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@InProceedings{Ohhashi:1985:HSC,
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title = "High-Speed Computation of Unary Functions",
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bibd+?indexsqlite_autoindex_bibtab_1bibtabrithm{\'e}tique} Binaire.
({French}) [{Explanation} of binary arithmetic]",
journal = "M{\'e}moires de math{\'e}matique et de physique de l
Acad{\'e}mie royale des sciences",
volume = "??",
number = "??",
pages = "85--89",
month = "????",
year = "1703",
bibdate = "Fri Mar 17 08:48:17 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Leibniz is often credited with the invention of the
binary number system, but there is other work from his
era, and detailed analysis of Leibniz's use of binary
numbers. See
\cite{Greve:1966:HLR,Glaser:1969:HMN,Glaser:1971:HBO,Lautz:1979:JLD,Glaser:1981:HBO,Esmay:2017:HNS,Strickland:2022:LBI,Zlatopolski:2023:PAV}",
URL = "https://hal.archives-ouvertes.fr/ads-00104781/document",
acknowledgement = ack-nhfb,
language = "French",
}
de physique de l Academie royale des sciences85--891703Fri Mar 17 08:48:17 2023https://www.math.utah.edu/pub/tex/bib/fparith.bib2023.03.17 08:48:17 ???Leibniz is often credited with the invention of the binary number system, but there is other work from his era, and detailed analysis of Leibniz's use of binary numbers. See cite Greve:1966:HLR,Glaser:1969:HMN,Glaser:1971:HBO,Lautz:1979:JLD,Glaser:1981:HBO,Esmay:2017:HNS,Strickland:2022:LBI,Zlatopolski:2023:PAVhttps://hal.archives-ouvertes.fr/ads-00104781/documentFrenchack-nhfbG.-W. LeibnizLeibniz is often credited with the invention of the binary number system, but there is other work from his era, and detailed analysis of Leibniz's use of binary numbers. See \cite{Greve:1966:HLR,Glaser:1969:HMN,Glaser:1971:HBO,Lautz:1979:JLD,Glaser:1981:HBO,Esmay:2017:HNS,Strickland:2022:LBI,Zlatopolski:2023:PAV}Explication de {l'Arithm{\'e}tique} Binaire. ({French}) [{Explanation} of binary arithmetic]
@Article{Leibniz:1703:EAB,
author = "G.-W. Leibniz",
title = "Explication de {l'Arithm{\'e}tique} Binaire.
({French}) [{Explanation} of binary arithmetic]",
journal = "M{\'e}moires de math{\'e}matique et de physique de l
Acad{\'e}mie royale des sciences",
volume = "??",
number = "??",
pages = "85--89",
month = "????",
year = "1703",
bibdate = "Fri Mar 17 08:48:17 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Leibniz is often credited with the invention of the
binary number system, but there is other work from his
era, and detailed analysis of Leibniz's use of binary
numbers. See
\cite{Greve:1966:HLR,Glaser:1969:HMN,Glaser:1971:HBO,Lautz:1979:JLD,Glaser:1981:HBO,Esmay:2017:HNS,Strickland:2022:LBI,Zlatopolski:2023:PAV}",
URL = "https://hal.archives-ouvertes.fr/ads-00104781/document",
acknowledgement = ack-nhfb,
language = "French",
}icus Perfectus Qui tria numerare nescit,
\ldots{}. ({Latin}) [{A} Perfect Arithmetic for who
does not know how to count to three]",
publisher = "????",
address = "Prague, Czechoslovakia",
pages = "????",
year = "1712",
bibdate = "Fri Mar 17 08:56:14 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://play.google.com/books/reader?id=cNxdAAAAcAAJ",
acknowledgement = ack-nhfb,
longtitle = "Arithmeticus Perfectus Qui tria numerare nescit, sen
Arithmetica dualis in qua Numerando non proceditur,
nisi ad duo, \& tamen omnes questiones Arithmetic{\ae}
negoti{\^o} facile enodar possunt ad perilsturem equite
Mathematic{\ae}. ({Latin}) [{A} Perfect Arithmetic for
who does not know how to count to three, is a dual
arithmetic in which he does not proceed to numbering
except to two, and yet all the questions of arithmetic
business can easily be entangled to the peril of the
mathematician]",
}to three]",
publisher = "????",
address = "Prague, Czechoslovakia",
pages = "????",
year = "1712",
bibdate = "Fri Mar 17 08:56:14 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://play.google.com/books/reader?id=cNxdAAAAcAAJ",
acknowledgement = ack-nhfb,
longtitle = "Arithmeticus Perfectus Qui tria numerare nescit, sen
Arithmetica dualis in qua Numerando non proceditur,
nisi ad duo, \& tamen omnes questiones Arithmetic{\ae}
negoti{\^o} facile enodar possunt ad perilsturem equite
Mathematic{\ae}. ({Latin}) [{A} Perfect Arithmetic for
who does not know how to count to three, is a dual
arithmetic in which he does not proceed to numbering
except to two, and yet all the questions of arithmetic
business can easily be entangled to the peril of the
mathematician]",
}
þþ‘s^ #-'1=o;„}y'…E‘articlefparith.bibLeibniz:1703:EABG.-W. LeibnizExplication de l'Arithmetique Binaire. (French) [Explanation of binary arithmetic]Memoires de mathematique et
‹‹Žj[ #/A‚9=o;uA‚“bookfparith.bibPelicano:1712:APQWenceslao Josepho PelicanoArithmeticus Perfectus Qui tria numerare nescit, ldots . (Latin) [A Perfect Arithmetic for who does not know how to count to three]Prague, Czechoslovakia1712Fri Mar 17 08:56:14 2023https://www.math.utah.edu/pub/tex/bib/fparith.bib2023.03.17 08:56:14 ???https://play.google.com/books/reader?id=cNxdAAAAcAAJack-nhfbWenceslao Josepho PelicanoArithmeticus Perfectus Qui tria numerare nescit, \ldots{}. ({Latin}) [{A} Perfect Arithmetic for who does not know how to count to three]
@Book{Pelicano:1712:APQ,
author = "Wenceslao Josepho Pelicano",
title = "Arithmeticus Perfectus Qui tria numerare nescit,
\ldots{}. ({Latin}) [{A} Perfect Arithmetic for who
does not know how to count unt of Negativo-Affirmative Arithmetick",
journal = j-PHILOS-TRANS-R-SOC-LOND,
volume = "34",
number = "392--398",
pages = "161--173",
month = "????",
year = "1726",
CODEN = "PTRSAV",
DOI = "https://doi.org/10.1098/rstl.1726.0032",
ISSN = "0370-2316 (print), 2053-9207 (electronic)",
bibdate = "Tue Jul 28 14:21:05 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith22.gforge.inria.fr/slides/s2-ercegovac.pdf",
acknowledgement = ack-nhfb,
fjournal = "Philosophical transactions of the Royal Society of
London",
journal-URL = "http://rsta.royalsocietypublishing.org/",
remark = "Early work on signed-digit arithmetic, reported by
Milo{\v{s}} Ercegovac in a talk at the ARITH'22
conference, Lyon, France, June 2015.",
}Colson:1726:SAN,
author = "John {Colson, F.R.S.}",
title = "A Short Account of Negativo-Affirmative Arithmetick",
journal = j-PHILOS-TRANS-R-SOC-LOND,
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number = "392--398",
pages = "161--173",
month = "????",
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bibdate = "Tue Jul 28 14:21:05 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
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acknowledgement = ack-nhfb,
fjournal = "Philosophical transactions of the Royal Society of
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journal-URL = "http://rsta.royalsocietypublishing.org/",
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conference, Lyon, France, June 2015.",
}
H¶HˆL[ ##-+u=o;a+iu‡s
unpublishedŽ?[ #+3s?Y5=o;y‚[7s
articlefparith.bibColson:1726:SANJohn Colson, F.R.S.A Short Account of Negativo-Affirmative Arithmetickj-PHILOS-TRANS-R-SOC-LOND34392--398161--1731726PTRSAVhttps://doi.org/10.1098/rstl.1726.00320370-2316 (print), 2053-9207 (electronic) OR 03702316 (print), 20539207 (electronic)Tue Jul 28 14:21:05 2015https://www.math.utah.edu/pub/tex/bib/fparith.bib2015.07.28 14:21:05 ???http://arith22.gforge.inria.fr/slides/s2-ercegovac.pdfPhilosophical transactions of the Royal Society of LondonEarly work on signed-digit arithmetic, reported by Milos Ercegovac in a talk at the ARITH'22 conference, Lyon, France, June 2015.ack-nhfbhttp://rsta.royalsocietypublishing.org/John {Colson, F.R.S.}A Short Account of Negativo-Affirmative Arithmetick
@Article{atical powers of the calculating engine",
month = dec,
year = "1837",
bibdate = "Wed Oct 13 11:09:59 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Manuscript held by Museum of the History of Science,
Oxford, UK. Reprinted in \cite[\S
2.1]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}fparith.bibBabbage:1837:MPCCharles BabbageOn the mathematical powers of the calculating engine161--173dec121837Wed Oct 13 11:09:59 2010https://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:09:59 ???Manuscript held by Museum of the History of Science, Oxford, UK. Reprinted in cite [ 2.1]Randell:1982:ODC.ack-nhfbCharles BabbageManuscript held by Museum of the History of Science, Oxford, UK. Reprinted in \cite[\S 2.1]{Randell:1982:ODC}.On the mathematical powers of the calculating engine
@Unpublished{Babbage:1837:MPC,
author = "Charles Babbage",
title = "On the mathematical powers of the calculating engine",
month = dec,
year = "1837",
bibdate = "Wed Oct 13 11:09:59 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Manuscript held by Museum of the History of Science,
Oxford, UK. Reprinted in \cite[\S
2.1]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}ct of a new system of arithmetic, weight, measure
and coins, proposed to be called the tonal system, with
sixteen to the base",
publisher = "J. B. Lippincott and Co.",
address = "Philadelphia, PA, USA",
pages = "106",
year = "1862",
LCCN = "QC96 .N95",
bibdate = "Sat Oct 29 10:28:27 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://unifoundry.com/tonal/;
https://catalog.hathitrust.org/Record/011602816;
https://lccn.loc.gov/04025433",
acknowledgement = ack-nhfb,
author-dates = "Johan Vilhelm Nystr{\"o}m (1824--1885)",
remark = "Thanks to Paul Hardy of Unifoundry in San Diego, CA,
USA, for information about Nystrom's promotion of
hexadecimal arithmetic, and for creating a Web site
about Nystrom's tonal system, as well as developing
Unicode-compatible fonts to represent the additional
digits needed by the system.",
subject = "Weights and measures; Numeration; base-16 arithmetic;
hexadecimal arithmetic",
}9 10:28:27 MDThttp://unifoundry.com/tonal/; https://catalog.hathitrust.org/Record/011602816; https://lccn.loc.gov/04025433Thanks 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.Weights and measures; Numeration; base-16 arithmetic; hexadecimal arithmeticack-nhfbJohan Vilhelm Nystrom (1824--1885)John W. (John William) NystromProject of a new system of arithmetic, weight, measure and coins, proposed to be called the tonal system, with sixteen to the base
@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",
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bibdate = "Sat Oct 29 10:28:27 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://unifoundry.com/tonal/;
https://catalog.hathitrust.org/Record/011602816;
https://lccn.loc.gov/04025433",
acknowledgement = ack-nhfb,
author-dates = "Johan Vilhelm Nystr{\"o}m (1824--1885)",
remark = "Thanks to Paul Hardy of Unifoundry in San Diego, CA,
USA, for information about Nystrom's promotion of
hexadecimal arithmetic, and for creating a Web site
about Nystrom's tonal system, as well as developing
Unicode-compatible fonts to represent the additional
digits needed by the system.",
subject = "Weights and measures; Numeration; base-16 arithmetic;
hexadecimal arithmetic",
}
,,“E_ #-I‚=7E';e„M%QI‚•bookfparith.bibNystrom:1862:PNSJohn W. (John William) NystromProject of a new system of arithmetic, weight, measure and coins, proposed to be called the tonal system, with sixteen to the baseJ. B. Lippincott and Co.Philadelphia, PA, USA1061862QC96 .N95Sat Oct 29 10:28:27 MDT 2016https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2016.10.2ations of Multiplication and
Division",
journal = j-SCI-AMER,
volume = "32",
number = "3",
pages = "41--42",
day = "16",
month = jan,
year = "1875",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican01161875-41",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Fri May 17 10:29:24 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciam1870.bib",
URL = "http://www.nature.com/scientificamerican/journal/v32/n3/pdf/scientificamerican01161875-41.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}onymousThe Arithmetical Operations of Multiplication and Division
@Article{Anonymous:1875:AOM,
author = "Anonymous",
title = "The Arithmetical Operations of Multiplication and
Division",
journal = j-SCI-AMER,
volume = "32",
number = "3",
pages = "41--42",
day = "16",
month = jan,
year = "1875",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican01161875-41",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Fri May 17 10:29:24 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciam1870.bib",
URL = "http://www.nature.com/scientificamerican/journal/v32/n3/pdf/scientificamerican01161875-41.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
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77>^ #1!w57EY;G3]articlefparith.bibAnonymous:1875:AOMAnonymousThe Arithmetical Operations of Multiplication and Divisionj-SCI-AMER32341--4216jan11875SCAMAChttps://doi.org/10.1038/scientificamerican01161875-410036-8733 (print), 1946-7087 (electronic) OR 00368733 (print), 19467087 (electronic)0036-8733 OR 00368733Fri May 17 10:29:24 MDT 2013https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sciam1870.bib2013.05.17 10:29:24 MDThttp://www.nature.com/scientificamerican/journal/v32/n3/pdf/scientificamerican01161875-41.pdfScientific Americanack-nhfbhttp://www.nature.com/scientificamericanAnviating Multiplication",
journal = j-SCI-AMER,
volume = "41",
number = "12",
pages = "184--184",
day = "20",
month = sep,
year = "1879",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican09201879-184",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Fri May 17 10:36:54 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciam1870.bib",
URL = "http://www.nature.com/scientificamerican/journal/v41/n12/pdf/scientificamerican09201879-184.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}ttp://www.nature.com/scientificamericanAnonymousThree Rules for Abbreviating Multiplication
@Article{Anonymous:1879:TRA,
author = "Anonymous",
title = "Three Rules for Abbreviating Multiplication",
journal = j-SCI-AMER,
volume = "41",
number = "12",
pages = "184--184",
day = "20",
month = sep,
year = "1879",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican09201879-184",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Fri May 17 10:36:54 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciam1870.bib",
URL = "http://www.nature.com/scientificamerican/journal/v41/n12/pdf/scientificamerican09201879-184.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
ll \ #1c!y57EY;K3]cŽOarticlefparith.bibAnonymous:1879:TRAAnonymousThree Rules for Abbreviating Multiplicationj-SCI-AMER4112184--18420sep91879SCAMAChttps://doi.org/10.1038/scientificamerican09201879-1840036-8733 (print), 1946-7087 (electronic) OR 00368733 (print), 19467087 (electronic)0036-8733 OR 00368733Fri May 17 10:36:54 MDT 2013https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/sciam1870.bib2013.05.17 10:36:54 MDThttp://www.nature.com/scientificamerican/journal/v41/n12/pdf/scientificamerican09201879-184.pdfScientific Americanack-nhfbh!$cy of use of the different digits
in natural numbers",
journal = j-AM-J-MATH,
volume = "4",
number = "1/4",
pages = "39--40",
year = "1881",
CODEN = "AJMAAN",
ISSN = "0002-9327 (print), 1080-6377 (electronic)",
ISSN-L = "0002-9327",
bibdate = "Thu Feb 15 16:35:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0002-9327%281881%294%3A1%2F4%3C39%3ANOTFOU%3E2.0.CO%3B2-K",
abstract = "That the ten digits do not occur with equal frequency
must be evident to any one making much use of
logarithmic tables, and noticing how much faster the
first pages wear out than the last ones. The first
significant figure is oftener 1 than any other digit,
and the frequency diminishes up to 9.",
acknowledgement = ack-nhfb,
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journal = "Technol. Q.",
volume = "1",
number = "??",
pages = "194--207",
month = "????",
year = "1888",
bibdate = "Mon May 21 17:12:03 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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@Article{AMD:1988:IFP,
author = "{Advanced Micro Devices}",
title = "{IEEE} float œM¹
@Article{Aamodt:2008:CTI,
author = "Tor M. Aamodt and Paul Chow",
title = "CompilUhˆ@‘
@Article{Abad:2023:HAT,
author = "Sudeh Shirkavand Saleh Abad and Mohammad Hossein
t'ˆW‘/
@Article{Abbasbandy:2004:USA,
author = "S. Abbasbandy and M. A. Fariborzi Araghi",
titleJŽI
@Article{Abbott:1999:ASS,
author = "P. H. Abbott and D. G. Brush and C. W. {Clark III} and<Ò’]¥;
@Article{Abbott:2012:TFA,
author = "John Abbott",
title = "Twin-float arithmetic"]ŠA•
@Article{Abdallah:2005:MRN,
author = "M. Abdallah and A. Skavantzos",
title = "OnMˆk‘W
@Article{Abdelfattah:2020:MMB,
author = "Ahmad Abdelfattah and Stanimire Tomov and Jack
n¡
rßL¹&“‡m[
@Article{Abdi:2023:FEF,
author = "Athena Abdi and Sina Shahoveisi",
title = "{FT-t*‡jU
@Article{Abed:2003:VIL,
author = "K. H. Abed and R. E. Siferd",
title = "{VLSI} iG•Š$”I
@Article{Aberbour:1998:PMF,
author = "M. Aberbour and A. Houelle and H. Mehrez and N.
;-†n]
@Article{Abtahi:2005:CFR,
author = "M. Abtahi and P. Siy",
title = "Core functionM‡Ž3
@Article{Abtahi:2007:FSD,
author = "M. Abtahi and P. Siy",
title = "The Factor-2 R’ˆ:u
@Article{Abu-El-Haija:1979:AER,
author = "A. Abu-El-Haija and A. Peterson",
title = õ…]‹;
@Article{Acha:1992:LOF,
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journal = j-AMER-MATH-MONTHLY,
volume = "4",
number = "8/9",
pages = "204--208",
month = aug # "\slash " # sep,
year = "1897",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:37:08 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
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number = "9",
pages = "77--91",
year = "1909",
CODEN = "SPRDAP",
ISSN = "0371-2303",
bibdate = "Wed Oct 13 11:14:08 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
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ŠeZ #-'UE'57=o;_oI'g]‹;articlefparith.bibBabbage:1910:BBAH. P. BabbageBabbage: Babbage's analytical enginej-MONTHLY-NOT-ROY-ASTRON-SOC70517--526, 6451910MNRAA40035-8711 (print), 1365-2966 (electronic) OR 00358711 (print), 13652966 (electronic)0035-8711 OR 00358711Wed Oct 13 11:12:08 2010https<is sur l'automatique. Sa definition. {{\'E}}tendue
th{\'e}orique de ses applications ({French}) [{Essays}
on automation. {Its} definition. {Theoretical} extent
of its applications]",
journal = j-REV-GEN-SCI-PURES-APPL,
volume = "??",
number = "??",
pages = "601--611",
day = "15",
month = nov,
year = "1915",
ISSN = "0370-7431",
bibdate = "Wed Oct 13 11:15:08 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 2.5]{Randell:1982:ODC}.
Translated by Mr. R. Basu.",
acknowledgement = ack-nhfb,
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language = "French",
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Square Roots of Integers",
journal = j-AMER-MATH-MONTHLY,
volume = "31",
number = "10",
pages = "482--484",
month = dec,
year = "1924",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:37:29 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
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acknowledgement = ack-nhfb,
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@Article{Adams:1967:SCP,
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title = "A stopping criterionÞ‹–%
@Article{Adams:2018:RFF,
author = "Ulf Adams",
title = "{Ry{\=u}}: fast float-to-hÙ\¡9
@Article{Adams:2019:RRP,
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title = n¥†ti
@Article{Adikari:2011:HBT,
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[P³~ç}
@Article{Agarwal:1986:NSV,
author = "Ramesh C. Agarwal and James W. Cooley and Fred G.
¹ŠN•
@Article{Agarwal:1987:CNS,
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ææ†Y #/;?9/=o;;?†QÓbookfparith.bibKarpinski:1925:HALouis Charles KarpinskiThe History of ArithmeticRand McNally & CompanyNew York, NY, USAxi + 2001925Fri Nov 28 18:09:05 2003https://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 18:09:05 ???ack-mfcLouis Charles KarpinskiThe History of Arithmetic
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Á‹!] ##;357E;GcIŒarticlefparith.bibJ:1930:RPRbR. A. J.Recent Publications: Reviews: em Standard Table of Square Roots, by L. M. Milne-Thomsonj-AMER-MATH-MONTHLY376314--314jun61930AMMYAE0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)0002-9890 OR 00029890Mon Jun 28 12:35:55 MDT 1999https://www.math.utah.edu/pSŒ4[ #+)e57Eƒ;QO)ikarticlefparith.bibCajori:1927:EAPFlorian CajoriThe Earliest Arithmetic Published in Americaj-ISIS93391--401dec121927ISISA40021-1753 (print), 1545-6994 (electronic) OR 00211753 (print), 15456994 (electronic)0021-1753 OR 00211753Tue Jul 30 21:57:45 MDT 2013http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i214411; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/isis1920.bib2013.07.30 21:57:45 MP {{\em Standard Table of
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ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:36:47 MDT 1999",
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acknowledgement = ack-nhfb,
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journal-URL = "https://www.jstor.org/journals/00029890.htm",
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number = "??",
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year = "1932",
ISSN = "0036-9713",
bibdate = "Thu Oct 26 11:15:25 2023",
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@Article{Simons:1932:IGA,
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}calculer, leurs principes, leur
{\'e}volution. ({French}) [{Calculating} machines,
their principles, their evolution]",
publisher = "Gauthier-Villars",
address = "Paris, France",
year = "1933",
bibdate = "Wed Oct 13 11:19:11 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Extracts reprinted in \cite[\S 3.2]{Randell:1982:ODC}.
Translated by Mr. R. Basu.",
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¡Šz] #/)!357E;Gc)!‹karticlefparith.bibKalbfell:1934:QDND. C. KalbfellQuestions, Discussions and Notes: On a Method for Calculating Square Rootsj-AMER-MATH-MONTHLY418504--506oct101934AMMYAE0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)0002-9890 OR 00029890Mon Jun 28 12:3cŠT] #3'‚-'=o;''/‚Šbookfparith.bibCouffignal:1933:MCLL. CouffignalLes machines a calculer, leurs principes, leur evolution. (French) [Calculating machines, their principles, their evolution]Gauthier-VillarsParis, France262--2641933Wed Oct 13 11:19:11 2010https://www.ma_sions and Notes: On a Method for
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˜˜rßL¹&“ˆ
@Article{Agrawal:1977:CNB,
author = "D. P. Agrawal",
title = "Comments on {``A No<‡-Ž[
@Article{Agrawal:1979:HSA,
author = "D. P. Agrawal",
title = "High-Speed Arithmetû‡qc
@Article{Agrawal:1980:NBA,
author = "D. P. Agrawal",
title = "On Negabinary-Binar‡C
@Article{Agrawal:1983:ICA,
author = "D. P. Agrawal and T. R. N. Rao",
title = "In&„S‰'
@Article{Agrawal:1984:ACB,
author = "V. K. Agrawal and S. Murugesan",
title = "Al8ˆL‘
@Article{Aharony:2012:IFP,
author = "Merav Aharony and Emanuel Gofman and Elena Guralnik
]©‹n—]
@Article{Ahmad:1972:ISH,
author = "M. Ahmad",
title = "Iterative schemes for high Æ†Œ
@Article{Ahmad:1987:IDA,
author = "M. Ahmad",
title = "Implementable Decimal Arit7:31 MDT 1999https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1999.06.28 12:37:31 MDTAmerican Mathematical Monthlyack-nhfbhttps://www.jstor.org/journals/00029890.htmD. C. KalbfellQuestions, Discussions and Notes: On a Method for Calculating Square Roots
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}jf Life Insurance",
publisher = "Life Office Management Association",
address = "New York",
pages = "xii + 132",
year = "1936",
LCCN = "HG8781 .L43",
bibdate = "Sat Aug 12 14:42:20 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
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URL = "http://hdl.handle.net/2027/mdp.39015017290688;
https://babel.hathitrust.org/cgi/pt?id=mdp.39015017290688",
abstract = "We have determined this item to be in the public
domain according to US copyright law through
information in the bibliographic record and/or US
copyright renewal records. The digital version is
available for all educational uses worldwide. Please
contact HathiTrust staff at hathitrust-help
umich.edu with any questions about this item. Life
insurance--Mathematics. (LCCN)3603410k3.
(OCoLC)ocm03161649. HG8781 .L43. HG 8781 .L66.
Http://hdl.handle.net/2027/mdp.39015017290688.",
acknowledgement = ack-nhfb,
remark = "While not about computer arithmetic, this book is
about practical applications of arithmetic in the life
insurance industry. It considers compound interest
calculations, present values of financial instruments,
mortality tables, insurance premiums, bond returns, and
so on. In Table 1, which shows the growth of an
investment at 3 percent over 10 years, the author
[amusingly] comments ``Mathematicians have already
worked out the multiplications and have incorporated
them into a table. With the use of this table, the
result can be obtained by a single multiplication.''.
