. Hertz",
title = "Computer Having Floating Point Multiplication",
howpublished = "US Patent 3,304,417.",
day = "14",
month = feb,
year = "1967",
bibdate = "Sat Mar 24 06:05:12 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Filed 1 October 1962.",
URL = "https://patentimages.storage.googleapis.com/47/86/c8/897ec6540ff584/US3304417.pdf;
https://patents.google.com/patent/US3304417",
abstract = "Prior art digital computers utilized fixed point
arithmetic processes in executing computer operations.
In performing fixed point arithmetic processes a
computer assumes the binary point (analogous to a
decimal point) to be between the sign of a number and
the most significant digit of the number. Thus the
number is considered to have an absolute value of less
than one. As explained in patent application filed
September 24, 1962, Serial No. 225,676, now abandoned,
for a ``Computer Having Floating Point Addition and
Floating Point Subtraction'' invented by me, in order
to execute fixed point addition and subtraction
operations, numbers to be operated upon by a computer
must first be appropriately scaled prior to computation
in order to obtain the scaling of the numbers is
accomplished prior to entering them into the computer
or by shifting them through programming afterwards.
Fixed point multiplication needs to have numbers scale
prior to performing computations with them. In
multiplication, shifting of the result through
programming is desirable in order to prevent loss of
significant portions which should be retained for use
in later computations. Particularly is it true where
after a multiplication operation has been performed,
the product must be added or subtracted from or with
other numbers, in which case scaling would first have
to be done before the additional computation could be
made.",
acknowledgement = ack-nhfb,
}
@Article{Howell:1967:MPA,
author = "K. M. Howell",
title = "Multiple precision arithmetic techniques",
journal = j-COMP-J,
volume = "9",
number = "4",
pages = "383--387",
month = feb,
year = "1967",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:56:19 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/090383.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/383.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/384.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/385.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/386.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/387.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Jarden:1967:EAL,
author = "Dov Jarden",
title = "Existence of Arbitrarily Long Sequences of Consecutive
Members in Arithmetic Progressions Divisible by
Arbitrarily Many Different Primes",
journal = j-FIB-QUART,
volume = "5",
number = "3",
pages = "280--??",
month = oct,
year = "1967",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:04:54 MDT 2011",
bibsource = "http://www.fq.math.ca/5-3.html;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/5-3/jarden1.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Krishnamurthy:1967:NRD,
author = "E. V. Krishnamurthy and S. K. Nandi",
title = "On the Normalization Requirement of Divisor in
Divide-and-Correct Methods",
journal = j-CACM,
volume = "10",
number = "12",
pages = "809--813",
month = dec,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Kuki:1967:CAE,
author = "H. Kuki",
title = "Comments on the {ANL} Evaluation of the {OS\slash 360
FORTRAN} Math Function Library",
journal = "{SHARE Secretary Distribution}",
volume = "SSD 169",
number = "C4773",
pages = "47--53",
year = "1967",
bibdate = "Fri Aug 20 09:42:04 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Lewis:1967:CFP,
author = "H. R. {Lewis, Jr.} and E. J. {Stovall, Jr.}",
title = "Comments on a Floating-Point Version of {Nordsieck}'s
Scheme for the Numerical Integration of Differential
Equations",
journal = j-MATH-COMPUT,
volume = "21",
number = "98",
pages = "157--161",
month = apr,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Long:1967:LAS,
author = "C. T. Long and J. H. Jordan",
title = "A Limited Arithmetic on Simple Continued Fractions",
journal = j-FIB-QUART,
volume = "5",
number = "2",
pages = "113--128",
month = apr,
year = "1967",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:04:52 MDT 2011",
bibsource = "http://www.fq.math.ca/5-2.html;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/5-2/long.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Mandelbaum:1967:CLS,
author = "David Mandelbaum",
title = "A Comparison of Linear Sequential Circuits and
Arithmetic Sequences",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-16",
number = "2",
pages = "151--157",
month = apr,
year = "1967",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1967.264810",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:01 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039022",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Massell:1967:RAP,
author = "E. Massell",
title = "{R67-41} An Analog Photoresistive Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-16",
number = "3",
pages = "380--380",
month = jun,
year = "1967",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1967.264730",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:03 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
note = "See comment \cite{Azgapetian:1968:CAP}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039094",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@InProceedings{Matula:1967:BCM,
author = "David W. Matula",
booktitle = "{Proceedings of the AFIPS 1967 Spring Joint Computer
Conference}",
title = "Base Conversion Mappings",
volume = "30",
publisher = pub-AFIPS,
address = pub-AFIPS:adr,
pages = "311--318",
year = "1967",
bibdate = "Wed Feb 14 19:18:24 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Book{McCalla:1967:INM,
author = "Thomas Richard McCalla",
title = "Introduction to Numerical Methods and {Fortran}
Programming",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xiii + 359",
month = jan,
year = "1967",
ISBN = "0-471-58125-9",
ISBN-13 = "978-0-471-58125-3",
LCCN = "QA297 .M25",
bibdate = "Sat Sep 27 17:58:26 MDT 1997",
bibsource = "http://www.amazon.com/exec/obidos/ISBN=0471581259/wholesaleproductA/;
http://www.cbooks.com/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$27.95",
URL = "http://www.cbooks.com/sqlnut/SP/search/gtsumt?source=&isbn=0471581259",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.; FORTRAN
(Computer program language); Numerical analysis.",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{McKeeman:1967:RER,
author = "W. M. McKeeman",
title = "Representation Error for Real Numbers in Binary
Computer Arithmetic",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-16",
number = "5",
pages = "682--683",
month = oct,
year = "1967",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1967.264781",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:05 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=4039164",
abstract = "Real numbers can be represented in a binary computer
by the form $ i \cdot B^e $ where $i$ is the integer
part, $B$ the base, and $e$ the exponent. The accuracy
of the representation will depend upon the number of
bits allocated to the integer part and exponent part as
well as what base is chosen. If $ L(i) $ and $ L(e) $
are the number of bits allocated to the magnitudes of
the integer and exponent parts and we define $ I =
2^{L(i)} $ and $ E = 2^{L(e)} $, the exponent range is
given by $ B^{\pm E} $, the maximum relative
representation error is given by $ B / 2 I $, and the
average relative representation error is given by $ (B
- 1) / (4 I \ln B) $. The formulas provide quantitative
comparison for the effectiveness of alternative formats
for real number representations.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
remark = "McKeeman discusses the maximum and average relative
errors in binary (with and without a hidden bit),
octal, and hexadecimal bases for floating-point
arithmetic with a 48-bit computer word. Errors are
smallest with binary and a hidden bit.",
}
@Article{Menzel:1967:AUA,
author = "M. Menzel and N. Metropolis",
title = "Algorithms in unnormalized arithmetic. {II}.
{Unrestricted} polynomial evaluation",
journal = j-NUM-MATH,
volume = "10",
number = "5",
pages = "451--462",
month = nov,
year = "1967",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF02162878",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.80",
MRnumber = "MR0255093 (40 \#8300)",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0225.65059",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Book{Minsky:1967:CFI,
author = "Marvin Lee Minsky",
title = "Computation: Finite and Infinite Machines",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xvii + 317",
year = "1967",
LCCN = "QA267 .M55",
bibdate = "Thu Oct 17 06:05:56 2019",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
author-dates = "1927--2016",
tableofcontents = "Physical machines and their abstract counterparts
\\
Part 1: Finite-state machines \\
Neural networks. Automata made up of parts \\
The memories of events in finite-state machines \\
Part 2: Infinite machines \\
Computability, effective procedures, and algorithms.
Infinite machines \\
Turing machines \\
Universal Turing machines \\
Limitations of effective computability: some problems
not solvable by instruction-obeying machines \\
The computable real numbers \\
The relations between Turing machines and recursive
functions \\
Models similar to digital computers \\
Part 3: Symbol-manipulation systems and computability
\\
The symbol-manipulation systems of post \\
Post's normal-form theorem \\
Very simple bases for computability \\
Solutions to selected problems",
}
@Article{Moler:1967:IRF,
author = "C. B. Moler",
title = "Iterative Refinement in Floating Point",
journal = j-J-ACM,
volume = "14",
number = "2",
pages = "316--321",
month = apr,
year = "1967",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Tue Nov 1 09:43:17 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "ir, nla, lud, iterative refinement",
}
@Article{Mosteller:1967:DSR,
author = "Frederick Mosteller and Cleo Youtz and Douglas Zahn",
title = "The Distribution of Sums of Rounded Percentages",
journal = j-DEMOGRAPHY,
volume = "4",
number = "2",
pages = "850--858",
month = jun,
year = "1967",
CODEN = "????",
ISSN = "0070-3370 (print), 1533-7790 (electronic)",
ISSN-L = "0070-3370",
bibdate = "Thu Nov 24 08:03:16 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Diaconis:1979:RP} for further work.",
URL = "http://muse.jhu.edu/journals/dem/;
http://www.biomedsearch.com/nih/Distribution-Sums-Rounded-Percentages/21318695.html;
http://www.jstor.org/stable/2060324",
abstract = "When percentages are computed for counts in several
categories or for several positive measurements0 each
taken as a fraction of their sum, the rounded
percentages often fail to add to 100 percent. We
investigate how frequently this failure occurs and what
the distributions of sums of rounded percentages are
for (1) an empirical set of data, (2) the multinomial
distribution in small samples, (3) spacings between
points dropped on an interval --- the broken-stick
model; and (4) for simulation for several categories.
The several methods produce similar distributions.We
find that the probability that the sum of rounded
percentages adds to exactly 100 percent is certain for
two categories, about three-fourths for three
categories, about two-thirds for four categories, and
about [Formula: see text] for larger numbers of
categories, c, on the average when categories are not
improbable.",
acknowledgement = ack-nhfb,
fjournal = "Demography",
pubmedid = "21318695",
}
@Article{Moursund:1967:OSV,
author = "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)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Nandi:1967:STD,
author = "Salil K. Nandi and E. V. Krishnamurthy",
title = "A simple technique for digital division",
journal = j-CACM,
volume = "10",
number = "5",
pages = "299--301",
month = may,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:13 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Sandberg:1967:FPR,
author = "I. W. Sandberg",
title = "Floating-Point-Roundoff Accumulation in Digital-Filter
Realizations",
journal = j-BELL-SYST-TECH-J,
volume = "46",
number = "8",
pages = "1775--1791",
month = oct,
year = "1967",
CODEN = "BSTJAN",
ISSN = "0005-8580",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1967/BSTJ.1967.4608.html;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol46/bstj46-8-1775.pdf",
abstract = "In this paper, several results are presented
concerning the effects of roundoff in the
floating-point realization of a general discrete filter
governed ideally by a stable difference equation of the
form\par
$$ w_n = \sum_{k = 0}^M b_k x_{n - k} - \sum {k = 1}^N
a_k w_{n - k}, \qquad n \geq N \qquad (1) $$ \par
in which $ \{ w_n \} $ and $ \{ x_n \} $ are output and
input sequences, respectively.\par
In particular, for a large class of filters it is
proved that there is a function $ f(K) $ with $ f(K)
\to 0 $ as $ K \to \infty $ and a constant $c$, both
dependent on the $ b_k $, the $ a_k $, the order in
which the products on the right side of (1) are summed
in the machine, and $t$, the number of bits allotted to
the mantissa, such that\par
$$ \langle e \rangle_K \leq c \langle y \rangle_K +
f(K) $$ \par
for all $ K \geq N $, in which, with the computed
output sequence of the realized filter,\par
$$ \langle y \rangle_K = \left (\frac {1}{K + 1}
\sum_{n = 0}^K |y_n|^2 \right)^{1 / 2} $$ \par
and\par
$$ \langle e \rangle_K = \left (\frac {1}{K + 1}
\sum_{n = 0}^K |w_n - y_n|^2 \right)^{1 / 2} $$
\par
Bounds on $ f(K) $ and $c$ are given that are not
difficult to evaluate, and which, in many realistic
cases, are informative. For example, for the
second-order bandpass filter:\par
$$ w_n = x_n - a_1 w_{n - 1} - a_2 w_{n - 2}, \qquad n
\geq 2 \qquad (2) $$ \par
with $ a_1 $ and $ a_2 $ chosen so that its poles arc
at approximately $ \pm 45^\circ $ and at distance
approximately (but not less than) $ 0.001 $ from the
unit circle, we find that $c$, an upper bound on the
``asymptotic output error-to-signal ratio'', is not
greater than $ 0.58 \times 10^{-4} $, assuming that $ t
= 27 $, that the terms on the right side of (2) are
summed in the machine in the order indicated (from
right to left), and that the $ x_n $ in (2) are machine
numbers. If the $ x_n $ are not machine numbers, and
hence must be quantized before processing, then $ c
\leq 0.76 \times 10^{-4} $.\par
In addition to error bounds, an inequality is derived
which, if satisfied, rules out certain types of
generally undesirable behavior such as self-sustained
output limit cycles due to roundoff effects. This
inequality is satisfied for the example described
above.",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Sasaki:1967:ASR,
author = "Akio Sasaki",
title = "Addition and Subtraction in the Residue Number
System",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-16",
number = "2",
pages = "157--164",
month = apr,
year = "1967",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1967.264811",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:01 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039023;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4039015",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
keywords = "residue arithmetic; residue number system",
summary = "Improved residue expression and new arithmetic
algorithms for addition and subtraction are proposed.
In the proposed system positive and negative integers
of any magnitude can be handled regardless of the
particular choice of the set of relatively \ldots{}",
}
@Book{Szabo:1967:RAA,
author = "Nicholas S. Szab{\'o} and Richard I. Tanaka",
title = "Residue arithmetic and its applications to computer
technology",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xvi + 236",
year = "1967",
LCCN = "QA247.35 .S95",
bibdate = "Fri Jun 24 16:02:00 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "McGraw-Hill series in information processing and
computers",
acknowledgement = ack-nhfb,
remark = "Based on the authors' Report on residue (modular)
arithmetic survey.",
subject = "Modular arithmetic; Algorithms; Computer programming",
}
@Article{Tomasulo:1967:EAE,
author = "R. M. Tomasulo",
title = "An Efficient Algorithm for Exploiting Multiple
Arithmetic Units",
journal = j-IBM-JRD,
volume = "11",
number = "1",
pages = "25--33",
month = jan,
year = "1967",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Fri Aug 26 10:27:10 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Book{Wilkinson:1967:BZW,
author = "J. H. Wilkinson",
title = "Bledy Zaokragle{\'n} w Procesach Algebraicznych.
({Polish}) [{Rounding} errors in algebraic Processes]",
publisher = "PWW",
address = "Warszawa, Poland",
pages = "????",
year = "1967",
bibdate = "Thu Aug 25 09:28:02 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Polish translation of \cite{Wilkinson:1963:REA}",
acknowledgement = ack-nhfb,
language = "Polish",
}
@Article{Winograd:1967:TRP,
author = "Shmuel Winograd",
title = "On the Time Required to Perform Multiplication",
journal = j-J-ACM,
volume = "14",
number = "4",
pages = "793--802",
month = oct,
year = "1967",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/321420.321438",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Sat Feb 8 10:29:30 2020",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Multi.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Yarbrough:1967:PCC,
author = "Lynn Yarbrough",
title = "Precision calculations of $e$ and $ \pi $ constants",
journal = j-CACM,
volume = "10",
number = "9",
pages = "537--537",
month = sep,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:15 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "floating-point arithmetic; number base conversion",
remark = "Gives decimal, octal, and hexadecimal values of $e$
and $ \pi $ to 100 digits, and notes ``The difficulty
arises because assemblers and compilers are hardly ever
designed to convert decimal constants to a precision of
more than a dozen or so digits. Thus, if calculations
to greater precision are to be done, constants usually
must be input in octal or other binary-derived
representation.''. Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Atkins:1968:HRD,
author = "D. E. Atkins",
title = "Higher-radix division using estimates of the divisor
and partial remainders",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "10",
pages = "925--934",
month = oct,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.226439",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Azen:1968:DMS,
author = "S. Azen and S. Derr",
title = "On the Distribution of the Most Significant
Hexadecimal Digit",
type = "Technical Report",
number = "RM 5496 PR",
institution = "Rand Report",
address = "Santa Monica, CA, USA",
year = "1968",
bibdate = "Wed Feb 14 17:22:53 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Azgapetian:1968:CAP,
author = "V. Azgapetian",
title = "Comment on {``An Analog Photoresistive Multiplier''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "2",
pages = "188--188",
month = feb,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.229083",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 17:40:47 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
note = "See \cite{Massell:1967:RAP}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687312",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Brennan:1968:FTA,
author = "J. F. Brennan",
title = "The Fastest Time of Addition and Multiplication",
journal = "IBM Research Reports",
volume = "4",
number = "1",
pages = "??--??",
month = "????",
year = "1968",
bibdate = "Fri Nov 09 10:43:37 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Dietmeyer:1968:GPI,
author = "D. L. Dietmeyer and J. R. Duley",
title = "Generating prime implicants via ternary encoding and
decimal arithmetic",
journal = j-CACM,
volume = "11",
number = "7",
pages = "520--523",
month = jul,
year = "1968",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363397.363565",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Aug 07 17:25:16 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Decimal arithmetic, ternary encoding of cubes, and
topological considerations are used in an algorithm to
obtain the extremals and prime implicants of Boolean
functions. The algorithm, which has been programmed in
the FORTRAN language, generally requires less memory
than other minimization procedures, and treats DON'T
CARE terms in an efficient manner.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "cubical complexes; extremal; minimization; prime
implicants; switching function; ternary encoding",
}
@Article{Elliott:1968:EAA,
author = "David Elliott",
title = "Error analysis of an algorithm for summing certain
finite series",
journal = j-J-AUSTRALIAN-MATH-SOC,
volume = "8",
number = "2",
pages = "213--221",
month = may,
year = "1968",
CODEN = "JAUMAX",
DOI = "https://doi.org/10.1017/s1446788700005267",
ISSN = "0004-9735 (print), 2059-9234 (electronic)",
ISSN-L = "0004-9735",
MRclass = "65.25",
MRnumber = "0230452",
MRreviewer = "U. C. Guha",
bibdate = "Fri Feb 9 15:20:35 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Australian Mathematical Society",
remark = "Analysis of Clenshaw algorithm for Chebyshev summation
\cite{Clenshaw:1955:NSC}, and report of region of
instability of that procedure",
}
@Book{Fike:1968:CEM,
author = "C. T. Fike",
title = "Computer Evaluation of Mathematical Functions",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xii + 227",
year = "1968",
LCCN = "QA297 .F5",
bibdate = "Thu Sep 1 10:12:51 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Fraser:1968:AUA,
author = "M. Fraser and N. Metropolis",
title = "Algorithms in unnormalized arithmetic. {III}. {Matrix}
inversion",
journal = j-NUM-MATH,
volume = "12",
number = "5",
pages = "416--428",
month = dec,
year = "1968",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.80",
MRnumber = "MR0255094 (40 \#8301)",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0184.37503",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Harman:1968:ADI,
author = "M. G. Harman",
title = "An Attempt to Design an Improved Multiplication
System",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "11",
pages = "1090--1090",
month = nov,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.226864",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 17:40:51 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687268",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Hart:1968:CAa,
author = "John F. Hart and E. W. Cheney and Charles L. Lawson
and Hans J. Maehly and Charles K. Mesztenyi and John R.
Rice and Henry G. {Thatcher, Jr.} and Christoph
Witzgall",
title = "Computer Approximations",
publisher = pub-R-E-KRIEGER,
address = pub-R-E-KRIEGER:adr,
pages = "x + 343",
year = "1968",
ISBN = "0-88275-642-7",
ISBN-13 = "978-0-88275-642-4",
LCCN = "QA 297 C64 1978",
bibdate = "Tue Dec 14 22:55:11 1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
note = "Reprinted 1978 with corrections.",
acknowledgement = ack-nhfb,
shorttableofcontents = "1: The Design of a Function Subroutine / 1 \\
2: General Methods of Computing Functions / 10 \\
3: Least Maximum Approximations / 42 \\
4: The Choice and Application of Approximations / 58
\\
5: Description and Use of the Tables / 82 \\
6: Function Notes / 89 \\
7: Tables of Coefficients / 155 \\
Appendix A: Conversion Algorithms / 307 \\
Appendix B: Bibliography of Approximations / 313 \\
Appendix C: Decimal and Octal Constants / 333 \\
References / 336 \\
Index / 341",
tableofcontents = "1: The Design of a Function Subroutine / 1 \\
1.1 Introduction / 1 \\
1.2 General Considerations in Writing a Function
Subroutine / 2 \\
1.3 Relation of the Function Subroutine to the Computer
System / 3 \\
1.4 The Three Main Types of Function Subroutine / 4 \\
1.5 Special Programming Techniques / 7 \\
1.6 Subroutine Errors / 7 \\
1.7 Final Steps / 9 \\
2: General Methods of Computing Functions / 10 \\
2.1 Introduction / 10 \\
2.2 Application of Infinite Expansions / 11 \\
2.3 Recurrence and Difference Relations / 23 \\
2.4 Iterative Techniques / 27 \\
2.5 Integral Representations / 28 \\
2.6 Differential Equations / 29 \\
2.7 Tabular Data / 32 \\
2.8 Convergence Acceleration / 33 \\
3: Least Maximum Approximations / 42 \\
3.1 Introduction / 42 \\
3.2 Properties of Least Maximum Approximations / 43 \\
3.3 Nearly Least Maximum Approximations / 46 \\
3.4 Rational Approximation / 51 \\
3.5 Segmented Approximation / 54 \\
3.6 Computation of the Tables / 55 \\
4: The Choice and Application of Approximations / 58
\\
4.1 Introduction / 5 8 \\
4.2 Domain Considerations / 58 \\
4.3 Machine Considerations / 62 \\
4.4 Conditioning of Approximations / 65 \\
4.5 Polynomial Forms / 67 \\
4.6 Rational Forms / 73 \\
4.7 Transformation Algorithms / 78 \\
5: Description and Use of the Tables / 82 \\
5.1 Introduction / 22 \\
5.2 Function Notes / 82 \\
5.3 Accuracy of the Coefficients / 83 \\
5.4 How to Use the Tables / 86 \\
5.5 Preparation of the Tables / 88 \\
6: Function Notes / 89 \\
6.1 Square Root, Cube Root / 89 \\
6.2 Exponential and Hyperbolic Functions / 96 \\
6.3 The Logarithm Function / 105 \\
6.4 Trigonometric Functions / 112 \\
6.5 The Inverse Trigonometric Functions / 120 \\
6.6 The Gamma Function and Its Logarithm / 130 \\
6.7 The Error Function / 136 \\
6.8 Bessel Functions / 141 \\
6.9 Complete Elliptic Integrals / 150 \\
7: Tables of Coefficients / 155 \\
Appendix A: Conversion Algorithms / 307 \\
Appendix B: Bibliography of Approximations / 313 \\
Appendix C: Decimal and Octal Constants / 333 \\
References / 336 \\
Index / 341",
}
@Book{Hart:1968:CAb,
author = "John F. Hart and E. W. Cheney and Charles L. Lawson
and Hans J. Maehly and Charles K. Mesztenyi and John R.
Rice and Henry G. {Thatcher, Jr.} and Christoph
Witzgall",
title = "Computer Approximations",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "x + 343",
year = "1968",
ISBN = "0-471-35630-1",
ISBN-13 = "978-0-471-35630-1",
LCCN = "QA297 .C64",
bibdate = "Sat Jan 14 14:53:06 2006",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "The SIAM series in applied mathematics",
acknowledgement = ack-nhfb,
}
@Book{IBM:1968:ISP,
author = "{IBM Corporation}",
title = "{IBM System}\slash 360 Principles of Operation",
publisher = pub-IBM,
address = pub-IBM:adr,
edition = "Eighth",
pages = "175",
year = "1968",
LCCN = "QA76.8.I12 I59 1968",
bibdate = "Wed Sep 14 23:12:39 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{Kahan:1968:ISS,
author = "W. Kahan",
title = "{7094-II} system support for numerical analysis",
howpublished = "SHARE Secretarial Distribution SSD-159.",
year = "1968",
bibdate = "Mon Sep 16 16:14:28 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaneko:1968:PSA,
author = "T. Kaneko and B. Liu",
title = "Round-off error of floating-point digital filters",
crossref = "Anonymous:1968:PSA",
pages = "219--227",
year = "1968",
MRclass = "65.80",
MRnumber = "41\#7878",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Matula:1968:BCT,
author = "David W. Matula",
title = "The Base Conversion Theorem",
journal = j-PROC-AM-MATH-SOC,
volume = "19",
number = "3",
pages = "716--723",
month = jun,
year = "1968",
CODEN = "PAMYAR",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
bibdate = "Fri Apr 21 07:26:39 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A demonstration that, in converting numbers from base
$ \beta $ to base $ \nu $, where $ \beta^i \neq \nu^j $
for any positive integers $ i, j $, a one-to-one
mapping exists only if $ \nu^{m - 1} \geq \beta^n - 1
$. Here $m$ is the number of digits in base $ \nu $ and
$n$ that in base $ \beta $.\par
The implications of this result are discussed in the
author's earlier paper [Proc. Amer. Fed. Information
Processing Soc. 30 (1967), 311--318].",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
received = "9 February 1967",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Matula:1968:C,
author = "David W. Matula",
title = "In-and-out conversions",
journal = j-CACM,
volume = "11",
number = "1",
pages = "47--50",
month = jan,
year = "1968",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/362851.362887",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.80",
MRnumber = "39\#2360",
bibdate = "Fri Nov 25 18:20:17 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Goldberg:1967:BED,Matula:1968:BCT}",
abstract = "By an in-and-out conversion we mean that a
floating-point number in one base is converted into a
floating-point number in another base and then
converted back to a floating-point number in the
original base. For all combinations of rounding and
truncation conversions the question is considered of
how many significant digits are needed in the
intermediate base to allow such in-and-out conversions
to return the original number (when possible), or at
least significant digit.",
acknowledgement = ack-nhfb # "\slash " # ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "floating-point numbers; number base conversion;
rounding error; significance; truncation error",
received = "April 1967 (revised August 1967)",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Metropolis:1968:ANA,
author = "N. Metropolis",
title = "Algorithms in un-normalized arithmetic: Polynomial
evaluation and matrix decomposition",
journal = "Colloques internationaux, Centre National de la
Recherche Scientifique, Paris",
volume = "165",
pages = "293--303",
year = "1968",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0207.15804",
acknowledgement = ack-nhfb,
classmath = "*65H05 (Single nonlinear equations (numerical
methods)) 65F05 (Direct methods for linear systems)",
}
@Article{Nathan:1968:IVS,
author = "A. Nathan and J. Molcho",
title = "Improved Voltage Selector and Cascade Multiplier
Circuits",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "4",
pages = "380--382",
month = apr,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.229386",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 17:40:48 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687350",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Nickel:1968:EBC,
author = "K. Nickel",
booktitle = "Proceedings of the IFIP Congress",
title = "Error Bounds and Computer Arithmetic",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "54--60",
year = "1968",
LCCN = "????",
bibdate = "Fri Aug 20 10:09:47 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Nievergelt:1968:CCP,
author = "J. Nievergelt",
title = "Computers and computing --- Past present Future",
journal = j-IEEE-SPECTRUM,
volume = "5",
number = "1",
pages = "57--61",
month = jan,
year = "1968",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1968.5215633",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Wed Jan 15 09:30:58 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "Computer science; Concurrent computing; Digital
arithmetic; Hardware; History; Instruments;
Maintenance; Manufacturing; Programming; Relays",
}
@Article{Padegs:1968:SAS,
author = "A. Padegs",
title = "Structural aspects of the {SYSTEM\slash 360 Model 85},
Part {III}: Extensions to floating-point architecture",
journal = j-IBM-SYS-J,
volume = "7",
number = "1",
pages = "22--29",
year = "1968",
CODEN = "IBMSA7",
ISSN = "0018-8670",
bibdate = "Tue Mar 19 17:38:46 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Systems Journal",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Phillips:1968:EME,
author = "G. M. Phillips",
title = "Estimate of the maximum error in best polynomial
approximations",
journal = j-COMP-J,
volume = "11",
pages = "110--111",
year = "1968",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Thu Sep 15 18:39:47 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
xxmonth = "(none)",
xxnumber = "(none)",
}
@Article{Rao:1968:ECL,
author = "T. R. N. Rao",
title = "Error-Checking Logic for Arithmetic-Type Operations of
a Processor",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "9",
pages = "845--849",
month = sep,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.229144",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 17:40:50 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687471",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Ross:1968:UMF,
author = "Richard D. Ross",
title = "{University of Mississippi} floating point subroutines
({UMFS})",
institution = "Computer Center, University of Mississippi",
address = "University",
pages = "31",
year = "1968",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic data processing.",
remark = "Cover title.",
}
@Article{Sasaki:1968:BIA,
author = "A. Sasaki",
title = "The Basis for Implementation of Additive Operations in
the Residue Number System",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "11",
pages = "1066--1073",
month = nov,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/TC.1968.226466",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 17:40:51 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687264;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35582",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "A new residue number system algebra has been
previously proposed by the author. The algebra has
solved an essential theoretical barrier in the residue
number system and has enabled one to pursue additive
operations in the residue \ldots{}",
}
@Article{Schmookler:1968:HSB,
author = "M. S. Schmookler",
title = "High Speed Binary to Decimal Conversion",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
pages = "506--508",
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.226913",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 28 19:09:15 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This note describes several methods of performing
fast, efficient, binary-to-decimal conversion. With a
modest amount of circuitry, an order of magnitude speed
improvement can is obtained. This achievement offers a
unique advantage to general-purpose computers requiring
special hardware to translate between binary and
decimal numbering systems.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "decimal floating-point arithmetic",
}
@Book{Scott:1968:OET,
author = "Th{\'e}odore G. Scott",
title = "Ordinateurs {\'e}lectroniques, techniques de
programmation: Computer programming techniques",
publisher = "Tournai, Ed. Gamma",
address = "Paris, France",
pages = "662",
year = "1968",
bibdate = "Thu May 09 09:52:34 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Cinq volumes. Version fran{\c{c}}aise de Juliette
Charbonneau-Kohiyama.",
acknowledgement = ack-nhfb,
contents = "1. Pr{\'e}sentation du Tutac. Etude du registre - base
et de ses fonctions. Le registre base. - 2. Les sous
programmes. L'entr{\'e}e. La sorite. - 3. La bande
magn{\'e}tique. La d{\'e}tection des erreurs. - 4. Les
calculs en virgule flottante. L'{\'e}dition des
programmes. - 5. La programmation symbolique. Le
language Cobol. Fortran et Algol",
}
@Manual{Smith:1968:CC,
author = "Smith, Robert E. (Robert Elijah)",
title = "Competence course",
organization = "Control Data Corp.",
address = "Minneapolis, MN, USA",
pages = "vi + 296",
year = "1968",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.; FORTRAN (Computer program
language)",
remark = "``Computer programming using FORTRAN and card inputs
without key punching!'' Cover title: Competence course,
FORTRAN computer programming. At head of title: School
computer-use plan.",
}
@Book{Stuart:1968:FP,
author = "Fredric Stuart",
title = "{Fortran} programming",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xix + 353",
year = "1968",
ISBN = "0-471-83477-7",
ISBN-13 = "978-0-471-83477-9",
LCCN = "QA76.5 .S8",
bibdate = "Sat Jan 27 13:40:57 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
{Fortran} (Computer program language)",
remark = "Cited in \cite{Sterbenz:1974:FPC}, but given year
1969.",
}
@Article{Tung:1968:DAS,
author = "Chin Tung",
title = "A Division Algorithm for Signed-Digit Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "9",
pages = "887--889",
month = sep,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.229150",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 17:40:50 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687477",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Urabe:1968:RED,
author = "Minoru Urabe",
title = "Roundoff Error Distribution in Fixed-Point
Multiplication and a Remark about the Rounding Rule",
journal = j-SIAM-J-NUMER-ANAL,
volume = "5",
number = "2",
pages = "202--210",
month = jun,
year = "1968",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Vitenko:1968:OAA,
author = "{\=I}. V. V{\=\i}ten'{k}o",
title = "Optimal algorithms for addition and multiplication on
machines with floating point. ({Russian})",
journal = "{\v{Z}}. Vy{\v{c}}isl. Mat. i Mat. Fiz",
volume = "8",
pages = "1076--1084",
year = "1968",
MRnumber = "40\#2250",
bibdate = "Sat Dec 16 16:45:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Russian",
reviewer = "J. Kuntzmann",
}
@TechReport{Yohe:1968:CPA,
author = "J. M. Yohe",
title = "Computer Programming for Accuracy",
type = "{MRC} Technical Summary Report",
number = "866",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
month = apr,
year = "1968",
bibdate = "Sun Dec 30 21:42:55 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In most computations, it is tacitly assumed that the
results produced by the program are 'accurate enough'.