Although the MARC record indicates the book is in the
public ldomain, the URL only permits download of a
single page at a time, although it is possible to page
through the book.",
tableofcontents = "Preface / vii \\
Index to Tables / xi \\
Notes on the Solution of Problems / xii \\
\\
I. Interest and Discount / 1 \\
Interest \\
Discount \\
Examples \\
Observations \\
Problems \\
\\
II. The Mortality Table and Easy Problems in Rate
Calculation at Age 90 / 6 \\
Natural or Net One-Year Term Premium \\
Net One-Year Pure Endowment \\
Net Single Premium Whole Life \\
Fundamental Principle \\
Observations \\
Problems \\
\\
III. Single Premium Contracts --- Age 35 / 14 \\
Mortality Table m\\
(Net) Single Premium 10-Year Term \\
(Net) Single Premium 10-Year Pure Endowment \\
(Net) Single Premium 10-Year Endowment \\
(Net) Single Premium Whole Life \\
(Net) Single Premium 10-Year Temporary Annuity \\
(Net) Single Premium Life Annuity \\
\\
IV. Development of Net Annual Premiums / 22 \\
Extension of Use of Discount \\
(Net) Annual Premium, Whole Life Policy \\
(Net) Annual Premium, 10-Payment Life \\
(Net) Annual Premium, 10-Year Term \\
(Net) Annual Premium, 10-Year Endowment \\
The ``Practical' and `More Exact' Premium \\
Alternative Method of Obtaining Net Annual Premiums \\
Problems \\
\\
V. More About Premiums / 30 \\
The Yearly Renewable Term Policy \\
nLoading the Premium \\
Partial or Instalment Premiums \\
Problems \\
\\
VI. Net Level Premium Reserves / 34 \\
10-Year Term Policy \\
10-Year Endowment Policy \\
Whole Life Policy \\
10-Payment Life Policy \\
Yearly Renewable Term \\
Problems \\
\\
VII. Reserve Fund, Mortality Fund and Cost of Insurance
/ 44 \\
Reserve Credit \\
Payment of Death Claims \\
The Reserve Fund and Mortality Fund \\
Cost of Insurance \\
Problems \\
\\
VIII. Full Preliminary Term Valuation \\
Gross Level Annual Premiums \\
Preliminary Term \\
Terminal Reserves Policy P \\
Full Preliminary Term Valuation \\
Modifoied Preliminary Term \\
Problems \\
\\
IX. Initial, Mean, and Calendar Year Reserves \\
\\
Initial Reserve \\
Mean Reserve \\
Calendar Year Reserve \\
Initial and Mean Reserves, F.P.T. Basis \\
Problems \\
\\
X. Non-Foreiture Options; Cash VALUE; Paid-Up and
Extended Insurance; Loan Value / 61 \\
The Cash Value \\
What Happens When Policy is Surrendered \\
Non-Forfeiture Options (Option 1, Option 2, and Option
3) \\
Cash Values under F.P.T. Basis of Valuation \\
Loan Values \\
Problems \\
\\
XI. Profits to a Life Insurance Company / 67 \\
Actual and Expected Mortality \\
Actual and Expected Expenses \\
Acptual and Expected Interest \\
Gain and Loss for the Year \\
Arithmetical Statement of Financial Status \\
Problems \\
\\
XII. Distribution of Surplus --- Dividend Options / 73
\\
Allocating Surplus to Policyholders \\
Share of Gain from Mortality, Loading and Interest \\
Dividend Formula \\
Variations in Dividend Formula \\
Dividend Options (Options 1 to 6) \\
Withdrawing the Dividend or Surrendering the Dividend
Credit \\
Problems \\
\\
XIII. Further Problems in Interest and Discount / 79
\\
Fundamental Principle \\
Annuity Certain (Present Value of) \\
Annuity Certain (Amount of) \\
Interest Compounded Oftener than Once a Year \\
Value qof a Bond \\
Problems \\
\\
XIV. Deferred Annuity --- Certain and Continuous
Annuity --- Optional Modes of Settlement / 91 \\
Deferred Life Annuity \\
``Combination'' Annuity Contract \\
Optional Modes of Settlement \\
Problems \\
\\
XV. Mortality Rates and Mortality Tables / 94 \\
Rate of Mortality \\
Building the Table \\
Changing Number at Initial Age \\
Selection and Select Tables \\
Indicating the Age (for Mortality Analysis) \\
Select Table \\
Ultimate Tables and Select and Ultimate Tables \\
Problems \\
\\
XVI. More About Reserves / 103 \\
Fundamental Principle Amended \\
Corollary to Amended Principle \\
Prospectirve and Retrospective Method of Obtaining the
Reserve \\
Reserves on Single Premium Policies \\
Reserves on Substandard Policies \\
Percentage Mortality Rating Table \\
Problems. \\
\\
XVII. Modified Preliminary Term Valuation / 109 \\
M.P.T. Basis of Valuation \\
Method A: M.P.T. Whole Life Basis \\
Method B: M.P.T. 20-Payment Life Basis \\
Method C: M.P.T. Original Plan Basis \\
Illinois Standard System of Valuation \\
Ohio Standard System of Valuation \\
New Jersey Standard System of Valuation \\
Problems \\
\\
Appendices: \\
I. Miscellaneous Examples / 118 \\
II. Chart 3B --- Single Premium Life Insurance (Age 35)
/ 121 \\
III. Chart 5B -- Single Premium Life Annuity (Age 35) /
122 \\
IV. Answers to Problems and Miscellaneous Examples 123
\\
Index / 127",
usmarc540 = "[US Library of Congress record]: We have determined
this item to be in the public domain according to US
copyright law through information in the bibliographic
record and/or US copyright renewal records. The digital
version is available for all educational uses
worldwide.",
}!tfparith.bibLeVita:1936:ALIMaurice H. Le VitaAn Arithmetic of Life InsuranceLife Office Management AssociationNew Yorkxii + 1321936HG8781 .L43Sat Aug 12 14:42:20 MDT 2023fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/fparith.bib2023.08.12 14:42:20 MDThttp://hdl.handle.net/2027/mdp.39015017290688; https://babel.hathitrust.org/cgi/pt?id=mdp.39015017290688We have determined this item to be in the public domain according to US copyright law through information in the bibliographic record and/or US copyright renewal records. The digital version is available for all educational uses worldwide. Please contact HathiTrust staff at hathitrust-help umich.edu with any questions about this item. Life insurance--Mathematics. (LCCN)36034103. (OCoLC)ocm03161649. HG8781 .L43. HG 8781 .L66. Http://hdl.handle.net/2027/mdp.39015017290688.While not about computer arithmetic, this book is about practical applications of arithmetic in the life insurance industry. It considers compound interest calculatuions, present values of financial instruments, mortality tables, insurance premiums, bond returns, and so on. In Table 1, which shows the growth of an investment at 3 percent over 10 years, the author [amusingly] comments ``Mathematicians have already worked out the multiplications and have incorporated them into a table. With the use of this table, the result can be obtained by a single multiplication.''. Although the MARC record indicates the book is in the public domain, the URL only permits download of a single page at a time, although it is possible to page through the book.Preface / vii Index to Tables / xi Notes on the Solution of Problems / xii I. Interest and Discount / 1 Interest Discount Examples Observations Problems II. The Mortality Table and Easy Problems in Rate Calculation at Age 90 / 6 Natural or Net One-Year Term Premium Net One-Year Pure Endowment Net Single Premium Whole Life Fundamental Principle Observations Problems III. Single Premium Contracts --- Age 35 / 14 Mortality Table (Netv) Single Premium 10-Year Term (Net) Single Premium 10-Year Pure Endowment (Net) Single Premium 10-Year Endowment (Net) Single Premium Whole Life (Net) Single Premium 10-Year Temporary Annuity (Net) Single Premium Life Annuity IV. Development of Net Annual Premiums / 22 Extension of Use of Discount (Net) Annual Premium, Whole Life Policy (Net) Annual Premium, 10-Payment Life (Net) Annual Premium, 10-Year Term (Net) Annual Premium, 10-Year Endowment The ``Practical' and `More Exact' Premium Alternative Method of Obtaining Net Annual Premiums Problems V. More About Premiums / 30 The Yearly Renewable Term Policy Loading the Premium Partial or Instalment Premiums Problems VI. Net Level Premium Reserves / 34 10-Year Term Policy 10-Year Endowment Policy Whole Life Policy 10-Payment Life Policy Yearly Renewable Term Problems VII. Reserve Fund, Mortality Fund and Cost of Insurance / 44 Reserve Credit Payment of Death Claims The Reserve Fund and Mortality Fund Cost of Insurance Problems VIII. Full Preliminary Term wValuation Gross Level Annual Premiums Preliminary Term Terminal Reserves Policy P Full Preliminary Term Valuation Modified Preliminary Term Problems IX. Initial, Mean, and Calendar Year Reserves Initial Reserve Mean Reserve Calendar Year Reserve Initial and Mean Reserves, F.P.T. Basis Problems X. Non-Foreiture Options; Cash VALUE; Paid-Up and Extended Insurance; Loan Value / 61 The Cash Value What Happens When Policy is Surrendered Non-Forfeiture Options (Option 1, Option 2, and Option 3) Cash Values under F.P.T. Basis of Valuation Loan Values Problems XI. Profits to a Life Insurance Company / 67 Actual and Expected Mortality Actual and Expected Expenses Actual and Expected Interest Gain and Loss for the Year Arithmetical Statement of Financial Status Problems XII. Distribution of Surplus --- Dividend Options / 73 Allocating Surplus to Policyholders Share of Gain from Mortality, Loading and Interest Dividend Formula Variations in Dividend Formula Dividend Options (Options 1 to 6) Withdrawing the Dividend xor Surrendering the Dividend Credit Problems XIII. Further Problems in Interest and Discount / 79 Fundamental Principle Annuity Certain (Present Value of) Annuity Certain (Amount of) Interest Compounded Oftener than Once a Year Value of a Bond Problems XIV. Deferred Annuity --- Certain and Continuous Annuity --- Optional Modes of Settlement / 91 Deferred Life Annuity ``Combination'' Annuity Contract Optional Modes of Settlement Problems XV. Mortality Rates and Mortality Tables / 94 Rate of Mortality Building the Table Changing Number at Initial Age Selection and Select Tables Indicating the Age (for Mortality Analysis) Select Table Ultimate Tables and Select and Ultimate Tables Problems XVI. More About Reserves / 103 Fundamental Principle Amended Corollary to Amended Principle Prospective and Retrospective Method of Obtaining the Reserve Reserves on Single Premium Policies Reserves on Substandard Policies Percentage Mortality Rating Table Problems. XVII. Modified Preliminary Term Valuation / 109 M.P.T. Baysis of Valuation Method A: M.P.T. Whole Life Basis Method B: M.P.T. 20-Payment Life Basis Method C: M.P.T. Original Plan Basis Illinois Standard System of Valuation Ohio Standard System of Valuation New Jersey Standard System of Valuation Problems Appendices: I. Miscellaneous Examples / 118 II. Chart 3B --- Single Premium Life Insurance (Age 35) / 121 III. Chart 5B -- Single Premium Life Annuity (Age 35) / 122 IV. Answers to Problems and Miscellaneous Examples 123 Index / 127ack-nhfbWe have determined this item to be in the public domain according to US copyright law through information in the bibliographic record and/or US copyright renewal records. The digital version is available for all educational uses worldwide. Please contact HathiTrust staff at hathitrust-help umich.edu with any questions about this item. Life insurance--Mathematics. (LCCN)36034103. (OCoLC)ocm03161649. HG8781 .L43. HG 8781 .L66. Http://hdl.handle.net/2027/mdp.39015017290688.Maurice H. {Le Vita}An Arithmetic of Life InsurancePzreface / vii \\ Index to Tables / xi \\ Notes on the Solution of Problems / xii \\ \\ I. Interest and Discount / 1 \\ Interest \\ Discount \\ Examples \\ Observations \\ Problems \\ \\ II. The Mortality Table and Easy Problems in Rate Calculation at Age 90 / 6 \\ Natural or Net One-Year Term Premium \\ Net One-Year Pure Endowment \\ Net Single Premium Whole Life \\ Fundamental Principle \\ Observations \\ Problems \\ \\ III. Single Premium Contracts --- Age 35 / 14 \\ Mortality Table \\ (Net) Single Premium 10-Year Term \\ (Net) Single Premium 10-Year Pure Endowment \\ (Net) Single Premium 10-Year Endowment \\ (Net) Single Premium Whole Life \\ (Net) Single Premium 10-Year Temporary Annuity \\ (Net) Single Premium Life Annuity \\ \\ IV. Development of Net Annual Premiums / 22 \\ Extension of Use of Discount \\ (Net) Annual Premium, Whole Life Policy \\ (Net) Annual Premium, 10-Payment Life \\ (Net) Annual Premium, 10-Year Term \\ (Net) Annual Premium, 10-Year Endowment \\ The ``Practical' and `More Exact'{ Premium \\ Alternative Method of Obtaining Net Annual Premiums \\ Problems \\ \\ V. More About Premiums / 30 \\ The Yearly Renewable Term Policy \\ Loading the Premium \\ Partial or Instalment Premiums \\ Problems \\ \\ VI. Net Level Premium Reserves / 34 \\ 10-Year Term Policy \\ 10-Year Endowment Policy \\ Whole Life Policy \\ 10-Payment Life Policy \\ Yearly Renewable Term \\ Problems \\ \\ VII. Reserve Fund, Mortality Fund and Cost of Insurance / 44 \\ Reserve Credit \\ Payment of Death Claims \\ The Reserve Fund and Mortality Fund \\ Cost of Insurance \\ Problems \\ \\ VIII. Full Preliminary Term Valuation \\ Gross Level Annual Premiums \\ Preliminary Term \\ Terminal Reserves Policy P \\ Full Preliminary Term Valuation \\ Modified Preliminary Term \\ Problems \\ \\ IX. Initial, Mean, and Calendar Year Reserves \\ \\ Initial Reserve \\ Mean Reserve \\ Calendar Year Reserve \\ Initial and Mean Reserves, F.P.T. Basis \\ Problems \\ \\ X. Non-Foreiture Options; Cash VALUE; Paid-Up and Extended Insuranc|e; Loan Value / 61 \\ The Cash Value \\ What Happens When Policy is Surrendered \\ Non-Forfeiture Options (Option 1, Option 2, and Option 3) \\ Cash Values under F.P.T. Basis of Valuation \\ Loan Values \\ Problems \\ \\ XI. Profits to a Life Insurance Company / 67 \\ Actual and Expected Mortality \\ Actual and Expected Expenses \\ Actual and Expected Interest \\ Gain and Loss for the Year \\ Arithmetical Statement of Financial Status \\ Problems \\ \\ XII. Distribution of Surplus --- Dividend Options / 73 \\ Allocating Surplus to Policyholders \\ Share of Gain from Mortality, Loading and Interest \\ Dividend Formula \\ Variations in Dividend Formula \\ Dividend Options (Options 1 to 6) \\ Withdrawing the Dividend or Surrendering the Dividend Credit \\ Problems \\ \\ XIII. Further Problems in Interest and Discount / 79 \\ Fundamental Principle \\ Annuity Certain (Present Value of) \\ Annuity Certain (Amount of) \\ Interest Compounded Oftener than Once a Year \\ Value of a Bond \\ Problems \\ \\ XIV. Defer}red Annuity --- Certain and Continuous Annuity --- Optional Modes of Settlement / 91 \\ Deferred Life Annuity \\ ``Combination'' Annuity Contract \\ Optional Modes of Settlement \\ Problems \\ \\ XV. Mortality Rates and Mortality Tables / 94 \\ Rate of Mortality \\ Building the Table \\ Changing Number at Initial Age \\ Selection and Select Tables \\ Indicating the Age (for Mortality Analysis) \\ Select Table \\ Ultimate Tables and Select and Ultimate Tables \\ Problems \\ \\ XVI. More About Reserves / 103 \\ Fundamental Principle Amended \\ Corollary to Amended Principle \\ Prospective and Retrospective Method of Obtaining the Reserve \\ Reserves on Single Premium Policies \\ Reserves on Substandard Policies \\ Percentage Mortality Rating Table \\ Problems. \\ \\ XVII. Modified Preliminary Term Valuation / 109 \\ M.P.T. Basis of Valuation \\ Method A: M.P.T. Whole Life Basis \\ Method B: M.P.T. 20-Payment Life Basis \\ Method C: M.P.T. Original Plan Basis \\ Illinois Standard System of Valuation \\ Ohio ~Standard System of Valuation \\ New Jersey Standard System of Valuation \\ Problems \\ \\ Appendices: \\ I. Miscellaneous Examples / 118 \\ II. Chart 3B --- Single Premium Life Insurance (Age 35) / 121 \\ III. Chart 5B -- Single Premium Life Annuity (Age 35) / 122 \\ IV. Answers to Problems and Miscellaneous Examples 123 \\ Index / 127
@Book{LeVita:1936:ALI,
author = "Maurice H. {Le Vita}",
title = "An Arithmetic of Life Insurance",
publisher = "Life Office Management Association",
address = "New York",
pages = "xii + 132",
year = "1936",
LCCN = "HG8781 .L43",
bibdate = "Sat Aug 12 14:42:20 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://hdl.handle.net/2027/mdp.39015017290688;
https://babel.hathitrust.org/cgi/pt?id=mdp.39015017290688",
abstract = "We have determined this item to be in the public
domain according to US copyright law through
information in the bibliographic record and/or US
copyright renewal records. The digital version is
available for all educational uses worldwide. Please
contact HathiTrust staff at hathitrust-help
umich.edu with any questions about this item. Life
insurance--Mathematics. (LCCN)36034103.
(OCoLC)ocm03161649. HG8781 .L43. HG 8781 .L66.
Http://hdl.handle.net/2027/mdp.39015017290688.",
acknowledgement = ack-nhfb,
remark = "While not about computer arithmetic, this book is
about practical applications of arithmetic in the life
insurance industry. It considers compound interest
calculations, present values of financial instruments,
mortality tables, insurance premiums, bond returns, and
so on. In Table 1, which shows the growth of an
€ investment at 3 percent over 10 years, the author
[amusingly] comments ``Mathematicians have already
worked out the multiplications and have incorporated
them into a table. With the use of this table, the
result can be obtained by a single multiplication.''.
Although the MARC record indicates the book is in the
public domain, the URL only permits download of a
single page at a time, although it is possible to page
through the book.",
tableofcontents = "Preface / vii \\
Index to Tables / xi \\
Notes on the Solution of Problems / xii \\
\\
I. Interest and Discount / 1 \\
Interest \\
Discount \\
Examples \\
Observations \\
Problems \\
\\
II. The Mortality Table and Easy Problems in Rate
Calculation at Age 90 / 6 \\
Natural or Net One-Year Term Premium \\
Net One-Year Pure Endowment \\
Net Single Premium Whole Life \\
Fundamental Principle \\
Observations \\
Problems \\
\\
III. Single Premium Contracts --- Age 35 / 14 \\
Mortality Table \\
(Net) Single Premium 10-Year Term \\
(Net) Single Premium 10-Year Pure Endowment \\
(Net) Single Premium 10-Year Endowment \\
(Net) Single Premium Whole Life \\
(Net) Single Premium 10-Year Temporary Annuity \\
(Net) Single Premium Life Annuity \\
\\
IV. Development of Net Annual Premiums / 22 \\
Extension of Use of Discount \\
(Net) Annual Premium, Whole Life Policy \\
(Net) Annual Premium, ‚10-Payment Life \\
(Net) Annual Premium, 10-Year Term \\
(Net) Annual Premium, 10-Year Endowment \\
The ``Practical' and `More Exact' Premium \\
Alternative Method of Obtaining Net Annual Premiums \\
Problems \\
\\
V. More About Premiums / 30 \\
The Yearly Renewable Term Policy \\
Loading the Premium \\
Partial or Instalment Premiums \\
Problems \\
\\
VI. Net Level Premium Reserves / 34 \\
10-Year Term Policy \\
10-Year Endowment Policy \\
Whole Life Policy \\
10-Payment Life Policy \\
Yearly Renewable Term \\
Problems \\
\\
VII. Reserve Fund, Mortality Fund and Cost of Insurance
/ 44 \\
Reserve Credit \\
ƒ Payment of Death Claims \\
The Reserve Fund and Mortality Fund \\
Cost of Insurance \\
Problems \\
\\
VIII. Full Preliminary Term Valuation \\
Gross Level Annual Premiums \\
Preliminary Term \\
Terminal Reserves Policy P \\
Full Preliminary Term Valuation \\
Modified Preliminary Term \\
Problems \\
\\
IX. Initial, Mean, and Calendar Year Reserves \\
\\
Initial Reserve \\
Mean Reserve \\
Calendar Year Reserve \\
Initial and Mean Reserves, F.P.T. Basis \\
Problems \\
\\
X. Non-Foreiture Options; Cash VALUE; Paid-Up and
Extended Insurance; Loan Value / 61 \\
The Cash Value \\
What Happens When Policy is Sur„rendered \\
Non-Forfeiture Options (Option 1, Option 2, and Option
3) \\
Cash Values under F.P.T. Basis of Valuation \\
Loan Values \\
Problems \\
\\
XI. Profits to a Life Insurance Company / 67 \\
Actual and Expected Mortality \\
Actual and Expected Expenses \\
Actual and Expected Interest \\
Gain and Loss for the Year \\
Arithmetical Statement of Financial Status \\
Problems \\
\\
XII. Distribution of Surplus --- Dividend Options / 73
\\
Allocating Surplus to Policyholders \\
Share of Gain from Mortality, Loading and Interest \\
Dividend Formula \\
Variations in Dividend Formula \\
Dividend Options (Options 1 to 6) \\
Withdrawing the Di…vidend or Surrendering the Dividend
Credit \\
Problems \\
\\
XIII. Further Problems in Interest and Discount / 79
\\
Fundamental Principle \\
Annuity Certain (Present Value of) \\
Annuity Certain (Amount of) \\
Interest Compounded Oftener than Once a Year \\
Value of a Bond \\
Problems \\
\\
XIV. Deferred Annuity --- Certain and Continuous
Annuity --- Optional Modes of Settlement / 91 \\
Deferred Life Annuity \\
``Combination'' Annuity Contract \\
Optional Modes of Settlement \\
Problems \\
\\
XV. Mortality Rates and Mortality Tables / 94 \\
Rate of Mortality \\
Building the Table \\
Changing Number at Initial Age \\
† Selection and Select Tables \\
Indicating the Age (for Mortality Analysis) \\
Select Table \\
Ultimate Tables and Select and Ultimate Tables \\
Problems \\
\\
XVI. More About Reserves / 103 \\
Fundamental Principle Amended \\
Corollary to Amended Principle \\
Prospective and Retrospective Method of Obtaining the
Reserve \\
Reserves on Single Premium Policies \\
Reserves on Substandard Policies \\
Percentage Mortality Rating Table \\
Problems. \\
\\
XVII. Modified Preliminary Term Valuation / 109 \\
M.P.T. Basis of Valuation \\
Method A: M.P.T. Whole Life Basis \\
Method B: M.P.T. 20-Payment Life Basis \\
Method C: M.P.T. Original Plan Basis \\
Illinois Standard System of Valuation \\
Ohio Standard System of Valuation \\
New Jersey Standard System of Valuation \\
Problems \\
\\
Appendices: \\
I. Miscellaneous Examples / 118 \\
II. Chart 3B --- Single Premium Life Insurance (Age 35)
/ 121 \\
III. Chart 5B -- Single Premium Life Annuity (Age 35) /
122 \\
IV. Answers to Problems and Miscellaneous Examples 123
\\
Index / 127",
usmarc540 = "[US Library of Congress record]: We have determined
this item to be in the public domain according to US
copyright law through information in the bibliographic
record and/or US copyright renewal records. The digital
version is available for all educational uses
worldwide.",
}
‘#¡Šx$] #+%%357E;Gc%%‹iarticlefparith.bibEscott:1937:QDNE. B. EscottQuestions, Discussions, and Notes: Rapid Method for Extracting a Square Rootj-AMER-MATH-MONTHLY4410644--646dec121937AMMYAE0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)0002-9890 OR 00029890Mon Jun 28 12:Šw#[ #'‚c=o;_Og‚wŠA#miscfparith.bibZuse:1936:VSDK. ZuseVerfahren zur selbsttatigen Durchfuhrung von Rechnungen mit Hilfe von Rechenmaschinen. (German) [Procedure for automatic execution of calculations by calculating machines]187--22111apr41936Wed Oct 13 11:22:03 2010https://www.math.utah.edu/pub/tex/bib/f‹‡o"Y #-)117=o;_W)g1ˆC#articlefparit‰Ÿw!a #+1KQ#E-;]‡M‹i¾‡M5KÅ™[books",
journal = j-J-INST-ACTUARIES,
volume = "67",
number = "??",
pages = "187--221",
year = "1936",
ISSN = "0020-2681",
bibdate = "Wed Oct 13 11:33:16 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.1]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Institute of Actuaries",
}"h.bibPhillips:1936:BCE. W. PhillipsBinary calculationj-J-INST-ACTUARIES67187--22119360020-2681 OR 00202681Wed Oct 13 11:33:16 2010https://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:33:16 ???Reprinted in cite [ 7.1]Randell:1982:ODC.Journal of the Institute of Actuariesack-nhfbE. W. PhillipsReprinted in \cite[\S 7.1]{Randell:1982:ODC}.Binary calculation
@Article{Phillips:1936:BC,
author = "E. W. Phillips",
title = "Binary calculation",
journal = j-J-INST-ACTUARIES,
volume = "67",
number = "??",
pages = "187--221",
year = "1936",
ISSN = "0020-2681",
bibdate = "Wed Oct 13 11:33:16 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.1]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Institute of Actuaries",
}n Durchfuhrung von
Rechnungen mit Hilfe von Rechenmaschinen}. ({German})
[{Procedure} for automatic execution of calculations by
calculating machines]",
howpublished = "German patent application Z23624.",
day = "11",
month = apr,
year = "1936",
bibdate = "Wed Oct 13 11:22:03 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 4.1]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
language = "German",
}#parith.bib2010.10.13 11:22:03 ???Reprinted in cite [ 4.1]Randell:1982:ODC.Germanack-nhfbGerman patent application Z23624.K. ZuseReprinted in \cite[\S 4.1]{Randell:1982:ODC}.{Verfahren zur selbstt{\"a}tigen Durchfuhrung von Rechnungen mit Hilfe von Rechenmaschinen}. ({German}) [{Procedure} for automatic execution of calculations by calculating machines]
@Misc{Zuse:1936:VSD,
author = "K. Zuse",
title = "{Verfahren zur selbstt{\"a}tigen Durchfuhrung von
Rechnungen mit Hilfe von Rechenmaschinen}. ({German})
[{Procedure} for automatic execution of calculations by
calculating machines]",
howpublished = "German patent application Z23624.",
day = "11",
month = apr,
year = "1936",
bibdate = "Wed Oct 13 11:22:03 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 4.1]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
language = "German",
}s, and Notes: Rapid Method for
Extracting a Square Root",
journal = j-AMER-MATH-MONTHLY,
volume = "44",
number = "10",
pages = "644--646",
month = dec,
year = "1937",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:38:44 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}$38:44 MDT 1999https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1999.06.28 12:38:44 MDTAmerican Mathematical Monthlyack-nhfbhttps://www.jstor.org/journals/00029890.htmE. B. EscottQuestions, Discussions, and Notes: Rapid Method for Extracting a Square Root
@Article{Escott:1937:QDN,
author = "E. B. Escott",
title = "Questions, Discussions, and Notes: Rapid Method for
Extracting a Square Root",
journal = j-AMER-MATH-MONTHLY,
volume = "44",
number = "10",
pages = "644--646",
month = dec,
year = "1937",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:38:44 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
} Watson",
title = "Mechanics, Molecular Physics, Heat, and Sound",
publisher = pub-MIT,
address = pub-MIT:adr,
pages = "????",
year = "1937",
bibdate = "Mon May 21 17:16:04 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See Appendix: Significant Figures and Notations by
Powers of Ten.",
acknowledgement = ack-nhfb,
remark = "Cited in \cite[ref. 22]{Carter:2013:ESF}.",
}%at, and Soundpub-MITpub-MIT:adr1937Mon May 21 17:16:04 2018https://www.math.utah.edu/pub/tex/bib/fparith.bib2018.05.21 17:16:04 ???See Appendix: Significant Figures and Notations by Powers of Ten.Cited in cite [ref. 22]Carter:2013:ESF.ack-nhfbRobert A. Millikan and Duane E. Roller and Earnest C. WatsonSee Appendix: Significant Figures and Notations by Powers of Ten.Mechanics, Molecular Physics, Heat, and Sound
@Book{Millikan:1937:MMP,
author = "Robert A. Millikan and Duane E. Roller and Earnest C.
Watson",
title = "Mechanics, Molecular Physics, Heat, and Sound",
publisher = pub-MIT,
address = pub-MIT:adr,
pages = "????",
year = "1937",
bibdate = "Mon May 21 17:16:04 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See Appendix: Significant Figures and Notations by
Powers of Ten.",
acknowledgement = ack-nhfb,
remark = "Cited in \cite[ref. 22]{Carter:2013:ESF}.",
}
CCI&[ '#-7s/_1=o;=
=O7=s¡'mastersthesisfparith.bibShannon:1937:SARClaude Elwood ShannonA Symbolic Analysis of Relay and Switching CircuitsMaster of ScienceDepartment of Electrical Engineering, MITCambridge, MA, USA7210aug81937Thu Nov 18 10:35:20 2010https://www.math.utah.edu/pub/tex/bib/fparith.bib2010.11.18 10:35:20 ???Not submitted until 1940http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425.pdfSmiley 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 publ“‰V%]#/g#=o;[g‰Kbookfparith.bibMillikan:1937:MMPRobert A. Millikan and Duane E. Roller and Earnest C. WatsonMechanics, Molecular Physics, He’bolic Analysis of Relay and Switching Circuits",
type = "{Master of Science}",
school = "Department of Electrical Engineering, MIT",
address = "Cambridge, MA, USA",
pages = "72",
day = "10",
month = aug,
year = "1937",
bibdate = "Thu Nov 18 10:35:20 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Not submitted until 1940",
URL = "http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425.pdf",
acknowledgement = ack-nhfb,
author-dates = "April 30, 1916--February 24, 2001",
remark = "Smiley \cite[p. 91]{Smiley:2010:MWI} claims: ``He
[Shannon] also had the insight, like Atanasoff, that
the binary arithmetic that relay switches represented
would simplify information systems. His master's
thesis, written when he as twenty-one and published
when he was twenty-two, is considered to be one of the
most important, if not the most important, master's
thesis of the twentieth century.''\par
Pages 59--61 of the thesis are a section called
``Electric Adder to the Base Two'', and pages 62--68,
``A Factor Table Machine'', describe a machine that
will print a table of factors and primes of all the
integers from 1 to 100,000,000. Shannon notes on page
68: ``As to the practicality of such a device, it might
be said that J. P. Kulik spent 20 years in constructing
a table of primes up to 100,000,000 and when finished
it was found to contain so many errors that it was not
worth publishing. The machine described here could
probably be made to handle 5 numbers per second so that
the table would require only about 2 months to
construct.''",
}&”ished 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.''ack-nhfbApril 30, 1916--February 24, 2001Claude Elwood ShannonNot submitted until 1940A Symbolic Analysis of Relay and Switching Circuits
@MastersThesis{Shannon:1937:SAR,
author = "Claude Elwood Shannon",
title =• "A Symbolic Analysis of Relay and Switching Circuits",
type = "{Master of Science}",
school = "Department of Electrical Engineering, MIT",
address = "Cambridge, MA, USA",
pages = "72",
day = "10",
month = aug,
year = "1937",
bibdate = "Thu Nov 18 10:35:20 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Not submitted until 1940",
URL = "http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425.pdf",
acknowledgement = ack-nhfb,
author-dates = "April 30, 1916--February 24, 2001",
remark = "Smiley \cite[p. 91]{Smiley:2010:MWI} claims: ``He
[Shannon] also had the insight, like Atanasoff, that
the binary arithmetic that relay switches represented
would simplify information systems. His master's
thesis, written when he as twenty-one and published
when he was twenty-two, is considered to be one of the
most important, if not the most important, master's
thesis of the twentieth century.''\par
Pages 59--61 of the thesis are a section called
``Electric Adder to the Base Two'', and pages 62--68,
``A Factor Table Machine'', describe a machine that
will print a table of factors and primes of all the
integers from 1 to 100,000,000. Shannon notes on page
68: ``As to the practicality of such a device, it might
be said that J. P. Kulik spent 20 years in constructing
a table of primes up to 100,000,000 and when finished
it was found to contain so many errors that it was not
worth publishing. The machine described here could
probably be made to handle 5 numbers per second so that
the table would require only about 2 months to
construct.''",
}—s Numbers",
journal = j-PROC-AMER-PHIL-SOC,
volume = "78",
number = "4",
pages = "551--572",
month = mar,
year = "1938",
CODEN = "PAPCAA",
ISSN = "0003-049X (print), 2326-9243 (electronic)",
ISSN-L = "0003-049X",
bibdate = "Thu Feb 15 16:28:28 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-G",
abstract = "It has been observed that the first pages of a table
of common logarithms show more wear than do the last
pages, indicating that more used numbers begin with the
digit 1 than with the digit 9. A compilation of some
20,000 first digits taken from widely divergent sources
shows that there is a logarithmic distribution of first
digits when the numbers are composed of four or more
˜ digits. An analysis of the numbers from different
sources shows that the numbers taken from unrelated
subjects, such as a group of newspaper items, show a
much better agreement with a logarithmic distribution
than do numbers from mathematical tabulations or other
formal data. There is here the peculiar fact that
numbers that individually are without relationship are,
when considered in large groups, in good agreement with
a distribution law---hence the name ``Anomalous
Numbers.''\par
A further analysis of the data shows a strong tendency
for bodies of numerical data to fall into geometric
series. If the series is made up of numbers containing
three or more digits the first digits form a
logarithmic series. If the numbers contain only single
™ digits the geometric relation still holds but the
simple logarithmic relation no longer applies.\par
An equation is given showing the frequencies of first
digits in the different orders of numbers 1 to 10, 10
to 100, etc.\par
The equation also gives the frequency of digits in the
second, third + place of a multi-digit number, and it
is shown that the same law applies to
reciprocals.\par
There are many instances showing that the geometric
series, or the logarithmic law, has long been
recognized as a common phenomenon in factual literature
and in the ordinary affairs of life. The wire gauge and
drill gauge of the mechanic, the magnitude scale of the
astronomer and the sensory response curves of the
psychologist are all particular examples of a
š 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.",
}'
++˜rßL¹&“Š]•;
@Article{Anderson:1988:MRE,
author = "Ned Anderson",
title = "Minimum relative er Ž!œC
@Article{Anderson:1999:DAF,
author = "I. J. Anderson",
title = "A Distillation Al<æˆ'
@Article{Anderson:2017:EMF,
author = "Andrew Anderson and Servesh Muralidharan and David
e‹†5Œk
@Article{Andrews:1978:EFM,
author = "M. Andrews and S. F. McCormick and G. D. Taylor",
t_…!ŠC
@Article{Andrews:1978:IAN,
author = "M. Andrews",
title = "Influence of architectb…!ŠC
@Article{Andrews:1978:UEF,
author = "M. Andrews and T. Mraz",
title = "Unified eld†U+
@Article{Andrews:1981:EFM,
author = "M. Andrews and D. Jaeger and S. F. McCormick and G. DH†2Œe
@Article{Andrews:1982:MMS,
author = "M. Andrews",
title = "Mathematical Microproc†5Œk
@Article{Andrews:1982:SRX,
author = "M. Andrews",
title = "Square-Root-{X} Comparjstor.org/sici?sici=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-GIt 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 numeržical 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 NumberŸs is thus a general probability law of widespread application.Proceedings of the American Philosophical Society held at Philadelphia for promoting useful knowledgeBenford's Law; Law of Anomalous Numbers; Zipf's LawFrom 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 su bject in subsequent years.'' The 2006 bibliography cite Hurlimann:2006:BLB cites 325 publications about Benford's Law.ack-nhfbhttp://www.jstor.org/journal/procamerphilsociIt 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 ``Anoma¡lous 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.Frank BenfordThe Law of Anomalous Numbers
@Article{Benford:1938:LAN,
author = "Frank Benford",
title = "The Law of Anomalous Numbers",
journal = j-PROC-AMER-PHIL-SOC,
volume = "78",
number = "4",
pages = "551--572",
month = mar,
year = "1938",
CODEN = "PAPCAA",
ISSN = "0003-049X (print), 2326-9243 (electronic)",
ISSN-L = "0003-049X",
bibdate = "Thu Feb 15 16:28:28 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-G",
abstract = "It has been observed that the first pages of a table
of common logarithms show more wear than do the last
pages, indicating that more used numbers begi£n 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 fact¥ual 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.",
}
KKÓ'_ #-'E557=o;CŸ]WsŽEgŸe'EÌUarticlefparith.bibBenford:1938:LANFrank BenfordThe Law of Anomalous Numbersj-PROC-AMER-PHIL-SOC784551--572mar31938PAPCAA0003-049X (print), 2326-9243 (electronic) OR 0003049X (print), 23269243 (electronic)0003-049X OR 0003049XThu Feb 15 16:28:28 2007https://www.math.utah.edu/pub/tex/bib/fparith.bib2007.02.15 16:28:28 ???http://links.œm{\'e}canique. Application aux machines
{\`a} calculer et aux calculs de la m{\'e}canique
c{\'e}leste. ({French}) [{On} mechanical analysis.
Application to calculating machines and to calculation
in celestial mechanics]",
publisher = "Gauthier-Villars",
school = "Facult{\'e} des Sciences de Paris",
address = "Paris, France",
year = "1938",
bibdate = "Wed Oct 13 11:17:22 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Extracts reprinted in \cite[\S 2.7]{Randell:1982:ODC}.
Translated by Mr. R. Basu.",
acknowledgement = ack-nhfb,
language = "French",
}( 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]
@PhdThesis{Couffignal:1938:AMA,
author = "L. Couffignal",
title = "Sur l'analyse m{\'e}canique. Application aux machines
{\`a} calculer et aux calculs de la m{\'e}canique
c{\'e}leste. ({French}) [{On} mechanical analysis.
Application to calculating machines and to calculation
in celestial mechanics]",
publisher = "Gauthier-Villars",
school = "Facult{\'e} des Sciences de Paris",
address = "Paris, France",
year = "1938",
bibdate = "Wed Oct 13 11:17:22 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Extracts reprinted in \cite[\S 2.7]{Randell:1982:ODC}.
Translated by Mr. R. Basu.",
acknowledgement = ack-nhfb,
language = "French",
}
n(] #3'ƒ7-G'=o;''/ƒ_phdthesisfparith.bibCouffignal:1938:AMAL. CouffignalSur l'analyse mecanique. Application aux machines a calculer et aux calculs de la mecanique celeste. (French) [On mechanical analysis. Application to calculating machines and to calculation in celestial mechanics]Gauthier-VillarsFaculte des Sciences de ParisParis, France551--5721938Wed Oct 13 11:17:22 2010https://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:17:22 ???Extracts reprinted in cite [ 2.7]Randell:1982:ODC. Translated by Mr. R. Basu.Frenchack-nhfbL. CouffignalExtracts reprinted in \cite[\S 2.7]{Randell:1982:ODC}. Translated by Mr. R. Basu.Sur l'analyse m{\'e}canique. Application aux¨ Maitland) Wright",
title = "An Introduction to the Theory of Numbers",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xvi + 403",
year = "1938",
LCCN = "QA241 .H28",
bibdate = "Fri Nov 30 06:49:15 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
})
>>‡?)[#)]!)!=o;]‡K£bookfparith.bibHardy:1938:ITNG. H. (Godfrey Harold) Hardy and E. M. (Edward Maitland) WrightAn Introduction to the Theory of Numberspub-OXFORDpub-OXFORD:adrxvi + 4031938QA241 .H28Fri Nov 30 06:49:15 2007https://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.30 06:49:15 ???ack-nhfbG. H. (Godfrey Harold) Hardy and E. M. (Edward Maitland) WrightAn Introduction to the Theory of Numbers
@Book{Hardy:1938:ITN,
author = "G. H. (Godfrey Harold) Hardy and E. M. (Edward
Maitland) Wright",
title = "An Introduction to the Theory of Numbers",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xvi + 403",
year = "1938",
LCCN = "QA241 .H28",
bibdate = "Fri Nov 30 06:49:15 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}ysis of Relay and Switching Circuits",
journal = j-TRANS-AMER-INST-ELEC-ENG,
volume = "57",
number = "??",
pages = "713--723",
month = dec,
year = "1938",
CODEN = "TAEEA5",
ISSN = "0096-3860",
bibdate = "Sat Nov 20 08:54:12 2010",
bibsource = "http://www2.research.att.com/~njas/doc/shannonbio.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Institute of Electrical
Engineers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714",
remark = "This is Shannon's first published paper (his Master's
thesis). In 1940, it received the Alfred Noble Prize of
the combined engineering societies of the United
States, an award given each year to a person not over
thirty for a paper published in one of the journals of
the participating societies. H. H. Goldstine
\cite{Goldstine:1972:CPN} called this work ``one of the
most important master's theses ever written \ldots{} a
landmark in that it helped to change digital circuit
design from an art to a science.''",
}*¯hesis). 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.''ack-nhfbhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714Claude E. ShannonA Symbolic Analysis of Relay and Switching Circuits
@Article{Shannon:1938:SAR,
author = "Claude E. Shannon",
title = "A Symbolic Analysis of Relay and Switching Circuits",
journal = j-TRANS-AMER-INST-ELEC-ENG,
volume = "57",
number = "??",
pages = "713--723",
month = dec,
year = "1938",
CODEN = "TAEEA5",
ISSN = "0096-3860",
bibdate = "Sat Nov 20 08:54:12 2010",
bibsource = "http://www2.research.att.com/~njas/doc/shannonbio.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Institute of Electrical
Engineers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714",
remark = "This is Shannon's first published paper (his Master's
thesis). In 1940, it received the Alfred Noble Prize of
the combined engineering societies of the United
States, an award given each year to a person not over
thirty for a paper published in one of the journals of
the participating societies. H. H. Goldstine
\cite{Goldstine:1972:CPN} called this work ``one of the
most important master's theses ever written \ldots{} a
landmark in that it helped to change digital circuit
design from an art to a science.''",
}
àà”*] #-/sA7=_; ˆ/s–aarticlefparith.bibShannon:1938:SARClaude E. ShannonA Symbolic Analysis of Relay and Switching Circuitsj-TRANS-AMER-INST-ELEC-ENG57713--723dec121938TAEEA50096-3860 OR 00963860Sat Nov 20 08:54:12 2010http://www2.research.att.com/~njas/doc/shannonbio.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib2010.11.20 08:54:12 ???Transactions of the American Institute of Electrical EngineersThis is Shannon's first published paper (his Master's t®The Artificial Arithmetick in Decimals of {Robert
Jager} ({London}, 1651)",
journal = j-ISIS,
volume = "31",
number = "1",
pages = "25--31",
month = nov,
year = "1939",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:26:49 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302217;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1930.bib",
URL = "http://www.jstor.org/stable/226014",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}+tersonThe Artificial Arithmetick in Decimals of {Robert Jager} ({London}, 1651)
@Article{Jager:1939:AAD,
author = "Robert Jager and Boyd C. Patterson",
title = "The Artificial Arithmetick in Decimals of {Robert
Jager} ({London}, 1651)",
journal = j-ISIS,
volume = "31",
number = "1",
pages = "25--31",
month = nov,
year = "1939",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:26:49 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302217;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1930.bib",
URL = "http://www.jstor.org/stable/226014",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
&&O+]#)Q57Eƒ;QOQŽgarticlefparith.bibJager:1939:AADRobert Jager and Boyd C. PattersonThe Artificial Arithmetick in Decimals of Robert Jager (London, 1651)j-ISIS31125--31nov111939ISISA40021-1753 (print), 1545-6994 (electronic) OR 00211753 (print), 15456994 (electronic)0021-1753 OR 00211753Tue Jul 30 21:26:49 MDT 2013http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i302217; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/isis1930.bib2013.07.30 21:26:49 MDThttp://www.jstor.org/stable/226014Isisack-nhfbhttp://www.jstor.org/journal/isisRobert Jager and Boyd C. Pat²decimal Arithmetic}}, by
George S. Terry}",
journal = j-J-R-STAT-SOC,
volume = "102",
number = "2",
pages = "299--300",
month = "????",
year = "1939",
DOI = "https://doi.org/10.2307/2980013",
ISSN = "0952-8385",
bibdate = "Sat Jan 24 11:18:08 MST 2015",
bibsource = "http://www.jstor.org/stable/i349540;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jrss-a-1930.bib",
URL = "http://www.jstor.org/stable/2980013",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society",
journal-URL = "http://www.jstor.org/journals/09528385.html",
},l of the Royal Statistical Societyack-nhfbhttp://www.jstor.org/journals/09528385.htmlM. G. K.Book Review: {{\booktitle{Duodecimal Arithmetic}}, by George S. Terry}
@Article{K:1939:BRBd,
author = "M. G. K.",
title = "Book Review: {{\booktitle{Duodecimal Arithmetic}}, by
George S. Terry}",
journal = j-J-R-STAT-SOC,
volume = "102",
number = "2",
pages = "299--300",
month = "????",
year = "1939",
DOI = "https://doi.org/10.2307/2980013",
ISSN = "0952-8385",
bibdate = "Sat Jan 24 11:18:08 MST 2015",
bibsource = "http://www.jstor.org/stable/i349540;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jrss-a-1930.bib",
URL = "http://www.jstor.org/stable/2980013",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society",
journal-URL = "http://www.jstor.org/journals/09528385.html",
}
°üx°‰=.\ #%5=o;‚#‚+5ˆmiscfparith.bibBush:1940:AMV. BushArithmetical Machine299--3001940Wed Oct 13 11:37:32 2010https://wwºˆy-[ !#1+/91'=o;_+g/ˆstechreportfparith.bibAtanasoff:19¸‹y,\ ##
)K7E‚';S]c?articlefparith.bibK:1939:BRBdM. G. K.Book Review: booktitle Duodecimal Arithmetic, by George S. Terryj-J-R-STAT-SOC1022299--3001939https://doi.org/10.2307/29800130952-8385 OR 09528385Sat Jan 24 11:18:08 MST 2015http://www.jstor.org/stable/i349540; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jrss-a-1930.bib2015.01.24 11:18:08 MSThttp://www.jstor.org/stable/2980013Journaµchine for the solution of large systems of
linear algebraic equations",
type = "Unpublished memorandum",
institution = "Iowa State College",
address = "Ames, IA, USA",
month = aug,
year = "1940",
bibdate = "Wed Oct 13 11:36:11 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}-40:CMSJ. V. AtanasoffComputing machine for the solution of large systems of linear algebraic equationsUnpublished memorandumIowa State CollegeAmes, IA, USA299--300aug81940Wed Oct 13 11:36:11 2010https://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:36:11 ???Reprinted in cite [ 7.2]Randell:1982:ODC.ack-nhfbJ. V. AtanasoffReprinted in \cite[\S 7.2]{Randell:1982:ODC}.Computing machine for the solution of large systems of linear algebraic equations
@TechReport{Atanasoff:1940:CMS,
author = "J. V. Atanasoff",
title = "Computing machine for the solution of large systems of
linear algebraic equations",
type = "Unpublished memorandum",
institution = "Iowa State College",
address = "Ames, IA, USA",
month = aug,
year = "1940",
bibdate = "Wed Oct 13 11:36:11 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}ished = "Vannevar Bush Papers, Container 18, Folder: Caldwell,
Samuel, 1939--1940",
year = "1940",
bibdate = "Wed Oct 13 11:37:32 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.3]{Randell:1982:ODC}.
Copyright interest in the unpublished writings of
Vannevar Bush has been dedicated to the public.",
acknowledgement = ack-nhfb,
}.w.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:37:32 ???Reprinted in cite [ 7.3]Randell:1982:ODC. Copyright interest in the unpublished writings of Vannevar Bush has been dedicated to the public.ack-nhfbVannevar Bush Papers, Container 18, Folder: Caldwell, Samuel, 1939--1940V. BushReprinted in \cite[\S 7.3]{Randell:1982:ODC}. Copyright interest in the unpublished writings of Vannevar Bush has been dedicated to the public.Arithmetical Machine
@Misc{Bush:1940:AM,
author = "V. Bush",
title = "Arithmetical Machine",
howpublished = "Vannevar Bush Papers, Container 18, Folder: Caldwell,
Samuel, 1939--1940",
year = "1940",
bibdate = "Wed Oct 13 11:37:32 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.3]{Randell:1982:ODC}.
Copyright interest in the unpublished writings of
Vannevar Bush has been dedicated to the public.",
acknowledgement = ack-nhfb,
}= "Unpublished memorandum",
institution = "Bell Telephone Laboratories",
address = "New York, NY, USA",
year = "1940",
bibdate = "Wed Oct 13 11:30:38 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.1]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}/
€€†}/Y !#)'9C/=o;_'g‡!techreportfparith.bibStibitz:1940:CG. R. StibitzComputerUnpublished memorandumBell Telephone LaboratoriesNew York, NY, USA299--3001940Wed Oct 13 11:30:38 2010https://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:30:38 ???Reprinted in cite [ 6.1]Randell:1982:ODC.ack-nhfbG. R. StibitzReprinted in \cite[\S 6.1]{Randell:1982:ODC}.Computer
@TechReport{Stibitz:1940:C,
author = "G. R. Stibitz",
title = "Computer",
type = "Unpublished memorandum",
institution = "Bell Telephone Laboratories",
address = "New York, NY, USA",
year = "1940",
bibdate = "Wed Oct 13 11:30:38 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.1]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}¾of electrical data recording and reading
mechanism",
type = "{M.S.} thesis",
school = "Iowa State College",
address = "Ames, IA, USA",
pages = "32",
year = "1941",
bibdate = "Thu Nov 18 11:18:18 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
author-dates = "1918--1963",
historical-note = "From
http://www.lib.iastate.edu/arch/rgrp/5-2-1-1.html:
``John Vincent Atanasoff received his M.S. (1926) in
Mathematics from Iowa State College (University) and
received his Ph.D. (1930) in Theoretical Physics from
the University of Wisconsin-Madison. He returned to
Iowa State in 1930 as Assistant Professor in
mathematics and physics and was promoted to Associate
Professor (1936). Atanasoff began developing concepts
for an electronic compu¿ting 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. DÀuring 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.",
}0Âd BerryDesign of electrical data recording and reading mechanismM.S. thesisIowa State CollegeAmes, IA, USA321941Thu Nov 18 11:18:18 2010https://www.math.utah.edu/pub/tex/bib/fparith.bib2010.11.18 11:18:18 ???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.ack-nhfb1918--1963Clifford Edward BerryDesign of electrical data recording and reading mechanism
@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 Ã= "Ames, IA, USA",
pages = "32",
year = "1941",
bibdate = "Thu Nov 18 11:18:18 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
author-dates = "1918--1963",
historical-note = "From
http://www.lib.iastate.edu/arch/rgrp/5-2-1-1.html:
``John Vincent Atanasoff received his M.S. (1926) in
Mathematics from Iowa State College (University) and
received his Ph.D. (1930) in Theoretical Physics from
the University of Wisconsin-Madison. He returned to
Iowa State in 1930 as Assistant Professor in
mathematics and physics and was promoted to Associate
Professor (1936). Atanasoff began developing concepts
for an electronic computing machine in 1937. It was
shortly thereafter that he, along with graduate student
Clifford Berry, started work on thÄe 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.",
}
²k².1[ #1/i/57Eƒ;SkW/iŽaarticlefparith.bibLancaster:1942:MMEOtis E. LancasterMachine Method for the Extraction of Cube Rootj-J-AM-STAT-ASSOC37217112--115mar31942JSTNAL0162-1459 (print), 1537-274X (electronic) OR 01621459 (print), 1537274X (electronic)0162-1459 OR 01621459Wed Jan 25 08:05:24 MST 2012http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314096; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib2012.01.25 08:05:24 MSThttp://www.jstor.org/stable/2279437Journal of the American Statistical Associationack-nhfbhttp://www.tandfonÈ ~0Z '#)7#1'=o;‡-!7³mmastersthesisfparith.bibBerry:1941:DEDClifford EdwarÁd for the Extraction of Cube Root",
journal = j-J-AM-STAT-ASSOC,
volume = "37",
number = "217",
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month = mar,
year = "1942",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:24 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314096;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
URL = "http://www.jstor.org/stable/2279437",
acknowledgement = ack-nhfb,
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@Article{Becker:2000:JST,
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title = "The Journeyman's Shop:?ò…p‹a
@Article{Becker:2000:JSWb,
author = "Pete Becker",
title = "The Journeyman's Shop?ôˆ
@Article{Becker:2018:NOS,
author = "Ruben Becker and Michael Sagraloff and Vikram Sharma
iŠ7”o
@Article{Beckmann:1993:FFTa,
author = "P. E. Beckmann and B. R. Musicus",
title = .HŠ7”o
@Article{Beckmann:1993:FFTb,
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title = .MJŸ
@Article{Beebe:2007:ETM,
author = "Nelson H. F. Beebe",
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@Article{Beebe:2009:NML,
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title = "A new math libraW+Š[•7
@Article{Behringer:1970:BFI,
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title = "{Eine bedingte â‡K
@Article{Belanovic:2002:LPF,
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@Article{Lancaster:1942:MME,
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bibsource = "http://www.jstor.org/journals/01621459.html;
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bibdate = "Wed Oct 13 11:52:54 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
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acknowledgement = ack-nhfb,
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acknowledgement = ack-nhfb,
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institution = "Research Laboratories, R.C.A. Manufacturing Company,
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month = apr,
year = "1942",
bibdate = "Sat Feb 8 10:28:55 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}3nic Predictors for Anti-Aircraft Fire ControlResearch Laboratories, R.C.A. Manufacturing Company, Inc.Camden, NJ, USA112--115apr41942Sat Feb 8 10:28:55 2020https://www.math.utah.edu/pub/tex/bib/fparith.bib2020.02.08 10:28:55 ???Reprinted in cite [ 7.4]Randell:1982:ODC.ack-nhfbJ. A. Rajchman and G. A. Morton and A. W. VanceReprinted in \cite[\S 7.4]{Randell:1982:ODC}.Report on Electronic Predictors for Anti-Aircraft Fire Control
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bibdate = "Sat Feb 8 10:28:55 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
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acknowledgement = ack-nhfb,
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bibdate = "Mon Jun 28 12:36:57 MDT 1999",
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JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}4 00029890Mon Jun 28 12:36:57 MDT 1999https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1999.06.28 12:36:57 MDTAmerican Mathematical Monthlyack-nhfbhttps://www.jstor.org/journals/00029890.htmW. S. H. CrawfordDiscussions and Notes: Square Roots from a Table of Cosines
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acknowledgement = ack-nhfb,
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bibdate = "Fri Jun 15 17:39:28 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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acknowledgement = ack-nhfb,
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Œf5] !#3+WQ7=o;‚9+[Stechreportfparith.bibRademacher:1943:MTIHans RademacherMathematical Topics of Interest in PX, Part Two: Summary of Articles Dealing with Rounding off ErrorsPX Report14Moore School of Electrical Engineering, Office of the Director Records, University of PennsylvaniaPhiladelphia, PA, USA190--19130nov111943Fri Jun 15 17:39:28 2018https://www.math.utah.edu/pub/tex/bib/fparith.bib2018.06.15 17:39:28 ???Cited on page 34 of Haigh, Priestley, and Rope, booktitle ENIAC in Action (2016) (ISBN 0-262-03398-4) as an annotated bibliÑÔignificant Figures of Numbers in Statistical Tables",
journal = j-NATURE,
volume = "154",
number = "3921",
pages = "800--801",
day = "23",
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year = "1944",
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DOI = "https://doi.org/10.1038/154800a0",
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bibdate = "Sun Sep 18 11:57:19 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf",
abstract = "A rough qualitative explanation of this fact can
easily be given. If we consider tables in which the
entries become rarer the larger they are, we can draw
the obvious conclusion that in any interval, say,
between 10 and 99, or 10,000 and 99,999, there are more
entries on the small side than on the large side.",
acknowledgement = ack-nhfb,
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}6Ö 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.NatureBenford's Law; Law of Anomalous Numbers; Zipf's Lawack-nhfbhttp://www.nature.com/nature/archive/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.S. A. Goudsmit and W. H. FurrySignificant Figures of Numbers in Statistical Tables
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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.",
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Significant Figures",
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number = "3924",
pages = "52--53",
day = "13",
month = jan,
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bibdate = "Sun Sep 18 11:51:37 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
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URL = "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf",
acknowledgement = ack-nhfb,
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@Article{Brent:1978:AMF,
author = "Richard P. Brent",
title = "Algorithm 524: {MP—…R‹%
@Article{Brent:1978:FMP,
author = "Richard P. Brent",
title = "{A Fortran} Multipš†J
@Article{Brent:1979:RMF,
author = "R. P. Brent",
title = "Remark on ``{Algorithm}ˆ>}
@Article{Brent:1980:AIB,
author = "Richard P. Brent and Judith A. Hooper and J. Michael
†Œ
@Article{Brent:1982:RLP,
author = "R. P. Brent and H. T. Kung",
title = "A regula(Ž5œk
@Article{Brent:2007:EBC,
author = "Richard Brent and Colin Percival and Paul Zimmermann",
RË‘n£]
@Article{Brent:2010:PAV,
author = "Richard P. Brent",
title = "On the precision aYu‡re
@Article{Breyer:2001:NGE,
author = "Laird Breyer and Gareth O. Roberts and Jeffrey S.