This assumption is not always valid. In this report, we
discuss several possible sources of error in digital
computation, and we list several steps which can be
taken to guard against some types of error and
determine an upper bound for the effects of other
types. We illustrate these techniques with our
experience in writing a program to locate zeros of the
Riemann zeta function.",
acknowledgement = ack-nhfb,
}
@Article{Anonymous:1969:VPD,
author = "Anonymous",
title = "Video Probability Distributions",
journal = j-IEEE-SPECTRUM,
volume = "6",
number = "4",
pages = "5--5",
month = apr,
year = "1969",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1969.5214042",
ISSN = "1939-9340",
ISSN-L = "0018-9235",
bibdate = "Wed Jan 15 11:58:06 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "Arithmetic; Circuit noise; Detectors; Distribution
functions; Gaussian noise; Probability distribution;
Signal to noise ratio; Tail; Testing; Voltage",
}
@InProceedings{Babuska:1969:NSM,
author = "Ivo Babu{\v{s}}ka",
title = "Numerical stability in mathematical analysis",
crossref = "Morrell:1969:IPP",
pages = "11--23",
year = "1969",
bibdate = "Tue Nov 22 05:36:22 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}
@Article{Banerji:1969:SDR,
author = "D. K. Banerji and J. A. Brzozowski",
title = "Sign Detection in Residue Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-18",
number = "4",
pages = "313--320",
month = apr,
year = "1969",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1969.222658",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 16:55:18 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671251;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35034",
abstract = "This paper is concerned with the sign detection
problem in residue number systems. The proposed
solution is applicable only to nonredundant systems. It
is shown that under rather general conditions an
explicit, closed formula for the sign function can be
obtained. In a special case, when one of the moduli is
$2$, the sign function becomes an EXCLUSIVE-OR
function. A sign detection algorithm is proposed and
methods of implementing the algorithm are presented.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
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)",
ISSN-L = "0001-0782",
MRclass = "68.00",
MRnumber = "43\#5755",
bibdate = "Mon Mar 24 21:38:51 MST 1997",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A digital computer is considered, whose memory words
are composed of $N$ $r$-state devices plus two sign
bits (two state devices). The choice of base $ \beta $
for the internal representation floating-point numbers
on such a computer is discussed. It is shown that in a
certain sense $ \beta = r $ is best.",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Bell Telephone Labs. Inc., Murray Hill, NJ, USA",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "accuracy; base choice; digital arithmetic;
floating-point; number representations",
}
@InProceedings{Clark:1969:SCE,
author = "N. W. Clark and W. J. Cody",
title = "Self-contained exponentiation",
crossref = "AFIPS:1969:ACPb",
volume = "35",
pages = "701--706",
year = "1969",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Cody:1969:PTF,
author = "W. J. Cody",
title = "Performance testing of function subroutines",
crossref = "AFIPS:1969:ACPa",
volume = "34",
pages = "759--763",
year = "1969",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Duke:1969:DFP,
author = "K. A. Duke",
title = "Decimal Floating Point Processor",
journal = j-IBM-TDB,
volume = "11-69",
pages = "862--862",
month = nov,
year = "1969",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Fri Nov 28 11:29:48 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
keywords = "decimal floating-point arithmetic",
remark = "Decimal arithmetic with unnormalized binary integers
of unspecified length for coefficient and exponent.",
}
@MastersThesis{Duncan:1969:FFA,
author = "Daniel D. A. Duncan",
title = "{FLOP}: a floating-point arithmetic package",
type = "Thesis ({M.S.})",
school = "University of Southwestern Louisiana",
address = "Lafayette, LA, USA",
pages = "108",
year = "1969",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Algorithms.; Arithmetic --- Foundations.; FLOP
(Computer program language).; Transformations
(Mathematics).",
}
@Article{Dunworth:1969:ECB,
author = "A. Dunworth and J. I. Roche",
title = "The Error Characteristics of the Binary Rate
Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-18",
number = "8",
pages = "741--745",
month = aug,
year = "1969",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1969.222757",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 16:55:20 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671350",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Ehrman:1969:SFP,
author = "J. R. Ehrman",
title = "A Study of Floating-Point Conversions in Some
{OS\slash 360} Components",
number = "SDD 196, C5207",
institution = "SHARE Secretary Distribution",
address = "????",
pages = "1--6",
year = "1969",
bibdate = "Wed Feb 14 18:50:19 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Fenstad:1969:NSM,
author = "Jens Erik Fenstad",
title = "Non-standard models for arithmetic and analysis",
journal = j-LECT-NOTES-MATH,
volume = "118",
pages = "30--47",
year = "1969",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0060250",
ISBN = "3-540-04907-X (print), 3-540-36246-0 (e-book)",
ISBN-13 = "978-3-540-04907-4 (print), 978-3-540-36246-3
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
bibdate = "Thu May 8 17:39:14 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/lnm1960.bib",
URL = "http://link.springer.com/chapter/10.1007/BFb0060250/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/BFb0060247",
book-URL = "http://www.springerlink.com/content/978-3-540-36246-3",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
}
@Article{Fenwick:1969:BMO,
author = "P. M. Fenwick",
title = "Binary Multiplication with Overlapped Addition
Cycles",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-18",
number = "1",
pages = "71--74",
month = jan,
year = "1969",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1969.222527",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 16:55:17 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671120",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Ferrari:1969:CDM,
author = "D. Ferrari",
title = "Correction to {``A Division Method Using a Parallel
Multiplier''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-18",
number = "10",
pages = "960--960",
month = oct,
year = "1969",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1969.222555",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 16:55:21 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
note = "See \cite{Ferrari:1967:DMU}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671148",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Field:1969:OFP,
author = "J. A. Field",
title = "Optimizing floating-point arithmetic via post addition
shift probabilities",
crossref = "AFIPS:1969:ACPa",
pages = "597--??",
year = "1969",
bibdate = "Tue Oct 09 07:54:02 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Flores:1969:BRB,
author = "Ivan Flores",
title = "Book Review: {{\booktitle{Residue Arithmetic and Its
Application to Computer Technology}} (Nicholas S. Szabo
and Richard I. Tanaka)}",
journal = j-SIAM-REVIEW,
volume = "11",
number = "1",
pages = "103--104",
month = "????",
year = "1969",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1011027",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:06:04 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/11/1;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1969",
}
@Book{Froberg:1969:INA,
author = "Carl Erik Fr{\"o}berg",
title = "Introduction to numerical analysis",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Second",
pages = "xii + 433",
year = "1969",
LCCN = "QA297 .F6813 1969",
bibdate = "Fri Aug 20 09:03:07 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Translation of Swedish original {\em L{\"a}robok i
numerisk analys}. Cited in \cite{Sterbenz:1974:FPC}.",
subject = "Numerical analysis",
}
@Article{Hammersley:1969:NAP,
author = "P. Hammersley",
title = "Note on {Algorithm 34}: Procedures for the Basic
Arithmetical Operations in Multi-Length Working",
journal = j-COMP-J,
volume = "12",
number = "1",
pages = "102--103",
month = feb,
year = "1969",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:51:33 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_01/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_01/tiff/102.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_01/tiff/103.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Manual{Hansen:1969:RCR,
author = "Per Brinch Hansen",
title = "{RC-4000 Computer} Reference Manual",
number = "RCSL No: 55-D1",
organization = "A/S Regnecentralen",
address = "Copenhagen, Denmark",
pages = "85",
month = jun,
year = "1969",
bibdate = "Sat Mar 09 14:14:25 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bitsavers.org/pdf/regnecentralen/RC_4000_Reference_Manual_Jun69.pdf;
http://www.math.utah.edu/~beebe/RC-4000",
acknowledgement = ack-nhfb,
remark = "The RC-4000 has a 24-bit word, and supplies 12-bit and
24-bit integer arithmetic, and 48-bit floating-point
arithmetic. The latter has a signed 36-bit normalized
two's-complement binary fraction stored at the left of
a double word, followed by a 12-bit two's-complement
signed exponent. The representable range is therefore
[-0x1p-2049, +0x1p2047), or about [-1.547e-617,
1.615e+161]. The sign, and zero value, can be
determined by examining only the first word. Its
floating-point arithmetic can exactly represent 35-bit
integer arithmetic.",
tableofcontents = "1. RC 4000 Specifications / 9 \\
2. Design Considerations / 11 \\
2.1. Word Length / 11 \\
2.2. Register Structure / 11 \\
2.3. Address Modification / 11 \\
2.4. Monitor Control / 12 \\
2.5. Input/Output Control / 13 \\
3. Data and Instruction Formats / 15 \\
3.1. Data Formats / 15 \\
3.2. Storage Addressing / 15 \\
3.3. Working Registers / 16 \\
3.4. Instruction Format / 17 \\
3.5. Address Modify Instruction / 18 \\
4. Integer Arithmetic / 19 \\
4.1. Number Representation / 19 \\
4.2. Byte Arithmetic / 19 \\
4.3. Multiplication and Division / 20 \\
4.4. Overflow and Carry Indication / 21 \\
5. Floating-Point Arithmetic / 22 \\
5.1. Number Representation / 22 \\
5.2. Arithmetic Operations / 23 \\
5.3. Normalization and Rounding / 23 \\
5.4. Precision Modes / 24 \\
5.5. Underflow, Overflow, and Non-Normalized Operands /
25 \\
5.6. Number Conversion / 26 \\
5.7. Exact Arithmetic with Floating-Point Instructions
/ 26 \\
6. Protection System / 28 \\
6.1. Storage Protection / 28 \\
6.2. Privileged Instructions / 29 \\
6.3. Summary of Protection System / 29 \\
6.4. An Example of Protected Areas / 30 \\
7. Interruption System / 32 \\
7.1. Interruption Logic / 32 \\
7.2. Interruption Conditions / 33 \\
8. Low-Speed Data Channel / 35 \\
8.1. Main Characteristics / 35 \\
8.2. Input/Output Instruction / 35 \\
8.3. Channel Operation / 36 \\
8.4. Disconnected and Busy Indication / 37 \\
8.5. Device Commands / 37 \\
8.6. Read / 37 \\
8.7. Sense / 37 \\
8.8. Write / 38 \\
8.9. Control / 39 \\
8.10. Summary of Low-Speed Channel / 39 \\
9. High-Speed Data Channel / 41 \\
10. Standard Peripheral Devices / 43 \\
10.1. Console Devices / 43 \\
10.2. Interval Timer / 43 \\
11. Operator Control Panel / 44 \\
11.1. Indicators and Control Keys / 44 \\
11.2. Machine Errors / 44 \\
11.3. Reset Control / 44 \\
11.4. Start Control / 45 \\
11.5. Autoload Control / 45 \\
11.6. Local/Remote Indication / 46 \\
12. Technical Control Panel / 47 \\
12.1. Operating Modes / 47 \\
12.2. Instruction Step Keys / 47 \\
12.3. Register Setting and Display / 47 \\
12.4. Microinstruction Selection and Display / 48 \\
12.5. Parity Control / 48 \\
13. Instruction Set / 49 \\
14. Definition of Instructions / 51 \\
14.1. Algol Notation / 51 \\
14.2. Register Structure / 51 \\
14.3. Elementary Operations / 54 \\
14.4. Control Panel Functions / 55 \\
14.5. Instruction Fetch Cycle / 55 \\
14.6. Protection Procedures / 56 \\
14.7. Arithmetic Procedures / 57 \\
14.8. Instruction Execution / 58 \\
Appendix / 79 \\
A.1. Reserved Storage Locations / 79 \\
A.2. Numeric Instruction Codes / 80 \\
A.3. Instruction Execution Times / 81 \\
Index / 83",
}
@Article{Holzwarth:1969:VBB,
author = "A. Holzwarth",
title = "{Ein Verfahren zur Bestimmung bester
Tscheb\-y\-scheff- Ap\-prox\-i\-ma\-tion\-en der
Quadratwurzelfunktion} \toenglish {A Method for
Determination of Best Chebyshev Approximations to the
Square Root Function} \endtoenglish",
journal = j-COMPUTING,
volume = "4",
number = "2",
pages = "168--177",
year = "1969",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
affiliation = "T{\"u}bingen, West Germany",
classification = "C4130",
description = "Chebyshev approximation; numerical analysis",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
language = "German",
}
@Article{Howell:1969:ASLa,
author = "Jo Ann Howell and Robert T. Gregory",
title = "An algorithm for solving linear algebraic equations
using residue arithmetic. {I}",
journal = j-BIT,
volume = "9",
pages = "200--224",
year = "1969",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65.35",
MRnumber = "MR0261775 (41 \#6388a)",
bibdate = "Thu Nov 8 14:50:15 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Howell:1969:ASLb,
author = "Jo Ann Howell and Robert T. Gregory",
title = "An algorithm for solving linear algebraic equations
using residue arithmetic. {II}",
journal = j-BIT,
volume = "9",
pages = "324--337",
year = "1969",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65.35",
MRnumber = "MR0261776 (41 \#6388b)",
MRreviewer = "J. Legras",
bibdate = "Thu Nov 8 14:50:18 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@MastersThesis{Huey:1969:DFP,
author = "Ben Milton Huey",
title = "Design of a floating point processor for the {PDP-9}
computer",
type = "Thesis ({M.S. - Electrical Engineering})",
school = "University of Arizona",
address = "Tucson, AZ, USA",
pages = "175",
year = "1969",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer storage devices.; Hybrid computers.",
}
@Article{Huttenhoff:1969:AUC,
author = "J. H. Huttenhoff and R. R. Shively",
title = "Arithmetic Unit of a Computing Element in a Global,
Highly Parallel Computer",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-18",
number = "8",
pages = "695--698",
month = aug,
year = "1969",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1969.222751",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 16:55:20 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671344",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{King:1969:LEN,
author = "Richard F. King and David L. Phillips",
title = "The Logarithmic Error and {Newton}'s Method for the
Square Root",
journal = j-CACM,
volume = "12",
number = "2",
pages = "87--88",
month = feb,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.50",
MRnumber = "44\#2333",
bibdate = "Fri Nov 25 18:20:24 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C4120 (Functional analysis)",
corpsource = "Argonne Nat. Lab., Argonne, IL, USA",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$\sqrt(x)$; elementary functions; function evaluation;
iterative methods",
}
@Article{Kirsch:1969:ACA,
author = "Arnold Kirsch",
title = "An analysis of commercial arithmetic",
journal = j-EDUC-STUD-MATH,
volume = "1",
number = "3",
pages = "300--311",
month = jan,
year = "1969",
CODEN = "EDSMAN",
DOI = "https://doi.org/10.1007/BF00558315",
ISSN = "0013-1954 (print), 1573-0816 (electronic)",
ISSN-L = "0013-1954",
bibdate = "Sat Jan 14 17:12:11 MST 2017",
bibsource = "http://www.math.utah.edu/pub/tex/bib/educstudmath.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer.com/accesspage/article/10.1007/BF00558315",
acknowledgement = ack-nhfb,
fjournal = "Educational Studies in Mathematics",
journal-URL = "http://link.springer.com/journal/10649",
}
@MastersThesis{Knight:1969:FPS,
author = "Douglas Wayne Knight",
title = "A floating point software package in {BCD} format for
small, fixed word length, digital computers",
type = "Thesis ({M.S.})",
school = "Arizona State University, Electrical Engineering",
address = "Tempe, AZ, USA",
pages = "151",
year = "1969",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Knuth:1969:SA,
author = "Donald E. Knuth",
title = "Seminumerical Algorithms",
volume = "2",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xi + 624",
year = "1969",
ISBN = "0-201-03802-1",
ISBN-13 = "978-0-201-03802-6",
LCCN = "QA76.5 .K57",
MRclass = "68.00 (65.00)",
MRnumber = "44 \#3531",
MRreviewer = "M. Muller",
bibdate = "Wed Dec 15 15:47:38 1993",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/cryptography.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\$19.75",
series = "The Art of Computer Programming",
acknowledgement = ack-nhfb,
remark = "Benford's Law is discussed on pp. 219--229. Cited in
\cite{Sterbenz:1974:FPC}.",
tableofcontents = "3: Random Numbers \\
3.1. Introduction / 1 \\
3.2. Generating Uniform Random Numbers / 9 \\
3.2.1. The Linear Congruential Method / 9 \\
3.2.1.1. Choice of modulus / 11 \\
3.2.1.2. Choice of multiplier / 15 \\
3.2.1.3. Potency / 21 \\
3.2.2. Other Methods / 25 \\
3.3. Statistical Tests / 34 \\
3.3.1. General Test Procedures for Studying Random Data
/ 35 \\
3.3.2. Empirical Tests / 54 \\
*3.3.3. Theoretical Tests / 69 \\
3.3.4. The Spectral Test / 82 \\
3.4. Other Types of Random Quantities / 100 \\
3.4.1. Numerical Distributions / 101 \\
3.4.2. Random Sampling and Shuffling / 121 \\
*3.5. What is a Random Sequence? / 127 \\
3.6. Summary / 155 \\
4: Arithmetic \\
4.1. Positional Number Systems / 162 \\
4.2. Floating-Point Arithmetic / 180 \\
4.2.1. Single-Precision Calculations / 180 \\
4.2.2. Accuracy of Floating-Point Arithmetic / 195 \\
*4.2.3. Double-Precision Calculations / 210 \\
4.2.4. Statistical Distribution / 218 \\
4.3. Multiple-Precision Arithmetic / 229 \\
4.3.1. The Classical Algorithms / 229 \\
*4.3.2. Modular Arithmetic / 248 \\
*4.3.3. How Fast Can We Multiply? / 258 \\
4.4. Radix Conversion / 280 \\
4.5. Rational Arithmetic / 290 \\
4.5.1. Fractions / 290 \\
4.5.2. The Greatest Common Divisor / 293 \\
*4.5.3. Analysis of Euclid's Algorithm / 316 \\
4.5.4. Factoring into Primes / 339 \\
4.6. Polynomial Arithmetic / 360 \\
4.6.1. Division of Polynomials / 363 \\
*4.6.2. Factorization of Polynomials / 381 \\
4.6.3. Evaluation of Powers / 398 \\
4.6.4. Evaluation of Polynomials / 422 \\
*4.7. Manipulation of Power Series / 444 \\
Answers to Exercises / 452 \\
Appendix A: MIX / 565 \\
1. Description of MIX / 565 \\
2. The MIX Assembly Language / 584 \\
Appendix B: Tables of Numerical Quantities / 596 \\
1. Fundamental Constants (decimal) / 596 \\
2. Fundamental Constants (octal) / 597 \\
3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
Numbers / 598 \\
Appendix C: Index to Notations / 600 \\
Index and Glossary / 605",
xxyear = "{\noopsort{1968c}}1969",
}
@Book{Knuth:ACP69-2,
author = "Donald E. Knuth",
title = "Seminumerical Algorithms",
volume = "2",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xi + 624",
year = "1969",
ISBN = "0-201-03802-1",
ISBN-13 = "978-0-201-03802-6",
LCCN = "QA76.5 .K57",
MRclass = "68.00 (65.00)",
MRnumber = "44 \#3531",
MRreviewer = "M. Muller",
bibdate = "Wed Dec 15 15:47:38 1993",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/cryptography.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\$19.75",
series = "The Art of Computer Programming",
acknowledgement = ack-nhfb,
remark = "Benford's Law is discussed on pp. 219--229.",
tableofcontents = "3: Random Numbers \\
3.1. Introduction / 1 \\
3.2. Generating Uniform Random Numbers / 9 \\
3.2.1. The Linear Congruential Method / 9 \\
3.2.1.1. Choice of modulus / 11 \\
3.2.1.2. Choice of multiplier / 15 \\
3.2.1.3. Potency / 21 \\
3.2.2. Other Methods / 25 \\
3.3. Statistical Tests / 34 \\
3.3.1. General Test Procedures for Studying Random Data
/ 35 \\
3.3.2. Empirical Tests / 54 \\
*3.3.3. Theoretical Tests / 69 \\
3.3.4. The Spectral Test / 82 \\
3.4. Other Types of Random Quantities / 100 \\
3.4.1. Numerical Distributions / 101 \\
3.4.2. Random Sampling and Shuffling / 121 \\
*3.5. What is a Random Sequence? / 127 \\
3.6. Summary / 155 \\
4: Arithmetic \\
4.1. Positional Number Systems / 162 \\
4.2. Floating-Point Arithmetic / 180 \\
4.2.1. Single-Precision Calculations / 180 \\
4.2.2. Accuracy of Floating-Point Arithmetic / 195 \\
*4.2.3. Double-Precision Calculations / 210 \\
4.2.4. Statistical Distribution / 218 \\
4.3. Multiple-Precision Arithmetic / 229 \\
4.3.1. The Classical Algorithms / 229 \\
*4.3.2. Modular Arithmetic / 248 \\
*4.3.3. How Fast Can We Multiply? / 258 \\
4.4. Radix Conversion / 280 \\
4.5. Rational Arithmetic / 290 \\
4.5.1. Fractions / 290 \\
4.5.2. The Greatest Common Divisor / 293 \\
*4.5.3. Analysis of Euclid's Algorithm / 316 \\
4.5.4. Factoring into Primes / 339 \\
4.6. Polynomial Arithmetic / 360 \\
4.6.1. Division of Polynomials / 363 \\
*4.6.2. Factorization of Polynomials / 381 \\
4.6.3. Evaluation of Powers / 398 \\
4.6.4. Evaluation of Polynomials / 422 \\
*4.7. Manipulation of Power Series / 444 \\
Answers to Exercises / 452 \\
Appendix A: MIX / 565 \\
1. Description of MIX / 565 \\
2. The MIX Assembly Language / 584 \\
Appendix B: Tables of Numerical Quantities / 596 \\
1. Fundamental Constants (decimal) / 596 \\
2. Fundamental Constants (octal) / 597 \\
3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
Numbers / 598 \\
Appendix C: Index to Notations / 600 \\
Index and Glossary / 605",
xxyear = "{\noopsort{1968c}}1969",
}
@Article{Linhardt:1969:DDT,
author = "R. J. Linhardt and H. S. Miller",
title = "Digit-by-Digit Transcendental-Function Computation",
journal = j-RCA-REV,
volume = "30",
number = "2",
pages = "209--247",
month = jun,
year = "1969",
CODEN = "RCARCI",
ISSN = "0033-6831",
bibdate = "Fri Sep 16 10:31:06 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "RCA review",
}
@Article{Liu:1969:EAD,
author = "B. Liu and T. Kaneko",
title = "Error analysis of digital filters realized with
floating-point arithmetic",
journal = j-PROC-IEEE,
volume = "57",
number = "10",
pages = "1735--1747",
month = oct,
year = "1969",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See correction \cite{Liu:1970:CEA}.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "This paper calculates the error at the output of a
digital filter using floating-point arithmetic
operations due to roundoff accumulation and input
quantization. Expressions are derived for the mean
square error for each of the three canonical forms
\ldots{}",
}
@InProceedings{Matula:1969:TAM,
author = "David W. Matula",
title = "Towards an Abstract Mathematical Theory of
Floating-Point Arithmetic",
crossref = "AFIPS:1969:ACPa",
pages = "765--772",
year = "1969",
bibdate = "Fri Oct 19 23:01:32 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Posnov:1969:FPR,
author = "N. N. Posnov and M. K. Buza and V. K. Kravcov",
title = "The floating point in a residue class number system.
({Russian})",
journal = "Vestnik Beloruss. Gos. Univ. Ser. I",
volume = "3",
pages = "21--27",
year = "1969",
MRclass = "10A10",
MRnumber = "45 3303e",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Russian",
reviewer = "J. B. Roberts",
}
@Book{Rice:1969:AFV,
author = "John R. Rice",
title = "The Approximation of Functions",
volume = "2",
publisher = pub-AW,
address = pub-AW:adr,
pages = "various",
year = "1969",
LCCN = "QA221 .R5 V.1-2",
bibdate = "Fri Dec 08 13:02:54 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@TechReport{Rigby:1969:DFP,
author = "G. W. Rigby",
title = "To draw a floating point number on the graph
plotter({PRP 2})",
type = "Group Research report",
institution = "British Steel Corporation",
address = "London, UK",
year = "1969",
bibdate = "Thu May 09 08:32:48 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Rosen:1969:ECH,
author = "Saul Rosen",
title = "Electronic Computers: a Historical Survey",
journal = j-COMP-SURV,
volume = "1",
number = "1",
pages = "7--36",
month = mar,
year = "1969",
CODEN = "CMSVAN",
DOI = "https://doi.org/10.1145/356540.356543",
ISSN = "0010-4892",
ISSN-L = "0360-0300",
bibdate = "Mon Sep 19 18:18:44 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The first large scale electronic computers were built
in connection with university projects sponsored by
government military and research organizations. Many
established companies, as well as new companies,
entered the computer field during the first generation,
1947-1959, in which the vacuum tube was almost
universally used as the active component in the
implementation of computer logic. The second generation
was characterized by the transistorized computers that
began to appear in 1959. Some of the computers built
then and since are considered super computers; they
attempt to go to the limit of current technology in
terms of size, speed, and logical complexity. From 1965
onward, most new computers belong to a third
generation, which features integrated circuit
technology and multiprocessor multiprogramming
systems.",
acknowledgement = ack-nhfb,
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
keywords = "computer history; electronic computers; magnetic drum
computers; super computers; time-sharing;
transistorized computers; university computer projects;
vacuum tube computers",
}
@Article{S:1969:BRQ,
author = "D. S.",
title = "Book Review: {{\em Square Roots of Integers $2$ to $
15 $ in Various Bases $2$ to $ 10 $: $ 88062 $ Binary
Digits or Equivalent} by W. A. Beyer, N. Metropolis,
and J. R. Neergaard}",
journal = j-MATH-COMPUT,
volume = "23",
number = "107",
pages = "679--679",
month = jul,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Mar 20 13:34:21 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0025-5718%28196907%2923%3A107%3C679%3ASROI2T%3E2.0.CO%3B2-C",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Shea:1969:NDN,
author = "Dale D. Shea",
title = "On the Number of Divisions Needed in Finding the
Greatest Common Divisor",
journal = j-FIB-QUART,
volume = "7",
number = "4",
pages = "337--340",
month = nov,
year = "1969",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:19 MDT 2011",
bibsource = "http://www.fq.math.ca/7-4.html;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/7-4/shea.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Sterbenz:1969:OSA,
author = "P. H. Sterbenz and C. T. Fike",
title = "Optimal Starting Approximations for {Newton}'s
Method",
journal = j-MATH-COMPUT,
volume = "23",
number = "106",
pages = "313--318",
month = apr,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Svoboda:1969:DAS,
author = "A. Svoboda",
title = "Decimal Adder with Signed Digit Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-18",
number = "3",
pages = "212--215",
month = mar,
year = "1969",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1969.222633",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jun 24 20:44:42 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "decimal floating-point arithmetic",
}
@Article{Troelstra:1969:EA,
author = "A. S. Troelstra",
title = "Elementary arithmetic",
journal = j-LECT-NOTES-MATH,
volume = "95",
pages = "12--13",
year = "1969",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0080646",
ISBN = "3-540-04614-3 (print), 3-540-36130-8 (e-book)",
ISBN-13 = "978-3-540-04614-1 (print), 978-3-540-36130-5
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
bibdate = "Thu May 8 17:39:14 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/lnm1960.bib",
URL = "http://link.springer.com/chapter/10.1007/BFb0080646",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/BFb0080643",
book-URL = "http://www.springerlink.com/content/978-3-540-36130-5",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
}
@Article{Turner:1969:CSI,
author = "L. Richard Turner",
title = "Comment on Some {IBM} Software",
journal = "{SHARE Secretary Distribution}",
volume = "SSD 199",
number = "C5279",
pages = "40--43",
year = "1969",
bibdate = "Fri Aug 20 10:23:55 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Turner:1969:DSC,
author = "L. Richard Turner",
title = "Difficulty in {\tt sin\slash cos} Routine",
journal = j-SIGNUM,
volume = "4",
number = "3",
pages = "13--13",
month = oct,
year = "1969",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Feb 15 15:23:23 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@TechReport{Turner:1969:IOC,
author = "L. R. Turner",
title = "Input-Output Conversion in {System\slash 360}",
number = "SSD 194, C5173",
institution = "SHARE Secretary Distribution",
address = "????",
pages = "1--8",
year = "1969",
bibdate = "Thu Feb 15 15:21:42 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Usow:1969:SSC,
author = "Karl H. Usow",
title = "{SIGNUM} subroutine certification committee",
journal = j-SIGNUM,
volume = "4",
number = "3",
pages = "15--18",
month = oct,
year = "1969",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Mon Mar 5 17:26:29 MST 2007",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Weinstein:1969:CCR,
author = "C. Weinstein and A. V. Oppenheim",
title = "Correction to {``A comparison of roundoff noise in
floating point and fixed point digital filter
realizations''}",
journal = j-PROC-IEEE,
volume = "57",
number = "8",
pages = "1466--1466",
month = aug,
year = "1969",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Weinstein:1969:CRN}.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}
@Article{Weinstein:1969:CRN,
author = "C. Weinstein and A. V. Oppenheim",
title = "A comparison of roundoff noise in floating point and
fixed point digital filter realizations",
journal = j-PROC-IEEE,
volume = "57",
number = "6",
pages = "1181--1183",
month = jun,
year = "1969",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See correction \cite{Weinstein:1969:CCR}.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "A statistical model for roundoff noise in floating
point digital filters, proposed by Kaneko and Liu, is
tested experimentally for first- and second-order
digital filters. Good agreement between theory and
experiment is obtained. The model is used to \ldots{}",
}
@Article{Weinstein:1969:RNF,
author = "C. Weinstein",
title = "Roundoff noise in floating point fast {Fourier}
transform computation",
journal = j-IEEE-TRANS-AUDIO-ELECTROACOUST,
volume = "17",
number = "3",
pages = "209--215",
month = sep,
year = "1969",
CODEN = "ITADAS",
ISSN = "0018-9278",
ISSN-L = "0018-9278",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Audio and Electroacoustics",
summary = "A statistical model for roundoff errors is used to
predict output noise-to-signal ratio when a fast
Fourier transform is computed using floating point
arithmetic. The result, derived for the case of white
input signal, is that the ratio of mean-square
\ldots{}",
}
@Article{Whipple:1969:CHR,
author = "W. L. Whipple",
title = "Comments on {``Higher-Radix Division Using Estimates
of the Divisor and Partial Remainders''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-18",
number = "2",
pages = "183--183",
month = feb,
year = "1969",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1969.222623",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 16:55:18 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
note = "See \cite{Atkins:1968:HRD}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671216",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Young:1969:SCN,
author = "David M. Young and Alvis E. McDonald",
title = "On the surveillance and control of number range and
accuracy in numerical computation (with discussion)",
crossref = "Morrell:1970:IPP",
pages = "145--152",
year = "1969",
MRclass = "65.80",
MRnumber = "40\#8303",
bibdate = "Thu Jan 18 13:48:21 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}, but given year
1968.",
}
@Article{Atkins:1970:DAU,
author = "D. E. Atkins",
title = "Design of the Arithmetic Units of {ILLIAC III}: Use of
Redundancy and Higher Radix Methods",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "720--723",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223022",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Oct 09 19:03:30 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Atkins.pdf",
abstract = "In keeping with the experimental nature of the
Illinois Pattern Recognition Computer (ILLIAC III), the
arithmetic units are intended to be a practical testing
ground for recent theoretical work in computer
arithmetic. This paper describes the use of redundant
number systems and the design of a structure with which
multiplication and division are executed radix 256. The
heart of the unit is the stored-sign subtracter, a
recently discovered member of the family of borrow-save
subtracters and carry-save adders. A cascade of these
subtracters, controlled by a multiplier recoder,
provides multiplication. The same structure, controlled
by a ``model division'' (a quotient recoder), performs
division.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "arithmetic unit; computer arithmetic; division; higher
radix arithmetic; ILLIAC III; multiplication; redundant
number systems; signed-digit subtracter; stored-sign
subtracter; stored-sign subtracter. Arithmetic unit",
remark = "Despite statements elsewhere that the ILLIAC III used
base 256, that is incorrect. The original manuals for
the machine clearly show an IBM System/360-style
base-16 encoding. This paper reveals the source of the
confusion: the multiplier uses a Wallace recoding
scheme, first defined for radix 4, but extended for the
ILLIAC III to radix 256. Thus, multiplication is done 8
bits at a time. Division is done 4 bits at a time.",
}
@Article{Avizienis:1970:UAB,
author = "Algirdas Avi{\v{z}}ienis and Chin Tung",
title = "A Universal Arithmetic Building Element ({ABE}) and
Design Methods for Arithmetic Processors",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "733--745",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223023",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Avizienis.pdf",
abstract = "The advent of large-scale integration of logic
circuits requires the definition of digital computer
structure in terms of large functional arrays of logic
of very few types. This paper describes a
single-package arithmetic processor called the
arithmetic building element (ABE). The ABE accepts
operands in either conventional or signed-digit radix-r
representation and produces signed-digit results, which
the ABE can reconvert to conventional form. Radix 16 is
chosen for illustrations. Arrays of ABE's may be
arranged to implement unit-time parallel addition,
all-combinational multiplication, and more complex
functions which are presently computed by subroutines.
To facilitate such arithmetic design, a graph model is
developed which permits a translation of the given
arithmetical algorithm into an interconnection diagram
of ABE's. The design procedure is illustrated by an
array for polynomial evaluation. Speed, cost, and
roundoff error of the array are considered. A computer
program has been written for the automatic translation
of the algorithm graph to an interconnection graph, and
for the evaluation of the cost and speed for a given
polynomial degree and a given precision requirement.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1",
}
@Article{Behringer:1970:BFI,
author = "F. A. Behringer",
title = "{Eine bedingte Form der Integral-Ungleichun von
Gronwal, leichte Verallgemeinerung eins
Stabilit{\"a}tsatzes von Perron und {\"u}berlauffreie
Skalierung von Analogrechenschaltungen}. ({German})
[{A} conditional version of the integral inequality of
{Gronwall}, a slight generalization of a stability
theorem of {Perron}, and overflow-free scaling of
analogue computer set-ups]",
journal = j-COMPUTING,
volume = "5",
number = "4",
pages = "333--348",
year = "1970",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:51 MST 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-ec # " and " # ack-nhfb,
affiliation = "Tech. Hochschule, M{\"u}nchen, West Germany",
classification = "C5460",
description = "analogue computer methods; differential equations",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
language = "German",
}
@Article{Beyer:1970:GST,
author = "W. A. Beyer and N. Metropolis and J. R. Neergaard",
title = "The Generalized Serial Test Applied to Expansions of
Some Irrational Square Roots in Various Bases",
journal = j-MATH-COMPUT,
volume = "24",
number = "111",
pages = "745--747",
month = jul,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.15",
MRnumber = "MR0273773 (42 \#8649)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
URL = "http://links.jstor.org/sici?sici=0025-5718%28197007%2924%3A111%3C745%3ATGSTAT%3E2.0.CO%3B2-2",
ZMnumber = "0227.10044",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Beyer:1970:SSD,
author = "W. A. Beyer and N. Metropolis and J. R. Neergaard",
title = "Statistical Study of Digits of Some Square Roots of
Integers in Various Bases",
journal = j-MATH-COMPUT,
volume = "24",
number = "110",
pages = "455--473",
month = apr,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "62.70",
MRnumber = "MR0272129 (42 \#7010)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
URL = "http://links.jstor.org/sici?sici=0025-5718%28197004%2924%3A110%3C455%3ASSODOS%3E2.0.CO%3B2-I",
ZMnumber = "0208.19505",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Brent:1970:ABN,
author = "R. Brent",
title = "On the Addition of Binary Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "758--759",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223027",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Brent.pdf",
abstract = "An upper bound is derived for the time required to add
numbers modulo $ 2^n $, using circuit elements with a
limited fan-in and unit delay, and assuming that all
numbers have the usual binary encoding. The upper bound
is within a factor $ (1 + \epsilon) $ of Winograd's
lower bound (which holds for all encodings), where $
\epsilon \rightarrow 0 $ as $ n \rightarrow \infty $,
and only $ O(n \log n) $ circuit elements are
required.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "addition; ARITH-1; binary numbers; computational
complexity; group multiplication; logic circuits;
logical design",
}
@TechReport{deLugish:1970:CAA,
author = "B. G. de Lugish",
title = "A Class of Algorithms for Automatic Evaluation of
Certain Elementary Function in a Binary Computer",
type = "Report",
number = "399",
institution = "Department of Computer Science, University of
Illinois",
pages = "??",
month = jun,
year = "1970",
bibdate = "Fri Sep 02 22:49:20 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Flynn:1970:DFI,
author = "M. J. Flynn",
title = "On Division by Functional Iteration",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "702--706",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223019",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite{Swartzlander:1990:CAa}.",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Flynn.pdf",
abstract = "In order to avoid the time delays associated with
linearly convergent division based on subtraction,
other iterative schemes can be used. These are based on
(1) series expansion of the reciprocal, (2)
multiplicative sequence, or (3) additive sequence
convergent to the quotient. These latter techniques are
based on finding the root of an arbitrary function at
either the quotient or reciprocal value. A
Newton--Raphson iteration or root finding iteration can
be used.