B¤d Distribution of Significant Figures
@Article{Furry:1945:DND,
author = "W. H. Furry and Henry Hurwitz",
title = "Distribution of Numbers and Distribution of
Significant Figures",
journal = j-NATURE,
volume = "155",
number = "3924",
pages = "52--53",
day = "13",
month = jan,
year = "1945",
CODEN = "NATUAS",
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bibdate = "Sun Sep 18 11:51:37 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
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URL = "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf",
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sWG;articlefparith.bibFurry:1945:DNDW. H. Furry and Henry HurwitzDistribution of Numbers and Distribution of Significant Figuresj-NATURE155392452--5313jan11945NATUAShttps://doi.org/10.1038/155052a00028-0836 (print), 1476-4687 (electronic) OR 00280836 (print), 14764687 (electronic)0028-0836 OR 00280836Sun Sep 18 11:51:37 2011https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib2011.09.18 11:51:37 ???http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdfNatureBenford's Law; Law of Anomalous Numbers; Zipf's Lawack-nhfbhttp://www.nature.com/nature/archive/W. H. Furry and Henry HurwitzDistribution of Numbers anÚDVAC}",
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day = "30",
month = jun,
year = "1945",
bibdate = "Mon Jun 06 19:17:03 2005",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
remark = "This is the report that got von Neumann's name
associated with the serial, stored-program, general
purpose, digital architecture upon which 99.99\% of all
computers today are based.",
xxnote = "Report prepared for U.S. Army Ordinance Department
under Contract W-670-ORD-4926. Reprinted in
\cite[pp.~177--246]{Stern:1981:EUA},
\cite[pp.~399--413]{Randell:1982:ODC},
\cite{vonNeumann:1993:FDR}, and
\cite{Laplante:1996:GPC}.",
}8EDVAC}",
institution = "University of Pennsylvania",
day = "30",
month = jun,
year = "1945",
bibdate = "Mon Jun 06 19:17:03 2005",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
remark = "This is the report that got von Neumann's name
associated with the serial, stored-program, general
purpose, digital architecture upon which 99.99\% of all
computers today are based.",
xxnote = "Report prepared for U.S. Army Ordinance Department
under Contract W-670-ORD-4926. Reprinted in
\cite[pp.~177--246]{Stern:1981:EUA},
\cite[pp.~399--413]{Randell:1982:ODC},
\cite{vonNeumann:1993:FDR}, and
\cite{Laplante:1996:GPC}.",
}
¨¨ŽM8[ !#3-UA=‚;_‚u-gY‘wtechreportfparith.bibvonNeumann:1945:FDRJohn von NeumannFirst Draft of a Report on the EDVACUniversity of Pennsylvania52--5330jun61945Mon Jun 06 19:17:03 2005ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib2005.06.06 19:17:03 ???Reprinted in cite [ 8.2]Randell:1982:ODC.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.ack-nhfbJohn von NeumannReprinted in \cite[\S 8.2]{Randell:1982:ODC}.First Draft of a Report on the {EDVAC}
@TechReport{vonNeumann:1945:FDR,
author = "John von Neumann",
title = "First Draft of a Report on the {Ýutomatic Sequence Controlled Calculator}",
journal = j-ELECTR-ENG,
volume = "65",
number = "??",
pages = "384--391, 449--454, 522--528",
year = "1946",
CODEN = "ELENAC",
ISSN = "0095-9197",
bibdate = "Wed Oct 13 11:26:29 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
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}9:1982:ODC.Electrical Engineering (American Institute of Electrical Engineers)ack-nhfbhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714H. H. Aiken and G. M. HopperReprinted in \cite[\S 5.2]{Randell:1982:ODC}.The {Automatic Sequence Controlled Calculator}
@Article{Aiken:1946:ASC,
author = "H. H. Aiken and G. M. Hopper",
title = "The {Automatic Sequence Controlled Calculator}",
journal = j-ELECTR-ENG,
volume = "65",
number = "??",
pages = "384--391, 449--454, 522--528",
year = "1946",
CODEN = "ELENAC",
ISSN = "0095-9197",
bibdate = "Wed Oct 13 11:26:29 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
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Electrical Engineers)",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714",
}
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Egi‹marticlefparith.bibAiken:1946:ASCH. H. Aiken and G. M. HopperThe Automatic Sequence Controlled Calculatorj-ELECTR-ENG65384--391, 449--454, 522--5281946ELENAC0095-9197 OR 00959197Wed Oct 13 11:26:29 2010https://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:26:29 ???Reprinted in cite [ 5.2]Randellàã
Neumann",
title = "Preliminary discussion of the logical design of an
electronic computing instrument",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "42",
day = "28",
month = jun,
year = "1946",
MRnumber = "MR22442",
bibdate = "Wed Oct 13 08:17:48 2004",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/arith.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Report to the U.S. Army Ordnance Department under
contract W-36-034-OKD-7481. Reprinted in \cite[Paper
ä2]{Taub:1963:JNCa}, \cite{Bell:1971:CSR}, \cite[pp.
221--259]{Swartzlander:1976:CDD} and \cite[pp.
97--146]{Aspray:1987:PJN}",
URL = "https://deepblue.lib.umich.edu/handle/2027.42/3972;
https://grch.com.ar/docs/p1/Apuntes/eng/Logical%20Design%20of%20an%20Electronic%20Computing%20Instrument.pdf",
acknowledgement = ack-nhfb,
author-dates = "John von Neumann (28 December 1903--8 February 1957)",
remark = "Discusses floating-point versus fixed-point
computation, and concludes that floating-point is
probably not justifiable. They wrote:\par
``There appear to be two major purposes in a `floating'
decimal point system both of which arise from the fact
that the number of digits in a word is a constant fixed
by design considerations for each particular machine.
The first of these purposes is to retain in a sum or
å 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.''",
}:ç-INST-ADV-STUDYinst-INST-ADV-STUDY:adr4228jun61946MR22442Wed Oct 13 08:17:48 2004https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/arith.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib2004.10.13 08:17:48 ???Report to the U.S. Army Ordnance Department under contract W-36-034-OKD-7481. Reprinted in cite [Paper 2]Taub:1963:JNCa, cite Bell:1971:CSR, cite [pp. 221--259]Swartzlander:1976:CDD and cite [pp. 97--146]Aspray:1987:PJNhttps://deepblue.lib.umich.edu/handle/2027.42/3972; https://grch.com.ar/docs/p1/Apuntes/eng/Logical%20Design%20of%20an%20Electronic%20Computing%20Instrument.pdfDiscusses floating-point versus fixed-point computation, and concludes that floating-point is probably not justifiable. They wrote:par ``There appear to beè 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 wéould 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.''ack-nhfbJohn von Neumann (28 December 1903--8 February 1957)Arthur W. Burks and Herman H. Goldstine and John von NeumannReport to the U.S. Army Ordnance Department under contract W-36-034-OKD-7481. Reprinted in \cite[Paper 2]{Taub:1963:JNCa}, \cite{Bell:1971:CSR}, \cite[pp. 221--259]{Swartzlander:1976:CDD} and \cite[pp. 97--146]{Aspray:1987:PJN}Preliminary discussion of the logical design of an electronic computing instrument
@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 = ê jun,
year = "1946",
MRnumber = "MR22442",
bibdate = "Wed Oct 13 08:17:48 2004",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/arith.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Report to the U.S. Army Ordnance Department under
contract W-36-034-OKD-7481. Reprinted in \cite[Paper
2]{Taub:1963:JNCa}, \cite{Bell:1971:CSR}, \cite[pp.
221--259]{Swartzlander:1976:CDD} and \cite[pp.
97--146]{Aspray:1987:PJN}",
URL = "https://deepblue.lib.umich.edu/handle/2027.42/3972;
https://grch.com.ar/docs/p1/Apuntes/engë/Logical%20Design%20of%20an%20Electronic%20Computing%20Instrument.pdf",
acknowledgement = ack-nhfb,
author-dates = "John von Neumann (28 December 1903--8 February 1957)",
remark = "Discusses floating-point versus fixed-point
computation, and concludes that floating-point is
probably not justifiable. They wrote:\par
``There appear to be two major purposes in a `floating'
decimal point system both of which arise from the fact
that the number of digits in a word is a constant fixed
by design considerations for each particular machine.
The first of these purposes is to retain in a sum or
product as many significant digits as possible and the
second of these is to free the human operator from the
burden of estimating and inserting into a problem
`scale factors' --- multiplicative constants which
serve to keep numbers within the limits of the
machine.\par
There is, of course, no denying the fact that human
time is consumed in arranging for the introduction of
suitable scale factors. We only argue that the time so
consumed is a very small percentage of the total time
we will spend in preparing an interesting problem for
our machine. The first advantage of the floating point
is, we feel, somewhat illusory. In order to have such a
floating point, one must waste memory capacity which
could otherwise be used for carrying more digits per
word. It would therefore seem to us not at all clear
whether the modest advantages of a floating binary
point offset the loss of memory capacity and the
increased complexity of the arithmetic and control
circuits.''",
},
journal = j-BELL-LABS-RECORD,
volume = "23",
number = "??",
pages = "457--460",
year = "1946",
CODEN = "BLRCAB",
ISSN = "0005-8564",
bibdate = "Wed Oct 13 11:31:47 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Bell Laboratories Record",
};h.bibCesareo:1946:RIO. CesareoThe Relay Interpolatorj-BELL-LABS-RECORD23457--4601946BLRCAB0005-8564 OR 00058564Wed Oct 13 11:31:47 2010https://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:31:47 ???Reprinted in cite [ 6.2]Randell:1982:ODC.Bell Laboratories Recordack-nhfbO. CesareoReprinted in \cite[\S 6.2]{Randell:1982:ODC}.The Relay Interpolator
@Article{Cesareo:1946:RI,
author = "O. Cesareo",
title = "The Relay Interpolator",
journal = j-BELL-LABS-RECORD,
volume = "23",
number = "??",
pages = "457--460",
year = "1946",
CODEN = "BLRCAB",
ISSN = "0005-8564",
bibdate = "Wed Oct 13 11:31:47 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Bell Laboratories Record",
}ïe True",
journal = j-NATURE,
volume = "158",
number = "4017",
pages = "567--568",
day = "26",
month = oct,
year = "1946",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/158567a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Wed Aug 9 07:30:09 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The black mark earned by the government of the day
more than a hundred years ago for its failure to see
Charles Babbage's difference engine brought to a
successful conclusion has still to be wiped out. It is
not too much to say that it cost Britain the leading
place in the art of mechanical computing. Babbage then
conceived and worked on his `ðanalytical engine',
designed to store numbers and operate on them according
to a sequence of processes conveyed to the machine by
cards similar to those used in the Jacquard loom. This,
however, was never completed.",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
remark = "The title in the Nature archive index is completely
wrong: it says ``A Manual of Operation for the
Automatic Sequence Controlled Calculator''. After the
critical introduction [see the abstract], the article
goes on to describe IBM's gift to Harvard of the
Automatic Sequence Controlled Calculator. It reports
about the ASCC: ``The machine contains seventy-two
storage counters, capable of holding twenty-three
digits and a sign. \ldots{} When working to the full
23-figure capacity of the machine, multiplication takes
about six seconds, and division twice as long;
additions and subtractions are done at the rate of
three a second, whatever their length.'' It then
describes the computation of logarithms via the Taylor
series expansion of $ \log (1 + x) $, and reports that
it can do exponential, trigonometric, and hyperbolic
functions as well.",
}<ò:1946:BDCL. J. ComrieBabbage's Dream Come Truej-NATURE1584017567--56826oct101946NATUAShttps://doi.org/10.1038/158567a00028-0836 (print), 1476-4687 (electronic) OR 00280836 (print), 14764687 (electronic)0028-0836 OR 00280836Wed Aug 9 07:30:09 2023https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib2023.08.09 07:30:09 ???The black mark earned by the government of the day more than a hundred years ago for its failure to see Charles Babbage's difference engine brought to a successful conclusion has still to be wiped out. It is not too much to say that it cost Britain the leading place in the art of mechanical computing. Babbage then conceived and worked on his `analytical engine', designed to store numbers and operate on them according to a sequence of processes conveyed to the machine by cards similar to those used in the Jacquard loom. This, however, was never completed.NatureThe title in the Nature archive index is completely wrong: it says `ó`A Manual of Operation for the Automatic Sequence Controlled Calculator''. After the critical introduction [see the abstract], the article goes on to describe IBM's gift to Harvard of the Automatic Sequence Controlled Calculator. It reports about the ASCC: ``The machine contains seventy-two storage counters, capable of holding twenty-three digits and a sign. ldots When working to the full 23-figure capacity of the machine, multiplication takes about six seconds, and division twice as long; additions and subtractions are done at the rate of three a second, whatever their length.'' It then describes the computation of logarithms via the Taylor series expansion of $ log (1 + x) $, and reports that it can do exponential, trigonometric, and hyperbolic functions as well.ack-nhfbhttp://www.nature.com/nature/archive/The black mark earned by the government of the day more than a hundred years ago for its failure to see Charles Babbage's difference engine brought to a successful conclusion has still to be wiped outô. It is not too much to say that it cost Britain the leading place in the art of mechanical computing. Babbage then conceived and worked on his `analytical engine', designed to store numbers and operate on them according to a sequence of processes conveyed to the machine by cards similar to those used in the Jacquard loom. This, however, was never completed.L. J. Comrie{Babbage}'s Dream Come True
@Article{Comrie:1946:BDC,
author = "L. J. Comrie",
title = "{Babbage}'s Dream Come True",
journal = j-NATURE,
volume = "158",
number = "4017",
pages = "567--568",
day = "26",
month = oct,
year = "1946",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/158567a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Wed Aug 9 07:30:09 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
https://www.math.utõah.edu/pub/tex/bib/fparith.bib",
abstract = "The black mark earned by the government of the day
more than a hundred years ago for its failure to see
Charles Babbage's difference engine brought to a
successful conclusion has still to be wiped out. It is
not too much to say that it cost Britain the leading
place in the art of mechanical computing. Babbage then
conceived and worked on his `analytical engine',
designed to store numbers and operate on them according
to a sequence of processes conveyed to the machine by
cards similar to those used in the Jacquard loom. This,
however, was never completed.",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
remark = "The title in the Nature archive index is completely
wrong: it says ``A Manual of Operation for the
Automatic Sequence Controlled Calculator''. After the
critical introduction [see the abstract], the article
goes on to describe IBM's gift to Harvard of the
Automatic Sequence Controlled Calculator. It reports
about the ASCC: ``The machine contains seventy-two
storage counters, capable of holding twenty-three
digits and a sign. \ldots{} When working to the full
23-figure capacity of the machine, multiplication takes
about six seconds, and division twice as long;
additions and subtractions are done at the rate of
three a second, whatever their length.'' It then
describes the computation of logarithms via the Taylor
series expansion of $ \log (1 + x) $, and reports that
it can do exponential, trigonometric, and hyperbolic
functions as well.",
}r Rechenautomat Ipm. Entwicklung Mathematischer
Instrumente in Deutschland 1939 bis 1945}. ({German})
[{The} {Ipm} Calculator. {The} development of
mathematical instruments in {Germany} 1939--1945]",
type = "{Bericht}",
number = "A3",
institution = "Institut f{\"u}r Praktische Mathematik, Technische
Hochschule",
address = "Darmstadt, West Germany",
day = "19",
month = aug,
year = "1946",
bibdate = "Wed Oct 13 11:20:15 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 3.3]{Randell:1982:ODC}.
Translated by Mr. and Mrs. P. Jones",
acknowledgement = ack-nhfb,
language = "German",
}=945}. ({German}) [{The} {Ipm} Calculator. {The} development of mathematical instruments in {Germany} 1939--1945]
@TechReport{Dreyer:1946:REM,
author = "H.-J. Dreyer and A. Walther",
title = "{Der Rechenautomat Ipm. Entwicklung Mathematischer
Instrumente in Deutschland 1939 bis 1945}. ({German})
[{The} {Ipm} Calculator. {The} development of
mathematical instruments in {Germany} 1939--1945]",
type = "{Bericht}",
number = "A3",
institution = "Institut f{\"u}r Praktische Mathematik, Technische
Hochschule",
address = "Darmstadt, West Germany",
day = "19",
month = aug,
year = "1946",
bibdate = "Wed Oct 13 11:20:15 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 3.3]{Randell:1982:ODC}.
Translated by Mr. and Mrs. P. Jones",
acknowledgement = ack-nhfb,
language = "German",
}
µµŽ@=]!#+Cƒ;=o;'C/ƒŽ%techreportfparith.bibDreyer:1946:REMH.-J. Dreyer and A. WaltherDer Rechenautomat Ipm. Entwicklung Mathematischer Instrumente in Deutschland 1939 bis 1945. (German) [The Ipm Calculator. The development of mathematical instruments in Germany 1939--1945]BerichtA3Institut fur Praktische Mathematik, Technische HochschuleDarmstadt, West Germany567--56819aug81946Wed Oct 13 11:20:15 2010https://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:20:15 ???Reprinted in cite [ 3.3]Randell:1982:ODC. Translated by Mr. and Mrs. P. JonesGermanack-nhfbH.-J. Dreyer and A. WaltherReprinted in \cite[\S 3.3]{Randell:1982:ODC}. Translated by Mr. and Mrs. P. Jones{Der Rechenautomat Ipm. Entwicklung Mathematischer Instrumente in Deutschland 1939 bis 1÷ "The {Electronic Numerical Integrator and Computer
(ENIAC)}",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "2",
number = "15",
pages = "97--110",
month = jul,
year = "1946",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
note = "Reprinted in \cite[\S 7.7]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
ajournal = "Math. Tables Other Aids Comput.",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}>fbMath. Tables Other Aids Comput.http://www.ams.org/mcom/H. H. Goldstine and Adele GoldstineReprinted in \cite[\S 7.7]{Randell:1982:ODC}.The {Electronic Numerical Integrator and Computer (ENIAC)}
@Article{Goldstine:1946:ENI,
author = "H. H. Goldstine and Adele Goldstine",
title = "The {Electronic Numerical Integrator and Computer
(ENIAC)}",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "2",
number = "15",
pages = "97--110",
month = jul,
year = "1946",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
note = "Reprinted in \cite[\S 7.7]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
ajournal = "Math. Tables Other Aids Comput.",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
ý‰q?\!#3]9-3;=y;]=Štechreportfparith.bibGoldstine:1947:PCPaHerman H. Goldstine and John von NeumannPlanning and coding of problems for an electronic computing instrument. ý‹x>[#1S}K7E;_oK=SgŒarticlefparith.bibGoldstine:1946:ENIH. H. Goldstine and Adele GoldstineThe Electronic Numerical Integrator and Computer (ENIAC)j-MATH-TABLES-OTHER-AIDS-COMPUT21597--110jul71946MTTCAS0891-6837 OR 08916837Tue Oct 13 08:44:19 MDT 1998https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:44:19 MDTReprinted in cite [ 7.7]Randell:1982:ODC.Mathematical Tables and Other Aids to Computationack-nhútle = "Planning and coding of problems for an electronic
computing instrument. {Part 1}, Vol. 1",
type = "Technical report",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "??",
month = "????",
year = "1947",
bibdate = "Fri Nov 16 16:35:14 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}?Part 1, Vol. 1Technical reportinst-INST-ADV-STUDYinst-INST-ADV-STUDY:adr1947Fri Nov 16 16:35:14 2012https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib2012.11.16 16:35:14 ???ack-nhfbHerman H. Goldstine and John von NeumannPlanning and coding of problems for an electronic computing instrument. {Part 1}, Vol. 1
@TechReport{Goldstine:1947:PCPa,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument. {Part 1}, Vol. 1",
type = "Technical report",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "??",
month = "????",
year = "1947",
bibdate = "Fri Nov 16 16:35:14 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}tle = "Planning and coding of problems for an electronic
computing instrument. {Part 2}, Vol. 1",
type = "Technical report",
number = "1",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "69",
day = "1",
month = apr,
year = "1947",
MRnumber = "MR22443",
bibdate = "Wed Jun 01 17:41:33 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Report prepared for U.S. Army Ordnance Department
under contract W-36-034-OKD-7481. Reprinted in
\cite[80--151]{Taub:1963:JNCa}. Knuth \cite[p.
278]{Knuth:1998:SA} cites pp. 142--151 of this report
as the first published treatment of double-precision
arithmetic on digital computers.",
acknowledgement = ack-nhfb,
}@
‹‹qÞL¹&“ˆo‘_
@Article{Ling:1981:HSB,
author = "Huey Ling",
title = "High-speed binary adder",
journal = ;‡I
@Article{Ling:1990:AIM,
author = "H. Ling",
title = "An approach to implementing &t„[‰7
@Article{Linhardt:1969:DDT,
author = "R. J. Linhardt and H. S. Miller",
title = "ˆd‘I
@Article{Linnainmaa:1974:ASK,
author = "Seppo Linnainmaa",
title = "Analysis of SoRŒ˜%
@Article{Linnainmaa:1975:TAS,
author = "Seppo Linnainmaa",
title = "Towards Accur
‘Œ{™w
@Article{Linnainmaa:1976:TEA,
author = "Seppo Linnainmaa",
title = "{Taylor} expaÛ…m‹[
@Article{Linnainmaa:1981:CEU,
author = "Seppo Linnainmaa",
title = "Combatting th>ˆ%K
@Article{Linnainmaa:1981:SDP,
author = "Seppo Linnainmaa",
title = "Software for Aechnical report1inst-INST-ADV-STUDYinst-INST-ADV-STUDY:adr691apr41947MR22443Wed Jun 01 17:41:33 2005https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib2005.06.01 17:41:33 ???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.ack-nhfbHerman H. Goldstine and John von NeumannReport 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.Planning and coding of problems for an electronic computing instrument. {Part 2}, Vol. 1
@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",
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year = "1947",
MRnumber = "MR22443",
bibdate = "Wed Jun 01 17:41:33 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Report prepared for U.S. Army Ordnance Department
under contract W-36-034-OKD-7481. Reprinted in
\cite[80--151]{Taub:1963:JNCa}. Knuth \cite[p.