The most useful techniques are quadratically convergent
(i.e., $ \mathrm {error}_{i + 1} = O((\mathrm
{error}_i)^2) $) . These techniques generally require
two arithmetic operations (add or multiply) to double
the precision of the quotient.",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1",
}
@Article{Forsythe:1970:PCW,
author = "George E. Forsythe",
title = "Pitfalls in Computation, or Why a Math Book Isn't
Enough",
journal = j-AMER-MATH-MONTHLY,
volume = "77",
number = "9",
pages = "931--956",
month = nov,
year = "1970",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "Contributed Item",
MRnumber = "MR1536090",
bibdate = "Tue Nov 22 09:08:17 MST 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
ZMnumber = "0207.15401",
acknowledgement = ack-nhfb,
classmath = "*65G50 Roundoff error 65Y20 Complexity and performance
of numerical algorithms",
fjournal = "The American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
@TechReport{Gardiner:1970:SDA,
author = "V. Gardiner and N. Metropolis",
title = "Significant Digit Arithmetic on a {CDC 6600}",
type = "Technical Report",
number = "LA--4470",
institution = inst-LASL,
address = inst-LASL:adr,
pages = "4",
day = "1",
month = jan,
year = "1970",
bibdate = "Tue Mar 20 11:46:17 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=4093265&query_id=0",
acknowledgement = ack-nhfb,
}
@Article{Good:1970:CIA,
author = "Donald I. Good and Ralph L. London",
title = "Computer Interval Arithmetic: Definition and Proof of
Correct Implementation",
journal = j-J-ACM,
volume = "17",
number = "4",
pages = "603--612",
month = oct,
year = "1970",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Sun Nov 6 11:55:54 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Habibi:1970:FM,
author = "A. Habibi and P. A. Wintz",
title = "Fast Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "2",
pages = "153--157",
month = feb,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222881",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 08:01:30 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671474",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Hamming:1970:DN,
author = "R. W. Hamming",
title = "On the Distribution of Numbers",
journal = j-BELL-SYST-TECH-J,
volume = "49",
number = "8",
pages = "1609--1625",
month = oct,
year = "1970",
CODEN = "BSTJAN",
DOI = "https://doi.org/10.1002/j.1538-7305.1970.tb04281.x",
ISSN = "0005-8580 (print), 2376-7154 (electronic)",
ISSN-L = "0005-8580",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://bstj.bell-labs.com/oldfiles/year.1970/BSTJ.1970.4908.html;
http://www.alcatel-lucent.com/bstj/vol49-1970/bstj-vol49-issue08.html;
http://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
http://www.math.utah.edu/pub/tex/bib/bstj1970.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol49/bstj49-8-1609.pdf;
http://www.alcatel-lucent.com/bstj/vol49-1970/articles/bstj49-8-1609.pdf",
abstract = "This paper examines the distribution of the mantissas
of floating-point numbers and shows how the arithmetic
operations of a computer transform various
distributions toward the limiting distribution $$ r(x)
= 1 / (x \ln b) \qquad (1 / b \leq x \leq 1) $$ (where
$b$ is the base of the number system). The paper also
gives a number of applications to hardware, software,
and general computing which show that this distribution
is not merely an amusing curiosity. A brief examination
of the distribution of exponents is included.",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Hansen:1970:APN,
author = "Rodney T. Hansen",
title = "Arithmetic of Pentagonal Numbers",
journal = j-FIB-QUART,
volume = "8",
number = "1",
pages = "83--86",
month = feb,
year = "1970",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:23 MDT 2011",
bibsource = "http://www.fq.math.ca/8-1.html;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/8-1/hansen.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Harris:1970:NND,
author = "V. C. Harris",
title = "Note on the Number of Divisions Required in Finding
the Greatest Common Divisor",
journal = j-FIB-QUART,
volume = "8",
number = "1",
pages = "104--??",
month = feb,
year = "1970",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:23 MDT 2011",
bibsource = "http://www.fq.math.ca/8-1.html;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/8-1/harris2.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@MastersThesis{Harvey:1970:SSP,
author = "Michael P. Harvey",
title = "A system study and problem solution in polynomial
evaluation",
type = "Thesis ({M.S.})",
school = "California State College",
address = "Long Beach, CA, USA",
pages = "vi + 119",
year = "1970",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers.; Numerical
calculations.; Polynomials.",
remark = "Title on spine: Automated floating point polynomial
evaluation.",
}
@TechReport{Hillstrom:1970:PSF,
author = "K. E. Hillstrom",
title = "Performance Statistics for the {FORTRAN IV (H)} and
{PL/I} (Version 5) Libraries in the {IBM OS\slash 360
Release 18}",
type = "Report",
number = "ANL-7666",
institution = inst-ANL,
address = inst-ANL:adr,
year = "1970",
bibdate = "Fri Aug 20 09:29:37 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Hornbuckle:1970:LMA,
author = "G. D. Hornbuckle and E. I. Ancona",
title = "The {LX-1} Microprocessor and Its Application to
Real-Time Signal Processing",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "710--720",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223021",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Hornbuckle.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1",
}
@Article{Howell:1970:SLE,
author = "Jo Ann Howell and Robert T. Gregory",
title = "Solving linear equations using residue arithmetic ---
{Algorithm II}",
journal = j-BIT,
volume = "10",
pages = "23--37",
year = "1970",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65.35",
MRnumber = "MR0261777 (41 \#6389)",
MRreviewer = "J. Legras",
bibdate = "Thu Nov 8 14:50:19 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Kailas:1970:AMC,
author = "M. V. Kailas",
title = "Another method of converting from hexadecimal to
decimal",
journal = j-CACM,
volume = "13",
number = "3",
pages = "193--193",
month = mar,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "There is a simple paper-and-pencil method of
converting a hexadecimal number N to decimal.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "digital arithmetic",
}
@Article{Knuth:1970:VNF,
author = "Donald E. Knuth",
title = "{Von Neumann}'s First Computer Program",
journal = j-COMP-SURV,
volume = "2",
number = "4",
pages = "247--260",
month = dec,
year = "1970",
CODEN = "CMSVAN",
DOI = "https://doi.org/10.1145/356580.356581",
ISSN = "0010-4892",
ISSN-L = "0360-0300",
bibdate = "Sat Mar 23 15:03:00 2002",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/compsurv.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/HBP/ACMCS.bib;
http://www.math.utah.edu/pub/tex/bib/compsurv.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite{Aspray:1987:PJN}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
}
@Article{Krishnamurthy:1970:OIS,
author = "E. V. Krishnamurthy",
title = "On Optimal Iterative Schemes For High-Speed Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "3",
pages = "227--231",
month = mar,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222901",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jan 08 23:09:36 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Krishnamurthy:1970:RTT,
author = "E. V. Krishnamurthy",
title = "On Range-Transformation Techniques for Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "2",
pages = "157--160",
month = feb,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222882",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 08:01:30 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671475",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Ling:1970:HSC,
author = "H. Ling",
title = "High-Speed Computer Multiplication Using a
Multiple-Bit Decoding Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "706--709",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223020",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Ling.pdf",
abstract = "This paper presents a method of performing the binary
multiplication beyond the scheme of multiple ADD and
SHIFT. The binary multiplication algorithm will be
discussed first, followed by block decoding method,
logic implementation, hardware consideration, and two
examples which are at the end of the discussion.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1",
}
@Article{Linz:1970:AFP,
author = "Peter Linz",
title = "Accurate Floating-Point Summation",
journal = j-CACM,
volume = "13",
number = "6",
pages = "361--362",
month = jun,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.25",
MRnumber = "44\#3468",
MRreviewer = "R. P. Brent",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "Compendex database;
ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1970.bib;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper describes an alternate method for summing a
set of floating-point numbers. Comparison of the error
bound for this method with that of the standard
summation method shows that it is considerably less
sensitive to propagation of round-off error.",
acknowledgement = ack-nhfb # "\slash " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "New York Univ., NY, USA",
descriptors = "Simulation; statistics; numeric calculation",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
journalabr = "Commun ACM",
keywords = "accurate floating-point summation; computers, data
processing; digital arithmetic; floating point
arithmetic; floating-point addition; mathematics;
numerical methods; round-off error; round-off errors;
round-off propagation; summation",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Liu:1970:CEA,
author = "B. Liu and T. Kaneko",
title = "Correction to {``Error analysis of digital filters
realized with floating-point arithmetic''}",
journal = j-PROC-IEEE,
volume = "58",
number = "3",
pages = "376--376",
month = mar,
year = "1970",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Liu:1969:EAD}.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}
@Article{Long:1970:LAS,
author = "C. T. Long and J. H. Jordan",
title = "A Limited Arithmetic on Simple Continued Fractions ---
{II}",
journal = j-FIB-QUART,
volume = "8",
number = "2",
pages = "135--157",
month = mar,
year = "1970",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:25 MDT 2011",
bibsource = "http://www.fq.math.ca/8-2.html;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/8-2/long.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@TechReport{Malcolm:1970:AFA,
author = "Michael Malcolm",
title = "An algorithm for floating-point accumulation of sums
with small relative error",
number = "STAN-CS-70-163",
institution = "Computer Science Department, Stanford University",
address = "Stanford, CA, USA",
pages = "21",
year = "1970",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; Algorithms.;
FORTRAN (Computer program language); Numerical
calculations --- Computer programs.",
remark = "Reproduced by National Technical Information Service.
AD 708 691.",
}
@MastersThesis{Marasa:1970:AAE,
author = "John D. Marasa",
title = "Accumulated arithmetic error in floating-point and
alternative logarithmic number systems",
type = "Thesis ({M.S.})",
school = "Washington University, Sever Institute of Technology,
Dept. of Applied Mathematics and Computer Science",
address = "St. Louis, MO, USA",
pages = "vii + 88",
year = "1970",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Programming (Mathematics)",
}
@Article{Matula:1970:ECA,
author = "David W. Matula",
title = "The emergence of computational arithmetic as a
component of the computer science curriculum",
journal = j-SIGCSE,
volume = "2",
number = "3",
pages = "41--44",
month = nov,
year = "1970",
CODEN = "SIGSD3",
DOI = "https://doi.org/10.1145/873641.873650",
ISSN = "0097-8418 (print), 2331-3927 (electronic)",
ISSN-L = "0097-8418",
bibdate = "Sun Nov 18 08:53:42 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/sigcse1970.bib",
acknowledgement = ack-nhfb,
fjournal = "SIGCSE Bulletin (ACM Special Interest Group on
Computer Science Education)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J688",
}
@Article{Matula:1970:FFP,
author = "D. W. Matula",
title = "A Formalization of Floating-Point Numeric Base
Conversion",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "681--692",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223017",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 08:01:35 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671610;
http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Matula.pdf",
abstract = "The process of converting arbitrary real numbers into
a floating-point format is formalized as a mapping of
the reals into a specified subset of real numbers. The
structure of this subset, the set of $n$ significant
digit base $b$ floating-point numbers, is analyzed and
properties of conversion mappings are determined. For a
restricted conversion mapping of the $n$ significant
digit base $b$ numbers to the $m$ significant-digit
base $d$ numbers, the one-to-one, onto, and
order-preserving properties of the mapping are
summarized. Multiple conversions consisting of a
composition of individual conversion mappings are
investigated and some results of the invariant points
of such compound conversions are presented. The
hardware and software implications of these results
with regard to establishing goals and standards for
floating-point formats and conversion procedures are
considered.",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1",
}
@Article{Nickel:1970:KBS,
author = "K. Nickel",
title = "{Das Kahan--Babu{\v{s}}kasche Summierungsverfahren in
Triplex-ALGOL 60}. ({German}) [{The
Kahan--Babu{\v{s}}ka} summation method in
{Triplex-ALGOL 60}]",
journal = j-Z-ANGE-MATH-MECH,
volume = "50",
pages = "369--373",
year = "1970",
CODEN = "ZAMMAX",
ISSN = "0044-2267 (print), 1521-4001 (electronic)",
ISSN-L = "0044-2267",
bibdate = "Tue Aug 28 06:12:04 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und
Mechanik}",
keywords = "accurate floating-point summation",
language = "German",
}
@Article{Ninomiya:1970:BRS,
author = "Ichizo Ninomiya",
title = "Best Rational Starting Approximations and Improved
{Newton} Iteration for the Square Root",
journal = j-MATH-COMPUT,
volume = "24",
number = "110",
pages = "391--404",
month = apr,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Nagoya Univ., Chikua ku, Japan",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "computing procedure; function approximation; iterative
methods; Newton iteration; rational approximation;
square root",
treatment = "T Theoretical or Mathematical",
}
@Article{Oppenheim:1970:RDF,
author = "A. Oppenheim",
title = "Realization of digital filters using
block-floating-point arithmetic",
journal = j-IEEE-TRANS-AUDIO-ELECTROACOUST,
volume = "18",
number = "2",
pages = "130--136",
month = jun,
year = "1970",
CODEN = "ITADAS",
ISSN = "0018-9278",
ISSN-L = "0018-9278",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Audio and Electroacoustics",
summary = "Recently, statistical models for the effects of
roundoff noise in fixed-point and floating-point
realizations of digital filters have been proposed and
verified, and a comparison between these realizations
presented. In this paper a structure for \ldots{}",
}
@Article{Phillips:1970:GLE,
author = "David L. Phillips",
title = "Generalized Logarithmic Error and {Newton}'s Method
for the $m$ th Root",
journal = j-MATH-COMPUT,
volume = "24",
number = "110",
pages = "383--389",
month = apr,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Rao:1970:BEC,
author = "T. R. N. Rao",
title = "Biresidue Error-Correcting Codes for Computer
Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "5",
pages = "398--402",
month = may,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222937",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 08:01:32 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671530",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Rao:1970:BLR,
author = "T. R. N. Rao and A. K. Trehan",
title = "Binary Logic for Residue Arithmetic Using Magnitude
Index",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "752--757",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223026",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Rao.pdf",
abstract = "We consider a residue number system using n pairwise
relatively prime moduli $ m_1, \ldots {}, m_n $ to
represent any integer $X$ in the range $ M / 2 \leq X >
M / 2 $, when $ M = \prod m_i $. The moduli $ m_i $ are
chosen to be of the $ 2 - 1 $ type, in order that the
residue arithmetic can be implemented by means of
binary registers and binary logic. Further, for each
residue number $X$, a magnitude index $ P_x $ is
maintained for all arithmetic operations. We
investigate the properties of such a system and derive
the addition, subtraction, multiplication, sign
determination, and overflow detection algorithms. The
proposed organization is found to improve the operation
times for sign detection and overflow detection
operations, while rendering multiplication to be a
difficult operation.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1; base extension; index generation logic;
magnitude index; modular adders; naturalized form;
overflow detection; residue multiplication; residue
number system; scale by 2; sign determination",
}
@Article{Robertson:1970:CBM,
author = "J. E. Robertson",
title = "The Correspondence Between Methods of Digital Division
and Multiplier Recoding Procedures",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "692--701",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223018",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Robertson.pdf",
abstract = "This paper relates previous analyses of the binary SRT
division to the theory of multiplier recoding. Since
each binary quotient digit has three possible values,
the quotient resulting from the SRT division is in
recoded form; in this paper it is shown that the
recoding is a function of the divisor, and the method
for determining the characteristic Boolean function of
the recoding is presented. The relationship between the
division and the recoding is established by scaling the
division in such a way that the scaled ``visor''
becomes a constant. Higher radix results are also
discussed.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1",
}
@TechReport{Rothmaier:1970:BQN,
author = "B. Rothmaier",
title = "{Die Berechnung der Quadratwurzel nebst Schranken auf
Dualmaschinen} \toenglish {The Computation of the
Square Root together with [Interval] Bounds on Binary
Machines} \endtoenglish",
type = "{Interner Bericht}",
number = "Nr. 70/17",
institution = "Institut f{\"u}r Informatik, Universit{\"a}t
Karlsruhe",
pages = "??",
year = "1970",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@TechReport{Rothmaier:1970:DSB,
author = "B. Rothmaier",
title = "{Dokumentation der Standardfunktionen des
Betriebssystems Hydra X8} \toenglish {Documentation} of
the Elementary Functions of the Operating System {Hydra
X8} \endtoenglish",
type = "{Interner Bericht}",
number = "Nr. 70/8",
institution = "Institut f{\"u}r Informatik, Universit{\"a}t
Karlsruhe",
pages = "??",
year = "1970",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Shively:1970:PFI,
author = "Richard R. Shively",
title = "Preface: {First IEEE Conference on Computer
Arithmetic, Minneapolis, Minnesota, June 16, 1969}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "679--680",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223016",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671609;
http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_contents.pdf;
http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Shively.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1",
}
@Article{Sikdar:1970:DMM,
author = "K. Sikdar",
title = "Determination of Multipliers Mapping an Arbitrary
Integer into a Range of Certain Type",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "12",
pages = "1221--1222",
month = dec,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222863",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 08:01:39 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671456",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Svoboda:1970:ADC,
author = "A. Svoboda",
title = "Adder With Distributed Control",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "749--751",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223025",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Svoboda.pdf",
abstract = "An adder is described for addition of a large number
of binary numbers $ x_j, j = 1, 2, \ldots {}, m $,
where $ x_j = \sum_i x_{j, i} 2^i, x_{j, i} = 0, 1, i =
0, 1, \ldots {}, n - 1 $. The adder's algorithm has two
parts: (1) the bits $ x_{j, i} $ are added
independently for each binary order $ i : s_i = \sum_j
x_{j, i} \leq m $ and the result expressed in the
binary form $ s_i = \sum_k a_{i, k} 2^k, a_{i, k} = 0,
1, k = 0, 1, \ldots {}, p - 1 $ (where $ 2^{p - 1} \leq
m < 2^p $) ; (2) the sum $ y = \sum_j x_j $ is formed
by adding terms $ s_{i, k} {2^{i + k}} $ as
contributions of the bit $ s_{i, k} $ to the total $y$.
A hardware implementation of this algorithm is
suggested where the sum $ s_i $ is obtained by a
sequential circuit which reorders the values $ x_{j,
i}' $ so that their sum $ s_i $, remains unchanged and
so that after the reordering the new values $ x_{j, i}'
$ obey the conditions $ x_{j + 1, i} \leq x_{j, i} $
for every $ j = 1, 2, \ldots {}, m - 1 $. The
implementation with integrated circuits should be quite
rewarding because the control of the circuit is done
with independent control elements distributed all over
the chip.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "adder; adder for large number of numbers; ARITH-1;
distributed control; reordering",
}
@Article{Taub:1970:ECS,
author = "D. M. Taub and C. E. Owen and B. P. Day",
title = "Experimental Computer for Schools",
journal = "Proceedings of the IEE",
volume = "117",
number = "2",
pages = "303--312",
month = feb,
year = "1970",
bibdate = "Fri Nov 28 19:30:38 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The computer is a small desk-top machine designed for
teaching schoolchildren how computers work. It works in
decimal notation and has a powerful instruction set
which includes 3-address floating-point instructions
implemented as `extracode' subroutines. Addressing can
be absolute, relative or indirect. For input it uses a
capacitive touch keyboard, and for output and display a
perfectly normal TV receiver is used. Another
input/output device is an ordinary domestic tape
recorder, used mainly for long term storage of
programs. To make the operation of the machine easy to
follow, it can be made to stop at certain stages in the
processing of an instruction and automaticaly display
the contents of all registers and storage locations
relevant at that time. The paper gives a description of
the machine and a discussion of the factors that hav
influenced its design.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "IBM Schools computer with scaled integer format, six
decimal digits and exponent range of $ [ - 6, 0] $.",
}
@Book{Thornton:1970:DCC,
author = "James E. Thornton",
title = "Design of a Computer: the {Control Data 6600}",
publisher = pub-SF,
address = pub-SF:adr,
pages = "v + 181",
year = "1970",
LCCN = "TK7889.C6 T5 1970",
bibdate = "Wed Sep 14 22:45:51 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://archive.computerhistory.org/resources/text/CDC/cdc.6600.thornton.design_of_a_computer_the_control_data_6600.1970.102630394.pdf",
acknowledgement = ack-nhfb,
remark = "See Table V: Nonstandard Floating Point Arithmetic on
page 79 for the rules governing Indefinite, Infinity,
and Negative Zero operands.",
tableofcontents = "I: Introduction / 1 \\
A. Justification for Large Computers / 1 \\
B. Building Blocks / 4 \\
C. The Approach / 5 \\
II: Organization of the 6600 / 9 \\
A. General / 9 \\
B. Peripheral Subsystem / 10 \\
C. Central Processor-CPU / 12 \\
D. Central Storage / 15 \\
E. Extended Core Storage / 17 \\
III: Basic Circuit Properties / 19 \\
A. The Silicon Transistor / 19 \\
B. DCTL Logic Circuits / 21 \\
C. Logic Symbols / 24 \\
D. Transmission Lines / 28 \\
E. Packaging / 32 \\
IV: Central Storage System / 37 \\
A. Storage Module / 37 \\
B. Theory of Interleaved Storage / 44 \\
C. Stunt Box / 47 \\
D. Storage Bus System / 51 \\
E. Extended Core Storage / 53 \\
F. ECS Coupler and Controller / 55 \\
V: Central Processor Functional Units / 57 \\
A. Boolean Unit / 59 \\
B. Fixed Add Unit / 63 \\
C. Data Trunks / 69 \\
D. Shift Unit / 71 \\
E. Add Unit / 77 \\
F. Multiply Unit / 88 \\
G. Divide Unit / 101 \\
H. Increment Unit / 105 \\
I. Branch Unit / 111 \\
J. ECS Coupler-Controller / 114 \\
VI: Central Processor Control / 117 \\
A. Exchange Jump / 117 \\
B. Instruction Fetch / 120 \\
C. Instruction Issue / 123 \\
D. Scoreboard / 125 \\
Register Entry/Exit Control / 134 \\
F. Summary / 137 \\
VII: Peripheral Subsystem / 141 A. Peripheral
Processors / 141 \\
B. Dead Start / 154 \\
C. Disk Storage / 157 \\
VIII: Systems Operation / 163 \\
A. Files / 163 \\
B. Tables / 165 \\
C. Circular Buffer for 1/0 / 166 \\
D. Job Processing / 167 \\
E. System Monitor MTR / 168 \\
F. Control Points / 169 \\
G. Summary / 171 \\
Appendix / 173 \\
Index / 177",
}
@Article{Tienari:1970:SMR,
author = "Martti Tienari",
title = "A Statistical Model of Roundoff Error for Varying
Length Floating-Point Arithmetic",
journal = j-BIT,
volume = "10",
number = "3",
pages = "355--365",
month = sep,
year = "1970",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01934204",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "68.00 (65.00)",
MRnumber = "42\#7108",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=10&issue=3&spage=355",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
reviewer = "R. W. Hamming",
}
@Article{Tung:1970:SDD,
author = "Chin Tung",
title = "Signed-Digit Division Using Combinational Arithmetic
Nets",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "746--748",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223024",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Tung.pdf",
abstract = "To meet the challenge created by the advent of large-
scale integration, a unique microelectronic arithmetic
building element and combinational arithmetic nets,
composed of the building elements, have been studied
and proposed for arithmetic processor design. A fast
division algorithm, particularly suitable for floating-
point arithmetic, has also been developed for
signed-digit arithmetic. This algorithm is
characterized by the need of preprocessing the divisor
and then exact generation of quotient digits. This
paper describes the implementation of this division
algorithm with the arithmetic building element and
combinational arithmetic nets. The intention here is to
explore the feasibility of applying large-scale
integration technology to arithmetic processors.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1; arithmetic building element; combinational
arithmetic net; division; large-scale integration;
microelectronic block; signed-digit number system",
}
@Article{Usow:1970:CB,
author = "K. H. Usow",
title = "Certification Bibliography",
journal = j-SIGNUM,
volume = "5",
number = "2",
pages = "14--15",
month = mar,
year = "1970",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Fri Aug 20 10:26:49 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Waksman:1970:WAI,
author = "A. Waksman",
title = "On {Winograd}'s Algorithm for Inner Products",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "4",
pages = "360--361",
month = apr,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222926",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Oct 09 18:54:12 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This correspondence demonstrates an improvement on
Winograd's algorithm for inner products as applied to
the multiplication of two matrices.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "fast matrix multiplication; product of matrices;
sufficient number of arithmetical operations",
}
@Article{Wilson:1970:OSA,
author = "M. Wayne Wilson",
title = "Optimal Starting Approximations for Generating Square
Root for Slow or No Divide",
journal = j-CACM,
volume = "13",
number = "9",
pages = "559--560",
month = sep,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.50",
MRnumber = "44\#2338",
MRreviewer = "J. E. {Dennis, Jr.}",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "On computing machines with slow or no division, it is
preferable to use an iterative scheme for the square
root different from the classical Heron scheme. The
problem of optimal initial approximants is considered,
and some optimal polynomial initial approximations are
tabulated.",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "IBM, Houston, TX, USA",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
journalabr = "Commun ACM",
keywords = "CACMA; digital arithmetic; ele; iterative methods;
mathematics; numerical methods; optimisation",
}
@TechReport{Yohe:1970:ACB,
author = "J. M. Yohe",
title = "Accurate Conversion Between Number Bases",
type = "{MRC} Technical Summary Report",
number = "1109",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
month = oct,
year = "1970",
bibdate = "Sun Dec 30 21:39:41 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The author presents and proves algorithms for taking a
number expressed in base gamma and finding, for a
predetermined floating point representation in base
beta, its least upper bound, greatest lower bound, and
closest approximation.",
acknowledgement = ack-nhfb,
}
@TechReport{Yohe:1970:BPF,
author = "J. M. Yohe",
title = "Best possible floating point arithmetic",
type = "{MRC} Technical Summary Report",
number = "1054",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
pages = "ii + 27",
month = mar,
year = "1970",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The report presents an algorithm for floating point
arithmetic, using single-length arithmetic registers,
which yields the most accurate approximation which can
be expressed in the given floating point format, the
greatest lower bound, or the least upper bound for the
result of the operation, whichever is specified by the
programmer. This makes the algorithm particularly
useful for implementation of interval arithmetic.",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.",
remark = "March 1970. Sponsored by Army Research Office, Durham,
N.C.",
}
@Article{Yong:1970:GBA,
author = "Lam Lay Yong",
title = "The Geometrical Basis of the {Ancient Chinese}
Square-Root Method",
journal = j-ISIS,
volume = "61",
number = "1",
pages = "92--102",
month = "Spring",
year = "1970",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:28:39 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302287;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/isis1970.bib",
URL = "http://www.jstor.org/stable/229151",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/page/journal/isis/about.html",
}
@Article{Zohar:1970:NRC,
author = "S. Zohar",
title = "Negative Radix Conversion",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "3",
pages = "222--226",
month = mar,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222900",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 08:01:31 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See comments \cite{Pawlak:1971:ACN,Wadel:1971:CNR}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671493",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
}
@Book{Zuse:1970:CML,
author = "Konrad Zuse",
title = "{Der Computer, mein Lebenswerk}",
publisher = "Verlag moderne Industrie",
address = "M{\"u}nchen, Germany",
pages = "221",
year = "1970",
LCCN = "QA76.2.Z8 A3",
bibdate = "Mon Nov 4 07:46:57 MST 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "computer engineers --- Germany --- biography;
computers --- Germany --- history; Zuse, Konrad",
}
@Article{Abdelmalek:1971:REA,
author = "Nabih N. Abdelmalek",
title = "Round-off Error Analysis for {Gram--Schmidt} Method
and Solution of Linear Least Squares Problems",
journal = j-BIT,
volume = "11",
number = "4",
pages = "345--367",
month = dec,
year = "1971",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01939404",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:12 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=11&issue=4;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=11&issue=4&spage=345",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Alway:1971:GFA,
author = "G. G. Alway",
title = "A general factorising algorithm",
journal = j-COMP-J,
volume = "14",
number = "2",
pages = "166--168",
month = may,
year = "1971",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:51:53 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/140166.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/tiff/166.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/tiff/167.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/tiff/168.tif",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Nat. Phys. Lab., Teddington, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "computer algorithm; digital arithmetic; general
factorising algorithm; primality of large numbers",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Banerji:1971:RAC,
author = "D. K. Banerji",
title = "Residue arithmetic in computer design",
institution = "University of Waterloo",
address = "Waterloo, ON, Canada",
year = "1971",
bibdate = "Thu Nov 18 09:13:45 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://books.google.com/books?id=YNVcPgAACAAJ",
acknowledgement = ack-nhfb,
}
@Article{Bataille:1971:GCW,
author = "M. Bataille",
title = "The {Gamma 60}: The computer that was ahead of its
time",
journal = "Honeywell Computer Journal",
volume = "5",
number = "3",
pages = "99--105",
month = "????",
year = "1971",
bibdate = "Thu Nov 25 09:37:15 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "The Gamma 60 decimal floating-point system provides 11
to 19 decimal digits with an exponent range of $ \pm 40
$.",
}
@Article{Berg:1971:SAO,
author = "R. O. Berg and L. L. Kinney",
title = "Serial Adders with Overflow Correction",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "6",
pages = "668--671",
month = jun,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223321",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:16 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671914",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Caprani:1971:ILR,
author = "Ole Caprani",
title = "Implementation of a Low Round-Off Summation Method",
journal = j-BIT,
volume = "11",
number = "3",
pages = "271--275",
month = sep,
year = "1971",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01931808",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Sat Nov 14 09:14:57 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=11&issue=3&spage=271",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "accurate floating-point summation; floating-point
arithmetic; rounding errors",
}
@Misc{Chen:1971:BAU,
author = "Tien Chi Chen",
title = "Binary arithmetic unit implementing a multiplicative
iteration for the exponential, logarithm, quotient and
square root functions",
howpublished = "United States Patent 3,631,230",
day = "28",
month = dec,
year = "1971",
bibdate = "Tue Jan 08 21:54:11 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.freepatentsonline.com/3631230.html",
abstract = "Apparatus and a method is described for efficiently
achieving arithmetic evaluations for functions such as
exponential, logarithm, quotient, and square root with
a minimum use of multiplications or divisions.
Basically, use is made of the fact that $ x(1 \pm
2^{-m}) $ can be evaluated by a shift followed by an
add. A pair of numbers $ (x_k, y_k) $ can represent a
function $ x : f(x) = g(x_k, y_k) $, such that $ g(l,
y_n) = y_n $ for logarithm, quotient and square root.