278]{Knuth:1998:SA} cites pp. 142--151 of this report
as the first published treatment of double-precision
arithmetic on digital computers.",
acknowledgement = ack-nhfb,
}
ûó÷û‰qB\!#3]9-3;=y;]=Štechreportfparith.bibGoldstine:1947:PCPdHerman H. Goldstine and John von NeumannPlanning and coding of problems for an electronic computing instrument. ‰qA\!#3]9-3;=y;]=Štechreportfparith.bibGoldstine:1947:PCPcHerman H. Goldstine and John von NeumannPlanning and coding of problems for an electronic computing instrument. ‘~@^!#3]9-3;=y;„;]„C=‘'techreportfparith.bibGoldstine:1947:PCPbHerman H. Goldstine and John von NeumannPlanning and coding of problems for an electronic computing instrument. Part 2, Vol. 1Ttle = "Planning and coding of problems for an electronic
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ÎÎŠ/E] #'a#+#Ca;+eŠbookfparith.bibHUCL:1946:MOAHarvard University. Computation LaboratoryA Manual of Operation for the Automatic Sequence Controlled Calculatorpub-HARVARDpub-HARVARD:adr5611946QA3 .H3 v.1Mon Nov 4 07:46:57 MST 2002htt
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URL = "http://www.emula3.com/docs/Turing_Report_on_ACE.pdf",
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`)»`ŒPH] '#-'Ck=1=o;‚''G‚;o‹Ainproceedingsfparith.bibMauchly:1947:PPEJ. W. MauchlyProceedings of a Symposium on Large Scale Digital Calculating Machinery, 7--10 January 1947Preparation of problems for EDVAC-type machinesHarvard University PressCambridge, MA, USA5--91947Wed Oct 13 11:55:58 2010https://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:55:58 ???Reprinted in em Annals of the Computation Laboratory of Harvard University, bf 16, 203--207 (1948). Reprinted in cite [ 8.2]Randell:1982:ODC.ack-nhfbJ. W. Mauchly{Pr‡bGY #'917=o;_=g9ˆMarticlefparit‰LFZ !#+%I%=‚;sm%I‹techreportfparith.bibTuring:1946:PECA. M. TuringProposed Electronic CalculatorReportE882inst-NPLinst-NPL:adr481946Fri journal = j-BELL-LABS-RECORD,
volume = "24",
number = "??",
pages = "5--9",
year = "1947",
CODEN = "BLRCAB",
ISSN = "0005-8564",
bibdate = "Wed Oct 13 11:32:38 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.3]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
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}Gh.bibJuley:1947:BCJ. JuleyThe Ballistic Computerj-BELL-LABS-RECORD245--91947BLRCAB0005-8564 OR 00058564Wed Oct 13 11:32:38 2010https://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:32:38 ???Reprinted in cite [ 6.3]Randell:1982:ODC.Bell Laboratories Recordack-nhfbJ. JuleyReprinted in \cite[\S 6.3]{Randell:1982:ODC}.The Ballistic Computer
@Article{Juley:1947:BC,
author = "J. Juley",
title = "The Ballistic Computer",
journal = j-BELL-LABS-RECORD,
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number = "??",
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ISSN = "0005-8564",
bibdate = "Wed Oct 13 11:32:38 2010",
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acknowledgement = ack-nhfb,
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bibdate = "Wed Oct 13 11:55:58 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
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acknowledgement = ack-nhfb,
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@InProceedings{Mauchly:1947:PPE,
author = "J. W. Mauchly",
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}tic 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;
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URL = "http://www.jstor.org/stable/226161",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
remark = "From the second paragraph: ``The earliest printed work
in English to discuss arithmetic, \booktitle{The
Myrrour of the World}, came from the press of William
Caxton in 1481. This work, however, contained only one
page devoted entirely to arithmetic. It is not until
1537 that we find another book printed in English
devoted entirely to arithmetic and dealing with the
Hindu--Arabic system of numbers. This is an anonymous
publication, from a press located at St. Albans, with
the title \booktitle{An Introduction for to Lerne to
Recken with the Pen, or with the Counters},'' This book
went through eight editions between 1537 and 1629. The
article quotes book sections on integer division.",
}I1947:FAPA. W. RichesonThe First Arithmetic Printed in Englishj-ISIS371--247--56may51947ISISA40021-1753 (print), 1545-6994 (electronic) OR 00211753 (print), 15456994 (electronic)0021-1753 OR 00211753Tue Jul 30 21:27:09 MDT 2013http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i302230; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/isis1940.bib2013.07.30 21:27:09 MDThttp://www.jstor.org/stable/226161IsisFrom the second paragraph: ``The earliest printed work in English to discuss arithmetic, booktitle The Myrrour of the World, came from the press of William Caxton in 1481. This work, however, contained only one page devoted entirely to arithmetic. It is not until 1537 that we find another book printed in English devoted entirely to arithmetic and dealing with the Hindu--Arabic system of numbers. This is an anonymous publication, from a press located at St. Albans, with the title booktitle An Introduction for to Lerne to Recken with the Pen, or with the Counters,'' This book went through eight editions between 1537 and 1629. The article quotes book sections on integer division.ack-nhfbhttp://www.jstor.org/journal/isisA. W. RichesonThe First Arithmetic Printed in {English}
@Article{Richeson:1947:FAP,
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bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
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in English to discuss arithmetic, \booktitle{The
Myrrour of the World}, came from the press of William
Caxton in 1481. This work, however, contained only one
page devoted entirely to arithmetic. It is not until
1537 that we find another book printed in English
devoted entirely to arithmetic and dealing with the
Hindu--Arabic system of numbers. This is an anonymous
publication, from a press located at St. Albans, with
the title \booktitle{An Introduction for to Lerne to
Recken with the Pen, or with the Counters},'' This book
went through eight editions between 1537 and 1629. The
article quotes book sections on integer division.",
}
~~¥lJ^#3]g!!571!;‹%;Mkg‡m!um]Ugª%Oarticlefparith.bibvonNeumann:1947:NIMJohn von Neumann and Herman H. GoldstineNumerical Inverting of Matrices of High Orderj-BULL-AMS53111021--1099nov111947BAMOAD0002-9904 (print), 1936-881X (electronic) OR 00029904 (print), 1936881X (electronic)0002-9904 OR 0002990465.0XMR0024235 (9,471b)E. BodewigThu Nov 8 14:49:36 2007https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/mirrors/ftp.ir˜lI\ #/)[57Eƒ;QŠgO)_œ
articlefparith.bibRicheson: = "Numerical Inverting of Matrices of High Order",
journal = j-BULL-AMS,
volume = "53",
number = "11",
pages = "1021--1099",
month = nov,
year = "1947",
CODEN = "BAMOAD",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
MRclass = "65.0X",
MRnumber = "MR0024235 (9,471b)",
MRreviewer = "E. Bodewig",
bibdate = "Thu Nov 8 14:49:36 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/auto.diff.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.1.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/Matrix.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/sparse.linear.systems.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Goldstine:1951:NIM} for Part II. Reprinted
in \cite[vol. 5, pp. 479--557]{Taub:1961:JNCa}.",
URL = "http://projecteuclid.org/euclid.bams/1183511222",
ZMnumber = "0031.31402",
acknowledgement = ack-nhfb # " and " # ack-jg,
author-dates = "John von Neumann (28 December 1903--8 February 1957)",
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
kwds = "nla, linear system, rounding error",
referred = "[Markov1999a].",
remark = "This may be the first journal publication about the
use of double-precision arithmetic on computers, used
for the accumulation of inner products and matrix
products. On pp. 1035--1038, the authors show that when
the sum of $m$ products of two $s$-digit numbers is
accumulated in precision $ 2 s $, with rounding to $s$
digits only after the final sum is complete, then the
rounding error is essentially one unit in the last
place, instead of $m$ times that value. Cited in
\cite{Sterbenz:1974:FPC}.",
}Ja.uka.de/bibliography/Math/auto.diff.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.1.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/Matrix.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/sparse.linear.systems.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.08 14:49:36 ???See cite Goldstine:1951:NIM for Part II. Reprinted in cite [vol. 5, pp. 479--557]Taub:1961:JNCa.http://projecteuclid.org/euclid.bams/1183511222Bulletin of the American Mathematical SocietyThis 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.0031.31402ack-nhfbJohn von Neumann (28 December 1903--8 February 1957)http://www.ams.org/journals/bull/all_issues.htmlJohn von Neumann and Herman H. GoldstineSee \cite{Goldstine:1951:NIM} for Part II. Reprinted in \cite[vol. 5, pp. 479--557]{Taub:1961:JNCa}.Numerical Inverting of Matrices of High Order
@Article{vonNeumann:1947:NIM,
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https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/auto.diff.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.1.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/Matrix.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/sparse.linear.systems.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Goldstine:1951:NIM} for Part II. Reprinted
in \cite[vol. 5, pp. 479--557]{Taub:1961:JNCa}.",
URL = "http://projecteuclid.org/euclid.bams/1183511222",
ZMnumber = "0031.31402",
acknowledgement = ack-nhfb # " and " # ack-jg,
author-dates = "John von Neumann (28 December 1903--8 February 1957)",
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
kwds = "nla, linear system, rounding error",
referred = "[Markov1999a].",
remark = "This may be the first journal publication about the
use of double-precision arithmetic on computers, used
for the accumulation of inner products and matrix
products. On pp. 1035--1038, the authors show that when
the sum of $m$ products of two $s$-digit numbers is
accumulated in precision $ 2 s $, with rounding to $s$
digits only after the final sum is complete, then the
rounding error is essentially one unit in the last
place, instead of $m$ times that value. Cited in
\cite{Sterbenz:1974:FPC}.",
}atories}' Computing
Machine---{I}",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "3",
number = "21",
pages = "1--13",
month = jan,
year = "1948",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
note = "Reprinted in \cite[\S 6.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
ajournal = "Math. Tables Other Aids Comput.",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}KC.Mathematical Tables and Other Aids to Computationack-nhfbMath. Tables Other Aids Comput.http://www.ams.org/mcom/Franz L. AltReprinted in \cite[\S 6.4]{Randell:1982:ODC}.A {Bell Telephone Laboratories}' Computing Machine---{I}
@Article{Alt:1948:BTLa,
author = "Franz L. Alt",
title = "A {Bell Telephone Laboratories}' Computing
Machine---{I}",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "3",
number = "21",
pages = "1--13",
month = jan,
year = "1948",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
note = "Reprinted in \cite[\S 6.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
ajournal = "Math. Tables Other Aids Comput.",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
gZ‚ÕgˆLNZ !#)'S7)1=‚W;'S‰9techreportfpa,‘M\ '#31E1=o;ˆE1E’=inproceedingsfparith.bibRademacher:1948:AEPHans A. RademacherOn the Accum)‰MLZ #)%?'5=o;_9W%g?Š5 articlefparith.bibEckert:1948:ECW. J. EckertElectrons and computationj-SCI-MONTHLY675315--323nov111948SCMOAA0096-3771 &‹KZ #'%uK7E;_oK=%g}Œ?
articlefparith.bibAlt:1948:BTLaFranz L. AltA Bell Telephone Laboratories' Computing Machine---Ij-MATH-TABLES-OTHER-AIDS-COMPUT3211--13jan11948MTTCAS0891-6837 OR 08916837Tue Oct 13 08:44:19 MDT 1998https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:44:19 MDTReprinted in cite [ 6.4]Randell:1982:OD#ion",
journal = j-SCI-MONTHLY,
volume = "67",
number = "5",
pages = "315--323",
month = nov,
year = "1948",
CODEN = "SCMOAA",
ISSN = "0096-3771 (print), 2327-7513 (electronic)",
bibdate = "Wed Oct 13 11:27:40 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.3]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "The Scientific Monthly",
journal-URL = "http://www.jstor.org/journal/sciemont",
}L(print), 2327-7513 (electronic) OR 00963771 (print), 23277513 (electronic)Wed Oct 13 11:27:40 2010https://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:27:40 ???Reprinted in cite [ 5.3]Randell:1982:ODC.The Scientific Monthlyack-nhfbhttp://www.jstor.org/journal/sciemontW. J. EckertReprinted in \cite[\S 5.3]{Randell:1982:ODC}.Electrons and computation
@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",
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bibdate = "Wed Oct 13 11:27:40 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.3]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "The Scientific Monthly",
journal-URL = "http://www.jstor.org/journal/sciemont",
}Integration on High-Speed Calculating Machines",
crossref = "Anonymous:1948:PSL",
pages = "176--187",
year = "1948",
bibdate = "Mon Jun 18 11:03:56 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "From page 186, remark by John W. Mauchly: ``I just
wanted to remark that this paper is probably one of the
first to appear as a result of the interaction between
computing machines and mathematics. I think many of us
have been looking forward with certainty to the day
when the advent of computing machines would influence
the course of mathematics, and there are still many
directions in which we can look forward to further such
impacts. This reaction is not, of course, one way.
Mathematics should also influence the computing
machine.''",
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@Book{Apple:1986:ANM,
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@Book{Apple:1988:ANM,
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@Book{Apple:1994:IMP,
author = "{Apple Computers, Inc.}",
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@Book{Arvo:1991:GGI,
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@Book{Aspray:1987:PJN,
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@Book{Bareiss:1978:PEA,
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@Book{Barna:1973:ICD,
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¯ê#ƒÔE
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@Book{Beliankov:1989:NPO,
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@InProceedings{Rademacher:1948:AEP,
author = "Hans A. Rademacher",
title = "On the Accumulation of Errors in Processes of
Integration on High-Speed Calculating Machines",
crossref = "Anonymous:1948:PSL",
pages = "176--187",
year = "1948",
bibdate = "Mon Jun 18 11:03:56 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "From page 186, remark by John W. Mauchly: ``I just
wanted to remark that this paper is probably one of the
first to appear as a result of the interaction between
computing machines and mathematics. I think many of us
have been looking forward with certainty to the day
when the advent of computing machines would influence
the course of mathematics, and there are still many
directions in which we can look forward to further such
impacts. This reaction is not, of course, one way.
Mathematics should also influence the computing
machine.''",
}re-root iteration",
type = "SRG Memorandum report",
number = "10",
institution = inst-PRINCETON,
address = inst-PRINCETON:adr,
pages = "18",
year = "1948",
bibdate = "Tue May 15 08:00:09 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}Nrith.bibTukey:1948:NSRJohn W. TukeyA note on the square-root iterationSRG Memorandum report10inst-PRINCETONinst-PRINCETON:adr181948Tue May 15 08:00:09 2012https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib2012.05.15 08:00:09 ???ack-nhfbJohn W. TukeyA note on the square-root iteration
@TechReport{Tukey:1948:NSR,
author = "John W. Tukey",
title = "A note on the square-root iteration",
type = "SRG Memorandum report",
number = "10",
institution = inst-PRINCETON,
address = inst-PRINCETON:adr,
pages = "18",
year = "1948",
bibdate = "Tue May 15 08:00:09 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}.n Matrix Processes",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "1",
pages = "287--308",
month = sep,
year = "1948",
CODEN = "QJMMAV",
ISSN = "0033-5614 (print), 1464-3855 (electronic)",
ISSN-L = "0033-5614",
MRclass = "65.0X",
MRnumber = "MR0028100 (10,405c)",
MRreviewer = "E. Bodewig",
bibdate = "Sat Nov 19 12:09:58 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/a/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite{Turing:1992:PM} with summary and
notes (including corrections)",
URL = "http://turing.ecs.soton.ac.uk/browse.php/B/18",
ZMnumber = "0033.28501",
acknowledgement = ack-nhfb,
fjournal = "Quarterly Journal of Mechanics and Applied
Mathematics",
journal-URL = "http://qjmam.oxfordjournals.org/content/by/year",
mynote = "The notes are not very good. They mainly correct
errors and fill in the gaps of derivations. Much better
would have been higher level comments from a numerical
analyst, e.g. on where Turing's ideas/predictions were
wrong.",
}O0tab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.19 12:09:58 ???Reprinted in cite Turing:1992:PM with summary and notes (including corrections)http://turing.ecs.soton.ac.uk/browse.php/B/18Quarterly Journal of Mechanics and Applied Mathematics0033.28501ack-nhfbhttp://qjmam.oxfordjournals.org/content/by/yearA. M. TuringReprinted in \cite{Turing:1992:PM} with summary and notes (including corrections)Rounding-Off Errors in Matrix Processes
@Article{Turing:1948:REM,
author = "A. M. Turing",
title = "Rounding-Off Errors in Matrix Processes",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "1",
pages = "287--308",
month = sep,
year = "1948",
CODEN = "QJMMAV",
ISSN = "0033-5614 (print), 1464-3855 (electronic)",
ISSN-L = "0033-5614",
MRclass = "65.0X",
MRnumber = "MR0028100 (10,405c)",
MRreviewer = "E. Bodewig",
bibdate = "Sat Nov 19 12:09:58 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/a/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite{Turing:1992:PM} with summary and
notes (including corrections)",
URL = "http://turing.ecs.soton.ac.uk/browse.php/B/18",
ZMnumber = "0033.28501",
acknowledgement = ack-nhfb,
fjournal = "Quarterly Journal of Mechanics and Applied
Mathematics",
journal-URL = "http://qjmam.oxfordjournals.org/content/by/year",
mynote = "The notes are not very good. They mainly correct
errors and fill in the gaps of derivations. Much better
would have been higher level comments from a numerical
analyst, e.g. on where Turing's ideas/predictions were
wrong.",
}
®®”CO] #+%[C573!=„;+gy!k%/[˜]articlefparith.bibTuring:1948:REMA. M. TuringRounding-Off Errors in Matrix Processesj-QUART-J-MECH-APPLIED-MATH1287--308sep91948QJMMAV0033-5614 (print), 1464-3855 (electronic) OR 00335614 (print), 14643855 (electronic)0033-5614 OR 0033561465.0XMR0028100 (10,405c)E. BodewigSat Nov 19 12:09:58 2005https://www.math.utah.edu/pub/bibnet/authors/a/turing-alan-mathison.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-s/ectronic digital computers",
journal = j-NATURE,
volume = "162",
number = "4117",
pages = "487--487",
day = "25",
month = sep,
year = "1948",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/162487a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Wed Oct 13 12:00:02 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
remark = "Letter submitted 3 August 1948. Describes a small
prototype digital computer with 32 31-bit words for
instructions, data, and working storage.",
}P
++˜rßL¹&“’t¥i
@Book{Kastner:2010:AOT,
author = "Ryan Kastner and Anup Hosangadi and Farzan Fallah",
tiYÜ†"ŒE
@Book{Katzan:1982:IAA,
author = "Harry Katzan",
title = "Invitation to {Ada} and —†zu
@Book{Katzan:1984:IA,
author = "Harry Katzan",
title = "Invitation to {Ada}",
pÛ…D‹
@Book{Kaucher:1987:CAS,
editor = "Edgar Kaucher and Ulrich Kulisch and Christian
y‹…H‹
@Book{Khinchin:1964:CF,
author = "Aleksandr Iakovlevich Khinchin",
title = "Contiš‡2Že
@Book{Khinchin:1997:CF,
author = "Aleksandr Iakovlevich Khinchin",
title = "Conti:°à
@Book{Kirk:2010:PMP,
author = "David B. Kirk and Wen-mei W. Hwu",
title = "PrograYå…Š/
@Book{Klatte:1991:PSB,
author = "R. Klatte and U. Kulisch and M. Neaga and D. Ratz and
)‚†/Œ_
@Book{Klatte:1991:PXP,
author = "R. Klatte and U. Kulisch and M. Neaga and D. Ratz and
)…Hn*¹HË<G£gÇO
@Article{Agarwal:1994:EFP,
author = "R. C. Agarwal and F. G. Gustavson and M. Zubair",
t1C,ˆ
@Article{Adam:2012:FPD,
author = "Sanda Adam and Gheorghe Adam",
title = "Floatin]¥+‰’'
@Article{Abdelmalek:1971:REA,
author = "Nabih N. Abdelmalek",
title = "Round-off Error Analysis for {Gram--Schmidt} Method
¸t+‡;Žw
@Article{Agrawal:1975:AAN,
author = "D. P. Agrawal",
title = "Arithmetic Algorith¨b†{w
@Article{Ahmadi:2008:PFS,
author = "O. Ahmadi and D. Hankerson and F.
RodUt†E
@Article{Ait-Ameur:1999:RRE,
author = "Y. Ait-Ameur",
title = "Refinement of rati<ßE'‡Ž7
@Article{Al-Twaijry:1998:SPB,
author = "H. A. Al-Twaijry and S. F. Oberman and S. T. Fu an;5M‡,ŽY
@Article{Alia:1991:VMM,
author = "G. Alia and E. Martinelli",
title = "A {VLSI} m'¶é.éZ<Ë]¦Šf•M
@Article{Alway:1971:GFA,
author = "G. G. Alway",
title = "A general factorising a¼<âu›k
@Article{Anderson:1967:ISMb,
author = "S. F. Anderson and J. G. Earle and R. E. Goldschmidäe‡=Ž{
@Article{Anonymous:1969:VPD,
author = "Anonymous",
title = "Video Probability Dis›‡K
@Article{Andrlon:2023:FNB,
author = "Mak Andrlon",
title = "Finding Normal Binaryt:1H„w‰o
@Article{Anonymous:1992:FPa,
author = "Anonymous",
title = "Floating Point",
jo+LeŒ„_‰?
@Article{Anonymous:1993:FPc,
author = "Anonymous",
title = "Floating Point",
jo.9„ˆ
@Article{Anonymous:1994:SPF,
author = "Anonymous",
title = "Signal Path: Floating1_8.4]{Randell:1982:ODC}.Electronic digital computers
@Article{Williams:1948:EDC,
author = "F. C. Williams and T. Kilburn",
title = "Electronic digital computers",
journal = j-NATURE,
volume = "162",
number = "4117",
pages = "487--487",
day = "25",
month = sep,
year = "1948",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/162487a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Wed Oct 13 12:00:02 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
remark = "Letter submitted 3 August 1948. Describes a small
prototype digital computer with 32 31-bit words for
instructions, data, and working storage.",
}
aP[ #/GEM57=o;_‚)WGgEarticlefparith.bibWilliams:1948:EDCF. C. Williams and T. KilburnElectronic digital computersj-NATURE1624117487--48725sep91948NATUAShttps://doi.org/10.1038/162487a00028-0836 (print), 1476-4687 (electronic) OR 00280836 (print), 14764687 (electronic)0028-0836 OR 00280836Wed Oct 13 12:00:02 2010https://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 12:00:02 ???Reprinted in cite [ 8.4]Randell:1982:ODC.NatureLetter submitted 3 August 1948. Describes a small prototype digital computer with 32 31-bit words for instructions, data, and working storage.ack-nhfbhttp://www.nature.com/nature/archive/F. C. Williams and T. KilburnReprinted in \cite[\S 6",
journal = j-SCI-AMER,
volume = "180",
number = "4",
pages = "28--39",
month = apr,
year = "1949",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican0449-28",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Sat May 18 16:12:10 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciam1940.bib",
URL = "http://www.jstor.org/stable/24967160;
http://www.nature.com/scientificamerican/journal/v180/n4/pdf/scientificamerican0449-28.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
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an introduction to the binary number system.",
}Q
jj×D±¹&“…@‹
@Article{Clarke:1996:VSD,
author = "E. M. Clarke and S. M. German and X. Zhao",
title = 7)‡#ŽG
@Article{Clarke:1999:VSD,
author = "Edmund M. Clarke and Steven M. German and Xudong
=V„|‰y
@Article{Clarkson:1961:DMI,
author = "W. K. Clarkson",
title = "A Divisionless Me9Žœ
@Article{Cleemput:2012:CMT,
author = "Jeroen V. Cleemput and Bart Coppens and Bjorn {De
^‰’%
@Article{Clenshaw:1955:NSC,
author = "C. W. Clenshaw",
title = "A note on the summation of {Chebyshev} series",
journal = Â…h‹Q
@Article{Clenshaw:1963:ASF,
author = "C. W. Clenshaw and G. F. Miller and M. Woodger",
t#Œq™c
@Article{Clenshaw:1984:BFP,
author = "C. W. Clenshaw and F. W. J. Olver",
title = j‹
–
@Article{Clenshaw:1986:GEL,
author = "C. W. Clenshaw and Daniel W. Lozier and F. W. J. Olvõarry M. Davis",
title = "Mathematical Machines",
journal = j-SCI-AMER,
volume = "180",
number = "4",
pages = "28--39",
month = apr,
year = "1949",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican0449-28",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Sat May 18 16:12:10 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciam1940.bib",
URL = "http://www.jstor.org/stable/24967160;
http://www.nature.com/scientificamerican/journal/v180/n4/pdf/scientificamerican0449-28.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
remark = "Description of counting devices before 1950, including
an introduction to the binary number system.",
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!!ˆR[ #-S{=o;SˆKarticlefpari=ŽfQ] #')7!o57EY;‚
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@Article{Davis:1949:MM,
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}Rth.bibHartree:1949:NSRDouglas R. (Douglas Rayner) HartreeNote On Systematic Roundoff Errors in Numerical IntegrationJournal of Research of the National Bureau of Standards4262--??1949Wed Feb 14 19:07:37 2007https://www.math.utah.edu/pub/tex/bib/fparith.bib2007.02.14 19:07:37 ???ack-nhfbDouglas R. (Douglas Rayner) HartreeNote On Systematic Roundoff Errors in Numerical Integration
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title = "Note On Systematic Roundoff Errors in Numerical
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acknowledgement = ack-nhfb,
}? Certain Procedure of Numerical
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journal = j-J-RES-NATL-BUR-STAND,
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month = jan,
year = "1949",
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bibdate = "Fri Aug 20 09:32:34 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "With an appendix by Douglas R. Hartree.",
abstract = "An example of numerical integration is given that
shows very systematic effects in the less significant
digits. This lack of randomness gives rounding-off
errors that exceed the predicted standard deviation by
a factor of three. The example considered in this paper
shows that systematic rounding-off errors can occur in
numerical in integration, irrespective of the number of
digits kept in the contributions to the integral. In
the appendix this phenomenon is examined, and criteria
are set up to detect the cases in which it may arise to
a serious extent.",
acknowledgement = ack-nhfb,
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
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}SAps://www.math.utah.edu/pub/tex/bib/fparith.bib2010.08.20 09:32:34 ???With an appendix by Douglas R. Hartree.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.Cited in cite Sterbenz:1974:FPC.ack-nhfbhttps://www.nist.gov/nist-research-library/journal-research-nist/past-papersAn 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 exampBle 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.H. D. HuskeyWith an appendix by Douglas R. Hartree.On the Precision of a Certain Procedure of Numerical Integration
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abstract = "An example of numerical integration is given that
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acknowledgement = ack-nhfb,
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title = "Transformation related to the angular and the
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\cite{Sterbenz:1974:FPC}.",
subject = "computers",
}Uof contract N6-ONR-240, Task 1. Cited in cite Sterbenz:1974:FPC.computersack-nhfbW. W. {Stifler, Jr.}High-speed computing devices
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\cite{Sterbenz:1974:FPC}.",
subject = "computers",
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articlefparith.bibStegun:1956:PCIrene A. Stegun and Milton AbramowitzPitfalls in computationJournal of the Society for Industrial and Applied Mathematics4207--2191956Tue Aug 28 06:16:28 2001https://www.math.utah.edu/pub/tex/bib/fparith.bib2001.08.28 06:16:28 ???Cited in cite Sterbenz:1974:FPC.ack-nhfbIrene A. Stegun and Milton AbramowitzPitfalls in computation
@Article{Stegun:1956:PC,
author = "Irene A. Stegun and Milton Abramowitz",
title = "Pitfalls in computation",
journal = "Journal of the Society for Industrial and Applied
Mathematics",
volume = "4",
pages = "207--219",
year = "1956",
bibdate = "Tue Aug 28 06:16:28 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
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month = jun,
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CODEN = "IRELAO",
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bibdate = "Thu Jun 30 15:46:21 MDT 2011",
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acknowledgement = ack-nhfb,
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journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}„d T. R. O'Meara and J. StrathmanAnalog Multipliers and Squarers Using a Multigrid Modulator
@Article{Sydnor:1956:AMS,
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GwŠg articlefparith.bibWeinberger:1956:OMAA. Weinberger and J. L. SmithA One-Microsecond Adder Using One-Megacycle Circuitryj-IRE-TRANS-ELEC-COMPUTù1^#+k;]7Ee;]
kŽOarticlefparith.bibSydnor:1956:AMSR. L. Sydnor and T. R. O'Meara and J. StrathmanAnalog Multipliers and Squarers Using a Multigrid Modulatorj-IRE-TRANS-ELEC-COMPUTEC-5282--85jun61956IRELAOhttps://doi.org/10.1109/TEC.1956.52198040367-9950 OR 03679950Thu Jun 30 15:46:21 MDT 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.06.30 15:46:21 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219804IRE Transactions on Electronic Computersack-nhfbhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885R. L. Sydnor anöA One-Microsecond Adder Using One-Megacycle
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journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-5",
number = "??",
pages = "65--73",
month = jun,
year = "1956",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Fri Nov 09 19:38:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
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@Article{Weinberger:1956:OMA,
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title = "A One-Microsecond Adder Using One-Megacycle
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}ng-Decimal Interpretive System for
the {IBM 650 Magnetic Drum Calculator}",
journal = "IBM Technical Newsletter",
volume = "??",
number = "11",
pages = "xxi + 63",
month = mar,
year = "1956",
bibdate = "Mon Sep 04 13:55:28 2023",
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URL = "https://babel.hathitrust.org/cgi/pt?id=coo.31924003945759&seq=7",
acknowledgement = ack-nhfb,
}†olontis:1956:CFDV. M. WolontisA Complete Floating-Decimal Interpretive System for the IBM 650 Magnetic Drum CalculatorIBM Technical Newsletter11xxi + 63mar31956Mon Sep 04 13:55:28 2023https://www.math.utah.edu/pub/tex/bib/fparith.bib2023.09.04 13:55:28 ???https://babel.hathitrust.org/cgi/pt?id=coo.31924003945759&seq=7ack-nhfbV. M. WolontisA Complete Floating-Decimal Interpretive System for the {IBM 650 Magnetic Drum Calculator}
@Article{Wolontis:1956:CFD,
author = "V. M. Wolontis",
title = "A Complete Floating-Decimal Interpretive System for
the {IBM 650 Magnetic Drum Calculator}",
journal = "IBM Technical Newsletter",
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month = mar,
year = "1956",
bibdate = "Mon Sep 04 13:55:28 2023",
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URL = "https://babel.hathitrust.org/cgi/pt?id=coo.31924003945759&seq=7",
acknowledgement = ack-nhfb,
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‹ˆó‹Œ\\#+IO57=o;M1SeIQSarticlefparith.bibErcoli:1957:EDOPaolo Ercoli and Roberto VaccaErrors Due to Overflow in Arithmetic Operations Particularly as Regards FINAC Electronic Computerj-J-ACM44450--455oct101957JACOAH0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)0004-5411 OR 00045411Thu Dec 08 09:28:48 2005https://www.math.utah.edu/pub/tex/bib/fparith.bib2005.12.08 09:28:48 ???See letter cite Ercoli:1960:LEE.Journal of the ACMfloating-point arithmetic; overflowack-nhfbhttp://portal.acm.org/browse‰ \ #%%%-=o;/%Š5Ybookfparith.bibAlt:1957:EDCFranz L. AltElectronþˆl\ #/)===o;)A‰'Tarticlefparith.bibWûs: Their Use in Science and
Engineering",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "x + 335",
year = "1957",
bibdate = "Sun Jun 17 18:53:23 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Section 2.3 discusses number representation and
decimal versus binary arithmetic.",
xxnote = "Check page count: incomplete view in Google books.