Then, multiplication by shifting is applied to $ x_k $
with suitable adjustments on $ y_k $, until $ x_k $ is
close to unity, at which time $ y_k $ represents the
desired answer. The exponential is computed by
essentially reversing the logarithm procedure. A
termination algorithm further improves accuracy. The
apparatus involves two registers for $ x_k $ and $ y_k
$, a local memory, an adder and a shift register.",
acknowledgement = ack-nhfb,
}
@Article{Chen:1971:BMS,
author = "Tien Chi Chen",
title = "A Binary Multiplication Scheme Based on Squaring",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "6",
pages = "678--680",
month = jun,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223325",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:16 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671918",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Misc{Chen:1971:DNC,
author = "Tien Chi Chen",
title = "Decimal Number Compression",
howpublished = "Internal IBM memo to Dr. Irving T. Ho.",
pages = "4",
day = "29",
month = mar,
year = "1971",
bibdate = "Fri Nov 28 16:24:59 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The fact that four bits can represent 16 different
states, but a decimal digit exploits only 10 of then
(0--9) has been a valid criticism against decimal
arithmetic.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Chen:1971:EAA,
author = "Tien Chi Chen",
title = "Efficient Arithmetic Apparatus and Method",
journal = j-IBM-TDB,
volume = "14",
number = "1",
pages = "328--330",
month = jun,
year = "1971",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Tue Jan 08 22:33:33 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
}
@InCollection{Clark:1971:SCP,
author = "N. W. Clark and W. J. Cody and H. Kuki",
title = "Self-Contained Power Routines",
crossref = "Rice:1971:MS",
pages = "399--415",
year = "1971",
bibdate = "Thu Sep 15 18:56:49 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Cody:1971:DHC,
author = "W. J. Cody",
title = "Desirable Hardware Characteristics for Scientific
Computation",
journal = j-SIGNUM,
volume = "6",
number = "1",
pages = "16--31",
month = jan,
year = "1971",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/1052614.1052616",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:49:57 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
xxtitle = "Hardware characteristics (pages missing from print)",
}
@InCollection{Cody:1971:SEF,
author = "W. J. Cody",
title = "Software for the Elementary Functions",
crossref = "Rice:1971:MS",
pages = "171--186",
year = "1971",
bibdate = "Thu Sep 15 18:56:47 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Dekker:1971:FPT,
author = "Theodorus J. Dekker",
title = "A Floating-Point Technique for Extending the Available
Precision",
journal = j-NUM-MATH,
volume = "18",
number = "3",
pages = "224--242",
year = "1971",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01397083",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "68A55",
MRnumber = "MR0299007 (45 \#8056)",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb # " and " # ack-nj,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "accurate floating-point summation; balanced ternary",
xxmonth = "(none)",
}
@Article{DeLong:1971:UPA,
author = "Howard DeLong",
title = "Unsolved Problems in Arithmetic",
journal = j-SCI-AMER,
volume = "224",
number = "3",
pages = "50--60",
month = mar,
year = "1971",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican0371-50",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Wed May 22 12:00:01 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/sciam1970.bib",
URL = "http://www.nature.com/scientificamerican/journal/v224/n3/pdf/scientificamerican0371-50.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@Article{Dutka:1971:SRD,
author = "Jacques Dutka",
title = "The Square Root of $2$ to $ 1, 000, 000 $ Decimals",
journal = j-MATH-COMPUT,
volume = "25",
number = "116",
pages = "927--930",
month = oct,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Gentleman:1971:OMC,
author = "W. Morven Gentleman",
title = "Optimal multiplication chains for computing a power of
a symbolic polynomial",
journal = j-SIGSAM,
volume = "??",
number = "18",
pages = "23--30",
month = apr,
year = "1971",
CODEN = "SIGSBZ",
DOI = "https://doi.org/10.1145/1093425.1093426",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Tue Jun 17 19:14:25 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper shows that in a certain model of symbolic
manipulation of algebraic formulae, the simple method
of computing a power of a symbolic polynomial by
repeated multiplication by the original polynomial is,
in essence, the optimal method.",
acknowledgement = ack-nhfb,
fjournal = "SIGSAM Bulletin",
issue = "18",
}
@TechReport{Ghest:1971:TCD,
author = "R. C. Ghest",
title = "A Two's Complement Digital Multiplier, the {Am25S05}",
type = "Technical report",
institution = "Advanced Micro Devices",
address = "Sunnyvale, CA, USA",
pages = "????",
year = "1971",
bibdate = "Fri Nov 09 18:50:36 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Ginsberg:1971:NID,
author = "Myron Ginsberg",
booktitle = "Proceedings of the First Annual Rocky Mountain
Symposium on Microprocessors",
title = "Numerical influences on the design of floating-point
arithmetic for microcomputers",
publisher = "????",
address = "????",
pages = "24--72",
year = "1971",
bibdate = "Fri Nov 09 18:52:22 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Golub:1971:CAC,
author = "G. H. Golub and L. B. Smith",
title = "{Chebyshev} Approximation of Continuous Functions by a
{Chebyshev} System of Functions",
journal = j-CACM,
volume = "14",
number = "11",
pages = "737--746",
month = nov,
year = "1971",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Aug 15 09:54:14 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "ACM Algorithm 414.",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Honey:1971:CCD,
author = "D. W. Honey",
title = "Correspondence: Calculation of a double-length square
root from a double length number using single precision
techniques",
journal = j-COMP-J,
volume = "14",
number = "4",
pages = "443--443",
month = nov,
year = "1971",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:51:58 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/140443.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/tiff/443.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Kagan:1971:FPS,
author = "Claude A. R. Kagan",
title = "Floating point sub-language of a string language",
journal = j-SIGPLAN,
volume = "6",
number = "10",
pages = "20--22",
month = nov,
year = "1971",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/1317448.1317449",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sat Dec 2 08:35:10 MST 2017",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/sigplan1970.bib",
URL = "https://dl.acm.org/citation.cfm?id=1317449",
abstract = "The facilities for floating point computation within
the framework of a string language currently operating
on the PDP-10 at the Western Electric Company
Engineering Research Center are considered to be a
sublanguage. This sublanguage is accessed through use
of the * (asterisk) as a function marker in lieu of the
colon, and such use causes execution of all of the
available arithmetic functions as well as a family of
additional functions whose names are the same as those
used in Fortran. The list of functions that will
execute in this sublanguage is displayed through
execution of ** (LF), expression.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@InProceedings{Kahan:1971:SEA,
author = "W. M. Kahan",
title = "A Survey of Error Analysis",
crossref = "Freiman:1971:PIC",
pages = "1214--1239",
year = "1971",
MRclass = "65G05",
MRnumber = "MR0458845 (56 \#17045)",
bibdate = "Tue Aug 28 05:24:53 2001",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Information Processing 71",
URL = "http://dblp.uni-trier.de/db/conf/ifip/ifip71-2.html#Kahan71",
acknowledgement = ack-jr # " and " # ack-nhfb,
keywords = "accurate floating-point summation",
remark = "This paper contains the modified compensating
summation algorithm wherein `e = (temp - s) + y' is
replaced by `f = 0; if (sign(temp) == sign(y)) {f =
(0.46*s - s) + s} e = ((temp - f) - (s - f)) + y',
cited in e.g.,
\cite{Dalhquist:1974:NM,Higham:1993:AFP}.",
}
@Article{Kan:1971:EAD,
author = "E. Kan and J. Aggarwal",
title = "Error analysis of digital filter employing
floating-point arithmetic",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "18",
number = "6",
pages = "678--686",
month = nov,
year = "1971",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See correction \cite{Kan:1973:CEA}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "The error accumulation in a digital filter employing
floating-point arithmetic is studied. Sources of errors
are considered to originate from (1) roundoff in the
arithmetic operations, (2) quantization of both the
input and the initial states, and (3) \ldots{}",
}
@Article{Kingsbury:1971:DFU,
author = "N. G. Kingsbury and P. J. W. Rayner",
title = "Digital filtering using logarithmic arithmetic",
journal = j-ELECT-LETTERS,
volume = "7",
number = "2",
pages = "56--58",
day = "28",
month = jan,
year = "1971",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:19710039",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Mon May 30 07:32:20 2016",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}
@Article{Krishnamurthy:1971:CTW,
author = "E. V. Krishnamurthy",
title = "Complementary Two-Way Algorithms for Negative Radix
Conversions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "5",
pages = "543--550",
month = may,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223288",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:14 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671881",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
}
@Article{Krishnamurthy:1971:EIR,
author = "E. V. Krishnamurthy",
title = "Economical Iterative and Range-Transformation Schemes
for Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "4",
pages = "470--472",
month = apr,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223270",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:14 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671863",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kuki:1971:FEP,
author = "H. Kuki and J. Ascoly",
title = "{FORTRAN} extended-precision library",
journal = j-IBM-SYS-J,
volume = "10",
number = "1",
pages = "39--61",
year = "1971",
CODEN = "IBMSA7",
ISSN = "0018-8670",
bibdate = "Thu Sep 15 18:51:32 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Systems Journal",
xxmonth = "(none)",
}
@InCollection{Kuki:1971:MFS,
author = "H. Kuki",
title = "Mathematical Function Subprograms for Basic System
Libraries\emdash Objectives, Constraints, and
Trade-Off",
crossref = "Rice:1971:MS",
pages = "187--199",
year = "1971",
bibdate = "Fri Sep 16 16:27:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Kulisch:1971:AAR,
author = "U. Kulisch",
title = "An axiomatic approach to rounded computations",
journal = j-NUM-MATH,
volume = "18",
number = "1",
pages = "1--17",
month = feb,
year = "1971",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01398455",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 16:12:48 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The present paper is intended to give an axiomatic
approach to rounded computations. A rounding is defined
as a monotone mapping of an ordered set into a subset,
which in general is called a lower respectively an
upper screen. The first chapter deals with roundings in
ordered sets. In the second chapter further properties
of roundings in linearly ordered sets are studied. The
third chapter deals with the two most important
applications, the approximation of the real arithmetic
on a finite screen and the approximation of the real
interval arithmetic on an upper screen. Beyond these
examples various further applications are possible.",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Kupka:1971:SRA,
author = "I. Kupka",
title = "Simulation of real arithmetic and real functions in
finite sets",
journal = j-NUM-MATH,
volume = "17",
number = "2",
pages = "143--152",
year = "1971",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C1220 (Simulation, modelling and identification);
C4110 (Error analysis in numerical methods)",
corpsource = "Univ. Hamburg, West Germany",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "error estimation; errors; estimation theory; finite
set; floating point arithmetic; real functions;
simulation",
language = "German",
treatment = "T Theoretical or Mathematical",
}
@Article{Majithia:1971:CAN,
author = "J. C. Majithia and R. Kitai",
title = "A Cellular Array for the Nonrestoring Extraction of
Square Roots",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "12",
pages = "1617--1618",
month = dec,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223191",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:22 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671784",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Majithia:1971:IAM,
author = "J. C. Majithia and R. Kitai",
title = "An Iterative Array for Multiplication of Signed Binary
Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "2",
pages = "214--216",
month = feb,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223216",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:12 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671809",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Malcolm:1971:AFP,
author = "Michael A. Malcolm",
title = "On Accurate Floating-Point Summation",
journal = j-CACM,
volume = "14",
number = "11",
pages = "731--736",
month = nov,
year = "1971",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/362854.362889",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65G05 (68-XX)",
MRnumber = "47 4434",
MRreviewer = "P. Brock",
bibdate = "Mon Jan 22 07:01:06 MST 2001",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm14.html#Malcolm71;
http://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Stanford Univ., CA, USA",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "accurate floating-point summation; digital arithmetic;
error analysis",
oldlabel = "Malcolm71",
treatment = "P Practical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Malcolm71",
}
@TechReport{Malcolm:1971:ARP,
author = "Michael A. Malcolm",
title = "Algorithm to reveal properties of floating-point
arithmetic",
institution = "Stanford University",
address = "Stanford, Ca.",
pages = "8",
year = "1971",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "AD-727 104",
acknowledgement = ack-nhfb,
keywords = "Algorithms.; Floating-point arithmetic.",
remark = "``STAN-CS-71-211.''",
}
@Article{Morris:1971:TFP,
author = "R. Morris",
title = "Tapered Floating Point: a New Floating-Point
Representation",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "12",
pages = "1578--1579",
month = dec,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223174",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:22 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671767",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Mullet:1971:NME,
author = "Gary M. Mullet and Tracy W. Murray",
title = "A New Method for Examining Rounding Error in
Least-Squares Regression Computer Programs",
journal = j-J-AM-STAT-ASSOC,
volume = "66",
number = "335",
pages = "496--498",
month = sep,
year = "1971",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:44 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314211;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib",
URL = "http://www.jstor.org/stable/2283514",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Nicoud:1971:IAR,
author = "Jean-Daniel Nicoud",
title = "Iterative Arrays for Radix Conversion",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "12",
pages = "1479--1489",
month = dec,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223160",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Oct 10 13:44:30 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The general study of the conversion of a number from
the radix p to the radix q number system leads to four
different algorithms for integers, and to four similar
ones for fractions. Most transform algorithms can be
implemented by iterative arrays of cells characterized
by simple equations. Such arrays are very attractive
with present-time large-scale integration technology.
Two kinds of cells, that is, two iterative arrays, are
sufficient for the near instantaneous conversion of
fixed-point numbers from radix p to radix q, or vice
versa. For the important special case of binary-decimal
conversion, the structure of the cells is studied, and
different realizations using the BCD code are
described. One of them is specially suited for an LSI
realization in MOS technology. The advantages of other
codes are discussed. In particular, the use of the
biquinary code allows the realization of the fastest
cells, with only one gate delay for each line of
cells.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "base conversion; binary-decimal conversion; cellular
arrays; code conversion; iterative arrays; large-scale
integration; MOS technology; number systems; radix
conversion algorithms",
}
@Article{Paker:1971:BFP,
author = "Y. Paker",
title = "A Binary Floating-Point Resistor",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "1",
pages = "7--11",
month = jan,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223074",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:11 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671667",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Paus:1971:FPA,
author = "Dag Paus",
title = "Floating point arithmetikk til {Nord-2B}",
type = "Hovedoppgave i fysikk",
institution = "Universitetet i Oslo",
address = "Oslo, Norway",
pages = "156",
year = "1971",
bibdate = "Thu May 09 08:11:14 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Norwegian",
}
@Article{Pawlak:1971:ACN,
author = "Z. Pawlak",
title = "Another Comment on {``Negative Radix Conversion''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "5",
pages = "587--587",
month = may,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223301",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:15 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Wadel:1971:CNR,Zohar:1970:NRC}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671894",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
}
@Article{Pezaris:1971:BBA,
author = "S. D. Pezaris",
title = "A 40ns 17-bit by 17-bit array multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "4",
pages = "442--447 (??)",
month = apr,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223261",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:12:55 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Pezaris:1971:NBB,
author = "S. D. Pezaris",
title = "A 40-ns 17-Bit by 17-Bit Array Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "4",
pages = "442--447",
month = apr,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223261",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:14 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671854",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Rhyne:1971:SPN,
author = "V. T. Rhyne",
title = "A Simple Postcorrection for Nonrestoring Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "2",
pages = "213--214",
month = feb,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223215",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:12 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671808",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@PhdThesis{Rothmaier:1971:BEF,
author = "B. Rothmaier",
title = "{Die Berechnung der elementaren Funktionen mit
beliebiger Genauigkeit} \toenglish {The Computation of
Elementary Functions with Arbitrary Accuracy}
\endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "??",
year = "1971",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Sarkar:1971:EPP,
author = "B. P. Sarkar and E. V. Krishnamurthy",
title = "Economic Pseudodivision Processes for Obtaining Square
Root, Logarithm, and Arctan",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "12",
pages = "1589--1593",
month = dec,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223178",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:22 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671771",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Schmookler:1971:HSD,
author = "Martin S. Schmookler and Arnold Weinberger",
title = "High speed decimal addition",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "8",
pages = "862--867",
month = aug,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223362",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 28 19:10:32 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Parallel decimal arithmetic capability is becoming
increasingly attractive with new applications of
computers in a multiprogramming environment. The direct
production of decimal sums offers a significant
improvement in addition over methods requiring decimal
correction. These techniques are illustrated in the
eight-digit adder which appears in the System/360 Model
195.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "decimal floating-point arithmetic",
}
@Article{Schonhage:1971:SMG,
author = "A. Sch{\"o}nhage and V. Strassen",
title = "{Schnelle Multiplikation gro{\ss}er Zahlen}.
({German}) [{Fast} multiplication of large numbers]",
journal = j-COMPUTING,
volume = "7",
number = "3--4",
pages = "281--292",
year = "1971",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Thu Jan 04 08:42:36 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
note = "Check pages??",
acknowledgement = ack-ec # " and " # ack-nhfb,
affiliation = "Univ., Konstanz, West Germany",
classification = "C5230",
description = "digital arithmetic",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
keywords = "algorithm; binary numbers; logical nets; multitape
Turing machines; product",
language = "German",
}
@Article{Shepherd:1971:RSL,
author = "B. J. Shepherd",
title = "Right Shift for Low-Cost Multiply and Divide",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "12",
pages = "1586--1589",
month = dec,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223177",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:22 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671770",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Stein:1971:IMA,
author = "Marvin L. Stein and William D. Munro",
title = "Introduction to machine arithmetic",
publisher = pub-AW,
address = pub-AW:adr,
pages = "viii + 295",
year = "1971",
LCCN = "QA76.5 .S752",
bibdate = "Fri Nov 9 19:20:08 MST 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
subject = "Electronic digital computers; Arithmetic",
}
@Article{Stein:1971:SMA,
author = "M. L. Stein and W. D. Munro",
title = "Scaling Machine Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "6",
pages = "675--678",
month = jun,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223324",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:16 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671917",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Wadel:1971:CNR,
author = "L. B. Wadel",
title = "Comment on {``Negative Radix Conversion''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "5",
pages = "587--587",
month = may,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223300",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:15 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Pawlak:1971:ACN,Zohar:1970:NRC}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671893",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
}
@Article{Walker:1971:BS,
author = "R. J. Walker",
title = "Binary Summation",
journal = j-CACM,
volume = "14",
number = "6",
pages = "417--417",
month = jun,
year = "1971",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:27:52 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm14.html#Walker71;
http://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Cornell Univ., Ithaca, NY, USA",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "binary summation; digital arithmetic; floating point;
roundoff errors; space; storage",
oldlabel = "Walker71",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Walker71",
}
@InProceedings{Walther:1971:UAE,
author = "J. S. Walther",
title = "A unified algorithm for elementary functions",
crossref = "AFIPS:1971:ACP",
volume = "38",
pages = "379--385",
year = "1971",
bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Wlodarski:1971:FLN,
author = "J. Wlodarski",
title = "{Fibonacci} and {Lucas} Numbers Tend to Obey
{Benford's Law}",
journal = j-FIB-QUART,
volume = "9",
number = "1",
pages = "87--88",
month = feb,
year = "1971",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:33 MDT 2011",
bibsource = "http://www.fq.math.ca/9-1.html;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/9-1/wlodarski2.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@InProceedings{Yohe:1971:R,
author = "J. M. Yohe",
booktitle = "Proceedings of the 1971 Army Numerical Analysis and
Computers Conference",
title = "Rounding",
publisher = "US Army Research Office",
address = "Durham, NC, USA",
pages = "213--223",
year = "1971",
LCCN = "????",
bibdate = "Sun Dec 30 21:37:46 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "ARO-D Report 71-4",
acknowledgement = ack-nhfb,
}
@MastersThesis{Abdelmagid:1972:DFP,
author = "Mohamed Nabil Fouad Abdelmagid",
title = "Design of a floating point arithmetic unit",
type = "Thesis ({M.S.})",
school = "Illinois Institute of Technology",
address = "Chicago, IL.",
pages = "v + 60",
year = "1972",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Ahmad:1972:ISH,
author = "M. Ahmad",
title = "Iterative schemes for high speed division",
journal = j-COMP-J,
volume = "15",
number = "4",
pages = "333--336",
month = nov,
year = "1972",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:52:07 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/150333.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/333.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/334.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/335.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/336.tif",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Univ. Manchester, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "digital arithmetic; digital computers; high speed
division; iterative methods; iterative schemes;
multiplicative",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Bandyopadhyay:1972:IAM,
author = "S. Bandyopadhyay and S. Basu and A. K. Choudhury",
title = "An Iterative Array for Multiplication of Signed Binary
Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "8",
pages = "921--922",
month = aug,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009055",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:46 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009055",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Banerji:1972:TAR,
author = "D. K. Banerji and J. A. Brzozowski",
title = "On Translation Algorithms in Residue Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "12",
pages = "1281--1285",
month = dec,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1972.223499",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:48 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672092;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35066",
abstract = "This paper considers translation problems in residue
number systems. The conversion from a fixed-base
representation to a residue representation can be done
using residue adders only; we show that relatively
simple combinational logic can be used to replace one
level of residue addition. In the reverse translation
problem, we examine the conditions under which base
extension can be used to compute the fixed-base digits
from a residue code number, and we study the efficiency
of the algorithm.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "base extension; input translation; modular arithmetic;
output translation; residue arithmetic; residue number
systems",
}
@Article{Brakefield:1972:OFP,
author = "James C. Brakefield",
title = "An optimal floating point format",
journal = j-COMP-ARCH-NEWS,
volume = "1",
number = "4",
pages = "16--17",
month = oct,
year = "1972",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 12 09:41:08 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{Chen:1972:ACE,
author = "Tien Chi Chen",
title = "Automatic Computation of Exponentials, Logarithms,
Ratios and Square Roots",
journal = j-IBM-JRD,
volume = "16",
number = "4",
pages = "380--388",
month = jul,
year = "1972",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "65D20",
MRnumber = "49 \#1738",
bibdate = "Tue Mar 25 14:26:59 MST 1997",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.research.ibm.com/journal/rd/164/chen.pdf",
abstract = "It is shown how a relatively simple device can
evaluate exponentials, logarithms, ratios and square
roots for fraction arguments, employing only shifts,
adds, high-speed table lookups, and bit counting. The
scheme is based on the cotransformation of a number
pair $ (x, y) $ such that the $ F(x, y) = f(x_0) $ is
invariant; when $x$ is driven towards a known value $
x_w $, $y$ is driven towards the result. For an $N$-bit
fraction about $ N / 4 $ iterations are required, each
involving two or three adds; then a termination
algorithm, based on an add and an abbreviated multiply,
completes the process, for a total cost of about one
conventional multiply time. Convergence, errors and
simulation using APL are discussed.",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "IBM, San Jose, CA, USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "adds; APL; bit counting; convergence;
cotransformation; digital arithmetic; errors;
exponentials; high speed table; iteration; logarithms;
lookups; ratios; shifts; simulation; square roots;
termination algorithm",
reviewer = "F. Gotze",
treatment = "P Practical",
}
@Article{Chiang:1972:NAB,
author = "A. C. L. Chiang and I. S. Reed",
title = "Notes on the Arithmetic {BN} Modulo {A} Codes",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "8",
pages = "891--894",
month = aug,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009046",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:46 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009046",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Chien:1972:ECH,
author = "R. T. Chien and Se June Hong",
title = "Error Correction in High-Speed Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "5",
pages = "433--438",
month = may,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1972.223538",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:43 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672131",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Chinal:1972:SCP,
author = "J. P. Chinal",
title = "Some Comments on Postcorrections for Nonrestoring
Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "12",
pages = "1385--1394",
month = dec,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1972.223511",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:49 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672104",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{DeMori:1972:PSS,
author = "R. {De Mori} and A. Serra",
title = "A Parallel Structure for Signed-Number Multiplication
and Addition",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "12",
pages = "1453--1454",
month = dec,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1972.223525",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:49 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672118",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Fenwick:1972:BRD,
author = "Peter M. Fenwick",
title = "A Binary Representation for Decimal Numbers",
journal = j-AUSTRALIAN-COMP-J,
volume = "4",
number = "4",
pages = "146--149",
month = nov,
year = "1972",
CODEN = "ACMJB2",
ISSN = "0004-8917",
bibdate = "Fri Nov 28 11:31:38 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Australian Computer Journal",
keywords = "decimal floating-point arithmetic",
}
@Article{Fettweis:1972:CBM,
author = "A. Fettweis",
title = "On the connection between multiplier word length
limitation and roundoff noise in digital filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "19",
number = "5",
pages = "486--491",
month = sep,
year = "1972",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "It is shown that for digital filters there exists a
direct and an indirect connection between the
generation of roundoff noise by a multiplier and the
effect that the coefficient word length limitation of
this multiplier has upon the response \ldots{}",
}
@Article{Franklin:1972:ZDA,
author = "J. W. Franklin",
title = "Zoned Decimal Arithmetic",
journal = j-IBM-TDB,
volume = "15",
number = "7",
pages = "2123--2124",
month = dec,
year = "1972",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
keywords = "decimal floating-point arithmetic",
}
@Book{Goldstine:1972:CPN,
author = "Herman H. Goldstine",
title = "The Computer: {From Pascal} to {von Neumann}",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "xii + 378",
year = "1972",
ISBN = "0-691-02367-0; 0-691-08104-2",
ISBN-13 = "978-0-691-02367-0; 978-0-691-08104-5",
bibdate = "Mon Jun 06 19:17:03 2005",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/Matrix.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/sparse.linear.systems.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/TUBScsd/1972.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Second printing, 1973. Paperback edition 1980. Fifth
printing, 1993 with new preface. Reprint 2000 by Books
on Demand, Ann Arbor, MI, USA.",
acknowledgement = ack-nhfb,
descriptor = "Computer, ENIAC, Entwicklung, Geschichte, Pascal, Von
Neumann",
kwds = "book, history, computer",
}
@TechReport{Gosper:1972:HCF,
author = "R. W. Gosper",
title = "{HAKMEM} 101: Continued Fractions",
type = "Memo",
number = "AIM 239",
institution = "MIT AI Laboratory",
address = "Cambridge, MA, USA",
pages = "37--44",
year = "1972",
bibdate = "Fri Nov 30 06:37:23 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.inwap.com/pdp10/hbaker/hakmem/cf.html#item101a",
acknowledgement = ack-nhfb,
remark = "From the document: ``The familiar transcendental
functions of rational arguments also have simple
continued fractions, but these are generally not
regular and cannot be reconstructed from numerical
values by a simple algorithm, since nonregular
representations aren't unique. The point is, however,
that numbers like e, pi, sqrt(2), sin .5, sqrt(7)
arctan sqrt(7), etc. can be expressed to unlimited
precision by simple programs which produce the terms on
demand.'' Also: ``Rational number arithmetic often
loses because numerators and denominators grow so large
as to require icky multiprecision. Algorithms for
arithmetic on continued fractions seem generally
unknown. The next items describe how to arithmetically
combine continued fractions to produce new ones, one
term at a time.'' and ``Continued fractions let us
perform numerical calculations a little at a time
without ever introducing any error, such as roundoff or
truncation. As if this weren't enough, the calculations
provide automatic error analysis, and obviate most
forms of successive approximation.''",
}
@Article{Gregory:1972:CFP,
author = "James Gregory",
title = "A Comparison of Floating Point Summation Methods",
journal = j-CACM,
volume = "15",
number = "9",
pages = "838--838",
month = sep,
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:46:23 MST 2001",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Gregory72;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Argonne Nat. Lab., IL, USA",
descriptors = "Simulation; statistics; numeric calculation",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "accurate floating-point summation; comparison; digital
arithmetic; error; error propagation; floating point
summation methods; truncation",
oldlabel = "Gregory72",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Gregory72",
}
@Article{Gregory:1972:URA,
author = "Robert Todd Gregory",
title = "The use of residue arithmetic with automatic digital
computers",
journal = "Delta (Waukesha)",
volume = "3",
number = "2",
pages = "1--27",
year = "1972\slash 1973",
MRclass = "68A10",
MRnumber = "MR0321348 (47 \#9881)",
MRreviewer = "A. D. Booth",
bibdate = "Thu Nov 8 14:50:21 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Hallin:1972:PAF,
author = "T. G. Hallin and M. J. Flynn",
title = "Pipelining of Arithmetic Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "8",
pages = "880--886",
month = aug,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009044",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 18:57:52 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Heising:1972:MM,
author = "W. Heising and M. O. Rabin and Shmuel Winograd",
title = "Multiplication Method",
journal = j-IBM-TDB,
volume = "15",
number = "4",
pages = "1147--1148",
month = sep,
year = "1972",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Manual{IBM:1972:ISR,
author = "{International Business Machines Corporation}",
title = "{IBM System\slash 360} reference data: direct
evaluation of floating point numbers in hexadecimal:
debugging aid",
organization = "IBM Corporation",
address = "White Plains, NY, USA",
pages = "18",
year = "1972",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "IBM 360 (Computer)",
remark = "``GX20-1787-0.''",
}
@Article{Kamal:1972:HSM,
author = "A. A. Kamal and M. A. N. Ghannam",
title = "High-Speed Multiplication Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "9",
pages = "1017--1021",
month = sep,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009082",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:46 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009082",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Liu:1972:REF,
author = "B. Liu and M. {Van Valkenburg}",
title = "On roundoff error of fixed-point digital filters using
sign-magnitude truncation",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "19",
pages = "536--537",
month = sep,
year = "1972",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "This correspondence gives the statistical mean squared
error at the output of a digital filter due to roundoff
accumulation when fixed-point arithmetic with
sign-magnitude truncation is \ldots{}",
}
@Article{Loevenbruck:1972:CNR,
author = "A. P. Loevenbruck",
title = "Conversion of Number Representations",
journal = j-IBM-TDB,
volume = "15",
number = "7",
pages = "2148--2151",
month = dec,
year = "1972",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Article{Majithia:1972:CAE,
author = "J. C. Majithia",
title = "Cellular Array for Extraction of Squares and Square
Roots of Binary Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "9",
pages = "1023--1024",
month = sep,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009084",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:46 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009084",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Malcolm:1972:ARP,
author = "M. A. Malcolm",
title = "Algorithms To Reveal Properties of Floating-Point
Arithmetic",
journal = j-CACM,
volume = "15",
number = "11",
pages = "949--951",
month = nov,
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:14:16 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Gentleman:1974:MAR}.",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Mandelbaum:1972:ECR,
author = "David Mandelbaum",
title = "Error correction in residue arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
pages = "538--545",
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009006",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "94A10 (94A20)",
MRnumber = "MR0345709 (49 \#10440)",
MRreviewer = "P. Deussen",
bibdate = "Thu Nov 8 14:50:21 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Manos:1972:CCA,
author = "Paul Manos and L. Richard Turner",
title = "Constrained {Chebyshev} approximations to some
elementary functions suitable for evaluation with
floating-point arithmetic",
type = "{NASA} Technical Note",
number = "TN D-6698",
institution = "NASA",
address = "Washington, DC, USA",
pages = "iii + 68",
month = mar,
year = "1972",
bibdate = "Mon May 22 11:27:24 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720010958_1972010958.pdf",
acknowledgement = ack-nhfb,
}
@MastersThesis{Maple:1972:FPA,
author = "Christopher Marion Maple",
title = "A floating point analog to digital and digital to
analog converter",
type = "Thesis ({B.S.})",
school = "Massachusetts Institute of Technology. Dept. of
Electrical Engineering",
address = "Cambridge, MA, USA",
pages = "18",
year = "1972",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Marino:1972:NAA,
author = "D. Marino",
title = "New Algorithms for the Approximate Evaluation in
Hardware of Binary Logarithms and Elementary
Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "21",
number = "12",
pages = "1416--1421",
month = dec,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1972.223516",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 08 08:05:51 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Matula:1972:NTF,
author = "David W. Matula",
title = "Number Theoretic Foundations of Finite Precision
Arithmetic",
crossref = "Zaremba:1972:ANT",
pages = "479--489",
year = "1972",
bibdate = "Fri Oct 19 22:58:55 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "base conversion; finite-precision rational arithmetic;
number theory; overflow; radix conversion; tape
updating problem",
}
@TechReport{Metropolis:1972:ABCa,
author = "N. Metropolis",
title = "Analyzed Binary Computing",
type = "Technical Report",
number = "LA-DC--72-783; CONF-720916--2",
institution = inst-LASL,
address = inst-LASL:adr,
pages = "4",
day = "12",
month = sep,
year = "1972",
bibdate = "Tue Mar 20 11:25:24 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=4647144&query_id=0",
acknowledgement = ack-nhfb,
}
@InProceedings{Metropolis:1972:ABCb,
author = "N. Metropolis",
title = "Analyzed Binary Computing",
crossref = "IEEE:1972:IAD",
pages = "81--84",
year = "1972",
bibdate = "Wed Mar 21 09:24:37 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A single format for the representation of numbers in a
computer is proposed to accommodate both exact and
inexact quantities. A consistent set of rules is
described for addition (subtraction), multiplication
and division of such quantities, both within their
separate types, as well as in combination. Error
correlation aside, the propagation of inherent errors
is monitored in operations with at least one imprecise
value. A definitive algorithm must, of course take into
account any correlations of inherent errors; these
correlations must be recognized and incorporated into
the algorithm by the numerical analyst, not by the
logical designer of the computer.",
acknowledgement = ack-nhfb,
}
@InProceedings{Metropolis:1972:ABCc,
author = "Nicholas C. Metropolis",
title = "Analyzed binary computing",
crossref = "IEEE:1972:ITS",
pages = "1--14",
year = "1972",
DOI = "https://doi.org/10.1109/ARITH.1972.6153912",
bibdate = "Tue Mar 5 08:31:37 MST 2013",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6153912",
acknowledgement = ack-nhfb,
journal-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6148543",
}
@MastersThesis{Miller:1972:DFD,
author = "Peter Edwin Miller",
title = "The design of a floating-point, double-precision
arithmetic unit for the {Digital Equipment
Corporation}'s {PDP-9} computer",
type = "Thesis ({M.S.})",
school = "Ohio State University",
address = "Columbus, OH, USA",
pages = "83",
year = "1972",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Arithmetic --- Computer programs; PDP-9 (Computer)",
}
@InProceedings{Neely:1972:CSN,
author = "Peter M. Neely",
title = "On conventions for systems of numerical
representation",
crossref = "ACM:1972:PAA",
pages = "644--561",
year = "1972",
bibdate = "Fri Nov 28 11:28:06 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Present conventions for numeric representation are
considered inadequate to serve the needs of applied
computing. Thus an augmented digital number system is
proposed for use in programming languages and in
digital computers. Special symbols are proposed for
numbers too large, too small or too close to zero to be
represented in the normal digital number system, or
which are undefined. Properties of mappings among and
between digital number systems are used to justify the
augments chosen. Finally a suggestion is made for a new
floating point word format that will serve all the
above needs and will greatly extend the exponent range
of floating point numbers.",
acknowledgement = ack-nhfb,
}
@Article{Oberman:1972:FRM,
author = "R. M. M. Oberman",
title = "A Flexible Rate Multiplier Circuit with Uniform Pulse
Distribution Outputs",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "8",
pages = "896--899",
month = aug,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009048",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:46 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009048",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Paris:1972:MA,
author = "J. B. Paris",
title = "On models of arithmetic",
journal = j-LECT-NOTES-MATH,
volume = "255",
pages = "251--280",
year = "1972",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0059548",
ISBN = "3-540-05744-7 (print), 3-540-37162-1 (e-book)",
ISBN-13 = "978-3-540-05744-4 (print), 978-3-540-37162-5
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
MRclass = "02H05 (02H13)",
MRnumber = "0392552 (52 \#13369)",
MRreviewer = "W. Marek",
bibdate = "Fri May 9 19:07:09 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/lnm1970.bib",
URL = "http://link.springer.com/chapter/10.1007/BFb0059548/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/BFb0059533",
book-URL = "http://www.springerlink.com/content/978-3-540-37162-5",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
}
@Article{Pettus:1972:IDC,
author = "C. Pettus",
title = "Indeterminate $ 0 \div 0 $ check in {APL}",
journal = j-SIGPLAN,
volume = "7",
number = "4",
pages = "40--41",
month = apr,
year = "1972",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Thu May 25 06:58:23 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "One unique feature of the APL system is the definition
$ (0 \div 0) = 1 $. Although there is obvious merit in
this decision, in real analysis $ (0 \div 0) $ is
indeterminate. If one wishes to be alerted to the fact
that a denominator is zero and does not want the result
$1$ if the numerator is also zero, one can replace the
expression $ X \div Y $ with $ X \times \div Y $. Then
if $X$ and $Y$ are both zero, a Domain Error will be
reported instead of yielding.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "floating-point arithmetic; zero divide",
}
@Article{Phillips:1972:ICF,
author = "C. Phillips",
title = "Instabilities caused by floating-point arithmetic
quantization",
journal = j-IEEE-TRANS-AUTOMAT-CONTR,
volume = "17",
number = "2",
pages = "242--243",
month = apr,
year = "1972",
CODEN = "IETAA9",
ISSN = "0018-9286",
ISSN-L = "0018-9286",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Automatic Control",
summary = "It is shown that an otherwise stable digital control
system may become unstable due to signal quantization
if the controller operates on floating-point
arithmetic. Sufficient conditions for instability are
developed \ldots{}",
}
@Article{Pichat:1972:CSA,
author = "M. Pichat",
title = "Correction d'une Somme en Arithm{\'e}tique {\`a}
Virgule Flottante. ({French}) {[Correction of a Sum in
Floating-Point Arithmetic]}",
journal = j-NUM-MATH,
volume = "19",
number = "5",
pages = "400--406",
year = "1972",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sat Sep 17 18:30:51 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "From Douglas Priest:
(\path=Douglas.Priest@eng.sun.com=) writing in Usenet
newsgroup sci.math.num-analysis on 13 Sep 1994 16:04:56
GMT: ``\ldots{} An iterative algorithm for computing a
protracted sum to working precision by repeatedly
applying the sum-and-roundoff method.''",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
corpsource = "Conservatoire Nat. Arts M{\'e}tiers, Paris, France",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "accurate floating-point summation; correction; digital
arithmetic; floating point arithmetic; rounding off
law; sum; truncature with guard digit",
language = "French",
treatment = "T Theoretical or Mathematical",
xxmonth = "(none)",
xxnumber = "(none)",
}
@Article{Ramamoorthy:1972:SPI,
author = "C. V. Ramamoorthy and James R. Goodman and K. H. Kim",
title = "Some Properties of Iterative Square-Rooting Methods
Using High-Speed Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "8",
pages = "837--847",
month = aug,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009039",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:45 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009039",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Randell:1972:ATO,
author = "Brian Randell",
title = "On {Alan Turing} and the origins of digital
computers",
type = "Technical report",
number = "33",
institution = "University of Newcastle upon Tyne, Computing
Laboratory",
address = "Newcastle upon Tyne, UK",
pages = "36",
year = "1972",
LCCN = "TK7888.3 .R35",
bibdate = "Wed Oct 13 09:24:25 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "University of Newcastle upon Tyne. Computing
Laboratory. Technical report series",
acknowledgement = ack-nhfb,
subject = "Von Neumann, John; Turing, Alan Mathison; Electronic
digital computers; History",
subject-dates = "1903--1957 (John von Neumann); 1912--1954 (Alan
Turing)",
}
@TechReport{Randell:1972:ODC,
author = "Brian Randell",
title = "The origins of digital computers: a bibliography",
type = "Technical report",
number = "38",
institution = "Computing Laboratory, University of Newcastle upon
Tyne",
address = "Newcastle upon Tyne, UK",
pages = "iii + 59",
year = "1972",
LCCN = "TK7888.3 .R35",
bibdate = "Wed Oct 13 09:24:25 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "University of Newcastle upon Tyne, Computing
laboratory. Technical report series",
acknowledgement = ack-nhfb,
subject = "Electronic digital computers; History; Bibliography",
}
@Article{Richman:1972:AEA,
author = "Paul L. Richman",
title = "Automatic Error Analysis for Determining Precision",
journal = j-CACM,
volume = "15",
number = "9",
pages = "813--817",
month = sep,
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65G05",
MRnumber = "47 2808",
bibdate = "Mon Jan 22 07:15:56 MST 2001",
bibsource = "Compendex database;
http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Richman72;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The problem considered is that of evaluating a
rational expression to within any desired tolerance on
a computer which performs variable-precision
floating-point arithmetic operations. An automatic
error analysis technique is given for determining,
directly from the results of a trial low-precision
interval arithmetic calculation, just how much
precision and data accuracy are required to achieve a
desired final accuracy. The technique given generalize
easily to the evaluation of many nonrational
expressions.",
acknowledgement = ack-nhfb,
classcodes = "B0290B (Error analysis in numerical methods); C4110
(Error analysis in numerical methods); C5230 (Digital
arithmetic methods)",
classification = "921",
corpsource = "Bell Telephone Labs. Inc., Denver, CO, USA",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
journalabr = "Commun ACM",
keywords = "automatic error analysis; control; digital arithmetic;
error analysis; floating point arithmetic; interval
arithmetic; mathematical techniques; precision;
precision control",
oldlabel = "Richman72",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Richman72",
}
@PhdThesis{Ripley:1972:PFP,
author = "Jerald Lester Ripley",
title = "On proofs of floating-point program correctness and a
measure of their relative efficiency",
type = "Thesis ({Ph.D.})",
school = "University of Oklahoma",
address = "????",
pages = "vi + 105",
year = "1972",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Numerical calculations.",
}
@Article{Rohl:1972:NCA,
author = "J. S. Rohl and J. A. Linn",
title = "A Note on Compiling Arithmetic Expressions",
journal = j-COMP-J,
volume = "15",
number = "1",
pages = "13--14",
month = feb,
year = "1972",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/15.1.13",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:49 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/15/1.toc;
http://www.math.utah.edu/pub/tex/bib/compj1970.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_01/",
URL = "http://comjnl.oxfordjournals.org/content/15/1/13.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_01/150013.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_01/tiff/13.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_01/tiff/14.tif",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques); C6150C (Compilers, interpreters
and other processors)",
corpsource = "Univ. Manchester, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "arithmetic expressions; compilers; compiling; data
handling; digital arithmetic; minimisation;
minimization; program; single accumulator; storing;
temporary",
treatment = "T Theoretical or Mathematical",
}
@Article{Samet:1972:CDL,
author = "P. A. Samet and D. W. Honey",
title = "Calculation of a Double-Length Square Root from
Double-Length Number using Single Precision
Techniques",
journal = j-COMP-J,
volume = "15",
number = "2",
pages = "116--116",
month = may,
year = "1972",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/15.2.116",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:49 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/15/2.toc;
http://www.math.utah.edu/pub/tex/bib/compj1970.bib;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/",
URL = "http://comjnl.oxfordjournals.org/content/15/2/116.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/tiff/116.tif",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Univ. Coll., London, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "digital arithmetic; double length; precision
techniques; single; square root",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Schulenberg:1972:RSS,
author = "Craig Schulenberg and James E. Kernan",
title = "Results of space shuttle computer floating-point
precision study",
type = "Report",
number = "E-2637",
institution = "M.I.T. Charles Stark Draper Laboratory",
address = "Cambridge",
pages = "various",
year = "1972",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic data processing --- Space trajectories.;
Reusable space vehicles.",
remark = "At head of title: Apollo guidance, navigation and
control.",
}
@Article{Schurmann:1972:MEA,
author = "A. Schurmann",
title = "On the minimum error in addition processes of positive
floating-point numbers",
journal = j-ZASTOS-MAT,
volume = "13",
pages = "351--366",
year = "1972--1973",
CODEN = "ZAMTAK",
MRclass = "65G05",
MRnumber = "48 3242",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Zastosowania Matematyki",
reviewer = "A. D. Booth",
}
@Article{Shaham:1972:NDA,
author = "Z. Shaham and Z. Riesel",
title = "A Note on Division Algorithms Based on
Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "5",
pages = "513--514",
month = may,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1972.223557",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:43 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672150",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Stallings:1972:CPM,
author = "W. T. Stallings and T. L. Boullion",
title = "Computation of Pseudoinverse Matrices Using Residue
Arithmetic",
journal = j-SIAM-REVIEW,
volume = "14",
number = "1",
pages = "152--163",
month = "????",
year = "1972",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1014005",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:06:35 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/14/1;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1972",
}
@Article{Stefanelli:1972:SHS,
author = "R. Stefanelli",
title = "A Suggestion for a High-Speed Parallel Binary
Divider",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "1",
pages = "42--55",
month = jan,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1972.223430",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jan 08 22:42:31 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "family of four procedures to compute the inverse $ 1 /
X $ of a given binary number $X$ normalized between 0.5
and 1 is described. The quotient is obtained in
redundant binary form, i.e., in a base 2 code in which
digits can assume any positive or negative integer
value. All methods here described can be implemented by
combinatorial networks; the dividers realized in this
way are very fast because all carry propagations take
place at the same time.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InCollection{Tung:1972:A,
author = "C. Tung",
title = "Arithmetic",
crossref = "Cardenas:1972:CS",
pages = "??--??",
year = "1972",
bibdate = "Sat May 18 14:39:14 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Urabae:1972:CEA,
author = "Minoru Urabae",
title = "Component-wise error analysis of iterative methods
practiced on a floating-point system",
type = "{MRC} Technical Summary Report",
number = "1268",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
pages = "57",
year = "1972",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Error analysis (Mathematics); Floating-point
arithmetic.; Iterative methods (Mathematics)",
remark = "``Received August 11, 1972.'' Sponsored by Army
Research Office, Durham, N.C.",
}
@Article{Varian:1972:LEB,
author = "Hal R. Varian",
title = "Letter to the {Editor}: {Benford's Law}",
journal = j-AMER-STAT,
volume = "26",
number = "3",
pages = "65--66",
month = jun,
year = "1972",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Fri Mar 30 11:34:37 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/amstat.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0003-1305%28197206%2926%3A3%3C62%3ALTTE%3E2.0.CO%3B2-Q",
abstract = "Around 1938 the physicist Frank Benford observed a
rather strange fact: tables of logarithms in libraries
tend to be dirtier at the beginning than at the end.