Price bibliography says 1958.",
}‡ic Digital Computers: Their Use in Science and Engineeringpub-ACADEMICpub-ACADEMIC:adrx + 3351957Sun Jun 17 18:53:23 2018https://www.math.utah.edu/pub/tex/bib/fparith.bib2018.06.17 18:53:23 ???Section 2.3 discusses number representation and decimal versus binary arithmetic.ack-nhfbFranz L. AltElectronic Digital Computers: Their Use in Science and Engineering
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publisher = pub-ACADEMIC,
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bibdate = "Sun Jun 17 18:53:23 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Section 2.3 discusses number representation and
decimal versus binary arithmetic.",
xxnote = "Check page count: incomplete view in Google books.
Price bibliography says 1958.",
}ors 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,
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CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
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bibdate = "Thu Dec 08 09:28:48 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See letter \cite{Ercoli:1960:LEE}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
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}ˆ_dl.cfm?idx=J401Paolo Ercoli and Roberto VaccaSee letter \cite{Ercoli:1960:LEE}.Errors Due to Overflow in Arithmetic Operations Particularly as Regards {FINAC} Electronic Computer
@Article{Ercoli:1957:EDO,
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title = "Errors Due to Overflow in Arithmetic Operations
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}ifre iniziali dei numeri
osservati. ({Italian}) [{On} the frequency of initial
digits of observed numbers]",
journal = "Bull. Inst. Internat. Stat.",
volume = "35",
number = "??",
pages = "57--76",
year = "1957",
bibdate = "Sun Sep 18 11:54:25 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "29th session, 2nd delivery, Rio de Janerio.",
URL = "",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
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}‰4:25 ???29th session, 2nd delivery, Rio de Janerio.Benford's Law; Law of Anomalous Numbers; Zipf's LawItalianack-nhfbCorrado Gini29th session, 2nd delivery, Rio de Janerio.Sulla frequenza delle cifre iniziali dei numeri osservati. ({Italian}) [{On} the frequency of initial digits of observed numbers]
@Article{Gini:1957:SFD,
author = "Corrado Gini",
title = "Sulla frequenza delle cifre iniziali dei numeri
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\ #+%‚=o;s%‚Šyarticlefparith.bibHerzel:1957:SDDAmato HerzelSulla distribuzione della cifre iniziali dei numeri statistici. (Italian) [On the frequency of initial digits of statistical numbers]Atti dell XV e XVII Riunione, Societa Italiana di StatiŠ [ #'%‚C=o;cs%c‚‹+articlefparith.bibGini:1957:SFDCorrado GiniSulla frequenza delle cifre iniziali dei numeri osservati. (Italian) [On the frequency of initial digits of observed numbers]Bull. Inst. Internat. Stat.3557--761957Sun Sep 18 11:54:25 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib2011.09.18 11:5ella cifre iniziali dei numeri
statistici. ({Italian}) [{On} the frequency of initial
digits of statistical numbers]",
journal = "Atti dell XV e XVII Riunione, Societa Italiana di
Statistica",
volume = "??",
number = "??",
pages = "??--??",
year = "1957",
bibdate = "Sun Sep 18 12:00:07 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
language = "Italian",
}Šstica??--??1957Sun Sep 18 12:00:07 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib2011.09.18 12:00:07 ???Benford's Law; Law of Anomalous Numbers; Zipf's LawItalianack-nhfbAmato HerzelSulla distribuzione della cifre iniziali dei numeri statistici. ({Italian}) [{On} the frequency of initial digits of statistical numbers]
@Article{Herzel:1957:SDD,
author = "Amato Herzel",
title = "Sulla distribuzione della cifre iniziali dei numeri
statistici. ({Italian}) [{On} the frequency of initial
digits of statistical numbers]",
journal = "Atti dell XV e XVII Riunione, Societa Italiana di
Statistica",
volume = "??",
number = "??",
pages = "??--??",
year = "1957",
bibdate = "Sun Sep 18 12:00:07 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
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}metric Resolution in Analog Computers by Means
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journal = j-IRE-TRANS-ELEC-COMPUT,
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number = "2",
pages = "86--92",
month = jun,
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221576",
acknowledgement = ack-nhfb,
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}‹e and E. G. GilbertTrigonometric Resolution in Analog Computers by Means of Multiplier Elements
@Article{Howe:1957:TRA,
author = "R. M. Howe and E. G. Gilbert",
title = "Trigonometric Resolution in Analog Computers by Means
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E%ŽGarticlefparith.bibHowe:1957:TRAR. M. Howe and E. G. GilbertTrigonometric Resolution in Analog Computers by Means of Multiplier Elementsj-IRE-TRANS-ELEC-COMPUTEC-6286--92jun61957IRELAOhttps://doi.org/10.1109/TEC.1957.52215760367-9950 OR 03679950Thu Jun 30 16:07:27 MDT 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.06.30 16:07:27 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221576IRE Transactions on Electronic Computersack-nhfbhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885R. M. HowAnalog Multiplier",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-6",
number = "2",
pages = "100--103",
month = jun,
year = "1957",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1957.5221579",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 16:07:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221579",
acknowledgement = ack-nhfb,
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}Œ79IRE Transactions on Electronic Computersack-nhfbhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885David C. KalbfellAn Electronic Analog Multiplier
@Article{Kalbfell:1957:EAM,
author = "David C. Kalbfell",
title = "An Electronic Analog Multiplier",
journal = j-IRE-TRANS-ELEC-COMPUT,
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ýý‹w\ #//K;]7Ee;]
/KAarticlefparith.bibKalbfell:1957:EAMDavid C. KalbfellAn Electronic Analog Multiplierj-IRE-TRANS-ELEC-COMPUTEC-62100--103jun61957IRELAOhttps://doi.org/10.1109/TEC.1957.52215790367-9950 OR 03679950Thu Jun 30 16:07:27 MDT 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.06.30 16:07:27 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=52215
on of $ e^n $ for $ - \infty < n < + \infty $
Using an Electronic Computer",
journal = j-IBM-JRD,
volume = "1",
number = "2",
pages = "110--115",
month = apr,
year = "1957",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Sep 06 18:04:49 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
˜˜rßL¹&“n›]
@Article{Robertson:1970:CBM,
author = "J. E. Robertson",
title = "The Correspondefˆ
@Article{Robertson:1973:SIC,
author = "James E. Robertson and Kishor S. Trivedi",
title U†qc
@Article{Robertson:1979:VPA,
author = "D. A. Robertson",
title = "Variable precisÌ„9ˆs
@Article{Robison:1983:USF,
author = "A. D. Robison",
title = "Use Squares for FasÍ…0Ša
@Article{Rodrigues:1981:HEM,
author = "M. R. D. Rodrigues and J. H. P. Zurawski and J. B.
šˆ
@Article{Rodriguez-Henriquez:2003:PMB,
author = "F. Rodriguez-Henriquez and {\c{C}}. K. KoI¢ˆG‘
@Article{Rodriguez-Henriquez:2008:LCB,
author = "F. Rodriguez-Henriquez and G. Morales-LunVŠˆ'O
@Article{Rodriguez-Henriquez:2018:SIH,
author = "Francisco Rodr{\'\i}guez-Henr{\'\i}quez ajãBM Journal of Research and Developmentack-njhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520E. G. KogbetliantzComputation of $ e^n $ for $ - \infty < n < + \infty $ Using an Electronic Computer
@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,
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number = "2",
pages = "110--115",
month = apr,
year = "1957",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Sep 06 18:04:49 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
õõ‹
^ #71/57=M;[13Œearticlefparith.bibKogbetliantz:1957:CENE. G. KogbetliantzComputation of $ e^n $ for $ - infty < n < + infty $ Using an Electronic Computerj-IBM-JRD12110--115apr41957IBMJAE0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)0018-8646 OR 00188646Tue Sep 06 18:04:49 1994ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.06 18:04:49 ???Iplication",
journal = j-IRE-TRANS-ELEC-COMPUT,
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number = "3",
pages = "204--205",
month = sep,
year = "1957",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1957.5222025",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 16:07:34 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222025",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}Žarnumber=5222025IRE Transactions on Electronic Computersack-nhfbhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885M. LehmanHigh-Speed Digital Multiplication
@Article{Lehman:1957:HSD,
author = "M. Lehman",
title = "High-Speed Digital Multiplication",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-6",
number = "3",
pages = "204--205",
month = sep,
year = "1957",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1957.5222025",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 16:07:34 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222025",
acknowledgement = ack-nhfb,
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journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
ááŠ&Z #'!mK7;M;oK=!y‹marticlefparith.bibLuke:1957:CLZY. L. LukeOn the Computation of $ log Z $ and $ arctan Z $j-MATH-TABLES-OTHER-AIDS-COMPUT1116--181957MTTCAS0891-6837 OR 08916837Thu Sep 1 10:16:09 1994ftp://garbo.uwasa.fi/pc/d‹a\ #+O;]7Ee;]
O1articlefparith.bibLehman:1957:HSDM. LehmanHigh-Speed Digital Multiplicationj-IRE-TRANS-ELEC-COMPUTEC-63204--205sep91957IRELAOhttps://doi.org/10.1109/TEC.1957.52220250367-9950 OR 03679950Thu Jun 30 16:07:34 MDT 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.06.30 16:07:34 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&log {Z} $ and $ \arctan {Z}
$",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "??",
pages = "16--18",
month = "????",
year = "1957",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "Math. Tables Other Aids Comput.",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}oc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:16:09 ???Mathematical Tables and Other Aids to Computationack-njMath. Tables Other Aids Comput.http://www.ams.org/mcom/Y. L. LukeOn the Computation of $ \log {Z} $ and $ \arctan {Z} $
@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",
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acknowledgement = ack-nj,
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}'s Complement Arithmetic Units
with Separate Carry or Borrow Storage",
type = "Report",
number = "81",
institution = "Digital Computer Laboratory, University of Illinois",
address = "Urbana, IL, USA",
pages = "77",
year = "1957",
bibdate = "Thu Nov 18 09:07:07 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Flores' book \cite[p. 485]{Flores:1963:LCA} cites this
report, and says that its conclusion is that the
disadvantages of one's complement arithmetic outweigh
the advantages.",
}cites this report, and says that its conclusion is that the disadvantages of one's complement arithmetic outweigh the advantages.ack-nhfbG. MetzeA Study of Parallel One's Complement Arithmetic Units with Separate Carry or Borrow Storage
@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",
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bibdate = "Thu Nov 18 09:07:07 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Flores' book \cite[p. 485]{Flores:1963:LCA} cites this
report, and says that its conclusion is that the
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the advantages.",
}
<œ` #+%oQ57E‚;‚†w['†w%oœ
articlefparith.bibMurphy:1957:PIAR. W. MurphyA Positive-Integer Arithmetic for Data Processingj-IBM-JRD12158--170apr41957IBMJAEhttps://doi.org/10.1147/rd.12.01580018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)0018-8646 OR 0018864668.0X18,939dTue Sep 11 15:35:33 MDT 2012http://www.research.ibm.com/journal/; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib‹8\ !#)Cs+=o;‚cCŒ-techreportfparith.bibMetze:1957:SPOG. MetzeA Study of Parallel One's Complement Arithmetic Units with Separate Carry or Borrow StorageReport81Digital Computer Laboratory, University of IllinoisUrbana, IL, USA771957Thu Nov 18 09:07:07 2010https://www.math.utah.edu/pub/tex/bib/fparith.bib2010.11.18 09:07:07 ???Flores' book cite [p. 485]Flores:1963:LCA ithmetic for Data Processing",
journal = j-IBM-JRD,
volume = "1",
number = "2",
pages = "158--170",
month = apr,
year = "1957",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.12.0158",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "68.0X",
MRnumber = "18,939d",
bibdate = "Tue Sep 11 15:35:33 MDT 2012",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392735;
http://www.research.ibm.com/journal/rd/012/ibmrd0102G.pdf",
abstract = "It is hypothesized that positive numbers suffice for
the expression of quantities in accounting. New
arithmetic operations are devised that yield
non-negative results in computation, and the
applicability of these operations to data processing is
studied. These operations permit a wide variety of
functions to be computed with fewer and less complex
steps and imply the feasibility of constructing less
complex data-processing machines.",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
reviewer = "C. C. Gotlieb",
}‘2012.09.11 15:35:33 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392735; http://www.research.ibm.com/journal/rd/012/ibmrd0102G.pdfIt 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.IBM Journal of Research and Developmentack-nhfbhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520C. C. GotliebIt 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.R. W. MurphyA Positive-Integer Arithmetic for Data Processing
@Article{Murphy:1957:PIA,
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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
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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",
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} negative basis in the
arithmometer of a digital computer",
journal = "Bull. Acad. Pol. Sci., Ser. Sci. Tech.",
volume = "5",
number = "??",
pages = "232--236",
month = "????",
year = "1957",
bibdate = "Thu Nov 06 05:56:32 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "negative base",
}’ith.bibPawlak:1957:UENZ. PawlakUse of expansions with a negative basis in the arithmometer of a digital computerBull. Acad. Pol. Sci., Ser. Sci. Tech.5232--2361957Thu Nov 06 05:56:32 2014https://www.math.utah.edu/pub/tex/bib/fparith.bib2014.11.06 05:56:32 ???negative baseack-nhfbZ. PawlakUse of expansions with a negative basis in the arithmometer of a digital computer
@Article{Pawlak:1957:UEN,
author = "Z. Pawlak",
title = "Use of expansions with a negative basis in the
arithmometer of a digital computer",
journal = "Bull. Acad. Pol. Sci., Ser. Sci. Tech.",
volume = "5",
number = "??",
pages = "232--236",
month = "????",
year = "1957",
bibdate = "Thu Nov 06 05:56:32 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "negative base",
}
c‘"c¼b#+eQ57E‚;‚™S[™YeµCarticlefparith.bibWalker:1957:EMAR. M. Walker and D. E. Rosenheim and P. A. Lewis and A. G. AndersonAn Experimental 50-Megacycle Arithmetic Unitj-IBM-JRD13257--278jul71957IBMJAEhttps://doi.org/10.1147/rd.13.02570018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)0018-8646 OR 00188646Tue Sep 11 15:35:35 MDT 2012http://www.research.ibm.com/journal/; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub*ˆyZ #)#E;7=o;]'
#EŠ+articlefparith.bibWadel:1957:NBNL. $v^ !#++‚u/Eo;‚E7‚+‚otechrepor!‡t[ #+/Y=o;'/ˆCarticlefpar-Interpreter): an automatic
programming, fixed and floating-point library of
subroutines for the {ERA} 1103 computer",
institution = "Operations Research Office, Johns Hopkins University",
address = "Bethesda, MD, USA",
pages = "43",
year = "1957",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Staff paper / Johns Hopkins University, Operations
Research Office; ORO-SP-32 Staff paper (Johns Hopkins
University. Operations Research Office); ORO-SP-32.",
acknowledgement = ack-nhfb,
keywords = "Military art and science --- Data processing.;
Military research --- Data processing.",
remark = "Cover title. ``Operating under contract with the
Department of the Army.'' ``Project COMPLAB.''
``October 1957.'' ORO-SP-32",
}“"tfparith.bibTaylor:1957:CCAW. Bruce TaylorCOIN (Compile-Interpreter): an automatic programming, fixed and floating-point library of subroutines for the ERA 1103 computerOperations Research Office, Johns Hopkins UniversityBethesda, MD, USA431957Sat Feb 24 15:01:45 MST 1996https://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MSTStaff paper / Johns Hopkins University, Operations Research Office; ORO-SP-32 Staff paper (Johns Hopkins University. Operations Research Office); ORO-SP-32.Military art and science --- Data processing.; Military research --- Data processing.Cover title. ``Operating under contract with the Department of the Army.'' ``Project COMPLAB.'' ``October 1957.'' ORO-SP-32ack-nhfbW. Bruce Taylor{COIN} (Compile-Interpreter): an automatic programming, fixed and floating-point library of subroutines for the {ERA} 1103 computer
@TechReport{Taylor:1957:CCA,
author = "W. Bruce Taylor",
title = "{COIN} (Compile-Interpreter): an automatic
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address = "Bethesda, MD, USA",
pages = "43",
year = "1957",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
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acknowledgement = ack-nhfb,
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``October 1957.'' ORO-SP-32",
}stems",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-6",
number = "??",
pages = "123--??",
month = jun,
year = "1957",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Thu Nov 06 05:53:55 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
keywords = "negative base",
}”B. WadelNegative base number systemsj-IRE-TRANS-ELEC-COMPUTEC-6123--??jun61957IRELAO0367-9950 OR 03679950Thu Nov 06 05:53:55 2014https://www.math.utah.edu/pub/tex/bib/fparith.bib2014.11.06 05:53:55 ???IRE Transactions on Electronic Computersnegative baseack-nhfbhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885L. B. WadelNegative base number systems
@Article{Wadel:1957:NBN,
author = "L. B. Wadel",
title = "Negative base number systems",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-6",
number = "??",
pages = "123--??",
month = jun,
year = "1957",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Thu Nov 06 05:53:55 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
keywords = "negative base",
}& A. G. Anderson",
title = "An Experimental 50-Megacycle Arithmetic Unit",
journal = j-IBM-JRD,
volume = "1",
number = "3",
pages = "257--278",
month = jul,
year = "1957",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.13.0257",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Sep 11 15:35:35 MDT 2012",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392687;
http://www.research.ibm.com/journal/rd/013/ibmrd0103H.pdf",
abstract = "An experimental 50-megacycle arithmetic unit has been
built which performs a repetitive multiplication
program and checks the results for errors. T'he 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",
}•
TTÁ.›ì“ƒk‡W
@InProceedings{Kiernan:1990:FAE,
author = "J. M. Kiernan and T. B. Blachowiak",
title = &Rˆ>}
@InProceedings{Kim:1991:NIC,
author = "S. W. Kim and T. Stouraitis",
booktitle = "{IE)‰n“]
@InProceedings{Kim:1993:FABa,
author = "S. W. Kim and T. Stouraitis and A. Skavantzos",
/††Œ9
@InProceedings{Kim:1993:FABb,
author = "Seon Wook Kim and T. Stouraitis and A. Skavantzos"/‹ˆm‘[
@InProceedings{Kim:1993:FABc,
author = "S. W. Kim and T. Stouraitis and A. Skavantzos",
booktitle /Ž†Œ9
@InProceedings{Kim:1993:FABd,
author = "Seon Wook Kim and T. Stouraitis and A. Skavantzos"/’‘¢3
@InProceedings{Kim:2019:CEI,
author = "HyunJin Kim and Min Soo Kim and Alberto A. {Del
Barrio} and Nader Bagherzadeh",
title = lêƒ0†a
@InProceedings{King:1997:DDT,
author = "E. J. King and E. E. {Swartzlander, Jr.}",
title:+/tex/bib/ibmjrd.bib2012.09.11 15:35:35 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392687; http://www.research.ibm.com/journal/rd/013/ibmrd0103H.pdfAn 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 stor,age 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.IBM Journal of Research and Developmentack-nhfbhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520An experimental 50-megacycle arithmetic unit has been built which pe-rforms 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.R. M. Walker and D. E. Rosenheim and P. A. Lewis and A. G. AndersonAn Experimental 50-Megacycle Arithmetic Unit
@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",
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ISSN-L = "0018-8646",
bibdate = "Tue Sep 11 15:35:35 MDT 2012",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392687;
http://www.research.ibm.com/journal/rd/013/ibmrd0103H.pdf",
abstract = "An experimental 50-megacycle arithmetic unit has been
built which performs a repetitive multiplication
program and checks the results for errors. The unit
uses pulse circuitry which has been developed to
perform digital operations at a 50-megacycle
pulse-repetition rate. This paper describes the
arithmetic system and the circuits which p0erform 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",
}og Multiplier Using Carriers",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-6",
number = "1",
pages = "30--34",
month = mar,
year = "1957",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1957.5221558",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 16:07:23 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221558",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}–Electronic Computersack-nhfbhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885Erich S. WeibelAn Electronic Analog Multiplier Using Carriers
@Article{Weibel:1957:EAM,
author = "Erich S. Weibel",
title = "An Electronic Analog Multiplier Using Carriers",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-6",
number = "1",
pages = "30--34",
month = mar,
year = "1957",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1957.5221558",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 16:07:23 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221558",
acknowledgement = ack-nhfb,
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journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
kÞÜkˆeZ !#1U+1Eo;eUŠtechreportfpari[Á_#+{ !-=U;eUÍ{i ÓÕoübookfparith.bibWilkes:1957:PPEMaurice V. Wilkes and David J. Wheeler and Stanley GillThe Preparation of Programs for an Electronic Digital Computerpub-BŒ\ #++i;]7Ee;]
+iSarticlefparith.bibWeibel:1957:EAMErich S. WeibelAn Electronic Analog Multiplier Using Carriersj-IRE-TRANS-ELEC-COMPUTEC-6130--34mar31957IRELAOhttps://doi.org/10.1109/TEC.1957.52215580367-9950 OR 03679950Thu Jun 30 16:07:23 MDT 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.06.30 16:07:23 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221558IRE Transactions on 25 Gill",
title = "The Preparation of Programs for an Electronic Digital
Computer",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Second",
pages = "xiv + 238",
year = "1957",
LCCN = "QA76.5 .W52 1957",
bibdate = "Mon Feb 10 09:42:47 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also first edition \cite{Wilkes:1951:PPE}.",
URL = "https://b-ok.org/book/3668116/b363ff",
acknowledgement = ack-nhfb,
remark-1 = "According to \cite{Anderson:2019:SAM}, this book
discusses the computation of integer population counts
on the Electronic Delay Storage Automatic Calculator
(EDSAC) computer using a recursive divide-and-conquer
algorithm. See also somewhat negative 1958 review by
Fernando J. Corbat{\'o}
6 \url{https://doi.org/10.1063/1.3062687}. Floating-point
arithmetic is discussed on pages 60, 90--91, and
135--137.",
remark-2 = "From page 5: ``Each storage location in the EDSAC
holds 17 binary digits. In words representing numbers,
the binary point is regarded as being to the right of
the extreme left-hand digit; this digit (the most
significant digit) is used as a sign indicator and is
referred to as the sign digit. \ldots{} the capacity of
the accumulator is 70 digits; there is, therefore,
plenty of room to hold the full 33-digit product of two
17-digit numbers. \ldots{} A negative number $-x$
(where $O < x \leq 1$) is represented by a $1$ in the
sign-digit position, followed by the digits of $(1 -
x)$; for example, $1.1100\ldots{}$ represents $-(1 -
7 3/4) = -1/4$. \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. 8Each 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 9page 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 o@f 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
A 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",
}—CAWpub-AW:adrSecondxiv + 2381957QA76.5 .W52 1957Mon Feb 10 09:42:47 2020https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib2020.02.10 09:42:47 ???See also first edition cite Wilkes:1951:PPE.https://b-ok.org/book/3668116/b363ffCHAPTER 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 / D25 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 / 5E6 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 F/ 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 fGloating-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 inputH routine of the EDSAC / 218 APPENDIX 4. Control combinations / 221 APPENDIX 5. Specimen solutions to programming exercises / 223 BIBLIOGRAPHY / 233 INDEX / 237ack-nhfbMaurice V. Wilkes and David J. Wheeler and Stanley GillSee also first edition \cite{Wilkes:1951:PPE}.The Preparation of Programs for an Electronic Digital ComputerCHAPTER 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 ordIer / 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 subrouJtines / 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 Kand 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 L\\ 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 \\ CATEMGORY 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
@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 09N:42:47 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also first edition \cite{Wilkes:1951:PPE}.",
URL = "https://b-ok.org/book/3668116/b363ff",
acknowledgement = ack-nhfb,
remark-1 = "According to \cite{Anderson:2019:SAM}, this book
discusses the computation of integer population counts
on the Electronic Delay Storage Automatic Calculator
(EDSAC) computer using a recursive divide-and-conquer
algorithm. See also somewhat negative 1958 review by
Fernando J. Corbat{\'o}
\url{https://doi.org/10.1063/1.3062687}. Floating-point
arithmetic is discussed on pages 60, 90--91, and
135--137.",
remark-2 = "From page 5: ``Each storage location in the EDSAC
holds 17 binary digits. In words representing numbers,
O 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 $1.0000\ldots{}$ reprPesents $-1$.''
[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, Qand 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
$a \cdot 10^p$, Rwhere $-10 \leq a \leq 10$ 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 fSrom
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;
T 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 comUbinations / 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 \\
V 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 \\
W 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 proXgrams / 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 FormuYla 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",
}rch memorandum 294",
type = "{AR} Memo",
number = "294 (AD 207929)",
institution = "Massachusetts Institute of Technology, Naval
Supersonic Laboratory",
address = "Cambridge, MA, USA",
pages = "7",
day = "23",
month = oct,
year = "1958",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Error functions.; Floating-point arithmetic.",
}˜th.bibAnonymous:1958:ARMAnonymousAnalysis and research memorandum 294AR Memo294 (AD 207929)Massachusetts Institute of Technology, Naval Supersonic LaboratoryCambridge, MA, USA723oct101958Sat Feb 24 15:01:45 MST 1996https://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MSTError functions.; Floating-point arithmetic.ack-nhfbAnonymousAnalysis and research memorandum 294
@TechReport{Anonymous:1958:ARM,
author = "Anonymous",
title = "Analysis and research memorandum 294",
type = "{AR} Memo",
number = "294 (AD 207929)",
institution = "Massachusetts Institute of Technology, Naval
Supersonic Laboratory",
address = "Cambridge, MA, USA",
pages = "7",
day = "23",
month = oct,
year = "1958",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Error functions.; Floating-point arithmetic.",
}r Square-Root Computation",
journal = j-CACM,
volume = "1",
number = "1",
pages = "6--7",
month = jan,
year = "1958",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 15 18:35:46 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}™
++˜rßL¹&“IŸ
@Article{Feldstein:1976:CED,
author = "Alan Feldstein and Richard Goodman",
title = ²‹y—s
@Article{Feldstein:1982:LSF,
author = "A. Feldstein and R. Goodman",
title = "LosiŽœ=
@Article{Feldstein:1986:OUS,
author = "Alan Feldstein and Peter Turner",
title = ŒI™
@Article{Feldstein:1996:OUM,
author = "Alan Feldstein and Peter R. Turner",
title = 7N‡V-
@Article{Feldstein:2006:GTO,
author = "Alan Feldstein and Peter R. Turner",
title = Q‡Ž!
@Article{Felt:1893:MA,
author = "Dorr E. Felt",
title = "Mechanical Arithmetic",
1‡zu
@Article{Fenn:1996:MDD,
author = "S. T. J. Fenn and M. Benaissa and D. Taylor",
title = 7SˆW‘/
@Article{Fenstad:1969:NSM,
author = "Jens Erik Fenstad",
title = "Non-standard moH‡Q#
@Article{Fenwick:1969:BMO,
author = "P. M. Fenwick",
title = "Binary MultiplicatiL00¡<1X—f¯M
@Article{Antao:2013:CFA,
author = "Samuel Ant{\~a}o and Leonel Sousa",
title = "T_&9C‰
’
@Article{Ardalan:1987:FPR,
author = "S. Ardalan and S. Alexander",
title = "Fixed-point roundoff error analysis of the
Wš_µ?