This indicated to Benford that people had more occasion
to calculate with numbers beginning with 1 or 2 than
with 8 or 9.\par
Benford also found that the frequency of the digit p
being the first digit of a decimal number was very
closely approximated by $ \log (p + 1) - \log p $
[i.e., $ \log (1 + 1 / p) $ ]. This has become known as
Benford's law.",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Book{Young:1972:SNM,
author = "David M. Young and Robert Todd Gregory",
title = "A Survey of Numerical Mathematics",
publisher = pub-AW,
address = pub-AW:adr,
pages = "x + 492 (A1--A18 and B1--B14 and I1--I19)",
year = "1972",
ISBN = "0-201-08773-1, 0-486-65691-8 (Dover paperback)",
ISBN-13 = "978-0-201-08773-4, 978-0-486-65691-5 (Dover
paperback)",
LCCN = "QA297 .Y63 1972",
MRclass = "65-02",
MRnumber = "53 11954a",
bibdate = "Wed Jan 17 10:57:04 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
http://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "D. Greenspan",
tableofcontents = "1: Numerical Analysis as a Subject Area \\
1.1 Introduction \\
1.2 Some pitfalls in computation \\
1.3 Mathematical and computer aspects of an algorithm
\\
1.4 Numerical instability of algorithms and
ill-conditioned problems \\
1.5 Typical problems of interest to the numerical
analyst \\
1.6 Iterative methods \\
2: Elementary Operations with Automatic Digital
Computers \\
2.1 Introduction \\
2.2 Binary arithmetic \\
2.3 Conversion from base $D$ to base $B$ representation
\\
2.4 Representation of integers on a binary computer \\
2.5 Floating-point representations \\
2.6 Computer-representable numbers \\
2.7 Floating-point arithmetic operations \\
2.8 Fortran analysis of a floating-point number \\
2.9 Calculation of elementary functions \\
3: Surveillance of Number Ranges \\
3.1 Introduction \\
3.2 Allowable number ranges \\
3.3 Basic real arithmetic operations \\
3.4 The quadratic equation \\
3.5 Complex arithmetic operations \\
4: Solution of Equations \\
4.1 Introduction \\
4.2 Attainable accuracy \\
4.3 Graphical methods \\
4.4 The method of bisection \\
4.5 The method of false position \\
4.6 The secant method \\
4.7 General properties of iterative methods \\
4.8 Generation of iterative methods \\
4.9 The Newton method \\
4.10 Muller's method \\
4.11 Orders of convergence of iterative methods \\
4.12 Acceleration of the convergence \\
4.13 Systems of nonlinear equations \\
5: Roots of Polynomial Equations \\
5.1 Introduction \\
5.2 General properties of polynomials \\
5.3 The Newton method and related methods \\
5.4 Muller's method and Cauchy's method \\
5.5 Location of the roots \\
5.6 Root acceptance and refinement \\
5.7 Matrix related methods: the modified Bernoulli
method \\
5.8 Matrix related methods: the IP method \\
5.9 Polyalgorithms \\
5.10 Other methods \\
6: Interpolation and Approximation \\
6.1 Introduction \\
6.2 Linear interpolation \\
6.3 Convergence and accuracy of linear interpolation
\\
6.4 Lagrangian interpolation \\
6.5 Convergence and accuracy of Lagrangian
interpolation \\
6.6 Interpolation with equal intervals \\
6.7 Hermite interpolation \\
6.8 Limitations on polynomial interpolation: smooth
interpolation \\
6.9 Inverse interpolation \\
6.10 Approximation by polynomials \\
6.11 Least squares approximation by polynomials \\
6.12 Rational approximation \\
6.13 Trigonometric interpolation and approximation \\
6.14 Interpolation in two variables \\
7: Numerical Differentiation and Quadrature \\
7.1 Introduction \\
7.2 The method of undetermined weights \\
7.3 Numerical differentiation \\
7.4 Numerical quadrature --- equal intervals \\
7.5 The Euler--MacLaurin formula \\
7.6 Romberg integration \\
7.7 Error determination \\
7.8 Numerical quadrature --- unequal intervals \\
8: Ordinary Differential Equations \\
8.1 Introduction \\
8.2 Existence and uniqueness \\
8.3 Analytic methods \\
8.4 Integral equation formulation --- the Picard method
of successive approximations \\
8.5 The Euler method \\
8.6 Methods based on numerical quadrature \\
8.7 Error estimation for predictor-corrector methods
\\
8.8 A numerical example \\
8.9 Runge--Kutta methods \\
8.10 Methods based on numerical differentiation \\
8.11 Higher-order equations and systems of first-order
equations \\
8.12 The use of high-speed computers \\
Appendix A \\
Appendix B \\
Appendix C \\
Bibliography \\
Index",
}
@Article{Aird:1973:SUM,
author = "T. Aird and D. Dodson and E. Houstis and J. Rice",
title = "Statistics on the Use of Mathematical Subroutines from
a Computer Center Library",
journal = j-SIGNUM,
volume = "8",
number = "4",
pages = "8--9",
month = oct,
year = "1973",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Sep 1 10:14:44 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
}
@MastersThesis{Anjoorian:1973:EME,
author = "Harry Anjoorian",
title = "An example of microprogrammed extended-precision
floating-point arithmetic",
type = "Thesis ({M.A.})",
school = "California State University, Chico",
address = "Chico, CA, USA",
pages = "ix + 94",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units.; Electronic
digital computers --- Design and construction.",
}
@Article{Atkins:1973:PCA,
author = "David E. {Atkins, III} and Harvey L. Garner",
title = "Preface: Computer Arithmetic: An Introduction and
Overview [{Second IEEE Symposium on Computer
Arithmetic, May 15--16, 1972, University of
Maryland}]",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "549--551",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009104",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009104;
http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Atkins.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Article{Avizienis:1973:AAE,
author = "Algirdas Avi{\v{z}}ienis",
title = "Arithmetic Algorithms for Error-Coded Operands",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "567--572",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009108",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Avizienis.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Book{Barna:1973:ICD,
author = "Arpad Barna and Dan I. Porat",
title = "Integrated Circuits in Digital Electronics",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xi + 483",
year = "1973",
ISBN = "0-471-05050-4",
ISBN-13 = "978-0-471-05050-6",
LCCN = "TK7868.D5 B43",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@Article{Barsi:1973:ECP,
author = "F. Barsi and P. Maestrini",
title = "Error Correcting Properties of Redundant Residue
Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "3",
pages = "307--315",
month = mar,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1973.223711",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:18 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672304;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35074",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "The error correcting properties of the redundant
residue number systems (RNS) are investigated through a
more natural a approach than was previously known. The
necessary and sufficient condition for the correction
of a given error affecting a single \ldots{}",
}
@Article{Baugh:1973:TCP,
author = "C. R. Baugh and B. A. Wooley",
title = "A Two's Complement Parallel Array Multiplication
Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "12",
pages = "1045--1047",
month = dec,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1973.223648",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:37 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See comments
\cite{Blankenship:1974:CTC,Kroft:1974:CTC}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672241",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Besslich:1973:MDS,
author = "P. W. Besslich and S. Raman",
title = "Multiplication, Division and Square Root Extraction
Methods for Electronic Desk Calculators",
journal = "Journal of the Institution of Telecommunication
Engineers (India)",
volume = "19",
number = "4",
month = apr,
year = "1973",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Brent:1973:PAV,
author = "Richard P. Brent",
title = "On the Precision Attainable with Various
Floating-Point Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "601--607",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009113",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:14:15 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Brent.pdf",
acknowledgement = ack-nj,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Article{Brent:1973:PEA,
author = "R. Brent and D. Kuck and K. Maruyama",
title = "The Parallel Evaluation of Arithmetic Expressions
Without Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "5",
pages = "532--534",
month = may,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1973.223757",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:23 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672350",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Cappa:1973:AIA,
author = "M. Cappa and V. C. Hamacher",
title = "An Augmented Iterative Array for High-Speed Binary
Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "2",
pages = "172--175",
month = feb,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1973.223680",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:15 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See comments \cite{Gardiner:1974:CAI}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672273",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Cody:1973:SDN,
author = "William J. {Cody, Jr.}",
title = "Static and Dynamic Numerical Characteristics of
Floating-Point Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "598--601",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009112",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:14:15 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Cody.pdf",
acknowledgement = ack-nj,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Article{Dorr:1973:REC,
author = "Fred W. Dorr and Cleve B. Moler",
title = "Roundoff error on the {CDC 6600\slash 7600}
computers",
journal = j-SIGNUM,
volume = "8",
number = "2",
pages = "24--26",
month = apr,
year = "1973",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:49:59 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Univ. California, Los Alamos, NM, USA",
fjournal = "ACM SIGNUM Newsletter",
keywords = "arithmetic; CDC 6600/7600 computers; computer; digital
arithmetic; program; roundoff error",
treatment = "P Practical; X Experimental",
}
@Article{Du:1973:CSS,
author = "Min-Wen Du and C. Dennis Weiss",
title = "Circuit Structure and Switching Function
Verification",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "618--625",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009116",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Du.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Article{Ercegovac:1973:REC,
author = "Milo{\v{s}} D. Ercegovac",
title = "Radix-16 Evaluation of Certain Elementary Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "561--566",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009107",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:15:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Ercegovac.pdf",
acknowledgement = ack-nj,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@TechReport{Erkio:1973:EAV,
author = "Hannu Erkio",
title = "An extension of {ALGOL} with variable precision
floating-point arithmetic",
type = "Series {A}. Report",
number = "1973/2",
institution = "University of Helsinki, Dept. of Computer Science",
address = "Helsinki",
pages = "ii + 20",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ALGOL (Computer program language); Floating-point
arithmetic",
}
@Article{Fettweis:1973:RNA,
author = "A. Fettweis",
title = "Roundoff noise and attenuation sensitivity in digital
filters with fixed-point arithmetic",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "20",
number = "2",
pages = "174--175",
month = mar,
year = "1973",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "A general expression is established which relates the
output roundoff noise generated by a fixed-point
multiplier in a digital filter to the sensitivity of
the filter attenuation with respect to the
corresponding multiplier coefficient. It confirms
\ldots{}",
}
@Article{Gelenbe:1973:UAE,
author = "Erol Gelenbe",
title = "A Unified Approach to the Evaluation of a Class of
Replacement Algorithms",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "611--618",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009115",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Gelenbe.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Article{Green:1973:NTF,
author = "D. H. Green and R. G. Kelsch",
title = "Nonlinear Ternary Feedback Shift Registers",
journal = j-COMP-J,
volume = "16",
number = "4",
pages = "360--367",
month = nov,
year = "1973",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:52:16 MDT 2000",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/160360.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/360.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/361.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/362.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/363.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/364.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/365.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/366.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/367.tif",
acknowledgement = ack-nhfb,
classcodes = "B1260 (Pulse circuits); B1265 (Digital electronics);
C5120 (Logic and switching circuits); C5230 (Digital
arithmetic methods)",
classification = "722",
corpsource = "Univ. Manchester Inst. Sci. Technol., UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "arithmetic; coding theory; communications; computers,
digital; digital arithmetic; digital computers;
feedback shift registers; functions; nonlinear;
polynomial domain representation; shift registers;
ternary",
treatment = "T Theoretical or Mathematical",
}
@Book{Hamming:1973:NMS,
author = "R. W. (Richard Wesley) Hamming",
title = "Numerical methods for scientists and engineers",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
edition = "Second",
pages = "ix + 721",
year = "1973",
ISBN = "0-07-025887-2",
ISBN-13 = "978-0-07-025887-7",
LCCN = "QA297 .H28 1973",
bibdate = "Fri Aug 20 09:12:08 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "International series in pure and applied mathematics",
acknowledgement = ack-nhfb,
subject = "Numerical analysis; Data processing",
}
@Article{Jacobsohn:1973:CDA,
author = "David H. Jacobsohn",
title = "A Combinatoric Division Algorithm for Fixed-Integer
Divisors",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "608--610",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009114",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Jacobsohn.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@TechReport{Kahan:1973:IAL,
author = "W. Kahan",
title = "Implementation of algorithms (lecture notes by {W. S.
Haugeland} and {D. Hough})",
type = "Technical report",
number = "20",
institution = "Department of Computer Science",
address = "Berkeley, CA, USA",
year = "1973",
bibdate = "Tue Aug 28 05:28:07 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
remark = "This paper contains the modified compensating
summation algorithm wherein `e = (temp - s) + y' is
replaced by `f = 0; if (sign(temp) == sign(y)) {f =
(0.46*s - s) + s} e = ((temp - f) - (s - f)) + y',
cited in e.g.,
\cite{Dalhquist:1974:NM,Higham:1993:AFP}. Kahan remarks
``The mysterious constant 0.46, which could perhaps be
any number between 0.25 and 0.50, and the fact that the
proof requires a consideration of known machines
designs, indicate that this algorithm is not an advance
in computer science.''",
}
@Article{Kan:1973:CEA,
author = "E. Kan and J. Aggarwal",
title = "Correction to {``Error Analysis of Digital Filters
Employing Floating-Point Arithmetic''}",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "20",
number = "5",
pages = "617--618",
month = sep,
year = "1973",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Kan:1971:EAD}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
}
@Article{Kanani:1973:NCS,
author = "Dhirubhai V. Kanani and Kenneth H. O'Keefe",
title = "A Note on Conditional-Sum Addition for Base $ - 2 $
Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "626--626",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009117",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:26 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009117;
http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Kanani.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2; negative base",
}
@Article{Kaneko:1973:LCO,
author = "T. Kaneko",
title = "Limit-cycle oscillations in floating-point digital
filters",
journal = j-IEEE-TRANS-AUDIO-ELECTROACOUST,
volume = "21",
number = "2",
pages = "100--106",
month = apr,
year = "1973",
CODEN = "ITADAS",
ISSN = "0018-9278",
ISSN-L = "0018-9278",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Audio and Electroacoustics",
summary = "In a digital filter realized with fixed-point
arithmetic, there is a peculiar phenomenon known as
limit-cycle oscillation, which is due to roundoff
errors. For floating-point arithmetic, it has been
conjectured that its amplitude is negligibly small,
\ldots{}",
}
@Article{Kaneko:1973:LRE,
author = "Toyohisa Kaneko and Bede Liu",
title = "On Local Roundoff Errors in Floating-Point
Arithmetic",
journal = j-J-ACM,
volume = "20",
number = "3",
pages = "391--398",
month = jul,
year = "1973",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/321765.321771",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "65G05",
MRnumber = "49 8318",
bibdate = "Tue Oct 09 10:18:49 2007",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A bound on the relative error in floating-point
addition using a single-precision accumulator with
guard digits is derived. It is shown that even with a
single guard digit, the accuracy can be almost as good
as that using a double-precision accumulator. A
statistical model for the roundoff error in
double-precision multiplication and addition is also
derived. The model is confirmed by experimental
measurements.",
acknowledgement = ack-nhfb # " and " # ack-nj,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
reviewer = "V. V. Ivanov",
}
@Article{Kielbasinski:1973:SAC,
author = "Andrzej Kie{\l}basi{\'n}ski",
title = "Summation algorithm with corrections and some of its
applications",
journal = j-MATH-STOS,
volume = "1",
pages = "22--41",
year = "1973",
bibdate = "Tue Aug 28 06:06:57 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "In Polish.",
acknowledgement = ack-nhfb,
fjournal = "Math. Stos.",
keywords = "accurate floating-point summation",
remark = "The author's name is correct [verified by a Polish
colleague who knows the author]: some references have
it incorrectly as Kie{\l}baszi{\'n}ski.",
}
@Article{Kinoshita:1973:GDS,
author = "E. Kinoshita and H. Kosako and Y. Kojima",
title = "General Division in the Symmetric Residue Number
System",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "2",
pages = "134--142",
month = feb,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1973.223674",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672267;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35073",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "In the residue number system, the arithmetic
operations of addition, subtraction, and multiplication
are executed in the same period of time without the
need for interpositional carry. There is a hope for
high-speed operation if residue arithmetic \ldots{}",
}
@Article{Kreifelts:1973:OBF,
author = "T. Kreifelts",
title = "{Optimale Basiswahl f{\"u}r eine
Gleitkomma-Arithmetik} \toenglish {Optimal Choice of
Basis for a Floating-Point Arithmetic} \endtoenglish",
journal = j-COMPUTING,
volume = "11",
number = "??",
pages = "353--363",
month = "????",
year = "1973",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Kreifelts:1973:OBG,
author = "Thomas Kreifelts",
title = "{Optimale Basiswahl f{\"u}r eine
Gleitkomma-Arithmetik}. ({German}) [{Optimal} Choice of
Basis for a Floating-Point Arithmetic]",
journal = j-COMPUTING,
volume = "11",
number = "4",
pages = "353--363",
month = dec,
year = "1973",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:51 MST 2001",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/computing.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
note = "See correction \cite{Kreifelts:1975:OBF}.",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "Inst. Numerische Datenverarbeitung, Bonn, West
Germany",
classification = "723; 921; C5230",
description = "digital arithmetic",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Comput (Vienna/NY)",
keywords = "base; computer programming; floating point arithmetic;
mathematical techniques; optimal choice; rounding
errors",
language = "German",
}
@Article{Kuki:1973:SSA,
author = "H. Kuki and W. J. Cody",
title = "A Statistical Study of the Accuracy of Floating Point
Number Systems",
journal = j-CACM,
volume = "16",
number = "4",
pages = "223--230",
month = apr,
year = "1973",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68A20 (65G05)",
MRnumber = "51 2344",
MRreviewer = "I. Kaufmann",
bibdate = "Wed Aug 31 13:47:33 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents the statistical results of tests
of the accuracy of certain arithmetic systems in
evaluating sums, products and inner products, and
analytic error estimates for some of the computations.
The arithmetic systems studied are 6-digit hexadecimal
and 22-digit binary floating point number
representations combined with the usual chop and round
modes of arithmetic with various numbers of guard
digits, and with a modified round mode with guard
digits. In a certain sense, arithmetic systems
differing only in their use of binary or hexadecimal
number representations are shown to be approximately
statistically equivalent in accuracy. Further, the
usual round mode with guard digits is shown to be
statistically superior in accuracy to the usual chop
mode in all cases save one. The modified round mode is
found to be superior to the chop mode in all cases.",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
classification = "723",
corpsource = "Univ. Chicago, IL, USA",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
journalabr = "Commun ACM",
keywords = "accuracy; arithmetic; computer programming; digital
arithmetic; error analysis; floating point arithmetic;
floating point number systems; guard digits; number
representation; rounding; statistical study",
oldlabel = "KukiC73",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/KukiC73",
}
@Article{Larson:1973:HSM,
author = "R. H. Larson",
title = "High Speed Multiply Using Four Input Carry Save
Adder",
journal = j-IBM-TDB,
volume = "??",
number = "??",
pages = "2053--2054",
month = dec,
year = "1973",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Fri Jun 24 20:46:32 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Article{Larson:1973:MSM,
author = "R. H. Larson",
title = "Medium Speed Multiply",
journal = j-IBM-TDB,
volume = "??",
number = "??",
pages = "2055--2055",
month = dec,
year = "1973",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Fri Jun 24 20:42:28 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
}
@PhdThesis{Lee:1973:SFP,
author = "Keng Ho Lee",
title = "Survey of floating-point software arithmetics and
basic library mathematical functions",
type = "Thesis ({Ph.D.})",
school = "Glasgow University",
address = "Glasgow, Scotland",
year = "1973",
bibdate = "Thu May 09 08:34:15 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Majithia:1973:NBL,
author = "J. C. Majithia and D. Levan",
title = "A note on base-2 logarithm computations",
journal = j-PROC-IEEE,
volume = "61",
number = "10",
pages = "1519--1520",
month = oct,
year = "1973",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 18:05:03 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "The well-known methods of iteration used suitably can
yield a more accurate and rapidly convergent
computation for the values of many functions. One
typical example is the base-2 logarithm-antilogarithm
computation. Some recently proposed techniques
\ldots{}",
}
@TechReport{Malcolm:1973:MAP,
author = "Michael A. Malcolm",
title = "A machine-independent {ALGOL} procedure for accurate
floating-point summation",
type = "Technical report",
number = "STAN-CS-73-374",
institution = "Stanford University, Computer Science Department",
address = "Stanford, CA, USA",
pages = "6",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ALGOL (Computer program language)",
}
@PhdThesis{Malcolm:1973:PAF,
author = "Michael A. Malcolm",
title = "Part {I}: On accurate floating-point summation; Part
{II}: Computation of nonlinear spline functions",
type = "Thesis ({Ph.D.})",
school = "Dept. of Computer Science, Stanford University",
address = "Stanford, CA, USA",
pages = "ix + 129",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; Interpolation;
spline theory",
}
@Article{Marasa:1973:SSC,
author = "John D. Marasa and David W. Matula",
title = "A simulated study of correlated error propagation in
various finite-precision arithmetics",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "587--597",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009111",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon May 20 05:07:23 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Marasa.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Article{Metropolis:1973:ABC,
author = "Nicholas C. Metropolis",
title = "Analyzed Binary Computing",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "573--576",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009109",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Mar 21 09:24:37 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A single format for the representation of numbers in a
computer is proposed to accommodate both exact and
inexact quantities. A consistent set of rules is
described for addition (subtraction), multiplication,
and division of such quantities, both within their
separate types, as well as in combination. Error
correlation aside, the propagation of inherent errors
is monitored in operations with at least one imprecise
value. A definitive algorithm must, of course take into
account any correlations of inherent errors; these
correlations must be recognized and incorporated into
the algorithm by the numerical analyst, not by the
logical designer of the computer.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2; control of propagated errors; floating-point
representation; representation error; significant digit
arithmetic",
}
@Article{Metropolis:1973:SAC,
author = "N. Metropolis and Gian-Carlo Rota and S. Tanny",
title = "Significance arithmetic: the carrying algorithm",
journal = j-J-COMB-THEORY-A,
volume = "14",
pages = "386--421",
month = may,
year = "1973",
CODEN = "JCBTA7",
ISSN = "0097-3165 (print), 1096-0899 (electronic)",
ISSN-L = "0097-3165",
MRclass = "10A30 (02E10)",
MRnumber = "MR0321857 (48 \#222)",
MRreviewer = "R. L. Goodstein",
bibdate = "Thu Nov 8 14:50:22 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0259.00001",
abstract = "It has been remarked that, in mathematics, a
notational deficiency is often a symptom of conceptual
obscurity. The starting point of this work is one such
deficiency. In ordinary binary arithmetic, a number
ending in a string of ones, such as $ 0.0110111 \ldots
{} $ is equal to the number obtained by replacing the
digit zero next to the string of ones by the digit one,
and the string of succeeding ones by zeros; in the
example, $ 0.0111000 $",
acknowledgement = ack-nhfb,
fjournal = "Journal of Combinatorial Theory. Series A",
}
@Article{Newbery:1973:EAF,
author = "A. C. R. Newbery",
title = "Error Analysis for {Fourier} Series Evaluation",
journal = j-MATH-COMPUT,
volume = "27",
number = "123",
pages = "639--644",
month = jul,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290B (Error analysis in numerical methods); C4110
(Error analysis in numerical methods)",
corpsource = "Univ. Kentucky, Lexington, KY, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "error analysis; evaluation; floating point; Fourier
series evaluation; numerical methods; polynomials;
recursive method; series (mathematics); trigonometric
polynomials",
treatment = "T Theoretical or Mathematical",
}
@Article{OKeefe:1973:RBE,
author = "Kenneth H. O'Keefe and John L. Wright",
title = "Remarks on Base Extension for Modular Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "9",
pages = "833--835",
month = sep,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009173",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:31 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009173",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@MastersThesis{Parker:1973:DHF,
author = "Tony Edwin Parker",
title = "Design of a hardware floating point processor for the
{PDP-8s}",
type = "Thesis ({B.S.})",
school = "Massachusetts Institute of Technology. Dept. of
Electrical Engineering",
address = "Cambridge, MA, USA",
pages = "19",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Paterson:1973:NNM,
author = "Michael S. Paterson and Larry J. Stockmeyer",
title = "On the Number of Nonscalar Multiplications Necessary
to Evaluate Polynomials",
journal = j-SIAM-J-COMPUT,
volume = "2",
number = "1",
pages = "60--66",
month = mar,
year = "1973",
CODEN = "SMJCAT",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
bibdate = "Mon Nov 29 10:57:40 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/2/1;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
Theory/Matrix.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
kwds = "na, polynomial, complexity",
xxnote = "Cited in \cite{govl:89}.",
}
@Article{Pittnauer:1973:AA,
author = "E. Pittnauer",
title = "{Eine Aussage {\"u}ber Alternanten} \toenglish {??}
\endtoenglish",
journal = j-NUM-MATH,
volume = "23",
number = "??",
pages = "427--432",
month = "????",
year = "1973",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Pittnauer:1973:NPK,
author = "E. Pittnauer",
title = "{Numerische Polynomapproximation mit Knotenpolynomen}
\toenglish {Numerical Polynomial Approximations with
Knot Polynomials} \endtoenglish",
journal = j-NUM-MATH,
volume = "21",
number = "3",
pages = "256--263",
year = "1973",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
xxmonth = "(none)",
}
@Book{Randell:1973:ODC,
editor = "Brian Randell",
title = "The origins of digital computers: selected papers",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 464",
year = "1973",
ISBN = "0-387-06169-X, 3-540-06169-X",
ISBN-13 = "978-0-387-06169-6, 978-3-540-06169-4",
LCCN = "TK7888.3 .R36",
bibdate = "Wed Oct 13 09:24:25 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "See also later editions
\cite{Randell:1975:ODC,Randell:1982:ODC}.",
}
@Article{Richman:1973:VPE,
author = "Paul L. Richman",
title = "Variable-Precision Exponentiation",
journal = j-CACM,
volume = "16",
number = "1",
pages = "38--40",
month = jan,
year = "1973",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65D20",
MRnumber = "51 4631",
MRreviewer = "V. V. Ivanov",
bibdate = "Mon Jan 22 07:15:57 MST 2001",
bibsource = "Compendex database;
http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Richman73;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A previous paper presented an efficient algorithm,
called the Recomputation Algorithm, for evaluating a
rational expression to within any desired tolerance on
a computer which performs variable-precision arithmetic
operations. The Recomputation Algorithm can be applied
to expressions involving any variable-precision
operations having $ O(10^( - p) + \sum_i|E_i|) $ error
bounds, where $p$ denotes the operation's precision and
$ E_i $ denotes the error in the operation's $i$-th
argument. \par
This paper presents an efficient variable-precision
exponential operation with an error bound of the above
order. Other operations such as log, sin, and cos,
which have simple series expansions, can be handled
similarly.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
classification = "723; 921",
corpsource = "Bell Telephone Labs. Inc., Denver, CO, USA",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
journalabr = "Commun ACM",
keywords = "computer programming; digital arithmetic; error
analysis; exponential function; exponentiation;
interval arithmetic; mathematical programming; variable
precision; variable-precision",
oldlabel = "Richman73",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Richman73",
}
@Article{Robertson:1973:SIC,
author = "James E. Robertson and Kishor S. Trivedi",
title = "The status of investigations into computer hardware
design based on the use of continued fractions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "555--560",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009106",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 8 14:50:24 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Robertson.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2; continued fractions",
}
@Article{Roy:1973:ARC,
author = "P. K. Sinha Roy and C. L. Sheng",
title = "Author's Reply to Comments on {``Decomposition Method
of Determining Maximum Compatibles''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "627--627",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009119",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Sureshchander:1973:CDM}.",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Sureshchander.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@MastersThesis{Rubinfield:1973:FM,
author = "Louis P. Rubinfield",
title = "A floating-point macromodule",
type = "Thesis ({M.S.})",
school = "Washington Univ., Dept. of Electrical Engineering",
address = "St. Louis, MO, USA",
pages = "vii + 111",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Design and
construction.",
}
@Article{Sankar:1973:AAN,
author = "P. V. Sankar and S. Chakrabarti and E. V.
Krishnamurthy",
title = "Arithmetic Algorithms in a Negative Base",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "2",
pages = "120--125",
month = feb,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1973.223671",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:14 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672264",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
}
@Article{Sankar:1973:DDA,
author = "P. V. Sankar and S. Chakrabarti and E. V.
Krishnamurthy",
title = "Deterministic Division Algorithm in a Negative Base",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "2",
pages = "125--128",
month = feb,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1973.223672",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:14 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672265",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
}
@Article{Schatte:1973:VMG,
author = "Peter Schatte",
title = "{Zur Verteilung der Mantisse in der
Gleitkommadarstellung einer Zufallsgr{\"o}{\ss}e}.
({German}) [Distribution of the mantissa in the
floating-point representation of a random variable]",
journal = j-Z-ANGE-MATH-MECH,
volume = "53",
number = "??",
pages = "553--565",
month = "????",
year = "1973",
CODEN = "ZAMMAX",
ISSN = "0044-2267 (print), 1521-4001 (electronic)",
ISSN-L = "0044-2267",
bibdate = "Mon Nov 14 16:35:28 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und
Mechanik}",
language = "German",
}
@Article{Schmid:1973:BLIa,
author = "H. Schmid",
title = "{BCD} logic {I}: {BCD} -- logic of many uses",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "13",
pages = "90--95",
month = jun,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 08 08:17:30 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
}
@Article{Schmid:1973:BLIb,
author = "H. Schmid",
title = "{BCD} logic {II}: {BCD} multiplication",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "14",
pages = "62--69",
month = jul,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
}
@Article{Schmid:1973:BLIc,
author = "H. Schmid",
title = "{BCD} logic {III}: {BCD} division",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "15",
pages = "86--92",
month = jul,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
}
@Article{Schmid:1973:BLId,
author = "H. Schmid",
title = "{BCD} logic {IV}: {BCD} decimal-point location",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "16",
pages = "80--84",
month = aug,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
keywords = "decimal floating-point arithmetic",
}
@Article{Schmid:1973:BLVa,
author = "H. Schmid",
title = "{BCD} logic {V}: {BCD} square root",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "17",
pages = "62--69",
month = aug,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
}
@Article{Schmid:1973:BLVb,
author = "H. Schmid",
title = "{BCD} logic {VI}: {BCD} logarithms and exponentials",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "18",
pages = "118--123",
month = sep,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
}
@Article{Schmid:1973:BLVc,
author = "H. Schmid",
title = "{BCD} logic {VII}: {BCD} trig and hyperbolic
functions",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "19",
pages = "68--73",
month = sep,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
}
@Article{Sentance:1973:FAB,
author = "W. A. Sentance",
title = "A Further Analysis of {Benford's Law}",
journal = j-FIB-QUART,
volume = "11",
number = "5",
pages = "490--494",
month = dec,
year = "1973",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:58:46 MDT 2011",
bibsource = "http://www.fq.math.ca/11-5.html;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/11-5/sentance.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Shea:1973:NDN,
author = "Dale D. Shea",
title = "On the Number of Divisions Needed in Finding the
Greatest Common Divisor",
journal = j-FIB-QUART,
volume = "11",
number = "5",
pages = "508--510",
month = dec,
year = "1973",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:58:46 MDT 2011",
bibsource = "http://www.fq.math.ca/11-5.html;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/11-5/shea.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Singh:1973:MOA,
author = "S. Singh and R. Waxman",
title = "Multiple Operand Addition and Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "2",
pages = "113--120",
month = feb,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1973.223670",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:14 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672263",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Sites:1973:FPS,
author = "Richard L. Sites",
title = "Floating point significance interrupt proposal",
journal = j-COMP-ARCH-NEWS,
volume = "2",
number = "1",
pages = "10--12",
month = jan,
year = "1973",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 12 09:40:28 MDT 2006",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The purpose of this proposal is to aid numerical
analysts in observing the significance of results in
floating-point calculations. This proposal is not a
cure-all, but it does attempt to a first, high-payoff
step in understanding and analyzing floating-point
algorithms. This proposal is specifically for IBM
360/370 architecture, but the ideas are applicable to
all machines.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
remark = "The author observes that register clearing by
subtraction is common, and is one of the reasons that
``all IBM language processors execute with significance
masked off.'' He proposes suppressing the significance
interrupt in subtractions when both operands are
equal.",
}
@Article{Sjoding:1973:NVR,
author = "T. Sjoding",
title = "Noise variance for rounded two's complement product
quantization",
journal = j-IEEE-TRANS-AUDIO-ELECTROACOUST,
volume = "21",
number = "4",
pages = "378--380",
month = aug,
year = "1973",
CODEN = "ITADAS",
ISSN = "0018-9278",
ISSN-L = "0018-9278",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Audio and Electroacoustics",
summary = "The Halyo-McAlpine discrete model for product
quantization is reconstructed using an error variable
set having an even number of members. It is shown in
this case that the noise variance associated with a
continuous model becomes an upper rather \ldots{}",
}
@Article{Spira:1973:CTA,
author = "Philip M. Spira",
title = "Computation Times of Arithmetic and {Boolean}
functions in $ (d, r) $ circuits",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "552--555",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009105",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Spira.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Book{Stone:1973:DMS,
author = "Harold S. Stone",
title = "Discrete mathematical structures and their
applications",
publisher = "Science Research Associates",
address = "Chicago, IL, USA",
pages = "401",
year = "1973",
LCCN = "QA162 .S877d; QA162 .S77",
bibdate = "Fri Nov 9 19:24:02 MST 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
series = "The SRA computer science series",
acknowledgement = ack-nhfb,
subject = "Algebra, Abstract; Group theory; Machine theory",
tableofcontents = "Foundations of discrete mathematics. \\
Groups. \\
The P\'olya theory of enumeration. \\
Applications of group theory to computer design. \\
Group codes. \\
Semigroups. \\
Finite-state machines. \\
Rings and fields. \\
Linear -finite-state machines. \\
Boolean algebra with applications to computer design.",
}
@Article{Sureshchander:1973:CDM,
author = "Sureshchander",
title = "Comments on {``Decomposition Method of Determining
Maximum Compatibles''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "627--627",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009118",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Roy:1973:ARC}.",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Sureshchander.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
xxnote = "Author has only a single name",
}
@Article{Swartzlander:1973:QSM,
author = "E. E. {Swartzlander, Jr.}",
title = "The Quasi-Serial Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "4",
pages = "317--321",
month = apr,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1973.223717",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:19 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672310",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@PhdThesis{Tanny:1973:SSA,
author = "Stephen Michael Tanny",
title = "Studies in Significance Arithmetic",
type = "{Ph.D.} thesis",
school = "Massachusetts Institute of Technology",
address = "Cambridge, MA, USA",
pages = "195",
year = "1973",
bibdate = "Tue Oct 22 06:18:19 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://search.proquest.com/pqdtglobal/docview/302720894",
acknowledgement = ack-nhfb,
remark = "Full text is not available in ProQuest.",
}
@Article{Urabe:1973:CEA,
author = "Minoru Urabe",
title = "Component-wise error analysis of iterative methods
practiced on a floating-point system",
journal = j-MEM-FAC-SCI-KYUSHU-UNIV-A,
volume = "27",
pages = "23--64",
year = "1973",
CODEN = "MFKAAF",
ISSN = "0373-6385",
ISSN-L = "0373-6385",
MRclass = "65H10",
MRnumber = "48 1457",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Memoirs of the Faculty of Science, Kyushu Imperial
University. Series A, Mathematics = Kyushu Teikoku
Daigaku Rigakubu kiyo",
reviewer = "D. C. Handscomb",
}
@PhdThesis{Wiatrowski:1973:DFP,
author = "Claude A. Wiatrowski",
title = "Design of a floating-point processor for digital
simulation",
type = "Thesis ({Ph.D.} - Electrical Engineering)",
school = "University of Arizona",
address = "Tucson, AZ, USA",
pages = "107",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units.; Computer storage
devices.",
}
@Article{Yau:1973:ECR,
author = "S. S.-S. Yau and Yu-Cheng Liu",
title = "Error Correction in Redundant Residue Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "1",
pages = "5--11",
month = jan,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1973.223594",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:11 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672187;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35069",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "Two error-correcting algorithms for redundant residue
number systems are presented, one for single
residue-error correction and the other for burst
residue-error correction. Neither algorithm requires
table lookup, and hence their implementation \ldots{}",
}
@TechReport{Yohe:1973:FFPa,
author = "J. M. Yohe",
title = "Foundations of floating point computer arithmetic",
type = "{MRC} Technical Summary Report",
number = "1302",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
pages = "25",
month = jan,
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A formal structure, within which computer arithmetic
operations may be defined, is described. Several
floating point arithmetic schemes are defined within
this context. The structure described in the paper
includes, as a sub-structure, the significance spaces
of Matula.",
acknowledgement = ack-nhfb,
keywords = "Computers.; Floating-point arithmetic.",
remark = "January 1973. Sponsored by Army Research Office,
Durham, NC, USA.",
}
@Article{Yohe:1973:IBS,
author = "J. M. Yohe",
title = "Interval Bounds for Square Roots and Cube Roots",
journal = j-COMPUTING,
volume = "11",
number = "1",
pages = "51--57",
year = "1973",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:51 MST 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-jr # " and " # ack-nhfb,
affiliation = "Univ. Wisconsin, Madison, WI, USA",
classification = "C5230",
description = "digital arithmetic; error analysis",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
keywords = "binary computers; cube roots; error analysis; interval
bounds; machine representable number; optimal upward
directed rounding; smallest machine representable
interval; square roots",
}
@Article{Yohe:1973:RFP,
author = "J. Michael Yohe",
title = "Roundings in Floating-Point Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "577--586",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009110",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:25 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009110;
http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Yohe.pdf",
abstract = "In this paper we discuss directed roundings and
indicate how hardware might be designed to produce
proper upward directed, downward directed, and certain
commonly used symmetric roundings. Algorithms for the
four binary arithmetic operations and for rounding are
presented, together with proofs of their correctness;
appropriate formulas for a priori error analysis of
these algorithms are presented. Some of the basic
applications of directed roundings are surveyed.",
acknowledgement = ack-jr # "\slash " # ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Article{Zohar:1973:DCR,
author = "Shalhav Zohar",
title = "{A/D} Conversion for Radix ($ - 2$)",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "7",
pages = "698--701",
month = jul,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009137",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:28 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009137",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
}
@Article{Agrawal:1974:NCL,
author = "D. P. Agrawal",
title = "Negabinary carry-look-ahead adder and fast
multiplier",
journal = j-ELECT-LETTERS,
volume = "10",
number = "??",
pages = "312--313",
month = jul,
year = "1974",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Thu Nov 06 06:16:38 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "negative base",
}
@Article{Banerji:1974:NIM,
author = "D. K. Banerji",
title = "A Novel Implementation Method for Addition and
Subtraction in Residue Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "1",
pages = "106--109",
month = jan,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1974.223790",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:29 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672383;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35077",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "This correspondence describes an implementation scheme
for the operations of addition and subtraction in the
residue number systems. The method is based on the
property that the set of residues modulo m form a
finite group under addition and \ldots{}",
}
@Article{Banerji:1974:URA,
author = "D. K. Banerji",
title = "On the Use of Residue Arithmetic for Computation",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "12",
pages = "1315--1317",
month = dec,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.223855",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:38 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672448",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Barsi:1974:EDC,
author = "F. Barsi and P. Maestrini",
title = "Error Detection and Correction by Product Codes in
Residue Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "9",
pages = "915--924",
month = sep,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1974.224055",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:35 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672648;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35088",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "The arithmetic error detecting and correcting
capabilities of product (AN) codes in residue number
systems (RNS) are described. The redundancy necessary
and sufficient to allow single residue digit error
detection or correction is determined, under \ldots{}",
}
@Article{Bauer:1974:CGR,
author = "F. L. Bauer",
title = "Computational Graphs and Rounding Error",
journal = j-SIAM-J-NUMER-ANAL,
volume = "11",
number = "1",
pages = "87--96",
month = mar,
year = "1974",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0711010",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65G05",
MRnumber = "356482",
MRreviewer = "L. B. Rall",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib;
http://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
JSTOR database; Theory/auto.diff.bib",
note = "In memoriam George Forsythe.",
URL = "https://www.jstor.org/stable/2156433",
ZMID = "03527739",
ZMnumber = "0337.65028",
acknowledgement = ack-nhfb,
author-dates = "Friedrich (``Fritz'') Ludwig Bauer (10 June 1924--26
March 2015)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
referred = "[Char91a]; [Irim91a].",
}
@Article{Blankenship:1974:CTC,
author = "P. E. Blankenship",
title = "Comments on {``A Two's Complement Parallel Array
Multiplication Algorithm''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "12",
pages = "1327--1327",
month = dec,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.223862",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:38 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Baugh:1973:TCP,Kroft:1974:CTC}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672455",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Boyes:1974:BNS,
author = "J. D. Boyes",
title = "Binary Noise Sources Incorporating Modulo-{$N$}
Dividers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "5",
pages = "550--552",
month = may,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.223980",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:33 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672573",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Brent:1974:FEP,
author = "Barry Brent",
title = "Functional Equations with Prime Roots from Arithmetic
Expressions for {$ G_\alpha $}",
journal = j-FIB-QUART,
volume = "12",
number = "2",
pages = "199--207",
month = apr,
year = "1974",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:58:50 MDT 2011",
bibsource = "http://www.fq.math.ca/12-2.html;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/12-2/brent1.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Brown:1974:BDE,
author = "D. A. H. Brown",
title = "Biquinary Decimal Error Detection Codes with One, Two
and Three Check Digits",
journal = j-COMP-J,
volume = "17",
number = "3",
pages = "201--204",
month = aug,
year = "1974",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/201.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/202.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/203.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/204.tif",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
classification = "722; 723",
corpsource = "Royal Radar Establ., Malvern, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "biquinary decimal error detection codes; check digits;
computer systems, digital; computers --- Debugging;
decimal floating-point arithmetic; digital arithmetic;
error detection codes; polynomial coding",
treatment = "T Theoretical or Mathematical",
}
@Article{Brown:1974:SEC,
author = "D. A. H. Brown",
title = "Some Error Correcting Codes for Certain Transposition
and Transcription Errors in Decimal Integers",
journal = j-COMP-J,
volume = "17",
number = "1",
pages = "9--12",
month = feb,
year = "1974",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Nov 28 16:12:29 2003",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/10.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/11.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/12.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/9.tif",
acknowledgement = ack-mfc # " and " # ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques)",
classification = "731",
corpsource = "Royal Radar Establ., Malvern, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "algorithm; block; codes, symbolic; cyclic; decimal
floating-point arithmetic; decimal integers; digital
arithmetic; error correcting codes; error correction
codes; modulus 11; transcription; transposition",
treatment = "P Practical",
}
@Article{Carta:1974:HLR,
author = "David G. Carta",
title = "Help!!: {The} Lost Reference: ({A} Modified {Newton}
Method for Square Roots)",
journal = j-SIGNUM,
volume = "9",
number = "4",
pages = "9--9",
month = oct,
year = "1974",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/1206085.1206086",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Jun 17 18:47:00 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Around 1970 I saw a journal article describing a
modified Newton iteration for square roots. It involved
changing the usual factor of 0.5 in $ x_{n + 1} = 0.5
(x_n + a / x_n) $ to $ c_n $ where $ c_n \rightarrow
0.5 $, thereby increasing the asymptotic rate of
convergence from $ e_{n + 1} = 0.5 e_n^2 $ to $ e_{n +
1} = 0.25 e_n^2 $.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
}
@Article{Catlin:1974:MR,
author = "Paul A. Catlin",
title = "On the Multiplication of Recurrences",
journal = j-FIB-QUART,
volume = "12",
number = "4",
pages = "365--367",
month = dec,
year = "1974",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:58:54 MDT 2011",
bibsource = "http://www.fq.math.ca/12-4.html;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/12-4/catlin2.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Chakrabarti:1974:DCA,
author = "S. Chakrabarti",
title = "Divide-and-Correct Algorithm for Division in a
Negative Base",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "9",
pages = "981--983",
month = sep,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.224066",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:35 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672659",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Chan:1974:REM,
author = "O. Chan and E. Jury",
title = "Roundoff error in multidimensional generalized
discrete transforms",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "21",
number = "1",
pages = "100--108",
month = jan,
year = "1974",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "The analysis of rounding error in the one-dimensional
fast Fourier transform (FFT) is extended to a class of
generalized orthogonal transforms [1] with a common
fast algorithm similar to the FFT algorithm. This class
includes the BInary FOurier \ldots{}",
}
@Book{Dahlquist:1974:NM,
author = "Germund Dahlquist and {\AA}ke Bj{\"o}rck and Ned
Anderson",
title = "Numerical Methods",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xviii + 573",
year = "1974",
ISBN = "0-13-627315-7",
ISBN-13 = "978-0-13-627315-8",
LCCN = "QA297 .D131 1969",
bibdate = "Tue Dec 14 22:44:59 1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
note = "Translated by Ned Anderson.",
series = "Prentice-Hall Series in Automatic Computation",
acknowledgement = ack-nhfb,
shorttableofcontents = "1: Some General Principles of Numerical
Calculation / 1 \\
2: How to Obtain and Estimate Accuracy in Numerical
Calculations / 21 \\
3: Numerical Uses of Series / 60 \\
4: Approximation of Functions / 81 \\
5: Numerical Linear Algebra / 137 \\
6: Nonlinear Equations / 218 \\
7: Finite Differences with Applications to Numerical
Integration, Differentiation, and Interpolation / 255
\\
8: Differential Equations / 330 \\
9: Fourier Methods / 405 \\
10: Optimization / 422 \\
11: The Monte Carlo Method and Simulation / 448 \\
12: Solutions to Problems / 465 \\
13: Bibliography and Published Algorithms / 536 \\
Index by Subject to Algorithms, 1960--1970 / 548 \\
Appendix Tables / 563 \\
Index / 565",
tableofcontents = "Preface / xvii \\
Conventions / xix \\
1: Some General Principles of Numerical Calculation / 1
\\
1.1. Introduction / 1 \\
1.2. Some Common Ideas and Concepts in Numerical
Methods / 2 \\
1.3. Numerical Problems and Algorithms / 13 \\
1.3.1. Definitions / 13 \\
1.3.2. Recursive Formulas; Homer's Rule / 14 \\
1.3.3. An Example of Numerical Instability / 16 \\
2: How to Obtain and Estimate Accuracy in Numerical
Calculations / 21 \\
2.1. Basic Concepts in Error Estimation / 21 \\
2.1.1. Introduction / 21 \\
2.1.2. Sources of Error / 22 \\
2.1.3. Absolute and Relative Errors / 23 \\
2.1.4. Rounding and Chopping / 24 \\
2.2 Propagation of Errors / 26 \\
2.2.1. Simple Examples of Error Analysis / 26 \\
2.2.2. The General Formula for Error Propagation;
Maximum Error and Standard Error / 29 \\
2.2.3. On the Practical Application of Error Estimation
/ 34 \\
2.2.4. The Use of Experimental Perturbations / 36 \\
2.2.5. Automatic Control of Accuracy / 37 \\
2.3. Number Systems; Floating and Fixed Representation
/ 42 \\
2.3.1. The Position System / 42 \\
2.3.2. Floating and Fixed Representation / 43 \\
2.3.3. Floating Decimal Point / 44 \\
2.3.4. Fixed Decimal Point / 46 \\
2.3.5. Round-off Errors in Computation with Floating
Arithmetic Operations / 46 \\
2.4. Backward Error Analysis; Condition Numbers / 51
\\
2.4.1. Backward Error Analysis / 51 \\
2.4.2. Condition Numbers for Problems and Algorithms /
53 \\
2.4.3. Geometrical Illustration of Error Analysis / 56
\\
3: Numerical Uses of Series / 60 \\
3.1. Elementary Uses of Series / 60 \\
3.1.1. Simple Examples / 60 \\
3.1.2. Estimating the Remainder / 62 \\
3.1.3. Power Series / 65 \\
3.2. Acceleration of Convergence / 71 \\
3.2.1. Slowly Converging Alternating Series / 71 \\
3.2.2. Slowly Converging Series with Positive Terms /
73 \\
3.2.3. Other Simple Ways to Accelerate Convergence / 74
\\
3.2.4. Ill-Conditioned Series / 75 \\
3.2.5. Numerical Use of Divergent Series / 77 \\
4: Approximation of Functions / 81 \\
4.1. Basic Concepts in Approximation / 81 \\
4.1.1. Introduction / 81 \\
4.1.2. The Idea of a Function Space / 84 \\
4.1.3. Norms and Seminorms / 85 \\
4.1.4. Approximation of Functions as a Geometric
Problem in Function Space / 87 \\
4.2. The Approximation of Functions by the Method of
Least Squares / 88 \\
4.2.t. Statement of the Problems / 88 \\
4.2.2. Orthogonal Systems / 89 \\
4.2.3. Solution of the Approximation Problem / 92 \\
4.3. Polynomials / 97 \\
4.3.1. Basic Terminology; the Weierstrass Approximation
Theorem / 97 \\
4.3.2. Triangle Families of Polynomials / 98 \\
4.3.3. A Triangle Family and Its Application to
Interpolation / 99 \\
4.3.4. Equidistant Interpolation and the Runge
Phenomenon / 101 \\
4.4. Orthogonal Polynomials and Applications / 104 \\
4.4.1. Tchebycheff Polynomials / 104 \\
4.4.2. Tchebycheff Interpolation and Smoothing / 106
\\
4.4.3. General Theory of Orthogonal Polynomials / 108
\\
4.4.4. Legendre Polynomials and Gram Polynomials / 113
\\
4.5. Complementary Observations on Polynomial
Approximation / 117 \\
4.5.1. Summary of the Use of Polynomials / 117 \\
4.5.2. Some Inequalities for $E_n(f)$ with Applications
to the Computation of Linear Functionals / 120 \\
4.5.3. Approximation in the Maximum Norm / 124 \\
4.5.4. Economization of Power Series; Standard
Functions / 125 \\
4.5.5. Some Statistical Aspects of the Method of Least
Squares / 126 \\
4.6. Spline Functions / 131 \\
5: Numerical Linear Algebra / 137 \\
5,1. Introduction / 137 \\
5.2. Basic Concepts of Linear Algebra / 138 \\
5.2.1. Fundamental Definitions / 138 \\
5.2.2. Partitioned Matrices / 140 \\
5.2.3. Linear Vector Spaces / 141 \\
5.2.4. Eigenvalues and Similarity Transformations / 142
\\
5.2.5. Singular-Value Decomposition and Pseudo-Inverse
/ 143 \\
5.3. Direct Methods for Solving Systems of Linear
Equations / 146 \\
5.3.1. Triangular Systems / 146 \\
5.3.2. Gaussian Elimination / 147 \\
5.3.3. Pivoting Strategies / 150 \\
5.3.4. $L U$-Decomposition / 152 \\
5.3.5. Compact Schemes for Gaussian Elimination / 157
\\
5.3.6. Inverse Matrices / 159 \\
5.4. Special Matrices / 162 \\
5.4.1. Symmetric Positive-Definite Matrices / 162 \\
5.4.2. Band Matrices / 165 \\
5.4.3. Large-Scale Linear Systems / 168 \\
5.4.4. Other Sparse Matrices / 169 \\
5.5. Error Analysis for Linear Systems / 174 \\
5.5.1. An Ill-Conditioned Example / 174 \\
5.5.2. Vector and Matrix Norms / 175 \\
5.5.3. Perturbation Analysis / 176 \\
5.5.4. Rounding Errors in Gaussian Elimination / 177
\\
5.5.5. Scaling of Linear Systems / 181 \\
5.5.6. Iterative Improvement of a Solution / 183 \\
5.6. Iterative Methods / 188 \\
5.7. Overdetermined Linear Systems / 196 \\
5.7.1. The Normal Equations / 197 \\
5.7.2. Orthogonalization Methods / 201 \\
5.7.3. Improvement of Least-Squares Solutions / 204 \\
5.7.4. Least-Squares Problems with Linear Constraints /
205 \\
5.8. Computation of Eigenvalues and Eigenvectors / 208
\\
5.8.1. The Power Method / 209 \\
5.8.2. Methods Based on Similarity Transformations /
211 \\
5.8.3. Eigenvalues by Equation Solving / 215 \\
5.8.4. The $Q R$-Algorithm / 216 \\
6: Nonlinear Equations / 218 \\
6.1. Introduction / 218 \\
6.2. Initial Approximations; Starting Methods / 219 \\
6.2.1. Introduction / 219 \\
6.2.2. The Bisection Method / 220 \\
6.3. Newton--Raphson's Method / 222 \\
6.4. The Secant Method / 227 \\
6.4.1. Description of the Method / 227 \\
6.4.2. Error Analysis for the Secant Method / 228 \\
6.4.3. Regula Falsi / 230 \\
6.4.4. Other Related Methods / 230 \\
6.5. General Theory of Iteration Methods / 233 \\
6.6. Error Estimation and Attainable Accuracy in
Iteration Methods / 238 \\
6.6.1. Error Estimation / 238 \\
6.6.2. Attainable Accuracy; Termination Criteria / 240
\\
6.7. Multiple Roots / 242 \\
6.8. Algebraic Equations / 243 \\
6.8.1. Introduction / 243 \\
6.8.2. Deflation / 245 \\
6.8.3. Ill-Conditioned Algebraic Equations / 246 \\
6.9. Systems of Nonlinear Equations / 248 \\
6.9.1. Iteration / 249 \\
6.9.2. Newton--Raphson's Method and Some Modifications
/ 249 \\
6.9.3. Other Methods / 251 \\
7: Finite Differences with Applications to Numerical
Integration, Differentiation, and Interpolation / 255
\\
7.1. Difference Operators and Their Simplest Properties
/ 255 \\
7.2. Simple Methods for Deriving Approximation Formulas
and Error Estimates / 263 \\
7.2.1. Statement of the Problems and Some Typical
Examples / 263 \\
7.2.2, Repeated Richardson Extrapolation / 269 \\
7.3. Interpolation / 275 \\
7.3.1. Introduction / 275 \\
7.3.2. When is Linear Interpolation Sufficient? / 276
\\
7.3.3. Newton's General Interpolation Formula / 277 \\
7.3.4. Formulas for Equidistant Interpolation / 279 \\
7.3.5. Complementary Remarks on Interpolation / 282 \\
7.3.6. Lagrange's Interpolation Formula / 284 \\
7.3.7. Hermite Interpolation / 285 \\
7.3.8. Inverse Interpolation / 286 \\
7.4. Numerical Integration / 290 \\
7.4.1. The Rectangle Rule, Trapezoidal Rule, and
Romberg's Method / 291 \\
7.4.2. The Truncation Error of the Trapezoidal Rule /
293 \\
7.4.3. Some Difficulties and Possibilities in Numerical
Integration / 294 \\
7.4.4. The Euler--Maclaurin Summation Formula / 297 \\
7.4.5. Uses of the Euler--Maclaurin Formula / 300 \\
7.4.6. Other Methods for Numerical Integration / 302
\\
7.5. Numerical Differentiation / 307 \\
7.6. The Calculus of Operators / 311 \\
7.6.1. Operator Algebra / 311 \\
7.6.2. Operator Series with Applications / 312 \\
7.7. Functions of Several Variables / 318 \\
7.7.1. Working with One Variable at a Time / 319 \\
7.7.2. Rectangular Grids / 319 \\
7.7.3. Irregular Triangular Grids / 322 \\
8: Differential Equations / 330 \\
8.1. Theoretical Background / 330 \\
8.1.1. Initial-Value Problems for Ordinary Differential
Equations / 330 \\
8.1.2. Error Propagation / 333 \\
8.1.3. Other Differential Equation Problems / 337 \\
8.2. Euler's Method, with Repeated Richardson
Extrapolation / 338 \\
8.3. Other Methods for Initial-Value Problems in
Ordinary Differential Equations / 342 \\
8.3.1. The Modified Midpoint Method / 342 \\
8.3.2. The Power-Series Method / 345 \\
8.3.3. Runge--Kutta Methods / 346 \\
8.3.4. Implicit Methods / 347 \\
8.3.5. Stiff Problems / 349 \\
8.3.6. Control of Step Size / 350 \\
8.3.7. A Finite-Difference Method for a Second-Order
Equation / 352 \\
8.4. Orientation on Boundary and Eigenvalue Problems
for Ordinary Differential Equations / 359 \\
8.4.1. Introduction / 359 \\
8.4.2. The Shooting Method / 359 \\
8.4.3. The Band Matrix Method / 361 \\
8.4.4. Numerical Example of an Eigenvalue Problem / 363
\\
8.5. Difference Equations / 367 \\
8.5.1. Homogeneous Linear Difference Equations with
Constant Coefficients / 368 \\
8.5.2. General Linear Difference Equations / 370 \\
8.5.3. Analysis of a Numerical Method with the Help of
a Test Problem / 372 \\
8.5.4. Linear Multistep Methods / 375 \\
8.6. Partial Differential Equations / 383 \\
8.6.1. Introduction / 383 \\
8.6.2. An Example of an Initial-Value Problem / 384 \\
8.6.3. An Example of a Boundary-Value Problem / 389 \\
8.6.4. Methods of Undetermined Coefficients and
Variational Methods / 392 \\
8.6.5. Finite-Element Methods / 395 \\
8.6.6. Integral Equations / 397 \\
9: Fourier Methods / 405 \\
9.1. Introduction / 405 \\
9.2. Basic Formulas and Theorems in Fourier Analysis /
406 \\
9.2.1. Functions of One Variable / 406 \\
9.2.2. Functions of Several Variables / 411 \\
9.3. Fast Fourier Analysis / 413 \\
9.3.1. An Important Special Case / 413 \\
9.3.2. Fast Fourier Analysis, General Case / 414 \\
9.4. Periodic Continuation of a Nonperiodic Function /
417 \\
9.5. The Fourier Integral Theorem / 419 \\
10: Optimization / 422 \\
10.1. Statement of the Problem, Definitions, and Normal
Form / 422 \\
10.2. The Simplex Method / 426 \\
10.3. Duality / 435 \\
10.4. The Transportation Problem and Some Other
Optimization Problems / 436 \\
10.5. Nonlinear Optimization Problems / 438 \\
10.5.1. Basic Concepts and Introductory Examples / 438
\\
10.5.2. Line Search / 440 \\
10.5.3. Algorithms for Unconstrained Optimization / 441
\\
10.5.4. Overdetermined Nonlinear Systems / 443 \\
10.5.5. Constrained Optimization / 444 \\
11: The Monte Carlo Method and Simulation / 448 \\
11.1. Introduction / 448 \\
11.2. Random Digits and Random Numbers / 449 \\
11.3. Applications; Reduction of Variance / 455 \\
11.4. Pseudorandom Numbers / 463 \\
12: Solutions to Problems / 465 \\
13: Bibliography and Published Algorithms / 536 \\
13.1. Introduction / 536 \\
13.2. General Literature in Numerical Analysis / 536
\\
13.3. Tables, Collections of Formulas, and Problems /
539 \\
13.4. Error Analysis and Approximation of Functions /
540 \\
13.5. Linear Algebra and Nonlinear Systems of Equations
/ 541 \\
13.6. Interpolation, Numerical Integration, and
Numerical Treatment of Differential Equations / 543 \\
13.7. Optimization; Simulation / 545 \\
13.8. Reviews, Abstracts and Other Periodicals / 547
\\
13.9. Survey of Published Algorithms / 548 \\
Index by Subject to Algorithms, 1960--1970 / 548 \\
Appendix Tables / 563 \\
Index / 565",
}
@Article{Davis:1974:USN,
author = "R. L. Davis",
title = "Uniform Shift Networks",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "3",
pages = "317--322",
month = mar,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224214",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 10:48:43 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Fateman:1974:PMP,
author = "Richard J. Fateman",
title = "Polynomial Multiplication, Powers, and asymptotic
Analysis: {Some} Comments",
journal = j-SIAM-J-COMPUT,
volume = "3",
number = "3",
pages = "196--213",
month = "????",
year = "1974",
CODEN = "SMJCAT",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
bibdate = "Mon Nov 29 10:57:57 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/3/3;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
Theory/auto.diff.bib; Theory/Comp.Alg.1.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
referred = "[Bren78a].",
}
@Article{Fettweis:1974:PFP,
author = "A. Fettweis",
title = "On properties of floating-point roundoff noise",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "22",
number = "2",
pages = "149--151",
month = apr,
year = "1974",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "The probability density and related properties of the
relative error due to rounding after floating-point
arithmetic operations can be computed from the
distributions of the mantissa and its absolute error.
Various results obtained, in particular, \ldots{}",
}
@Article{Fischer:1974:FLI,
author = "Michael J. Fischer and Larry J. Stockmeyer",
title = "Fast on-line integer multiplication",
journal = j-J-COMP-SYS-SCI,
volume = "9",
number = "3",
pages = "317--331",
month = dec,
year = "1974",
CODEN = "JCSSBM",
DOI = "https://doi.org/10.1016/S0022-0000(74)80047-4",
ISSN = "0022-0000 (print), 1090-2724 (electronic)",
ISSN-L = "0022-0000",
bibdate = "Tue Jan 29 15:25:28 MST 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jcompsyssci.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022000074800474",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computer and System Sciences",
journal-URL = "http://www.sciencedirect.com/science/journal/00220000",
}
@MastersThesis{Fischer:1974:FPP,
author = "David Michael Fischer",
title = "Floating point processor for teleoperator studies",
type = "Thesis ({M.S.})",
school = "Massachusetts Institute of Technology. Dept. of
Mechanical Engineering",
address = "Cambridge, MA, USA",
pages = "35 + 14",
year = "1974",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Gardiner:1974:CAI,
author = "A. B. Gardiner",
title = "Comments on {``An Augmented Iterative Array for High
Speed Division''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "3",
pages = "326--327",
month = mar,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.223931",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:31 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Cappa:1973:AIA}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672524",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Gentleman:1974:MAR,
author = "W. Morven Gentleman and Scott B. Marovich",
title = "More on Algorithms that Reveal Properties of Floating
Point Arithmetic Units",
journal = j-CACM,
volume = "17",
number = "5",
pages = "276--277",
month = may,
year = "1974",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/360980.361003",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:43:47 MST 2001",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#GentlemanM74;
http://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Malcolm:1972:ARP}.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Univ. Waterloo, Ont., Canada",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "algorithms; base of the arithmetic; digital
arithmetic; floating point arithmetic units; high
level; languages; trailing digits",
oldlabel = "GentlemanM74",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/GentlemanM74",
}
@Book{Hildebrand:1974:INA,
author = "Francis Begnaud Hildebrand",
title = "Introduction to numerical analysis",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
edition = "Second",
pages = "xiii + 669",
year = "1974",
ISBN = "0-07-028761-9",
ISBN-13 = "978-0-07-028761-7",
LCCN = "QA297 .H54 1974",
bibdate = "Fri Aug 20 09:19:58 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "International series in pure and applied mathematics",
acknowledgement = ack-nhfb,
remark = "Reprinted in \cite{Hildebrand:1987:INA}.",
subject = "Numerical analysis",
}
@Article{Hill:1974:RFF,
author = "Bruce M. Hill",
title = "The rank-frequency form of {Zipf}'s law",
journal = j-J-AM-STAT-ASSOC,
volume = "69",
number = "348",
pages = "1017--1026",
month = dec,
year = "1974",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
MRclass = "62E15",
MRnumber = "0426242 (54 \#14188)",
MRreviewer = "S. M. Samuels",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
ZMnumber = "Zbl 0301.60011",
acknowledgement = ack-nhfb,
classification = "B0240 (Probability and statistics); C1140
(Probability and statistics)",
corpsource = "Dept. of Statistics, Univ. of Michigan, Ann Arbor, MI,
USA",
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
keywords = "Bose--Einstein allocation; distribution; random
processes; rank frequency form; statistics; Zipf's
law",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Hull:1974:LFM,
author = "T. E. Hull and J. J. Hofbauer",
title = "Language facilities for multiple precision floating
point computation, with examples, and the description
of a preprocessor",
type = "Technical report",
number = "63",
institution = "University of Toronto, Dept. of Computer Science",
address = "Toronto, ON, Canada",
pages = "vi + 84",
year = "1974",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic; Electronic digital
computers --- Programming",
}
@Article{Kinoshita:1974:FPA,
author = "Eisuke Kinoshita and Hideo Kosako and Yoshiaki
Kojima",
title = "Floating-Point Arithmetic Algorithms in the Symmetric
Residue Number System",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "1",
pages = "9--20",
month = jan,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1974.223772",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "68A10",
MRnumber = "50 9042",
bibdate = "Tue Jul 12 11:27:29 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672365;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35077",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
reviewer = "M. S. Cheema",
summary = "The residue number system is an integer number system
and is inconvenient to represent numbers with
fractional parts. In the symmetric residue system, a
new representation of floating-point numbers and
arithmetic algorithms for its addition, \ldots{}",
}
@Article{Kroft:1974:CTC,
author = "D. Kroft",
title = "Comments on {``A Two's Complement Parallel Array
Multiplication Algorithm''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "12",
pages = "1327--1328",
month = dec,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.223863",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:38 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Baugh:1973:TCP,Blankenship:1974:CTC}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672456",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Kulisch:1974:PCC,
author = "U. Kulisch",
title = "Formalization and implementation of floating-point
arithmetics",
crossref = "Panagiotopoulos:1974:PCC",
pages = "328--369",
year = "1974",
MRclass = "65G05",
MRnumber = "57 14392",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "R. H. Bartels",
}
@Article{Ling:1974:CSA,
author = "Robert F. Ling",
title = "Comparison of several algorithms for computing sample
means and variances",
journal = j-J-AM-STAT-ASSOC,
volume = "69",
number = "348",
pages = "859--866",
month = dec,
year = "1974",
CODEN = "JSTNAL",
DOI = "https://doi.org/10.1080/01621459.1974.10480219",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:46 MST 2012",
bibsource = "Distributed/QLD.bib; Distributed/QLD/1974.bib;
http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314230;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib;
Theory/Matrix.bib",
URL = "http://www.jstor.org/stable/2286154;
https://www.tandfonline.com/doi/abs/10.1080/01621459.1974.10480219;
https://www.tandfonline.com/doi/pdf/10.1080/01621459.1974.10480219",
acknowledgement = ack-nhfb,
country = "USA",
date = "13/05/93",
descriptors = "Simulation; statistics; numeric calculation",
enum = "7605",
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
keywords = "mean; standard deviation; stat; updating; variance",
location = "SEL: Wi",
remark = "This is an early paper on the numerical difficulties
associated with two important statistical algorithms.