@Article{Arnold:1990:RLA,
author = "M. G. Arnold and T. A. Bailey and J. R. Cowles and J.
%GEQ‡Ž?
@Article{Asai:1983:SOM,
author = "Hitohisa Asai and C. K. Cheng",
title = "Speedi7%†;Œw
@Article{Asprey:1993:PFP,
author = "T. Asprey and G. Averill and E. DeLano and R. Mason
.Ò‹%–K
@Article{Atkins:1979:FSC,
author = "D. E. Atkins",
title = "{Fourth Symposium on tronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Thu Sep 15 18:35:46 1994ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.15 18:35:46 ???Communications of the ACMack-njhttps://dl.acm.org/loi/cacmRobert W. BemerA Machine Method for Square-Root Computation
@Article{Bemer:1958:MMS,
author = "Robert W. Bemer",
title = "A Machine Method for Square-Root Computation",
journal = j-CACM,
volume = "1",
number = "1",
pages = "6--7",
month = jan,
year = "1958",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 15 18:35:46 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
ÿÿŠ\ #-';7=o;]O
' ‹articlefparith.bibCouleur:1958:BBDJ. F. CouleurBIDEC --- a Binary-to-Decimal or Decimal-to-Binary Converterj-IRE-TRANS-ELEC-COMPUTEC-7313--3161958IRELAO0367-9950 OR 03679950Fd‰g[ #)#i57;M;?C#iŠiarticlefparith.bibBemer:1958:SMCR. W. BemerA Subroutine Method for Calculating Logarithmsj-CACM155--7may51958CACMA20001-0782 (print), 1557-7317b‰o[ #)+e57=M;?C+eŠoarticlefparith.bibBemer:1958:MMSRobert W. BemerA Machine Method for Square-Root Computationj-CACM116--7jan11958CACMA20001-0782 (print), 1557-7317 (elec_ Calculating Logarithms",
journal = j-CACM,
volume = "1",
number = "5",
pages = "5--7",
month = may,
year = "1958",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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ÆÆŒ.\ #+%‚{!77=[;%ƒŒoarticlefparith.bibHammer:1958:PSTFranz HammerNicht Pascal sondern der Tubinger Professor Wilhelm Schickard erfand die Rechenmaschine!. (German) [Not Pascal, but the Tubingen professor William Schickard, invented the calculator!]Buromarkt201023--102519580007-3148 OR 000731480007-3148 OR 00073148Sat Jul 27 11:05:26 2013https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/scicontext.bib2013.07.27 11:05:26 ???Germanack-nhfbFranz Hammmion of Arctan {$N$} for $ - \infty < {N} < +
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ÞÞŒ$\ #31[;]7Ee;]
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}¥ SchmidA Transistorized Four-Quadrant Time-Division Multiplier with an Accuracy of 0.1 Per Cent
@Article{Schmid:1958:TFQ,
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title = "A Transistorized Four-Quadrant Time-Division
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DOI = "https://doi.org/10.1109/TEC.1958.5222094",
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bibdate = "Thu Jul 14 15:56:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
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)=ŽGarticlefparith.bibSchmid:1958:TFQHermann SchmidA Transistorized Four-Quadrant Time-Division Multiplier with an Accuracy of 0.1 Per Centj-IRE-TRANS-ELEC-COMPUTEC-7141--47mar31958IRELAOhttps://doi.org/10.1109/TEC.1958.52220940367-9950 OR 03679950Thu Jul 14 15:56:43 MDT 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 15:56:43 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222094IRE Transactions on Electronic Computersack-nhfbhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885Hermann€ƒl Redundancy Check",
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volume = "1",
number = "5",
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CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
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bibdate = "Mon Jan 22 07:22:12 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Sisson58;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "As more emphasis is placed on improving the accuracy
of data fed into automatic computing systems, more
emphasis will be placed on redundancy checking of
predictable fields within the input. Two systems (at
least) of checking a field of decimal digits have been
proposed. In both of these it is assumed that the field
to be checked is all numeric and that the redundancy
must be of only one digit.",
acknowledgement = ack-nhfb,
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@Article{Roegel:2015:MCA,
author = "Denis Roegel",
title = "A Mechanical Calculatc™‡[7
@Article{Roesler:2002:NOH,
author = "Eric Roesler and Brent Nelson",
title = "NovG‘D£
@Article{Rogers:1995:UMP,
author = "John Rogers",
title = "Using the Multiple Precision Library",
journal = j-DDJ,
volume = "20",
number = "1",
pages = 6"›
@Article{Rohl:1972:NCA,
author = "J. S. Rohl and J. A. Linn",
title = "A Note on
cˆ
@Article{Rohn:2014:VLD,
author = "Jiri Rohn",
title = "Verification of Linear (Inaä‡n]
@Article{Rokne:1975:ACI,
author = "J. Rokne and P. Lancaster",
title = "Algorithm† all numeric and that the redundancy must be of only one digit.Communications of the ACMdecimal floating-point arithmeticack-nhfbhttps://dl.acm.org/loi/cacmAs 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.Roger L. SissonAn Improved Decimal Redundancy Check
@Article{Sisson:1958:IDR,
author = "Roger L. Sisson",
title = "An Improved Decimal Redundancy Check",
journal = j-CACM,
volume = "1",
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of data fed into automatic computing systems, more
emphasis will be placed on redundancy checking of
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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,
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ÐÐ– &] #++U57Em;†'?OC†'+U–Earticlefparith.bibSisson:1958:IDRRoger L. SissonAn Improved Decimal Redundancy Checkj-CACM1510--12may51958CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Mon Jan 22 07:22:12 MST 2001http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Sisson58; https://www.math.utah.edu/pub/tex/bib/fparith.bib2001.01.22 07:22:12 MSTAs 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…ication and Division for
Automatic Binary Computers",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "11",
number = "3",
pages = "364--384",
month = "????",
year = "1958",
CODEN = "QJMMAV",
ISSN = "0033-5614 (print), 1464-3855 (electronic)",
ISSN-L = "0033-5614",
bibdate = "Thu Apr 2 08:38:35 1998",
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acknowledgement = ack-sfo # " and " # ack-nhfb,
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}§b/tex/bib/fparith.bib1998.04.02 08:38:35 ???Quarterly Journal of Mechanics and Applied Mathematicsack-sfohttp://qjmam.oxfordjournals.org/content/by/yearK. D. TocherTechniques of Multiplication and Division for Automatic Binary Computers
@Article{Tocher:1958:TMD,
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title = "Techniques of Multiplication and Division for
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journal = j-QUART-J-MECH-APPLIED-MATH,
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pages = "364--384",
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bibdate = "Thu Apr 2 08:38:35 1998",
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šZš‹4([ #)#I57E‚;?C#I_articlefparith.bibWadey:1958:TSRW. G. WadeyTwo Square-Root Approximationsj-CACM11113--14nov111958CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Wed Jul 14 15:48:22 MDT 2004http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Wadey58; http://portal.acm.org/; https://www.math.utah.edu/Œ‹'\ #+%C57;o;yk%Œ-articlefparith.bibTocher:1958:TMDK. D. TocherTechniques of Multiplication and Division for Automatic Binary Computersj-QUART-J-MECH-APPLIED-MATH113364--3841958QJMMAV0033-5614 (print), 1464-3855 (electronic) OR 00335614 (print), 14643855 (electronic)0033-5614 OR 00335614Thu Apr 2 08:38:35 1998https://www.math.utah.edu/pu‰mations",
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number = "11",
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month = nov,
year = "1958",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
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bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Wadey58;
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}¨pub/tex/bib/fparith.bib2004.07.14 15:48:22 MDTCommunications of the ACMack-nhfbhttps://dl.acm.org/loi/cacmW. G. WadeyTwo Square-Root Approximations
@Article{Wadey:1958:TSR,
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title = "Two Square-Root Approximations",
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}Žitle = "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",
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MRclass = "68.00",
MRnumber = "MR0105833 (21 \#4568)",
MRreviewer = "H. H. Goldstine",
bibdate = "Fri Dec 08 13:06:24 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
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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,
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@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",
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ISSN = "0004-5411 (print), 1557-735X (electronic)",
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bibdate = "Fri Dec 08 13:06:24 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
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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,
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QHQk*] #//57Eq;?OC/‘ articlefparith.bibBuchholz:1959:FFCWilfried BuchholzFingers or Fists? (The Choice of Decimal or Binary Representation)j-CACM2123--111959CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Mon Jan 22 06:28:45 MST 2001http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Buchholz59; https://www.math.utah.edu/pub/tex/bib/fparith.bib2001.01.22 06:28:45 MSTCommunications of the ACMdecimal floating-point arithmeticack-nhfbhttps://dl.acm.org/loi/cacmWilfried BuchholzFingers or Fists? (The Choice of Decimal or Binary Representation)
@Article{Buchholz:1959:FFC,
author = "Wilfried Buchholz",
•™$)]#3eYW577+=‚_;†3q!e†3eY˜}articlefparith.bibAshenhurst:1959:UFPRobert L. Ashenhurst and Nicholas Metropolists? (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;
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acknowledgement = ack-nhfb,
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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.",
}ª
ëëXßL¹&“…x‹s
@Article{Garver:1932:QDNb,
author = "Raymond Garver",
title = "Questions, DiscussWˆ}‘{
@Article{Garwick:1961:AFP,
author = "Jan V. Garwick",
title = "The Accuracy of Floating Point Computers",
O†o_
@Article{Garwick:1961:RAF,
author = "J. V. Garwick",
title = "Reply to {``On the S„n‰]
@Article{Gavrielov:1983:CSF,
author = "M. Gavrielov and A. Kaminker and Y.-T. Sidi",
titÍ’%¤K
@Article{Gavrielov:1986:NFP,
author = "Moshe Gavrielov and Lev Epstein",
title = ‡Ž7
@Article{Gavrilova:2009:ESC,
author = "Marina L. Gavrilova",
title = "An ExplicitWüŽœ
@Article{Gay:1999:SAF,
author = "David M. Gay and Eric Grosse",
title = "Self-ada=Õtitle = "Fingers or Fists? (The Choice of Decimal or Binary
Representation)",
journal = j-CACM,
volume = "2",
number = "12",
pages = "3--11",
month = "????",
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:28:45 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Buchholz59;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
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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.",
} Floating Point Arithmetic",
journal = j-CACM,
volume = "2",
number = "5",
pages = "10--15",
month = may,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:23 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Carr59a;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Carr59a",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Carr59a",
}«8:23 MDTCommunications of the ACMack-nhfbhttps://dl.acm.org/loi/cacmJohn W. {Carr III}Error Analysis in Floating Point Arithmetic
@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",
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‹i+[ #'-c57E‚;?C1cŽarticlefparith.bibCarr:1959:EAFJohn W. Carr IIIError Analysis in Floating Point Arithmeticj-CACM2510--15may51959CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Wed Jul 14 15:48:23 MDT 2004http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Carr59a; http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib2004.07.14 15:4—bbe and Simon Ramo and Dean E.
Wooldridge",
booktitle = "Handbook of Automation, Computation, and Control",
title = "Programming and Coding",
publisher = pub-WILEY,
address = pub-WILEY:adr,
bookpages = "????",
year = "1959",
LCCN = "TJ213 .G72",
bibdate = "Fri Aug 20 08:41:16 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
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note = "Chapter 2.",
acknowledgement = ack-nhfb,
remark = "1958--1961: Volume 1. Control fundamentals. Volume 2.
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subject = "automation; mathematics; computers; operations
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}¬gene M. Grabbe and Simon Ramo and Dean E. WooldridgeChapter 2.Programming and Coding
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title = "Programming and Coding",
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bookpages = "????",
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LCCN = "TJ213 .G72",
bibdate = "Fri Aug 20 08:41:16 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
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note = "Chapter 2.",
acknowledgement = ack-nhfb,
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P"P‰F-Z #-'U;7=o;]O
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journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "5",
pages = "335--339",
month = sep,
year = "1959",
CODEN = "IRELAO",
ISSN = "0367-9950",
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}335--339sep91959IRELAO0367-9950 OR 03679950Thu Sep 08 08:14:00 1994https://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.08 08:14:00 ???IRE Transactions on Electronic Computersdecimal floating-point arithmeticack-njhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885D. H. DaggettDecimal-Binary Conversions in {CORDIC}
@Article{Daggett:1959:DBC,
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journal = j-CACM,
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bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#ErcoliV59;
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https://www.math.utah.edu/pub/tex/bib/fparith.bib",
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hh.]#+I!57E‚;?CI!articlefparith.bibErcoli:1959:BADPaolo Ercoli and Roberto VaccaBinary Arithmetic for Discretely Variable Word Length in a Serial Computerj-CACM2413--15apr41959CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Wed Jul 14 15:48:22 MDT 2004http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#ErcoliV59; http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib2004.07.14 15:48:22 MDTCommunications of the ACMack-nhfbhttps://dl.acm.org/loi/cacmPaolo Ercoli and Roberto VaccaBinary ArithmŸ¢Note on Rounding-Off Errors",
journal = j-SIAM-REVIEW,
volume = "1",
number = "1",
pages = "66--67",
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year = "1959",
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bibsource = "http://epubs.siam.org/toc/siread/1/1;
https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
ZMnumber = "0168.14002",
acknowledgement = ack-nhfb,
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journal-URL = "http://epubs.siam.org/sirev",
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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
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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.''",
}¯¤:24 MDT 2014http://epubs.siam.org/toc/siread/1/1; https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib2014.03.27 09:04:24 MDTSIAM Reviewnumerical analysis; random rounding-off procedureFrom 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.''0168.14002ack-nhfbhttp://epubs.siam.org/sirevJanuary 1959George ¥E. ForsytheReprint of a Note on Rounding-Off Errors
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https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
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ii›/\ #/1]'K577E…S;#oˆ!C%1]Ÿarticlefparith.bibForsythe:1959:RNRGeorge E. ForsytheReprint of a Note on Rounding-Off Errorsj-SIAM-REVIEW1166--67jan11959SIREADhttps://doi.org/10.1137/10010110036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)0036-1445 OR 0036144565.00MR0099119 (20 \#5563)Thu Mar 27 09:04£the Study of Multiplication for
Complement Codes",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "1",
pages = "25--30",
month = mar,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5222757",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:44 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222757",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}°pl/RecentIssue.jsp?punumber=5407885Harvey L. GarnerA Ring Model for the Study of Multiplication for Complement Codes
@Article{Garner:1959:RMS,
author = "Harvey L. Garner",
title = "A Ring Model for the Study of Multiplication for
Complement Codes",
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Œe0^ #+-;]7Ee;]
-Žarticlefparith.bibGarner:1959:RMSHarvey L. GarnerA Ring Model for the Study of Multiplication for Complement Codesj-IRE-TRANS-ELEC-COMPUTEC-8125--30mar31959IRELAOhttps://doi.org/10.1109/TEC.1959.52227570367-9950 OR 03679950Thu Jul 14 15:56:44 MDT 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 15:56:44 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222757IRE Transactions on Electronic Computersack-nhfbhttps://ieeexplore.ieee.org/x¨r System",
journal = j-IRE-TRANS-ELEC-COMPUT,
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bibdate = "Thu Jul 14 15:56:44 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219515",
acknowledgement = ack-nhfb,
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}±=&arnumber=5219515IRE Transactions on Electronic Computersack-nhfbhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885Harvey L. GarnerThe Residue Number System
@Article{Garner:1959:RNS,
author = "Harvey L. Garner",
title = "The Residue Number System",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "2",
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‰o2]'#'A7'%=o;A;‰kinproceedingsfparith.bibGray:1959:NFPH. L. Gray and C. HarrisonProceedings of the Eastern Joint Computer Conference, Boston, MA, December 1--3, 1959®‹^1\ #+-?;]7Ee;]
-?/articlefparith.bibGarner:1959:RNSHarvey L. GarnerThe Residue Number Systemj-IRE-TRANS-ELEC-COMPUTEC-82140--147jun61959IRELAOhttps://doi.org/10.1109/TEC.1959.52195150367-9950 OR 03679950Thu Jul 14 15:56:44 MDT 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 15:56:44 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp«ceedings of the Eastern Joint Computer Conference,
Boston, {MA}, December 1--3, 1959",
title = "Normalized floating-point arithmetic with an index of
significance",
volume = "16",
publisher = pub-AFIPS,
address = pub-AFIPS:adr,
pages = "244--248",
year = "1959",
LCCN = "TK7885.A1 J6",
bibdate = "Tue Oct 09 09:43:31 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}²Normalized floating-point arithmetic with an index of significance16pub-AFIPSpub-AFIPS:adr244--2481959TK7885.A1 J6Tue Oct 09 09:43:31 2007https://www.math.utah.edu/pub/tex/bib/fparith.bib2007.10.09 09:43:31 ???ack-nhfbH. L. Gray and C. HarrisonProceedings of the Eastern Joint Computer Conference, Boston, {MA}, December 1--3, 1959Normalized floating-point arithmetic with an index of significance
@InProceedings{Gray:1959:NFP,
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acknowledgement = ack-nhfb,
}title = "Proceedings of the International Conference on
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Differential Equations",
publisher = "????",
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LCCN = "????",
bibdate = "Fri Aug 20 09:11:32 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}³iciProceedings of the International Conference on Information Processing, {UNESCO}Theoretical and Experimental Studies on the Accumulation of Error in the Numerical Solution of Initial Value Problems for Systems of Ordinary Differential Equations
@InProceedings{Henrici:1959:TES,
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acknowledgement = ack-nhfb,
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ØØŒ3] '#-''‚U=o;M'+‚UŒinproceedingsfparith.bibHenrici:1959:TESPeter HenriciProceedings of the International Conference on Information Processing, UNESCOTheoretical and Experimental Studies on the Accumulation of Error in the Numerical Solution of Initial Value Problems for Systems of Ordinary Differential Equations36--431959Fri Aug 20 09:11:32 2010https://www.math.utah.edu/pub/tex/bib/fparith.bib2010.08.20 09:11:32 ???Cited in cite Sterbenz:1974:FPC.ack-nhfbPeter Henr°on of $ \sin {N} $, $ \cos {N} $, and {$M$
th} Root of {$N$} Using an Electronic Computer",
journal = j-IBM-JRD,
volume = "3",
number = "2",
pages = "147--152",
month = apr,
year = "1959",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}´
˜˜rßL¹&“‡+ŽW
@Article{Rolfe:1987:FIS,
author = "Timothy J. Rolfe",
title = "On a Fast Integer ž†iS
@Article{Romano:2011:NLR,
author = "Paul K. Romano and Harry McLaughlin",
title = ]I‡#ŽG
@Article{Romanov:2021:APB,
author = "Aleksandr Yu. Romanov and Alexander L. Stempkovsky anr‡Y3
@Article{Romanovski:2011:ASS,
author = "Valery G. Romanovski and Mateja Presern",
title ]MuŸk
@Article{Rosen:1969:ECH,
author = "Saul Rosen",
title = "Electronic Computers: a ‹–
@Article{Ross:1965:RTE,
author = "D. R. Ross",
title = "Reducing Truncation ErrorL†hQ
@Article{Rothstein:1959:RBN,
author = "Jerome Rothstein",
title = "Residues of BiÂ†V-
@Article{Roughan:2019:PSS,
author = "Matthew Roughan",
title = "Practically surremÔvelopmentack-njhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520E. G. KogbetliantzComputation of $ \sin {N} $, $ \cos {N} $, and {$M$ th} Root of {$N$} Using an Electronic Computer
@Article{Kogbetliantz:1959:CSC,
author = "E. G. Kogbetliantz",
title = "Computation of $ \sin {N} $, $ \cos {N} $, and {$M$
th} Root of {$N$} Using an Electronic Computer",
journal = j-IBM-JRD,
volume = "3",
number = "2",
pages = "147--152",
month = apr,
year = "1959",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
ÒÒŒ"4^ #71=57;M;[1Qarticlefparith.bibKogbetliantz:1959:CSCE. G. KogbetliantzComputation of $ sin N $, $ cos N $, and $M$ th Root of $N$ Using an Electronic Computerj-IBM-JRD32147--152apr41959IBMJAE0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)0018-8646 OR 00188646Thu Sep 1 10:15:56 1994ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:56 ???IBM Journal of Research and De´ns for Digital Computers Using a
Modified Reflected Binary Code",
journal = j-IRE-TRANS-ELEC-COMPUT,
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number = "4",
pages = "449--458",
month = dec,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5222057",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222057",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}µ85Harold M. LucalArithmetic Operations for Digital Computers Using a Modified Reflected Binary Code
@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,
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articlefparith.bibLucal:1959:AODHarold M. LucalArithmetic Operations for Digital Computers Using a Modified Reflected Binary Codej-IRE-TRANS-ELEC-COMPUTEC-84449--458dec121959IRELAOhttps://doi.org/10.1109/TEC.1959.52220570367-9950 OR 03679950Thu Jul 14 15:56:45 MDT 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 15:56:45 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222057IRE Transactions on Electronic Computersack-nhfbhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=54078·ethods for Generating Normal Deviates
on Digital Computers",
journal = j-J-ACM,
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number = "3",
pages = "376--383",
month = jul,
year = "1959",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Tue Nov 1 09:33:26 1994",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
descriptors = "RVG",
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}¶ite Sterbenz:1974:FPC.ack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401Mervin E. MullerA Comparison of Methods for Generating Normal Deviates on Digital Computers
@Article{Muller:1959:CMG,
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title = "A Comparison of Methods for Generating Normal Deviates
on Digital Computers",
journal = j-J-ACM,
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CODEN = "JACOAH",
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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;
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acknowledgement = ack-nhfb,
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××Œ6] #+-#57;w;1Me-#;articlefparith.bibMuller:1959:CMGMervin E. MullerA Comparison of Methods for Generating Normal Deviates on Digital Computersj-J-ACM63376--383jul71959JACOAH0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)0004-5411 OR 00045411Tue Nov 1 09:33:26 1994ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib1994.11.01 09:33:26 ???Journal of the ACMCited in cºmputer based on the `$ - 2 $'
system",
journal = "Bull. Acad. Pol. Sci., Ser. Sci. Tech.",
volume = "7",
number = "??",
pages = "713--722",
month = "????",
year = "1959",
bibdate = "Thu Nov 06 05:58:31 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "negative base",
}·
˜˜rßL¹&“†I
@Article{Spielberg:1961:ECF,
author = "Kurt Spielberg",
title = "Efficient Contin~†$ŒI
@Article{Spielberg:1961:RPS,
author = "K. Spielberg",
title = "Representation of †P!