See also entry \cite{McCullough:2019:WTS} in
fparith.bib that shows that even after 45 years, some
statistics code in database software remains poor.",
revision = "16/01/94",
xxtitle = "Comparison of Several Algorithms for Computing Means
and Variances",
}
@Article{Linnainmaa:1974:ASK,
author = "Seppo Linnainmaa",
title = "Analysis of Some Known Methods of Improving the
Accuracy of Floating-Point Sums",
journal = j-BIT,
volume = "14",
number = "2",
pages = "167--202",
month = jun,
year = "1974",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01932946",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65G05",
MRnumber = "MR0483373 (58 \#3381)",
bibdate = "Fri Dec 08 13:05:19 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=14&issue=2&spage=167",
acknowledgement = ack-nj,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "accurate floating-point summation; floating-point
arithmetic; rounding errors",
reviewer = "H. Ratschek",
}
@InCollection{Metropolis:1974:SAA,
author = "N. Metropolis and Gian-Carlo Rota",
booktitle = "Studies in numerical analysis (papers in honour of
{Cornelius Lanczos} on the occasion of his 80th
birthday)",
title = "Significance arithmetic---on the algebra of binary
strings",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "241--251",
year = "1974",
MRclass = "02F43 (68A15)",
MRnumber = "MR0354335 (50 \#6815)",
MRreviewer = "Stephen Tanny",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0311.65031",
acknowledgement = ack-nhfb,
}
@InProceedings{Miller:1974:CCN,
author = "Webb Miller",
title = "Computational complexity and numerical stability",
crossref = "ACM:1974:CRS",
pages = "317--322",
year = "1974",
bibdate = "Wed Nov 24 12:46:29 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Manual{Moon:1974:MRM,
author = "David A. Moon",
title = "{MacLISP} Reference Manual",
organization = "MIT Project MAC",
address = "Cambridge, MA, USA",
month = apr,
year = "1974",
bibdate = "Wed Jan 29 16:47:55 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "From \cite{Steele:2004:RHP}: ``In early 1971, he
[White] began to analyze the machine-language algorithm
used in the implementation of MacLisp (described in
this report) to convert PDP-10 floating-point numbers
into decimal notation.''",
}
@Article{Neumaier:1974:REV,
author = "A. Neumaier",
title = "{Rundungsfehleranalyse Einiger Verfahren Zur Summation
Endlicher Summen}. ({German}) [{Rounding} error
analysis of a method for summation of finite sums]",
journal = j-Z-ANGE-MATH-MECH,
volume = "54",
pages = "39--51",
year = "1974",
CODEN = "ZAMMAX",
ISSN = "0044-2267 (print), 1521-4001 (electronic)",
ISSN-L = "0044-2267",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-jr,
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und
Mechanik}",
keywords = "accurate floating-point summation",
language = "German",
}
@Article{Newbery:1974:EAP,
author = "A. C. R. Newbery",
title = "Error Analysis for Polynomial Evaluation",
journal = j-MATH-COMPUT,
volume = "28",
number = "127",
pages = "789--793",
month = jul,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290B (Error analysis in numerical methods); B0290D
(Functional analysis); C4110 (Error analysis in
numerical methods); C4120 (Functional analysis)",
corpsource = "Univ. Kentucky, Lexington, KY, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "analysis; Chebyshev; computable error bound; error
analysis; floating point error; function evaluation;
Horner's scheme; polynomial evaluation; polynomials",
treatment = "T Theoretical or Mathematical",
}
@MastersThesis{Prezas:1974:FPA,
author = "Pericles Panos Prezas",
title = "Floating point arithmetic unit",
type = "Thesis ({M.S.})",
publisher = "The author",
school = "Illinois Institute of Technology",
address = "Chicago, IL.",
pages = "ix + 77",
year = "1974",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Renner:1974:RRN,
author = "K. Renner and S. Gupta",
title = "Reduction of roundoff noise in wave digital filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "21",
number = "2",
pages = "305--310",
month = mar,
year = "1974",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "Roundoff noise generated by arithmetic operations in a
digital-filter computational sequence is undesirable in
that it serves to distort the true signal at the
output. Furthermore, coefficient wordlength is directly
related to the generated noise. \ldots{}",
}
@Book{Scaife:1974:SNA,
editor = "B. K. P. Scaife",
title = "Studies in numerical analysis",
publisher = "The Royal Irish Academy",
address = "Dublin, Ireland",
pages = "xxii + 333",
year = "1974",
MRclass = "65-06",
MRnumber = "MR0347039 (49 \#11759)",
bibdate = "Thu Nov 8 19:02:54 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Papers in honour of Cornelius Lanczos on the occasion
of his 80th birthday",
acknowledgement = ack-nhfb,
}
@Book{Schmid:1974:DC,
author = "Hermann Schmid",
title = "Decimal Computation",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xi + 266",
year = "1974",
ISBN = "0-471-76180-X",
ISBN-13 = "978-0-471-76180-8",
LCCN = "QA75 .S34",
bibdate = "Thu Sep 1 10:14:05 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted \cite{Schmid:1983:DC}.",
acknowledgement = ack-nj,
keywords = "decimal floating-point arithmetic",
}
@Article{Sites:1974:SBD,
author = "R. L. Sites",
title = "Serial Binary Division by Ten",
journal = j-IEEE-TRANS-COMPUT,
volume = "23",
number = "12",
pages = "1299--1301",
month = dec,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.223849",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Aug 07 18:02:35 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A technique is presented for dividing a positive
binary integer by ten, in which the bits of the input
are presented serially, low-order bit first. A complete
division by ten is performed in two word times
(comparable to the time needed for two serial
additions). The technique can be useful in serial
conversions from binary to decimal, or in scaling
binary numbers by powers of 10.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "decimal arithmetic",
}
@Book{Sterbenz:1974:FPC,
author = "Pat H. Sterbenz",
title = "Floating Point Computation",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xiv + 316",
year = "1974",
ISBN = "0-13-322495-3",
ISBN-13 = "978-0-13-322495-5",
LCCN = "QA76.8.I12 S771 1974",
MRclass = "68A05 (65G05)",
MRnumber = "50 1556",
bibdate = "Sat May 29 08:01:36 1999",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/mathcw.bib",
series = "Prentice-Hall Series in Automatic Computation.",
acknowledgement = ack-nj # " and " # ack-nhfb,
keywords = "Compiling (Electronic computers); Computation by
computer systems --- Floating point representation;
Floating-point arithmetic; IBM 360 (Computer) ---
Programming",
remark = "From p. 116: ``There is general agreement that the
mantissas of floating-point numbers are not uniformly
distributed. [See Hamming (1962)
[\cite{Hamming:1962:NMS}], Pinkham (1961)
[Pinkham:1961:DFS], or Knuth (1969) [Knuth:1969:SNM].]
Instead, it is customary to assume that they are
distributed logarithmically, that is, that the
probability density function is
$$ (3.12.9) f(m) = \frac {1}{m \ln r}, \qquad r^{-1}
\leq m \leq 1. $$
This assumption is based on the following observations:
First, this distribution reproduces itself under
multiplication, but a uniform distribution does not.
[See Hamming (1962) [\cite{Hamming:1962:NMS}] and
Exercise 20.] A second justification is based on the
fact that many of the numbers that arise in computation
represent measurable quantities such as lengths,
forces, etc., and it is reasonable to believe that the
distribution of the mantissas of such quantities is
independent of the units in which they are measured.
Pinkham (1961) shows that this leads to the conclusion
that the distribution of mantissas must be
logarithmic.''",
reviewer = "F. J. Murray",
tableofcontents = "Preface / ix \\
1. Floating-Point Number Systems / 1 \\
1.1 Fixed-Point Calculation / 1 \\
1.2 Floating-Decimal Representation of Numbers / 4 \\
1.3 Floating-Decimal Arithmetic / 6 \\
1.4 Floating-Point Number Systems / 9 \\
1.5 FP(r, p, c) and FP(r, p, R) / 12 \\
1.6 Laws of Algebra / 14 \\
1.7 Inequalities in FP(r,p, c) / 21 \\
1.8 FP(r, p, clq) / 22 \\
1.9 The Solution of a * x = b in FP(r,p, c) / 29 \\
1.10 Division / 33 \\
Exercises / 35 \\
2. Floating-Point Overflow and Underflow / 39 \\
2.1 Bounds for Exponents / 39 \\
2.2 $\Omega$-Zero Fixup / 41 \\
2.3 Interrupt / 44 \\
2.4 Messages and Tests / 46 \\
2.5 ON OVERFLOW and ON UNDERFLOW in PL/I / 49 \\
2.6 Example / 50 \\
2.7 Counting Mode / 57 \\
2.8 Gradual Underflow / 59 \\
2.9 Imprecise Interrupt / 61 \\
2.10 Changing the Treatment of Spill / 62 \\
2.11 Virtual Overflow and Underflow / 64 \\
2.12 Division by Zero and Indeterminant Forms / 66 \\
Exercises / 67 \\
3. Error Analysis / 71 \\
3.1 Significant Digits / 71 \\
3.2 Relative Error / 73 \\
3.3 Relative Error in FP(r,p, clq) / 75 \\
3.4 Approximate Laws of Algebra / 80 \\
3.5 Propagation of Rounding Error / 87 \\
3.6 X**N / 92 \\
3.7 Condition / 98 \\
3.8 Error Analysis of a Program / 103 \\
3.9 Backward Error Analysis / 105 \\
3.10 Examples / 107 \\
3.11 Changing the Problem / 109 \\
3.12 Statistical Error Analysis / 113 \\
Exercises / 117 \\
4. Example / 123 \\
4.1 Quadrature / 123 \\
4.2 Power Series / 130 \\
4.3 Exact Sums and Differences in FP(r, p, clq) / 137
\\
4.4 Dismantling Floating-Point Numbers / 143 \\
Exercises / 146 \\
5. Double-Precision Calculation / 154 \\
5.1 Programs Using Double-Precision Arithmetic / 155
\\
5.2 Implicit Typing of Names / 162 \\
5.3 Routines to Perform Double-Precision Arithmetic /
163 \\
5.4 Double-Precision Multiplication / 165 \\
5.5 Double-Precision Addition and Subtraction / 168 \\
5.6 Double-Precision Division / 171 \\
5.7 Writing Double-Precision Programs Without Language
Support / 178 \\
5.8 Uses of Double-Precision / 180 \\
5.9 Higher-Precision Arithmetic / 185 \\
Exercises / 186 \\
6. Rounding / 189 \\
6.1 General Considerations / 189 \\
6.2 Uses of Rounding / 191 \\
6.3 Implementation of Rounding / 192 \\
6.4 Bias Removal / 194 \\
6.5 Other ``Rounding'' Procedures / 197 \\
Exercises / 198 \\
7. Automatic Analysis of Error / 201 \\
7.1 Introduction / 201 \\
7.2 Significance Arithmetic / 202 \\
7.3 Noisy Mode / 205 \\
7.4 Interval Arithmetic / 207 \\
7.5 Rerunning the Program in Higher-Precision / 213 \\
Exercises / 222 \\
8. Radix Conversion / 224 \\
8.1 Equivalent Number of Digits / 224 \\
8.2 Properties of Conversion Transformations / 228 \\
8.3 Conversion Techniques / 232 \\
Exercises / 238 \\
9/ Carefully Written Programs / 240 \\
9.1 Introduction / 240 \\
9.2 Average Problem / 240 \\
9.3 Quadratic Equation / 246 \\
Exercises / 252 \\
10. Checking and Testing / 255 \\
10.1 Range Checking / 255 \\
10.2 Mathematical Checks / 256 \\
10.3 Testing / 259 \\
Exercises / 261 \\
11. Language Features for Floating-Point Computation /
263 \\
11.1 Introduction / 263 \\
11.2 Predictability, Controllability, Observability /
264 \\
11.3 Ease of Programming / 265 \\
11.4 Machine Independence / 267 \\
Exercises / 269 \\
12. Floating-Point Hardware / 271 \\
12.1 Choice of Radix / 271 \\
12.2 The Representation of Floating-Point Numbers / 273
\\
12.3 FP(r, p, c) and FP(r, p, R) / 277 \\
12.4 Unnormalized Numbers and Unnormalized Arithmetic /
278 \\
Exercises / 282 \\
13. Complex Numbers / 285 \\
13.1 Programs Using Complex Numbers / 285 \\
13.2 Relative Error / 286 \\
13.3 Complex Arithmetic / 287 \\
Exercises / 297 \\
Bibliography / 301 \\
Glossary of Symbols / 309 \\
Index / 311",
}
@Article{Suter:1974:MAA,
author = "B. W. Suter",
title = "The Modular Arithmetic of Arbitrarily Long Sequences
of Digits",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "12",
pages = "1301--1303",
month = dec,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.223850",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:38 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672443",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Syslo:1974:RAP,
author = "M. M. Syslo",
title = "Remarks on addition processes of positive
floating-point numbers",
journal = j-ZASTOS-MAT,
volume = "14",
pages = "415--417",
year = "1974",
CODEN = "ZAMTAK",
MRclass = "65G05",
MRnumber = "50 8953",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Zastosowania Matematyki",
reviewer = "Sven-{\AA}ke Gustafson",
}
@PhdThesis{Thompson:1974:IUF,
author = "Jackie Lloyd Thompson",
title = "An implementation of user-oriented floating point
arithmetic",
type = "Dissertation ({Ph.D.} in {Computing Science})",
school = "Texas A\&M University",
address = "College Station, TX, USA",
pages = "150",
year = "1974",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Tsao:1974:DSD,
author = "Nai Kuan Tsao",
title = "On the Distributions of Significant Digits and
Roundoff Errors",
journal = j-CACM,
volume = "17",
number = "5",
pages = "269--271",
month = may,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65G05",
MRnumber = "49 6595",
MRreviewer = "N. N. Abdelmalek",
bibdate = "Mon Jan 22 07:26:38 MST 2001",
bibsource = "Compendex database;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Tsao74;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Generalized logarithmic law is derived for the
distribution of the first $t$ significant digits of a
random digital integer. This result is then used to
determine the distribution of the roundoff errors in
floating-point operations, which is a mixture of
uniform and reciprocal distributions.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
classification = "921",
corpsource = "Aerospace Res. Labs., Wright-Patterson AFB, OH, USA",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
journalabr = "Commun ACM",
keywords = "Benford's Law; digital arithmetic; digital integer;
distributions; error analysis; floating point
operations; Law of Anomalous Numbers; logarithmic law;
mathematical techniques; mean value; random;
reciprocal; roundoff errors; significant digits;
uniform distribution; variance; Zipf's Law",
oldlabel = "Tsao74",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Tsao74",
}
@Article{Tsao:1974:SPE,
author = "Nai-Kuan Tsao",
title = "Some a Posteriori Error Bounds in Floating-Point
Computations",
journal = j-J-ACM,
volume = "21",
number = "1",
pages = "6--17",
month = jan,
year = "1974",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "65G05",
MRnumber = "49 8319",
bibdate = "Fri Dec 08 13:06:33 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
reviewer = "N. N. Abdelmalek",
}
@Article{Walker:1974:FGU,
author = "A. J. Walker",
title = "Fast generation of uniformly distributed pseudorandom
numbers with floating-point representation",
journal = j-ELECT-LETTERS,
volume = "10",
number = "25--26",
pages = "533--534",
day = "12",
month = dec,
year = "1974",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:19740423",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Fri Dec 30 16:39:46 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4245313",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}
@Article{Agrawal:1975:AAN,
author = "D. P. Agrawal",
title = "Arithmetic Algorithms in a Negative Base",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "10",
pages = "998--1000",
month = oct,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224109",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:57 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672702",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Agrawal:1975:OAL,
author = "Dharma P. Agrawal",
title = "Optimum Array-Like Structures for High-Speed
Arithmetic",
crossref = "IEEE:1975:SCA",
pages = "208--219",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Agrawal.pdf",
abstract = "Array-like structures for high-speed multiplication,
division, square and square-root operations have been
described in this paper. In these designs the division
and square-rooting time have been made to approach to
that of multiplication operation. These structures are
optimum from speed and versatility point of view. Most
of the cellular arrays described in the literature are
adequately slow. The time delay is particularly
significant in the division and square-rooting
operations due to the ripple effect of the carries.
Though the carry-save technique has been widely
utilized for multiplication operation, it has been only
recently employed by Cappa et al. in the design of a
nonrestoring divider array. This requires sign-bit
detection that makes the array non-uniform. Such an
array has been named as an array-like structure. The
carry-save method has been extended here for restoring
division operation. Due to sign-detection and overflow
correction requirements, the restoring method is
slightly complex. But the main advantage of such
restoring array is in its simple extension for
multiplication operation. The array for the two
operations, when pipelined, will have more computing
power than all other multiplier-divider arrays.
Suggestions have also been included for further speed
improvement.\par
The technique applied for division operation is as well
applicable for the square-rooting and an array-like
structure for square-square-rooting operations has also
been given. For performing any one of the four
operations, the only manipulation to be done is to
combine the two arrays; one for multiplication-division
and another for square-square-rooting. Possible.
methods of combining the two arrays have been indicated
and their relative advantages and disadvantages have
been mentioned. Finally, a generalized pipeline
array-like structure with complete internal details and
for 4-bit operation, has been shown. Due consideration
has also been given to the possibility of
large-scale-integration of different arrays presented
in this paper.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Atkins:1975:HRN,
author = "Daniel E. Atkins",
title = "Higher Radix, Non-restoring Division: History and
recent Developments",
crossref = "IEEE:1975:SCA",
pages = "158--167",
year = "1975",
bibdate = "Wed Nov 14 17:43:08 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Atkins.pdf",
abstract = "This paper reviews work related to the theory and
application of higher-radix. non-restoring division as
originally defined by Robertson in 1958.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Avizienis:1975:RNR,
author = "Algirdas Avi{\v{z}}ienis",
title = "Redundancy in Number Representations as an Aspect of
Computational Complexity of Arithmetic Functions",
crossref = "IEEE:1975:SCA",
pages = "87--89",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Avizienis.pdf",
abstract = "Recent research has led to the derivation of bounds
for the time required to perform arithmetic operations
by means of logical elements with a limited number of
inputs [1--4]. The model of a $ (d, r) $ logical
circuit $C$ employed in these studies consists of a set
of $ (d, r) $ logical elements and a rule of
interconnection with designated sets of input and
output lines. The $ (d, r) $ logical element has $r$
input lines and one output line; these lines can assume
one of $d$ distinct states. The $ (d, r) $ logical
element has a unit time delay; that is, the state of
the output line at the time $ t + 1 $ is a function of
the states of the input lines at time $t$.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Baker:1975:MER,
author = "P. W. Baker",
title = "More Efficient Radix-2 Algorithms for Some Elementary
Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "11",
pages = "1049--1054",
month = nov,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224132",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:15:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Banerji:1975:CLS,
author = "D. K. Banerji",
title = "On Combinational Logic for Sign Detection in Residue
Number Systems",
crossref = "IEEE:1975:SCA",
pages = "113--116",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Banerji.pdf",
abstract = "This paper is concerned with the algebraic sign
detection of a number in a residue number system. The
proposed solution is applicable only to nonredundant
systems. The method utilizes a systematic decomposition
of the sign function $S$ that is based on some special
properties of $S$. Starting with the canonical
sum-of-products expression for $S$, we transform the
expression to a form whose realization is simpler than
the canonical form realization and, if possible, also
simpler than the minimal sum-of-products realization.
In some cases, the proposed method yields savings as
high as 85\% compared to the minimal sum-of-products
realization for $S$.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Basu:1975:SPN,
author = "D. Basu and T. Jayashree",
title = "On a Simple Postcorrection for Nonrestoring Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "10",
pages = "1019--1020",
month = oct,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224116",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:57 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672709",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Benedek:1975:DLB,
author = "M. Benedek",
title = "Developing Large Binary to {BCD} Conversion
Structures",
crossref = "IEEE:1975:SCA",
pages = "188--196",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Benedek.pdf",
abstract = "Static binary to BCD conversion has been described in
many papers during the last decade, but none of the
methods presented were practical for the conversion of
large number of binary bits.\par
In this paper it is intended to further develop static
conversions by the expansion of the original BIDEC
method (Ref. 1). There are quite a few static
conversion schemes published which use other methods of
conversion. The static method, developed from the
BIDEC, lends itself best for the expansion to larger
structures as in its original ``correct and shift''
form there were no basic limitations on the size of the
binary words to be converted. with the appearance of
large bipolar ROMs and the even larger but somewhat
slower MOS ROMs there is a renewed interest in large
structures for fast binary to BCD conversions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Bivins:1975:SAA,
author = "R. L. Bivins and N. Metropolis",
title = "Significance Arithmetic: Application to a Partial
Differential Equation",
crossref = "IEEE:1975:SCA",
pages = "64--66",
year = "1975",
DOI = "https://doi.org/10.1109/ARITH.1975.6156973",
bibdate = "Mon Mar 19 18:17:32 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Also available as Los Alamos Technical Report
LA-UR-75-1763 CONF-751103-1.",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Bivins.pdf",
abstract = "The methods of significance arithmetic are applied to
the numerical solution of a nonlinear partial
differential equation. The authors approach permits the
use of initial values having imprecision considerably
greater than that of rounding error; moreover, the
intermediate and final quantities are monitored so that
at any stage the precision of such quantities is
available. An algorithm is found that represents
faithfully the solution to a difference equation
approximation to Burger's equation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3; significance arithmetic",
}
@InProceedings{Bohlender:1975:FPC,
author = "G. Bohlender",
title = "Floating-Point Computation of Functions with Maximum
Accuracy",
crossref = "IEEE:1975:SCA",
pages = "14--23",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Bohlender.pdf",
abstract = "Algorithms are given which compute multiple sums and
products and arbitrary roots of floating-point numbers
with maximum accuracy. The summation algorithm can be
applied to compute scalar products, matrix products,
etc. For all these functions, simple error formulas and
the smallest floating-point intervals containing the
exact result can be obtained.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@TechReport{Brent:1975:FMP,
author = "R. P. Brent",
title = "A {Fortran} Multiple-Precision Arithmetic Package",
type = "Technical report",
institution = "Department of Computer Science, Australian National
University",
address = "Canberra, Australia",
year = "1975",
bibdate = "Fri Jan 06 07:38:05 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic; multiple-precision
arithmetic",
}
@TechReport{Brent:1975:MZM,
author = "R. P. (Richard P.) Brent",
title = "Multiple-precision zero-finding methods and the
complexity of elementary function evaluation",
institution = "Department of Computer Science, Carnegie-Mellon
University",
address = "Pittsburgh, PA, USA",
pages = "26",
year = "1975",
bibdate = "Sat Jan 11 10:14:06 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Iterative methods (Mathematics)",
searchkey = "ti:elementary n1 function",
}
@Article{Brubaker:1975:MUL,
author = "T. A. Brubaker and J. C. Becker",
title = "Multiplication Using Logarithms Implemented with
Read-Only Memory",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "8",
pages = "761--765",
month = aug,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224307",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:56 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672900",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Caprani:1975:REF,
author = "Ole Caprani",
title = "Round-off Errors in Floating-Point Summation",
journal = j-BIT,
volume = "15",
number = "1",
pages = "5--9",
month = mar,
year = "1975",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01932993",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65G05",
MRnumber = "58 19088",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "accurate floating-point summation; floating-point
arithmetic; rounding errors",
xxtitle = "Roundoff errors in floating-point summation",
}
@Article{Chen:1975:SER,
author = "Tien Chi Chen and Irving T. Ho",
title = "Storage-Efficient Representation of Decimal Data",
journal = j-CACM,
volume = "18",
number = "1",
pages = "49--52",
month = jan,
year = "1975",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "94A15 (68A20)",
MRnumber = "50 16105",
MRreviewer = "R. N. Goss",
bibdate = "Mon Jan 22 06:30:44 MST 2001",
bibsource = "Compendex database;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#ChenH75;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Collection of articles honoring {Alston S.
Householder}. See comment \cite{Smith:1975:CPC}.",
abstract = "Usually $n$ decimal digits are represented by $ 4 n $
bits in computers. Actually, two BCD digits can be
compressed optimally and reversibly into $7$ bits, and
three digits into $ 10 $ bits, by a very simple
algorithm based on the fixed-length combination of two
variable field-length encodings. In over half of the
cases the compressed code results from the conventional
BCD code by simple removal of redundant $0$ bits. A
long decimal message can be subdivided into three-digit
blocks, and separately compressed; the result differs
from the asymptotic minimum length by only $ 0.34 $
percent. The hardware requirement is small, and the
mappings can be done manually.",
acknowledgement = ack-nhfb,
classcodes = "C6130 (Data handling techniques)",
classification = "722; 921",
corpsource = "IBM San Jose Res. Lab., CA, USA",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
journalabr = "Commun ACM",
keywords = "asymptotic minimum; binary coded decimal; codes;
compressed code; data compression; data storage units;
decimal data; decimal floating-point arithmetic; fixed
length combination; hardware; length; length encodings;
mathematical techniques --- Digital Arithmetic;
representation; storage efficient; variable field",
oldlabel = "ChenH75",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/ChenH75",
}
@InProceedings{Chinal:1975:LMA,
author = "Jean P. Chinal",
title = "The Logic of Modulo $ 2^k + 1 $ Adders",
crossref = "IEEE:1975:SCA",
pages = "126--136",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Chinal_2.pdf",
abstract = "The design of modulo $ 2^k + 1 $ adders for arbitrary
$k$ is considered, with the objective of achieving a
logic structure as regular as possible so as to allow a
convenient implementation in large-scale integration
technology (LSI). It is shown how the design problem
can be reduced. to the recursive generation of a
subtract signal and to the merging, in various degrees,
of the corresponding logic with the logic of an
ordinary adder or, alternately, of a so-called {\em
signed-carry adder\/} which is defined and designed
itself in general, with both recursive and explicit
carry schemes. Modulo $ 2^k + 1 $ adder designs are
given, one with conventional adder, another based on
signed-carry adder and a third, derived from the
signed-carry scheme, where subtract signal generation
and carry logic are merged. This last scheme can be set
up with two backward recursion chains and five or six
forward ones. Two more basic variants are finally
indicated for this integrated scheme, aiming at
reducing as much as possible the residual logic
structure irregularity presented by the most
significant position in the word.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Chinal:1975:MA,
author = "Jean P. Chinal",
title = "Mirror Arithmetic",
crossref = "IEEE:1975:SCA",
pages = "98--107",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Chinal_1.pdf",
abstract = "Mirror coding for signed numbers is defined by means
of a set of primitive powers of two $ \{ + 2^n, - 2^{n
- 1}, \ldots {}, - 2^0 \} $ where signs of the usual
set used in 2's complement representation are reversed.
Use of the mirror representation is shown as an
alternate design approach and is illustrated by a
special purpose adder design in mirror code, by an
alternate proof of a basic property of signed-digit
arithmetic and as another interpretation of cells used
in some array multipliers for signed numbers. Lastly,
the concept is used to define a variable mode redundant
coding, allowing simple sign-flipping without
overflow.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Cobb:1975:IPS,
author = "Gary W. Cobb",
title = "The Impact of Parallelism on Software",
crossref = "IEEE:1975:SCA",
pages = "220--222",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Cobb.pdf",
abstract = "There seems to be a tug-of-war raging between computer
procurement technical evaluation committees, computer
designers and scholars of computer science and
numerical analysis over the issue of parallelism in
computations. Caught in the middle seems to be the user
community and the compiler writers. For the scope of
this paper, the term ``user community'' will be assumed
to be Fortran programmers who are involved in solving
problems that require large computer resources, e.g.,
plasma research, weather prediction, ray tracing,
seismic analysis, econometric modeling, weapons
research, reactor calculation, etc.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{DeMori:1975:MMM,
author = "Renato {De Mori} and Michele Elia and Angelo Serra",
title = "Minimization Methods for Macrocellular Arithmetic
Networks",
crossref = "IEEE:1975:SCA",
pages = "232--240",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_DeMori.pdf",
abstract = "This paper presents a new method to study arithmetic
combinatorial circuits. Using polynomial associated to
the input-output sequences and to the system, it is
possible to solve the problem of minimization of the
number of the component blocks. Particularly, the
important case of the multiple outputs elementary units
can be treated.\par
Applications of the introduced procedures to multiplier
and to fast networks for performing convolution are
presented.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Deverell:1975:PIA,
author = "J. Deverell",
title = "Pipeline Iterative Arithmetic Arrays",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "3",
pages = "317--322",
month = mar,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224214",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 18:46:50 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@PhdThesis{Ercegovac:1975:GMEa,
author = "Milo{\v{s}} Dragutin Ercegovac",
title = "A General Method for Evaluation of Functions and
Computations in a Digital Computer",
type = "{Ph.D.} Thesis",
school = "Department of Computer Science, University of Illinois
at Urbana-Champaign",
address = "Urbana-Champaign, IL, USA",
pages = "viii + 109",
month = jul,
year = "1975",
bibdate = "Mon Feb 10 07:18:12 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://search.proquest.com/pqdtglobal/docview/302756306",
acknowledgement = ack-nhfb,
advisor = "James E. Robertson",
}
@InProceedings{Ercegovac:1975:GMEb,
author = "Milo{\v{s}} D. Ercegovac",
title = "A General Method for Evaluation of Functions in a
Digital Computer",
crossref = "IEEE:1975:SCA",
pages = "147--157",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Ercegovac.pdf",
abstract = "This paper presents a recently discovered general
computational method, amenable for efficient
implementation in digital computing systems. The method
provides a unique, simple and fast algorithm for
solving many computational problems, such as the
evaluation of polynomials, rational functions and
arithmetic expressions, or solving a class of systems
of linear equations, or performing the basic
arithmetics. In particular, the method is well suited
for fast evaluation of commonly used mathematical
functions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@MastersThesis{Fawcett:1975:MCR,
author = "B. K. Fawcett",
title = "Maximal Clocking Rates for Pipelined Digital Systems",
type = "{M.S.} thesis",
school = "Department of Electrical Engineering, University of
Illinois at Urbana-Champaign",
address = "Urbana-Champaign, IL, USA",
year = "1975",
bibdate = "Fri Nov 09 10:50:56 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Foster:1975:CNM,
author = "Caxton Foster and Edward Riseman and Fred Stockton and
Conrad Wogrin",
title = "{CHARGOGGAGGOGGMANCHAUGAGOGGCHAUBUNAGUNGAMAUG}: a
Novel Multiply-by-Three Circuit",
crossref = "IEEE:1975:SCA",
pages = "185--187",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Foster.pdf",
abstract = "Recently, while considering the connection of a 48 bit
word computer to a 16 bit computer, we felt the need
for a fast and inexpensive device that would multiply a
binary address by a factor of three. Since $ 3 N = N +
2 N $, there is an obvious solution of providing a
normal adder circuit and presenting one set of inputs
with $N$ and the other with $N$-shifted left one place.
But, there is a great deal of redundancy here since
knowing one input we have complete knowledge of the
other.\par
Seeking to take advantage of this redundancy, we have
spent some twenty man hours and have saved one gate per
stage over a conventional full adder. Since the
ultimate circuit is to be a ``one-of'' this is scarcely
economic, but it has been fun. Before going further,
the interested reader may enjoy puzzling over the
problem for himself. We make no pretense of minimality,
but we have a circuit with 6 gates per stage and a
propagation delay of one gate per stage.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
remark = "Footnote to title: The title of this paper refers to
the Indian name of a lake in Massachusetts which
reputedly means ``You fish on your side, I fish on my
side, nobody fish in the middle.'",
}
@InProceedings{Gabrielian:1975:FSN,
author = "Armen Gabrielian",
title = "Formal Systems of Numerals",
crossref = "IEEE:1975:SCA",
pages = "76--81",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Gabrielian.pdf",
abstract = "A new system of numerals is introduced for
representing numbers in base $ 2^N $, for $ N \leq 8 $.
The new notation greatly simplifies arithmetical
operations on numbers. For example, for $ N = 3 (4) $
one obtains a notation for octal (hexadecimal) numbers
in which one can perform addition and multiplication
much more easily than in the standard notation. For $ N
= 8 $ one obtains a practical way of representing
numbers to the base 256. A simplification of the
decimal notation is also presented.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{George:1975:ARR,
author = "James E. George",
title = "Algorithms to Reveal the Representation of Characters,
Integers, and Floating-Point Numbers",
journal = j-TOMS,
volume = "1",
number = "3",
pages = "210--216",
month = sep,
year = "1975",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355644.355647",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Aug 26 23:44:16 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Gibson:1975:SCT,
author = "J. A. Gibson and R. W. Gibbard",
title = "Synthesis and Comparison of Two's Complement Parallel
Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "10",
pages = "1020--1027",
month = oct,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224117",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:57 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672710",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Ginsberg:1975:DUFa,
author = "Myron Ginsberg and Dennis J. Frailey",
title = "The design and use of a floating-point (software)
simulator for testing the arithmetic behavior of
mathematical software",
type = "Technical report",
number = "CP 74028",
institution = "Department of Computer Science, Institute of
Technology, Southern Methodist University",
address = "Dallas",
edition = "Revised Oct. 1975.",
pages = "26",
year = "1975",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units --- Testing.;
Computer programs --- Testing.; Floating-point
arithmetic.",
}
@InProceedings{Ginsberg:1975:DUFb,
author = "Myron Ginsberg and Dennis J. Frailey",
title = "The Design and Use of a Floating-Point (Software)
Simulator for Testing the Arithmetic Behavior of
Mathematical Software",
crossref = "IEEE:1975:SCA",
pages = "56--63",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Ginsberg.pdf",
abstract = "An important aspect of any evaluative procedure for
developing high quality mathematical software is
testing the effects of arithmetic behavior on
algorithmic implementations. This paper describes a
proposed design approach and various applications of a
high-level language floating-point simulator which has
two inputs: the program to be tested and a description
of the floating-point arithmetic under which the
routine is to be executed. A brief discussion of the
motivation for this approach is given along with a
review of existing efforts to study the influences of
computer arithmetic on the accuracy and reliability of
mathematical. software. An overview of the simulator's
structure is presented as well as suggestions for
experiments to assist in determining the effects of
floating-point behavior across several different
computer architectures. Present and future uses of the
simulator are also indicated.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Goodman:1975:REP,
author = "R. Goodman and A. Feldstein",
title = "Round-Off Error in Products",
journal = j-COMPUTING,
volume = "15",
number = "3",
pages = "263--273",
month = sep,
year = "1975",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/BF02242373",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:52 MST 2001",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "Dept. of Math., Univ. of Miami, Coral Gables, FL,
USA",
classification = "921; C5230",
description = "digital arithmetic",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Comput (Vienna/NY)",
keywords = "digit by digit deviation; floating point numbers;
fraction; logarithmic distribution; mathematical
techniques; mean; multiplication; products; roundoff
errors; variance",
}
@InProceedings{Goyal:1975:DAE,
author = "Lakshmi N. Goyal",
title = "Design of an Arithmetic Element for Serial Processing
in an Iterative Structure",
crossref = "IEEE:1975:SCA",
pages = "223--231",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Goyal.pdf",
abstract = "This paper describes the arithmetic and logic design
of the digit processing logic of an arithmetic element.
The arithmetic element is used in an iterative
structure and arithmetic processing takes place
serially on a digit by digit basis with the most
significant digit first. Starting from the arithmetic
specification of the digit processing logic, the
arithmetic design (namely, the choice of number system,
number representation and the digit algorithm) is
developed. Algebraic and logic designs of the logic
necessary to execute the digit algorithm and its
implication for LSI implementation are discussed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Grant:1975:TAS,
author = "J. A. Grant and G. D. Hitchins",
title = "Two Algorithms for the Solution of Polynomial
Equations to Limiting Machine Precision",
journal = j-COMP-J,
volume = "18",
number = "3",
pages = "258--264",
month = aug,
year = "1975",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/18.3.258",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:56 MST 2012",
bibsource = "Compendex database;
http://comjnl.oxfordjournals.org/content/18/3.toc;
http://www.math.utah.edu/pub/tex/bib/compj1970.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/",
URL = "http://comjnl.oxfordjournals.org/content/18/3/258.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/258.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/259.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/260.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/261.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/262.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/263.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/264.tif",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
classification = "723; 921",
corpsource = "Dept. of Math., Univ. of Bradford, Bradford, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "algorithms; complex coefficients; computer programming
--- Subroutines; limiting machine; mathematical
techniques; polynomial equations; polynomials;
precision; real coefficients",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Gregory:1975:BCR,
author = "Robert Todd Gregory and David W. Matula",
title = "Base Conversion in Residue Number Systems",
crossref = "IEEE:1975:SCA",
pages = "117--125",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Gregory.pdf",
abstract = "We are concerned in this paper with the representation
of an integer in a (multiple-modulus) residue number
system and, in particular, with an algorithm for
changing the base vector of the residue number system.
Szabo and Tanaka [1, p.47] describe such an algorithm
when each modulus of the second base vector is
relatively prime to each modulus of the first base
vector. However, we show that a much simpler algorithm
exists if we allow the moduli of the second base vector
to have factors in common with the moduli of the first
base vector (even though the moduli of the second base
vector are pairwise relatively prime among
themselves).",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Hunter:1975:QMP,
author = "G. Hunter",
title = "A quantitative measure of precision",
journal = j-COMP-J,
volume = "18",
number = "3",
pages = "231--233",
month = aug,
year = "1975",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/231.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/232.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/233.tif",
abstract = "The precision $ z_b $ of a real number is defined
quantitatively in terms of the fractional error in the
number, and the base of the arithmetic in which it is
represented. The definition is an extension of the
traditional rough measure of precision as the number of
signification digits in the number. In binary
arithmetic the integral part of $ z_b $ is the number
of binary digits required to store the number.
Conversion of the precision from one base to another
(such as binary/decimal) is discussed, and applied to
consideration of the intrinsic precision of
input/output routines and floating point arithmetic.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
classification = "723; 921",
corpsource = "York Univ., Dept. of Chem., Downsview, Ont., Canada",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "binary arithmetic; digital arithmetic; digits;
floating; fractional error; input/output routines;
mathematical techniques; point arithmetic; precision;
real number; significant",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Kehl:1975:MMA,
author = "T. H. Kehl and Kenneth Burkhardt",
title = "A Minicomputer Microprogrammable, Arithmetic
Processor",
crossref = "IEEE:1975:SCA",
pages = "174--178",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kehl.pdf",
abstract = "Except for a few notable examples, all computers have
been designed as ``adder-central'' architectures.
``Adder-central,'' as used here, refers to an
organization which places the Arithmetic Logic Unit
(ALU) at that junction of the system through which all
data must flow --- thus creating a bottleneck. In the
early days, when adders were expensive, cost
considerations precluded more than one ALU. Nowadays
powerful ALU's are available at very low cost and a
designer, even of minicomputers, can consider placing
more than one ALU in a system.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Keir:1975:CNR,
author = "Roy A. Keir",
title = "Compatible number representations",
crossref = "IEEE:1975:SCA",
pages = "82--87",
year = "1975",
bibdate = "Fri Nov 28 11:38:18 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Keir_2.pdf",
abstract = "A compatible number system for mixed fixed-point and
floating-point arithmetic is described in terms of
number formats and opcode sequences (for hardwired or
microcoded control). This inexpensive system can be as
fast as fixed-point arithmetic on integers, is faster
than normalized arithmetic in floating point, gets
answers identical to those of normalized arithmetic,
and automatically satisfies the Algol-60 mixed-mode
rules. The central concept is the avoidance of
meaningless ``normalization'' following arithmetic
operations. Adoption of this system could lead to
simpler compilers.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3; decimal floating-point arithmetic",
}
@InProceedings{Keir:1975:PCR,
author = "Roy A. Keir",
title = "Programmer-controlled roundoff and the selection of a
stable roundoff rule",
crossref = "IEEE:1975:SCA",
pages = "73--76",
year = "1975",
bibdate = "Fri Nov 28 18:11:30 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Keir_1.pdf",
abstract = "The author suggests that every computer with
floating-point addition and subtraction should have PSW
controllable roundoff facilities. Yohe's catalog should
be included. There should also be a stable roundoff
mode using the round-to-off [{\em -odd\/}] or
round-to-even rule based on whether the radix is
divisible by four or only by two.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
keywords = "ARITH-3",
}
@Article{Keir:1975:SSR,
author = "R. A. Keir",
title = "Should the stable rounding rule be radix-dependent?",
journal = j-INFO-PROC-LETT,
volume = "3",
number = "6",
pages = "188--189",
day = "??",
month = jul,
year = "1975",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Tue Nov 17 10:49:43 MST 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
corpsource = "Dept. of Computer Sci., Univ. of Utah, Salt Lake City,
UT, USA",
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
keywords = "digital arithmetic; drift; floating point addition;
radices; round to even rule; round to odd rule; stable
rounding rule",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Kent:1975:CSU,
author = "Jan G. Kent",
title = "Comparison Sets: a Useful Partitioning of the Space of
Floating-Point Operand Pairs",
crossref = "IEEE:1975:SCA",
pages = "36--39",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kent.pdf",
abstract = "In this paper the definition of comparison sets and a
discussion of their usefulness are presented based on
the research work reported in (14). In addition some
new results concerning the distribution of floating
point (FLP) operand pairs over comparison sets are
given.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Klatte:1975:CPI,
author = "R. Klatte and Ch. Ullrich",
title = "Consequences of a Properly Implemented Computer
Arithmetic for Periodicities of Iterative Methods",
crossref = "IEEE:1975:SCA",
pages = "24--32",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Klatte.pdf",
abstract = "In ordered sets it is possible to show under certain
assumptions two basic theorems concerning the cycle
length of sequences of iterates generated by monotone
operators. These results are applied to different
iterative methods, where the conclusions are valid for
the sequences of iterates produced by the numerical
computations only, if the used computer arithmetic is
properly implemented.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3; cycle, weakly cyclic vector function;
floating-point arithmetic; Rounding invariant
structures",
}
@InProceedings{Kornerup:1975:UND,
author = "Peter Kornerup",
title = "A Unified Numeric Data Type in {Pascal}",
crossref = "IEEE:1975:SCA",
pages = "40--47",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kornerup.pdf",
abstract = "It is proposed to substitute the standard data type
{\em real\/} of a high level language, with a unified
data representation which can include a variety of
interpretations as well as formats, in order to allow
experiments with an environment containing a spectrum
of non-standard arithmetics, as well as
standard.\par
The implementation of a system is described where
syntactic extensions to a language are made to support
a microprogrammed virtual arithmetic unit which can
treat variants such as integers, normalized, and
unnormalized floating point numbers and intervals,
within a unified representation.\par
More specifically Pascal is chosen as the base
language, because it allows the user to define new data
types, and the extension then mainly consists in
substituting the simple (unstructured) data type {\em
real\/} with a skeletal structured type (which will be
called {\em numeric\/}).\par
The system is intended to be implemented on a
microprogrammable processor (called MATHILDA) with a 64
bit wide datapath. The language Pascal has already been
partially implemented based on a stack machine
specifically designed for that language, and realized
by interpretation in microcode. The present compiler
was constructed with the aid of a parser-generator
system, which will allow the language extensions to be
made with a moderate effort.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Kreifelts:1975:OBF,
author = "T. Kreifelts",
title = "{Optimale Basiswahl f{\"u}r eine Gleitkomma-Arithmetik
(Berichtigung)} \toenglish {Optimal Basis Choice for a
Floating-Point Arithmetic (Correction)} \endtoenglish",
journal = j-COMPUTING,
volume = "14",
number = "??",
pages = "313--314",
month = "????",
year = "1975",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@InProceedings{Krishnamurthy:1975:MPU,
author = "E. V. Krishnamurthy",
title = "Matrix Processors Using $p$-{ADIC} Arithmetic for
Exact Linear Computations",
crossref = "IEEE:1975:SCA",
pages = "92--97",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Krishnamurthy.pdf",
abstract = "A unique code (called Hensel's code) is derived for a
rational number, by truncating its infinite $p$-adic
expansion. The four basic arithmetic algorithms for
these codes are described and their application to
rational matrix computations is demonstrated by solving
a system of linear equations exactly, using the
Gaussian elimination procedure.\par
A comparative study of the computational complexity
involved in this arithmetic and the multiple prime
module arithmetic is made with reference to matrix
computations. On this basis, a multiple $p$-adic scheme
is suggested for the design of a highly parallel matrix
processor.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Ku:1975:FPC,
author = "W. Ku and Siu-Ming Ng",
title = "Floating-point coefficient sensitivity and roundoff
noise of recursive digital filters realized in ladder
structures",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "22",
number = "12",
pages = "927--936",
month = dec,
year = "1975",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "Coefficient sensitivity and roundoff error with
floating-point rounding have been investigated for
several digital ladder filter structures. It is found
that in all the cases studied, the ladder structures
first proposed by Fettweis show a much lower \ldots{}",
}
@InProceedings{Kuck:1975:RRN,
author = "D. J. Kuck and D. S. Parker and A. H. Sameh",
title = "{ROM}-Rounding: a New Rounding Scheme",
crossref = "IEEE:1975:SCA",
pages = "67--72",
year = "1975",
bibdate = "Thu Sep 01 12:13:06 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kuck.pdf",
abstract = "ROM-rounding is introduced and is shown to compare
favorably with existing floating-point rounding methods
on design considerations and on performance over a
series of error tests. The error-retarding value of
guard digits, of rounding the aligned operand, and of
rounding in general are discussed.",
acknowledgement = ack-nj,
keywords = "ARITH-3",
}
@Article{Kulisch:1975:FIF,
author = "U. Kulisch",
title = "Formalization and implementation of floating-point
arithmetics",
journal = j-COMPUTING,
volume = "14",
number = "4",
pages = "323--348",
year = "1975",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G05 (68A10)",
MRnumber = "53 14897",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
reviewer = "A. D. Booth",
}
@InProceedings{Kulisch:1975:MFC,
author = "U. Kulisch",
title = "Mathematical Foundation of Computer Arithmetic",
crossref = "IEEE:1975:SCA",
pages = "1--13",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kulisch.pdf",
abstract = "During the last years a number of papers concerning a
mathematical foundation of computer arithmetic have
been written. Some of these papers are still
unpublished. The papers consider the spaces which occur
in numerical computations on computers in dependence of
a properly defined computer arithmetic. The following
treatment gives a summary of the main ideas of these
papers. Many of the proofs had to be sketched or
completely omitted. In such cases the full information
can be found in the references.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Lacroix:1975:PEM,
author = "Arild Lacroix",
title = "Limit cycles in floating point digital filters",
crossref = "Swamy:1975:PEM",
pages = "475--479",
year = "1975",
MRclass = "94A05",
MRnumber = "55 12278",
bibdate = "Fri Dec 08 12:19:10 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "Krzysztof Sapiecha",
}
@Article{Landauro:1975:ODC,
author = "A. Landauro and J. Lienard",
title = "On Overflow Detection and Correction in Digital
Filters",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "12",
pages = "1226--1228",
month = dec,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224168",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:59 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672761",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Lang:1975:DPA,
author = "Allan L. Lang and Bruce D. Shriver",
title = "The Design of a Polymorphic Arithmetic Unit",
crossref = "IEEE:1975:SCA",
pages = "48--55",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Lang.pdf",
abstract = "This paper presents results which stem from a research
effort concerned with the specification and design of
arithmetic units which can execute nonstandard integer
and floating-point arithmetic. An arithmetic unit is
proposed whose characteristics are based on user
specifications and subsequently is termed a Polymorphic
Arithmetic Unit (PAU). The user binds the identity of
the PAU by specifying the contents of various
descriptors and semantic interpretation tables which
the PAU accesses during its execution. This capability
removes several of the restrictions found in
commercially available arithmetic units and potentially
assists in making mathematically software portable.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Laurie:1975:PIR,
author = "D. P. Laurie",
title = "Propagation of Initial Rounding Error in
{Romberg}-Like Quadrature",
journal = j-BIT,
volume = "15",
number = "3",
pages = "277--282",
month = sep,
year = "1975",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01933660",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:14 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=15&issue=3;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=15&issue=3&spage=277",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Lemeire:1975:CEI,
author = "Frans Lemeire",
title = "Computation of Equivalent Inherent Rounding Errors in
the Solution of a Set of Linear Equations",
journal = j-BIT,
volume = "15",
number = "1",
pages = "65--71",
month = mar,
year = "1975",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01932997",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:14 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=15&issue=1;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=15&issue=1&spage=65",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Linnainmaa:1975:TAS,
author = "Seppo Linnainmaa",
title = "Towards Accurate Statistical Estimation of Rounding
Errors in Floating-Point Computations",
journal = j-BIT,
volume = "15",
number = "2",
pages = "165--173",
month = jun,
year = "1975",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01932690",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65G05",
MRnumber = "58 19090",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=15&issue=2&spage=165",
abstract = "A new method of estimating a posteriori the
statistical characteristics of the rounding errors of
an arbitrary algorithm is presented. This method is
based on a discrete model of the distribution of
rounding errors which makes more accurate estimates
possible. The analysis is given for both rounding and
truncating arithmetic. Finally, some experimental
results are reported.",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@InProceedings{Lipovski:1975:RND,
author = "G. J. Lipovski",
title = "On Residue Number {A/D} and {D/A} Converters",
crossref = "IEEE:1975:SCA",
pages = "197--199",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Lipovski.pdf",
abstract = "A very simple analog to digital converter and digital
to analog converter is described for residue number
digital processing. These simple devices make it
feasible to replace analog components with
comparatively inexpensive digital processors that use
residue, or modulus, arithmetic capable of operating at
very high speeds. Using off-the-shelf integrated
circuits, addition, subtraction or multiplication of
about 15 bits of accuracy can easily be done in as
little as fifty nanoseconds. Any function using these
operations (polynomial expansions, linear filters, Fast
Fourier Transforms) can be economically implemented in
a pipeline or other structure to get very fast systems.
Moreover, a stage in the pipeline can correct for
nonlinearities in the A/D or D/A converters. The simple
devices described herein make residue arithmetic
digital processors extremely attractive for use in fast
analog systems.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3; residue number system",
}
@Article{Liu:1975:REF,
author = "B. Liu and T. Kaneko",
title = "Roundoff error in fast {Fourier} transforms",
journal = j-PROC-IEEE,
volume = "63",
number = "6",
pages = "991--992",
month = jun,
year = "1975",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "The finite word length used in the computer causes
round-off error in the calculation of Fourier
coefficients. When the fast Fourier transform method is
used, the statistical mean-square error has been
previously determined [3] for the case of the
\ldots{}",
}
@Article{Lorez:1975:BGB,
author = "H. Lorez and F. J. Urbanek and H. Will and R. Weiss
and W. Baron and others",
title = "{Buchbesprechungen} ({German}) {Book Reviews}",
journal = j-COMPUTING,
volume = "14",
number = "3",
pages = "315--322",
month = sep,
year = "1975",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/computing.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Kreifelts:1973:OBG}.",
acknowledgement = ack-nj,
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
language = "German",
}
@Book{Luke:1975:MFT,
author = "Y. L. Luke",
title = "Mathematical Functions and their Approximations",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xvii + 568",
year = "1975",
ISBN = "0-12-459950-8",
ISBN-13 = "978-0-12-459950-5",
LCCN = "QA55 .M418",
bibdate = "Thu Sep 1 10:13:15 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
tableofcontents = "Front Matter \\
Copyright \\
Dedication \\
Preface \\
I: The Gamma Function and Related Functions / 1--23 \\
II: The Binomial Function / 24--35 \\
III: Elementary Functions / 36--76 \\
IV: Incomplete Gamma Functions / 77--153 \\
V: The Generalized Hypergeometric Function $_PF_Q$ and
the $G$-Function / 154--256 \\
VI: The Gaussian Hypergeometric Function $_2F_1$ /
257--283 \\
VII: The Confluent Hypergeometric Function / 284--297
\\
VIII: Identification of the $_PF_Q$ and $G$-Functions
with the Special Functions / 298--310 \\
IX: Bessel Functions and Their Integrals / 311--412 \\
X: Lommel Functions, Struve Functions, and Associated
Bessel Functions / 413--427 \\
XI: Orthogonal Polynomials / 428--482 \\
XII: Computation by Use of Recurrence Formulas /
483--489 \\
XIII: Some Aspects of Rational and Polynomial
Approximations / 490--504 \\
XIV: Miscellaneous Topics / 505--516 \\
Bibliography / 517--544 \\
Notation Index / 545--550 \\
Subject Index / 551--568",
}
@Article{Martinson:1975:DMF,
author = "L. Martinson and R. Smith",
title = "Digital matched filtering with pipelined floating
point fast {Fourier} transforms ({FFT}'s)",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "23",
number = "2",
pages = "222--234",
month = apr,
year = "1975",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "A special floating point arithmetic technique for fast
Fourier transform (FFT) processors has been developed.
The implementation of a high-speed pipeline FFT matched
filter using the method employs significantly fewer
components than a fixed-point \ldots{}",
}
@InProceedings{Matula:1975:FSF,
author = "D. W. Matula",
title = "Fixed-Slash and Floating-Slash Arithmetic",
crossref = "IEEE:1975:SCA",
pages = "90--91",
year = "1975",
bibdate = "Wed Nov 14 17:45:51 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Matula.pdf",
abstract = "A finite precision rational number system provides for
representation of a collection of rational numbers
subject to limitations on numerator and denominator
magnitude. In fixed-point and floating-point radix
number systems, only rationals of the form $ i /
\beta^j $, where $ \beta $ is the base, can be
realized. In contrast, a finite precision rational
number system will allow representation of practically
all simple fractions encountered in applications.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{McDonald:1975:TCQ,
author = "T. G. McDonald and R. K. Guha",
title = "The Two's Complement Quasi-Serial Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "12",
pages = "1233--1235",
month = dec,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224170",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:59 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672763",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Meo:1975:ANT,
author = "A. R. Meo",
title = "Arithmetic Networks and Their Minimization Using a New
Line of Elementary Units",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "3",
pages = "258--280",
month = mar,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224207",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:51 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672800",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Miller:1975:SRA,
author = "Webb Miller",
title = "Software for Roundoff Analysis",
journal = j-TOMS,
volume = "1",
number = "2",
pages = "108--128",
month = jun,
year = "1975",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355637.355639",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65G05",
MRnumber = "53 \#9622",
bibdate = "Fri Aug 26 23:44:16 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
reviewer = "James H. Wilkinson",
}
@Article{Nance:1975:IFR,
author = "Richard E. Nance and Claude {Overstreet, Jr.}",
title = "Implementation of {Fortran} Random Number Generators
on Computers with One's Complement Arithmetic",
journal = j-J-STAT-COMPUT-SIMUL,
volume = "4",
number = "3",
pages = "235--243",
month = "????",
year = "1975",
CODEN = "JSCSAJ",
DOI = "https://doi.org/10.1080/00949657508810126",
ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
ISSN-L = "0094-9655",
bibdate = "Thu Jan 05 10:58:18 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fortran1.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/00949657508810126",
abstract = "Random number generators can be programmed in FORTRAN
using several methods on 1's complement machines. We
have presented several methods for the SRU 1107--1108
and CDC 6000 and CYBER series, the two most popular
that utilize 1's complement arithmetic. We believe the
logical mask method to be the most efficient technique
based on execution time on both machines. This method
requires only a little more than one-half the time of
the signed residue method on the SRU 1107--1108 and a
little more than two thirds the time of the unsigned
residue method on the CDC 6000--CYBER. A fast composite
generator in FORTRAN uses the logical mask method
combined with the FLD function to implement the table
approach of MacLaren and Marsaglia (1965). This
generator proves to be more than twice as fast as a
previous one for the SRU 1108, Marsaglia and Bray
(1968)",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Computation and Simulation",
journal-URL = "http://www.tandfonline.com/loi/gscs20",
onlinedate = "20 Mar 2007",
}
@Article{Nelson:1975:PPF,
author = "James M. Nelson and Charles E. Cohn",
title = "Parallel Processing in {FORTRAN} with Floating-Point
Hardware",
journal = j-SPE,
volume = "5",
number = "1",
pages = "65--68",
month = jan # "\slash " # mar,
year = "1975",
CODEN = "SPEXBL",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Sat May 31 13:36:16 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/spe.bib",
acknowledgement = ack-nhfb,
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}
@Article{Newbery:1975:PES,
author = "A. C. R. Newbery",
title = "Polynomial Evaluation Schemes",
journal = j-MATH-COMPUT,
volume = "29",
number = "132",
pages = "1046--1050",
month = oct,
year = "1975",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Dept. of Computer Sci., Univ. of Kentucky, Lexington,
KY, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "floating; function evaluation; point arithmetic;
polynomial evaluation algorithm; polynomials; round off
error",
treatment = "T Theoretical or Mathematical",
}
@Manual{NSC:1975:IFP,
author = "{National Semiconductor Corporation}",
title = "{IMP-16F\slash 400} floating point firmware technical
description",
type = "Publication - National Semiconductor Corporation no.
4200072A",
organization = "National Semiconductor Corporation",
address = "Santa Clara, CA, USA",
pages = "16",
year = "1975",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Microprocessors --- Handbooks, manuals, etc.;
Microprogramming --- Handbooks, manuals, etc.",
remark = "At head of title: Integrated microprocessor-16.",
}
@Article{OKeefe:1975:NFB,
author = "K. H. O'Keefe",
title = "A Note on Fast Base Extension for Residue Number
Systems with Three Moduli",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "11",
pages = "1132--1133",
month = nov,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1975.224147",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:58 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672740;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35091",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "An algorithm is given for the base-extension (BE)
computation in residue number systems that requires the
standard four steps (for systems with three moduli) but
which saves hardware. Furthermore, for the particular
moduli m-1, m, and m+1 it is \ldots{}",
}
@InCollection{Phillips:1975:BC,
author = "E. William Phillips",
title = "Binary Calculation",
crossref = "Randell:1975:ODC",
pages = "293--304",
year = "1975",
bibdate = "Wed Oct 13 09:51:37 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "The 1936 epigraph credited to this author in
\cite[Chapter 7]{Coonen:1984:CPS} says: ``The ultimate
aim is to persuade all of the civilized world to
abandon the decimal numeration and to use octonal in
its place; to discontinue counting in tens and to count
in eights instead. However, it seems unlikely that the
whole civilized world will be persuaded to complete
this change during the next twelve months, having
previously declined similar invitations.''",
}
@InProceedings{Rao:1975:TIS,
author = "T. R. N. Rao and D. W. Matula",
title = "The {Third IEEE Symposium on Computer Arithmetic}:
Foreword",
crossref = "IEEE:1975:SCA",
pages = "v--v",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_contents.pdf;
http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_foreword.pdf;
http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_preface.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Reiser:1975:EDFa,
author = "John F. Reiser and Donald E. Knuth",
title = "Evading the drift in floating-point addition",
journal = j-INFO-PROC-LETT,
volume = "3",
number = "3",
pages = "84--87",
month = jan,
year = "1975",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Sun Dec 04 12:21:37 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Reiser:1975:EDFb}.",
acknowledgement = ack-nhfb # "\slash " # ack-nj,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@Article{Reiser:1975:EDFb,
author = "John F. Reiser and Donald E. Knuth",
title = "Erratum: ``{Evading} the drift in floating-point
addition''",
journal = j-INFO-PROC-LETT,
volume = "3",
number = "5",
pages = "164--164",
month = may,
year = "1975",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Sun Dec 04 12:21:42 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Reiser:1975:EDFa}.",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@Article{Rokne:1975:ACI,
author = "J. Rokne and P. Lancaster",
title = "Algorithm 86. Complex Interval Arithmetic",
journal = j-COMP-J,
volume = "18",
number = "1",
pages = "83--85",
month = feb,
year = "1975",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods); C7310 (Mathematics
computing)",
corpsource = "Univ. Calgary, Alta., Canada",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "algorithm; complex interval arithmetic; digital
arithmetic; floating point; real numbers; subroutines",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Rubinfield:1975:PMB,
author = "L. P. Rubinfield",
title = "A Proof of the Modified {Booth}'s Algorithm for
Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "10",
pages = "1014--1015",
month = oct,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224114",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:57 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672707",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Senzig:1975:CA,
author = "Don Senzig",
title = "Calculator Algorithms",
journal = "IEEE Compcon Reader Digest",
pages = "139--141",
year = "1975",
bibdate = "Fri Nov 28 19:19:40 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 75CH0920-9C.",
abstract = "This paper discusses algorithms for generating the
trigonometric, exponential, and hyperbolic functions
and their inverses. No invention is claimed here. The
algorithm for logarithm was used by Briggs in compiling
his table of logarithms in the 1600's. Other earlier
references are [cited]. The development presented here
is, perhaps, more direct than those given in the above
references but leads to the same result.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@Article{Shimizu:1975:REF,
author = "Tatsujiro Shimizu and Tsunemichi Oohashi",
title = "Rounding errors in floating point addition",
journal = "TRU Math.",
volume = "11",
pages = "41--50",
year = "1975",
MRclass = "65G05",
MRnumber = "55 4646",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "R. P. Brent",
}
@InProceedings{Shriver:1975:BCA,
author = "B. D. Shriver and E. K. Reuter",
title = "A Bibliography on Computer Arithmetic",
crossref = "IEEE:1975:SCA",
pages = "241--249",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Biography.pdf",
abstract = "This bibliography on computer arithmetic uses, by and
large, the format and abbreviations employed by
Computing Reviews. It is presented in alphabetical
order only and not by individual topics. The topics
included, however, span the abstract and implementation
problems associated with finite precision computer
arithmetic.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Shriver:1975:UUN,
author = "Bruce D. Shriver and Peter Kornerup",
title = "The {UNRAU} --- a {Unified Numeric Representation
Arithmetic Unit}",
crossref = "IEEE:1975:SCA",
pages = "179--184",
year = "1975",
bibdate = "Wed Nov 14 17:46:23 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Shriver.pdf",
abstract = "A companion paper entitled, ``A Unified Numeric Data
Type in Pascal'', proposes the substitution of the
standard data type {\em real\/} of the language Pascal
with a unified data representation termed {\em
numeric}. The {\em numeric\/} data type can represent a
variety of arithmetic operands such as integers,
normalized floating point numbers, and centered-radius
intervals.\par
This paper describes an arithmetic unit which is
capable of executing the standard arithmetic operations
(addition, subtraction, multiplication, and division)
on pairs of operands specified to be of the {\em
numeric\/} data type. This arithmetic unit, called the
UNRAU --- Unified Numeric Representation Arithmetic
Unit, supports operations on operands externally
represented as 5-tuples $ (t, a, e, f, r) $. The UNRAU
provides for automatic conversion among the various
data types and can also be used to perform an explicit
conversion on a single operand.\par
It is intended to implement the UNRAU on a dynamically
microprogrammable microprocessor to determine what host
facilities are required to efficiently realize such an
arithmetic unit and to experiment with the high level
language support of such a unit.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Smith:1975:CPC,
author = "Alan Jay Smith",
title = "Comments on a paper by {T. C. Chen} and {I. T. Ho}",
journal = j-CACM,
volume = "18",
number = "8",
pages = "463--463",
month = aug,
year = "1975",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:22:40 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#Smith75a;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Chen:1975:SER}.",
acknowledgement = ack-nhfb,
classcodes = "C6130 (Data handling techniques)",
corpsource = "Univ. of California, Berkeley, CA, USA",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "advantages; alternatives; binary coded decimal; codes;
coding; compression of numbers; data handling; decimal
data; decimal floating-point arithmetic; decoding;
deletions; Huffman codes; insertions; permutations;
storage efficient representation; variable length
codes",
oldlabel = "Smith75a",
treatment = "G General Review; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Smith75a",
}
@Article{Smith:1975:SCO,
author = "Cyril Stanley Smith",
title = "A {Seventeenth-Century} Octonary Arithmetic",
journal = j-ISIS,
volume = "66",
number = "3",
pages = "390--394",
month = sep,
year = "1975",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:29:19 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302314;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/isis1970.bib",
URL = "http://www.jstor.org/stable/228846",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/page/journal/isis/about.html",
}
@Article{Soule:1975:AAB,
author = "Stephen Soule",
title = "Addition in an Arbitrary Base Without Radix
Conversion",
journal = j-CACM,
volume = "18",
number = "6",
pages = "344--346",
month = jun,
year = "1975",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:23:30 MST 2001",
bibsource = "Compendex database;
ftp://ftp.ira.uka.de/pub/bibliography/Theory/Seiferas/1975.bib;
http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#Soule75;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents a generalization of an old
programming technique; using it, one may add and
subtract numbers represented in any radix, including a
mixed radix, and stored one digit per byte in bytes of
sufficient size. Radix conversion is unnecessary, no
looping is required, and numbers may even be stored in
a display (I/O) format. Applications to Cobol, MIX, and
hexadecimal sums are discussed.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques)",
classification = "723; 921",
corpsource = "Univ. of Calgary, Calgary, Alta., Canada",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
journalabr = "Commun ACM",
keywords = "add; addition; arbitrary base; arbitrary radix
arithmetic; Cobol display arithmetic; computer systems
programming; data handling; decimal arithmetic; decimal
floating-point arithmetic; digital arithmetic;
mathematical techniques --- Digital Arithmetic; MIX
arithmetic; mixed radix arithmetic; numbers;
programming; radix conversion; subtract; subtraction;
without radix conversion",
oldlabel = "Soule75",
treatment = "A Application; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Soule75",
}
@InProceedings{Stephenson:1975:CSP,
author = "Charles Stephenson",
title = "Case Study of the Pipelined Arithmetic Unit for the
{TI Advanced Scientific Computer}",
crossref = "IEEE:1975:SCA",
pages = "168--173",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Stephenson.pdf",
abstract = "Many scientific applications today require computers
which are very fast and capable of processing large
amounts of data. Some advances in scientific processing
have been slowed due to the lack of supercomputer
capabilities which are required primarily in the area
of Central Processor speed and the availability of
large amounts of high speed memory. Particularly in the
fields of modeling and simulation, additional speed and
memory capacity are desired to allow increased
resolution of the experiment. Technological
developments :In such things as integrated circuits,
multilayer printed circuit boards, memory speeds, and
others have contributed to the ability of computer
manufacturers to serve this market. In addition to
these developments, however, large advances had to be
realized from the standpoint of the basic computer
architecture. The concept of pipelining has provided an
answer to the large data execution rate required.
Pipelined capabilities in the form of arithmetic units
and special purpose functional units are included in
machines such as the CDC 7600, IBM 360/195, CDC
STAR-100, etc. The Texas Instruments Advanced
Scientific Computer (ASC) uses the pipeline concept
throughout the Central Processor and carries the
concept throughout the Central Processor and carries
the concept further to include vector instructions in
response to the high execution rates required. 3",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Sterbenz:1975:UA,
author = "Pat H. Sterbenz",
title = "Understandable Arithmetic",
crossref = "IEEE:1975:SCA",
pages = "33--35",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Sterbenz.pdf",
abstract = "Since the floating-point operations form the basic
steps in our programs, the programmer has to understand
the results that will be produced by these operations.
This paper discusses operations which have been or
might be implemented in the hardware. The emphasis is
on making the results easy for the user to
understand.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Book{Stone:1975:ICA,
editor = "Harold S. Stone and Tien Chi Chen and Michael J. Flynn
and Samuel H. Fuller and others",
title = "Introduction to computer architecture",
publisher = "Science Research Associates",
address = "Chicago, IL, USA",
pages = "x + 565",
year = "1975",
ISBN = "0-574-18405-8",
ISBN-13 = "978-0-574-18405-4",
LCCN = "QA76.5 .I7; QA76.9.A73 I57; QA76.5 .I63; QA76.9.A73
I57 1975",
bibdate = "Fri Nov 9 19:22:07 MST 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
series = "SRA computer science series",
acknowledgement = ack-nhfb,
subject = "Electronic digital computers",
}
@InProceedings{Svoboda:1975:SCA,
author = "Antonin Svoboda",
title = "Self-Checking Adder for Large Scale Integration",
crossref = "IEEE:1975:SCA",
pages = "108--112",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Svoboda.pdf",
abstract = "The testing of LSI chips is expensive and
unsatisfactory. On the other hand there are cases (as
in space ship computers) where a damaged chip must be
localized and replaced. The use of self-checking chips
seems to be one of several possible solutions of this
problem. The theory of the structure of self-checking
logical circuit is covered by literature at least at
the fundamental form (see References). However, even
when the design principles are supposed to be known,
their application to the actual creation of a
self-checking circuit of an average complexity is and
will remain an art. The reason is quite simple and
fundamental optimization of design criteria
(engineering qualifications, performance and physical
properties of components of the circuits are entities
possessing different physical dimensions --- it is
impossible to qualify, for instance, two circuits A, B
designed for the same task by comparing their speeds
and costs if A is faster than B but B is cheaper than
A) will never be objective and independent of the
talent or whim of the circuit designer.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Swartzlander:1975:SLN,
author = "E. E. {Swartzlander, Jr.} and A. G. Alexopoulos",
title = "The Sign\slash Logarithm Number System",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "12",
pages = "1238--1242",
month = dec,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224172",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:59 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Hongyuan:1986:CSL}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672765",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Toma:1975:CLA,
author = "C. I. Toma",
title = "Cellular Logic Array for High-Speed Signed Binary
Number Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "9",
pages = "932--935",
month = sep,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224340",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:57 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672933",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Trivedi:1975:LAD,
author = "Kishor S. Trivedi and Milo{\v{s}} D. Ercegovac",
title = "On-Line Algorithms for Division and Multiplication",
crossref = "IEEE:1975:SCA",
pages = "161--177",
year = "1975",
bibdate = "Fri Dec 08 10:45:59 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Trivedi_2.pdf",
abstract = "In this paper we are considering problems of division
and multiplication in a computational environment in
which all but basic arithmetic operations satisfy
``on-line'' property: to generate $ j^{\mbox {th}} $
digits of the result it is necessary and sufficient to
have argument(s) available up to the $ (j +
\delta)^{\mbox {th}} $ digit, where the index
difference $ \delta $ is a small positive
constant.
Such an environment, due to its potential to perform a
sequence of operations in an overlapped fashion, could
conveniently speed up an arithmetic multiprocessor
structure it could be useful in certain real-time
applications, with inherent on-line properties. The
on-line property implies a left-to-right digit-by-digit
type of algorithm and consequently, a redundant
representation, at least of the results. For addition
and subtraction such algorithms satisfying on-line
property can be easily specified. Multiplication
requires a somewhat more elaborate approach and there
are several possible ways of defining an on-line
algorithm. However, the existence of an on-line
division algorithm is not obvious and its analysis
appears interesting.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Trivedi:1975:UCF,
author = "Kishor S. Trivedi",
title = "On the Use of Continued Fractions for Digital Computer
Arithmetic",
crossref = "IEEE:1975:SCA",
pages = "137--146",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Trivedi_1.pdf",
abstract = "Recently, there has been some interest in the use of
continued fractions for digital hardware calculations.
We require that the coefficients of the continued
fractions be integral powers of two. As a result well
known continued fraction expansions of functions cannot
be used. Methods of expansion of a large number of
functions are presented.\par
We show that the problem of selection of coefficients
of the continued fractions does not have practical
solution in most of the cases we have considered. We
conjecture that the solution of a polynomial equation
is the only problem that can be solved in our
formulation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@MastersThesis{Tzaferos:1975:EBD,
author = "Konstantina Tzaferos",
title = "Error bounds due to index of significance
specifications in floating-point operations with
encoded mantissa lengths",
type = "Thesis ({M.S.})",
school = "California State University, Chico",
address = "Chico, CA, USA",
pages = "vi + 43",
year = "1975",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.",
}
@Article{Wakerly:1975:DUM,
author = "J. F. Wakerly",
title = "De