@Article{Spielberg:1962:PCF,
author = "Kurt Spielberg",
title = "Polynomial and C„Y‰3
@Article{Spielberg:1966:CEU,
author = "K. Spielberg",
title = "Computation of $ eÍ‡;Žw
@Article{Spira:1973:CTA,
author = "Philip M. Spira",
title = "Computation Times o‡‡6Žm
@Article{Spiteri:2002:PPA,
author = "Pierre Spiteri and Jean-Claude Miellou and Didier El
GB—Z¯5
@Article{Squire:1991:ANS,
author = "Jon S. Squire",
title = "{Ada} numerics stand*„F‰
@Article{Sreedharan:1985:ASS,
author = "J. Sreedharan and A. Dhurkadas",
title = _
GG‡57[ #+Y=o;'ˆ
articlefparith.bibPawlak:1959:EDCZ. PawlakAn electronic digital computer based on the `$ - 2 $' systemBull. Acad. Pol. Sci., Ser. Sci. Tech.7713--7221959Thu Nov 06 05:58:31 2014https://www.math.utah.edu/pub/tex/bib/fparith.bib2014.11.06 05:58:31 ???negative baseack-nhfbZ. PawlakAn electronic digital computer based on the `$ - 2 $' system
@Article{Pawlak:1959:EDC,
author = "Z. Pawlak",
title = "An electronic digital computer based on the `$ - 2 $'
system",
journal = "Bull. Acad. Pol. Sci., Ser. Sci. Tech.",
volume = "7",
number = "??",
pages = "713--722",
month = "????",
year = "1959",
bibdate = "Thu Nov 06 05:58:31 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "negative base",
} Multiplier Using Triangular Waves,
Diodes, Resistors, and Operational Amplifiers",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "2",
pages = "222--227",
month = jun,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5219526",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219526",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}¸ Multiplier Using Triangular Waves, Diodes, Resistors, and Operational Amplifiers
@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,
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number = "2",
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month = jun,
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CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5219526",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219526",
acknowledgement = ack-nhfb,
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**J8^ #/-M;]7Ee;]
-MŽcarticlefparith.bibPfeiffer:1959:FQMPaul E. PfeifferA Four-Quadrant Multiplier Using Triangular Waves, Diodes, Resistors, and Operational Amplifiersj-IRE-TRANS-ELEC-COMPUTEC-82222--227jun61959IRELAOhttps://doi.org/10.1109/TEC.1959.52195260367-9950 OR 03679950Thu Jul 14 15:56:45 MDT 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 15:56:45 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219526IRE Transactions on Electronic Computersack-nhfbhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885Paul E. PfeifferA Four-QuadrantÀnary Numbers Modulo Three",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "2",
pages = "229--229",
month = jun,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5219529",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219529",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}¹ons on Electronic Computersack-nhfbhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885Jerome RothsteinResidues of Binary Numbers Modulo Three
@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",
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DOI = "https://doi.org/10.1109/TEC.1959.5219529",
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ççŒ
9\ #1-[;]7Ee;]
-[Qarticlefparith.bibRothstein:1959:RBNJerome RothsteinResidues of Binary Numbers Modulo Threej-IRE-TRANS-ELEC-COMPUTEC-82229--229jun61959IRELAOhttps://doi.org/10.1109/TEC.1959.52195290367-9950 OR 03679950Thu Jul 14 15:56:45 MDT 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 15:56:45 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219529IRE TransactiÃomputation of Square Roots Without
Using Division",
journal = j-CACM,
volume = "2",
number = "11",
pages = "23--24",
month = nov,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:24 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sarafyan59;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See comments \cite{Traub:1960:CNM}.",
acknowledgement = ack-nhfb,
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}º Without Using Division
@Article{Sarafyan:1959:NMC,
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**J:] #/)57E‚!;O?C)SWarticlefparith.bibSarafyan:1959:NMCDiran SarafyanA New Method of Computation of Square Roots Without Using Divisionj-CACM21123--24nov111959CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Wed Jul 14 15:48:24 MDT 2004http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sarafyan59; http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib2004.07.14 15:48:24 MDTSee comments cite Traub:1960:CNM.Communications of the ACMack-nhfbhttps://dl.acm.org/loi/cacmDiran SarafyanSee comments \cite{Traub:1960:CNM}.A New Method of Computation of Square RootsÆ Translator Compiler of the {IBM FORTRAN
Automatic Coding System}",
journal = j-CACM,
volume = "2",
number = "2",
pages = "9--21",
month = feb,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sheridan59;
http://ei.cs.vt.edu/~cs4304/bibliography.html;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
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@Article{Sheridan:1959:ATC,
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title = "The Arithmetic Translator Compiler of the {IBM FORTRAN
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acknowledgement = ack-nhfb,
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f;] #//'57E‚;?C/+
articlefparith.bibSheridan:1959:ATCPeter B. SheridanThe Arithmetic Translator Compiler of the IBM FORTRAN Automatic Coding Systemj-CACM229--21feb21959CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Wed Jul 14 15:48:22 MDT 2004http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sheridan59; http://ei.cs.vt.edu/~cs4304/bibliography.html; http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib2004.07.14 15:48:22 MDTCommunications of the ACMack-nhfbhttps://dl.acm.org/loi/cacmPeter B. SheridanThe Arithmetic Translator Compiler of the {IBM FORTRAN Automatic Coding SystemÉ root of a complex number",
journal = j-COMP-J,
volume = "2",
number = "2",
pages = "89--89",
month = jul,
year = "1959",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/2.2.89",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:55:11 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/020089.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/tiff/89.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}¼racheyOn taking the square root of a complex number
@Article{Strachey:1959:TSR,
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title = "On taking the square root of a complex number",
journal = j-COMP-J,
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number = "2",
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Decimal Fraction",
journal = j-CACM,
volume = "2",
number = "7",
pages = "27--27",
month = jul,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:25:37 MST 2001",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Taranto59;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "decimal floating-point arithmetic",
oldlabel = "Taranto59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Taranto59",
}½ction
@Article{Taranto:1959:BCF,
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title = "Binary Conversion, with Fixed Decimal Precision, of a
Decimal Fraction",
journal = j-CACM,
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number = "7",
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month = jul,
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acknowledgement = ack-nj,
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'#'‰p>[ #+%e;7;M;]
%i‹ articlefparith.bibVolder:1959:CTCJ. E. VolderThe CORDIC Trigonometric Computing Techniquej-IRE-TRANS-ELEC-COMPUTEC-85330--334sep91959IRELAO0367-9950 OR ÒQ=] #-)57E‚M;?OC){articlefparith.bibTaranto:1959:BCFDonald TarantoBinary Conversion, with Fixed Decimal Precision, of a Decimal Fractionj-CACM2727--27jul71959CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Mon Jan 22 07:25:37 MST 2001ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Taranto59; https://www.math.utah.edu/pub/tex/bib/fparith.bib2001.01.22 07:25:37 MSTCommunications of the ACMdecimal floating-point arithmeticack-njhttps://dl.acm.org/loi/cacmDonald TarantoBinary Conversion, with Fixed Decimal Precision, of a Decimal FraÏetric Computing Technique",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "5",
pages = "330--334",
month = sep,
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CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}¾03679950Thu Sep 1 10:15:31 1994ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:31 ???IRE Transactions on Electronic Computersack-njhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885J. E. VolderThe {CORDIC} Trigonometric Computing Technique
@Article{Volder:1959:CTC,
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CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:55:07 MDT 2000",
bibsource = "Compiler/semantics.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/010163.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/163.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/164.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/165.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/166.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/167.tif",
acknowledgement = ack-nhfb,
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@Article{Wensley:1959:CNA,
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polynomials. {I}",
journal = j-NUM-MATH,
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pages = "150--166",
month = dec,
year = "1959",
CODEN = "NUMMA7",
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ISSN = "0029-599X (print), 0945-3245 (electronic)",
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bibdate = "Mon Oct 18 01:28:20 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}À//link.springer.com/journal/211J. H. WilkinsonThe evaluation of the zeros of ill-conditioned polynomials. {I}
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Ž-articlefparith.bibWilkinson:1959:EZIbJ. H. WilkinsonThe evaluation of the zeros of ill-conditioned polynomials. IIj-NUM-MATH1167--180dec121959NUMMA7https://doi.org/10.1007/BF013863820029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)0029-599X OR 0029599X65.00MR0109435 (22 \#321)H. RutishauserMon Oct 18 01:28:20 MDT 1999https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib1999.10.18 01:28:20 MDTNumerische Mathematikack-nhfbhttp://Üsome methods of numerical integration using
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year = "1959",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}Âsfparith.bibYoung:1959:SSMJohn Mackay YoungA study of some methods of numerical integration using floating point arithmeticThesis (M.S. in Mathematics)Texas A.&M. CollegeCollege Station, TX, USA501959Sat Feb 24 15:01:45 MST 1996https://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MSTack-nhfbJohn Mackay YoungA study of some methods of numerical integration using floating point arithmetic
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acknowledgement = ack-nhfb,
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bibdate = "Thu Jul 14 15:34:12 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
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acknowledgement = ack-nhfb,
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@Article{Brown:1960:EDC,
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journal = j-SCRIPTA-MATH,
volume = "25",
number = "??",
pages = "221--228",
month = "????",
year = "1960",
ISSN = "0036-9713",
ISSN-L = "0036-9713",
MRclass = "10.00",
MRnumber = "118694",
MRreviewer = "H. Bergstr{\"{o}}m",
bibdate = "Thu Oct 26 11:15:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
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acknowledgement = ack-nhfb,
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}Å116.27101ack-nhfbScripta Math.Eckford CohenThe elementary arithmetical functions
@Article{Cohen:1960:EAF,
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title = "The elementary arithmetical functions",
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CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1960.5219830",
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bibdate = "Thu Jul 14 15:34:11 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219830",
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ŽŽûhÕ¹&“Š>”}
@Article{Jenkins:1981:SPC,
author = "W. K. Jenkins and M. H. Etzel",
title = "SpeŠ”
@Article{Jenkins:1982:RNS,
author = "W. K. Jenkins",
title = "Residue number syst‰Œ'˜O
@Article{Jenkins:1983:DEC,
author = "W. K. Jenkins",
title = "The Design of Error‰Z“5
@Article{Jenkins:1988:SCP,
author = "W. K. Jenkins and E. J. Altman",
title = "Self-checking properties of residue number error
checkers based on mixed radix conversion",
journal = Ó À#
@Article{Jeon:2018:HMP,
author = "Dong-Ik Jeon and Kyeong-Bin Park and Ki-Seok Chung",
tjˆ0a
@Article{Jeong:2004:CEP,
author = "Jong-Chul Jeong and Woo-Chan Park and Woong Jeong and
K«”.¨]
@Article{Jessani:1996:FPU,
author = "R. M. Jessani and C. H. Olson",
title = "The7çctions on Electronic Computersack-nhfbhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885John E. CroyImproved Arrangement of a Decimal Multiplier
@Article{Croy:1960:IAD,
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title = "Improved Arrangement of a Decimal Multiplier",
journal = j-IRE-TRANS-ELEC-COMPUT,
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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/;
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acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}Çs of the ACMack-nhfbhttps://dl.acm.org/loi/cacmPaolo ErcoliSee \cite{Ercoli:1957:EDO}.Letter to the {Editor}: {Errors} Due to Overflow in Arithmetic Operations
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55?H[ #)!57Eƒ5;?C!sarticlefparith.bibGurzi:1960:HSMFred GurziA High-Speed Multiplication Process for Digital Computersj-CACM34241--245apr41960CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Fri Nov 25 18:19:26 MST 2005http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Gurzi60; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:26 MSTCommunications of the ACMack-nhfbhttps://dl.acm.org/loi/cacmFred GurziA High-Speed Multiplication Process for Digital ñs for floating point trigonometric,
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abstract = "Conversion of integers in both directions between the
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ìì–J] #+)uW57Eƒ7;„=?9C„=)u—%articlefparith.bibKanner:1960:NUAHerbert KannerA Note on the Use of the Abacus in Number Conversionj-CACM33167--167mar31960CACMA2https://doi.org/10.1145/367149.3671660001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Fri Nov 25 18:19:26 MST 2005http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Kanner60; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:26 MSTConversion of integers in both directions between the base ten and any desired base can be accomplished with remarkable simplicity by use of the abacus.øü System",
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abstract = "For centuries the decimal number system reigned
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}‰kQ[#'AG57;M;?CAGŠmarticlefparith.bibPope:1960:MPAD. A. Pope and M. L. SteinMultiple Precision Arithmeticj-CACM312652--654dec121960CACMA20001-0782 (print), 1557-7317arithmetic",
crossref = "Alt:1960:AC",
pages = "231--308",
year = "1960",
bibdate = "Sat May 18 14:36:56 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}Òutation of square roots through
continued squaring",
journal = j-CACM,
volume = "3",
number = "5",
pages = "319--321",
month = may,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.00",
MRnumber = "22\#8639",
bibdate = "Fri Nov 25 18:19:26 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions",
ZMreviewer = "M. Lotkin",
}ÓyanDivisionless computation of square roots through continued squaring
@Article{Sarafyan:1960:DCS,
author = "Diran Sarafyan",
title = "Divisionless computation of square roots through
continued squaring",
journal = j-CACM,
volume = "3",
number = "5",
pages = "319--321",
month = may,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.00",
MRnumber = "22\#8639",
bibdate = "Fri Nov 25 18:19:26 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions",
ZMreviewer = "M. Lotkin",
}
bbS] #/)57E‚9;?MC)Žyarticlefparith.bibSarafyan:1960:DCSDiran SarafyanDivisionless computation of square roots through continued squaringj-CACM35319--321may51960CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 0001078265.0022\#8639Fri Nov 25 18:19:26 MST 2005http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:26 MSTCommunications of the ACM$sqrt (x)$; elementary functionsack-nhfbhttps://dl.acm.org/loi/cacmDiran Sarafr}: Rounding in Floating-Point
Arithmetic",
journal = j-CACM,
volume = "3",
number = "12",
pages = "A9--A9",
month = dec,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:29 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point arithmetic; rounding errors",
}Ô
NNrßL¹&“‰-’[
@Article{Tasche:2001:WAC,
author = "Manfred Tasche and Hansmartin Zeuner",
title = "Worst and average case roundoff error analysis for
{FFD¬Š ”
@Article{Tatsaki:1995:ICB,
author = "A. Tatsaki and T. Stouraitis and C. Goutis",
title 6{Ž,œY
@Article{Taub:1970:ECS,
author = "D. M. Taub and C. E. Owen and B. P. Day",
title = ƒ‡/Ž_
@Article{Tay:2016:NIM,
author = "T. Fatt Tay and C. Chang",
title = "A Non-Iterate_˜/°_
@Article{Taylor:1981:FPR,
author = "Fred J. Taylor and Chao H. Huang",
title = "AÌ†Œ-
@Article{Taylor:1982:ARM,
author = "F. J. Taylor and C. H. Huang",
title = "An Auõ‡5Žk
@Article{Taylor:1982:VRA,
author = "F. J. Taylor",
title = "A {VLSI} Residue Aritù‡.Ž]
@Article{Taylor:1983:OFR,
author = "F. J. Taylor",
title = "An Overflow-Free Resi ACMfloating-point arithmetic; rounding errorsack-nhfbhttps://dl.acm.org/loi/cacmRoland SilverLetter to the {Editor}: Rounding in Floating-Point Arithmetic
@Article{Silver:1960:LER,
author = "Roland Silver",
title = "Letter to the {Editor}: Rounding in Floating-Point
Arithmetic",
journal = j-CACM,
volume = "3",
number = "12",
pages = "A9--A9",
month = dec,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:29 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point arithmetic; rounding errors",
}
ÍÍŒ'T] #+'57E‚9;?aC'Oarticlefparith.bibSilver:1960:LERRoland SilverLetter to the Editor: Rounding in Floating-Point Arithmeticj-CACM312A9--A9dec121960CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Fri Nov 25 18:19:29 MST 2005http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:29 MSTCommunications of thetion Logic",
journal = j-TRANS-IRE,
volume = "EC-9",
number = "2",
pages = "226--230",
month = jun,
year = "1960",
bibdate = "Fri Nov 09 19:17:08 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the IRE",
}Õ
ÇÇ†5UY #/#I#=o;;#I‡articlefparith.bibSklansky:1960:CSAJ. SklanskyConditional Sum Addition Logicj-TRANS-IREEC-92226--230jun61960Fri Nov 09 19:17:08 2007https://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.09 19:17:08 ???Transactions of the IREack-nhfbJ. SklanskyConditional Sum Addition Logic
@Article{Sklansky:1960:CSA,
author = "J. Sklansky",
title = "Conditional Sum Addition Logic",
journal = j-TRANS-IRE,
volume = "EC-9",
number = "2",
pages = "226--230",
month = jun,
year = "1960",
bibdate = "Fri Nov 09 19:17:08 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the IRE",
}[{``A New Method of
Computation of Square Roots Without Using
Division''}]",
journal = j-CACM,
volume = "3",
number = "2",
pages = "86--86",
month = feb,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:25 MST 2005",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Traub60;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Sarafyan:1959:NMC}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Traub60",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Traub60",
}Ör [{``A New Method of
Computation of Square Roots Without Using
Division''}]",
journal = j-CACM,
volume = "3",
number = "2",
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month = feb,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:25 MST 2005",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Traub60;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Sarafyan:1959:NMC}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Traub60",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Traub60",
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88˜}
@Article{Ashenhurst:1959:UFP,
author = "Robert L. Ashenhurst and Nicholas Metropolis",
t…Š#
@Article{Ashenhurst:1964:FEU,
author = "R. L. Ashenhurst",
title = "Function Evalp‰/’_
@Article{Ashenhurst:1965:EEC,
author = "R. L. Ashenhurst and N. Metropolis",
title = "Error Estimation in Computer Calculation",
journal = j-AMER-MATHÇƒo‡_
@Article{Ashton:1989:AFP,
author = "C. Ashton",
title = "The {Am29C327} floating "OI›
@Article{Aspinwall:1983:MVM,
author = "David B. Aspinwall and Yale N. Patt",
title = <‘Y£3
@Article{Aspinwall:1985:RVM,
author = "D. B. Aspinwall and Y. N. Patt",
title = "Retrofitting the {VAX-11\slash 780} Microarchitecture
for {IEEE} Floating Point Arithmetic --- Implementa{–'¬O
@Article{Aspray:1990:BBS,
author = "William Aspray",
title = "Back to Basics: The%R'. 87--88]j-NORDISK-TIDSKR-INFORM-BEHAND13220--222sep91961BITTEL, NBITABhttps://doi.org/10.1007/BF019334340006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)0006-3835 OR 00063835Wed Jan 4 18:52:07 MST 2006http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=3; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib2006.01.04 18:52:07 MSTSee cite Garwick:1961:AFP,Garwick:1961:RAF.http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=3&spage=220floating-point accuracy; floating-point arithmeticack-nhfbhttp://link.springer.com/journal/10543O. Amble and Jan V. GarwickSee \cite{Garwick:1961:AFP,Garwick:1961:RAF}.On the Accuracy of Floating Point Computers {[BIT {\bf 1}(2), 1961, pp. 87--88]}
@Article{Amble:1961:AFP,
author = "O. Amble and Jan V. Garwick",
title = "On the Accuracy of Floating Point Computers {[BIT {\bf
1}(2), 1961, pp. 87--88]}",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "3",
pages = "220--222",
month = sep,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01933434",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=3;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Garwick:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=3&spage=220",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
xxpages = "220--221??",
}
‘UY^#)C#I)Q57Cƒ;cKqYCg-’{articlefparith.bibAmble:1961:AFPO. Amble and Jan V. GarwickOn the Accuracy of Floating Point Computers [BIT bf 1(2), 1961, pp&xzèz„‰Ž“˜¢§¬±¶»ÀÅÊÏÔÙÞãèíò÷ü$).38=BGLQV[`ejoty~ƒˆ’—œ¡¦«°µº¿ÄÉÎÓØÝâçìòøþ
"(.4:@FLRX^djpv|‚ˆŽ”š ¦¬²¸¾ÄÊÐÖÜâèîôú"')
03
8=@CHKNQV[`f ‡$&¦'©(«)°*³+¶.¼/Å1Ë4Ò5×6Û7Þ8á<ø=û?B EHJ$N1O7P;RCTHUKVNZV[[]b^e`}cˆdŒf‘hŸi¡k¬mµn¸p½tÇxÑyÓzÖ{Ù|Ü}â~çêô÷ü
3`finq t!y#~$%‡&Š(’*˜+›- .¦/©0¬2±3µ4¸5»6¾7Á8Ä9Ç:Ê;Í<Ð>×?Ú@ÝBâCåDof]flrx~„Š–œ¢¨®´ºÀÆÌÒØÞäêðöü &,28>DJPV\bhntz€†Œ’˜ž¤ª°¶¼ÂÈÎÔÚàæìòøþ
"(.4:@FLRX^djpv|‚ˆŽ”š ¦¬²¸¾ÄÊÐÖÜâèîôúìFïGòHõIúJLMN
PRSTUV!X(Y,Z/[5\8^@_CbRdXf^hciejikllwmzn}o€q‡rst’uÊwÏxÒyÖ{ß|â~ç‚ì‚ð‚õ‚ø‚ý‚‚ ‚‚‚‚"‚'‚,‚7‚:‚B‚H‚K‚N‚ T‚"Y‚#_‚$a‚%d‚'o‚+{‚.…‚1’‚3—‚6ž‚8¤‚;«‚>µ‚?·‚@º‚CÁ‚EÊ‚IÕ‚KÚ‚LÝ‚Mâ‚Nä‚Oç‚Pê‚Qî‚Uþ‚V‚W‚X ‚Y‚[‚\‚]‚^‚_‚b%‚d*‚e-‚f1‚i:‚k?‚mD‚pK‚qP‚rS‚sW‚tZ‚uethods",
type = "Notes on Applied Science",
number = "16",
institution = "National Physical Laboratory",
address = "Her Majesty's Stationery Office, London",
year = "1961",
bibdate = "Fri Aug 20 10:05:25 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}Ú
II‡3ZY !#1==E[=o;M=ˆtechreportfparith.bibAnonymous:1961:MCMAnonymousModern Computing MethodsNotes on Applied Science16National Physical LaboratoryHer Majesty's Stationery Office, London220--2221961Fri Aug 20 10:05:25 2010https://www.math.utah.edu/pub/tex/bib/fparith.bib2010.08.20 10:05:25 ???Cited in cite Sterbenz:1974:FPC.ack-nhfbAnonymousModern Computing Methods
@TechReport{Anonymous:1961:MCM,
author = "Anonymous",
title = "Modern Computing Methods",
type = "Notes on Applied Science",
number = "16",
institution = "National Physical Laboratory",
address = "Her Majesty's Stationery Office, London",
year = "1961",
bibdate = "Fri Aug 20 10:05:25 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}-Digit Number Representations for Fast Parallel
Arithmetic",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "3",
pages = "389--400",
month = sep,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219227",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219227",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}Ûunumber=5407885Algirdas Avi{\v{z}}ienisSigned-Digit Number Representations for Fast Parallel Arithmetic
@Article{Avizienis:1961:SDN,
author = "Algirdas Avi{\v{z}}ienis",
title = "Signed-Digit Number Representations for Fast Parallel
Arithmetic",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "3",
pages = "389--400",
month = sep,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219227",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219227",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
tt[^ #11
;]7Ee;]
=
Ž7articlefparith.bibAvizienis:1961:SDNAlgirdas AvizienisSigned-Digit Number Representations for Fast Parallel Arithmeticj-IRE-TRANS-ELEC-COMPUTEC-103389--400sep91961IRELAOhttps://doi.org/10.1109/TEC.1961.52192270367-9950 OR 03679950Thu Jul 14 14:45:04 MDT 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:04 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219227IRE Transactions on Electronic Computersack-nhfbhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?p.1relator Based on the Residue Number
System",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "1",
pages = "63--70",
month = mar,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219154",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219154",
abstract = "A system design for a digital correlator based on the
application of the residue number system for
computation is presented. Areas of investigation
include sampling, analog-to-residue conversion, logical
design of the arithmetic units, residue-to-analog
conversion, and modes of operation of the proposed
digital correlator. The advantages of speed of
computation and simplicity of logic due to the use of a
residue number system are shown to result in a
significantly faster and simpler system than if a
conventional number system were used. The resulting
digital correlator is designed for megacycle sampling
and computation with a 0.1 per cent system precision.",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}Ü3-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.IRE Transactions on Electronic Computersack-nhfbhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885A 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 simpler4 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.Philip Warren CheneyA Digital Correlator Based on the Residue Number System
@Article{Cheney:1961:DCB,
author = "Philip Warren Cheney",
title = "A Digital Correlator Based on the Residue Number
System",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "1",
pages = "63--70",
month = mar,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219154",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219154",
abstract = "A system design for a digital correlator based on the
application of the residue number system for
computation is presented. Areas of investigation
include sampling, analog-to-residue conversion, logical
design of the arithmetic units, residue-to-analog
conversion, and modes of operation of the proposed
digital correlator. The advantages of speed of
computation and simplicity of logic due to the use of a
residue number system are shown to result in a
significantly faster and simpler system than if a
conventional number system were used. The resulting
digital correlator is designed for megacycle sampling
and computation with a 0.1 per cent system precision.",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
îî~\^ #+5{;]7Ee;Š=]
Š=5{œarticlefparith.bibCheney:1961:DCBPhilip Warren CheneyA Digital Correlator Based on the Residue Number Systemj-IRE-TRANS-ELEC-COMPUTEC-10163--70mar31961IRELAOhttps://doi.org/10.1109/TEC.1961.52191540367-9950 OR 03679950Thu Jul 14 14:45:02 MDT 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:02 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219154A 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, residue2w algorithms for rational approximation",
journal = j-NUM-MATH,
volume = "3",
number = "1",
pages = "72--75",
month = dec,
year = "1961",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01386002",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 19:01:15 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}Ýb/nummath.bib1999.10.17 19:01:15 MDTNumerische Mathematikack-nhfbhttp://link.springer.com/journal/211E. W. Cheney and H. L. LoebTwo new algorithms for rational approximation
@Article{Cheney:1961:TNA,
author = "E. W. Cheney and H. L. Loeb",
title = "Two new algorithms for rational approximation",
journal = j-NUM-MATH,
volume = "3",
number = "1",
pages = "72--75",
month = dec,
year = "1961",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01386002",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 19:01:15 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
MàM‰^Z #/)c57=o;?C)c‰yarticlefparith.bibClarkson:1961:DMIW. K. Clarkso:Œ][#+Cg!Q57E‚;;7UCg+articlefparith.bibCheney:1961:TNAE. W. Cheney and H. L. LoebTwo new algorithms for rational approximationj-NUM-MATH3172--75dec121961NUMMA7https://doi.org/10.1007/BF013860020029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)0029-599X OR 0029599XSun Oct 17 19:01:15 MDT 1999https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bi7thod of Integer Conversion",
journal = j-CACM,
volume = "4",
number = "7",
pages = "315--316",
month = jul,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 08:14:59 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}ÞnA Divisionless Method of Integer Conversionj-CACM47315--316jul71961CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Thu Sep 08 08:14:59 1994https://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.08 08:14:59 ???Communications of the ACMack-njhttps://dl.acm.org/loi/cacmW. K. ClarksonA Divisionless Method of Integer Conversion
@Article{Clarkson:1961:DMI,
author = "W. K. Clarkson",
title = "A Divisionless Method of Integer Conversion",
journal = j-CACM,
volume = "4",
number = "7",
pages = "315--316",
month = jul,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 08:14:59 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}< on Multiple Precision Arithmetic",
journal = j-CACM,
volume = "4",
number = "8",
pages = "353--353",
month = aug,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/366678.366693",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Dec 03 14:07:44 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Since computers have means to detect overflow on
addition or subtraction, this can be used in a multiple
precision addition-subtraction subroutine to obviate a
sign analysis. Consider all integers in the computer to
be expressed ``radix t'', that is, in the form $ a =
a_0 + a_1 t + \cdots + a_n t^n $ where $ a_i $ are of
like sign and have magnitudes less than $t$. $t$ is a
positive integer determined by the word length of the
computer. Consider the expression $ c = a \pm b = (a_0
\pm b_0) + (a_1 \pm b_1)t + \cdots + (a_n \pm b_n)t^n$.
Here $ a_i \pm b_i$ may exceed the storage capacity of
one word or may have a sign different from $c$.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}ß>ltiple 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 $c$.Communications of the ACMack-nhfbhttps://dl.acm.org/loi/cacmSince 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 leng?th 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 $c$.Albert G. Cox and H. A. LutherA Note on Multiple Precision Arithmetic
@Article{Cox:1961:NMP,
author = "Albert G. Cox and H. A. Luther",
title = "A Note on Multiple Precision Arithmetic",
journal = j-CACM,
volume = "4",
number = "8",
pages = "353--353",
month = aug,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/366678.366693",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Dec 03 14:07:44 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Since computers have means to detect overflow on
addition or subtraction, this can be used in a multiple
precision addition-subtraction subroutine to obviate a
sign analysis. Consider all integers in the computer to
be expressed ``radix t'', that is, in the form $ a =
a_0 + a_1 t + \cdots + a_n t^n $ where $ a_i $ are of
like sign and have magnitudes less than $t$. $t$ is a
positive integer determined by the word length of the
computer. Consider the expression $ c = a \pm b = (a_0
\pm b_0) + (a_1 \pm b_1)t + \cdots + (a_n \pm b_n)t^n$.
Here $ a_i \pm b_i$ may exceed the storage capacity of
one word or may have a sign different from $c$.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
557_] #%I[W57=ƒ;Š?CŠI[›5articlefparith.bibCox:1961:NMPAlbert G. Cox and H. A. LutherA Note on Multiple Precision Arithmeticj-CACM48353--353aug81961CACMA2https://doi.org/10.1145/366678.3666930001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Sat Dec 03 14:07:44 2005ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib2005.12.03 14:07:44 ???Since computers have means to detect overflow on addition or subtraction, this can be used in a mu=al or Machine Binary-to-Decimal
Integer Conversion Using Decimal Radix Arithmetic",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "4",
pages = "777--777",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219286",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:05 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219286",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}àl or Machine Binary-to-Decimal Integer Conversion Using Decimal Radix Arithmetic
@Article{Croy:1961:RTM,
author = "John E. Croy",
title = "Rapid Technique of Manual or Machine Binary-to-Decimal
Integer Conversion Using Decimal Radix Arithmetic",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "4",
pages = "777--777",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219286",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:05 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219286",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
($µ(°mb`!#+[U51=o;#Žy‹Žy[Uy
techreportfparith.bibGarner:1961:RNIˆaa[ #-'!=o;+'‹
articlefparEP`^ #'%];]7Ee;]
%]Žearticlefparith.bibCroy:1961:RTMJohn E. CroyRapid Technique of Manual or Machine Binary-to-Decimal Integer Conversion Using Decimal Radix Arithmeticj-IRE-TRANS-ELEC-COMPUTEC-104777--777dec121961IRELAOhttps://doi.org/10.1109/TEC.1961.52192860367-9950 OR 03679950Thu Jul 14 14:45:05 MDT 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:05 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219286IRE Transactions on Electronic Computersack-nhfbhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885John E. CroyRapid Technique of ManuaBs of certain binary division
algorithms",
journal = j-IRE-PROC,
volume = "49",
number = "1",
pages = "91--103",
month = jan,
year = "1961",
bibdate = "Mon Sep 16 16:12:21 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IRE Proceedings",
xxnote = "Check author name: I have found this paper cited both
as Freiman and as Frieman?? Hennessy and Patterson
\cite{Hennessy:2002:CAQ} have Freiman.",
}áith.bibFreiman:1961:SACC. V. FreimanStatistical analysis of certain binary division algorithmsj-IRE-PROC49191--103jan11961Mon Sep 16 16:12:21 2002https://www.math.utah.edu/pub/tex/bib/fparith.bib2002.09.16 16:12:21 ???IRE Proceedingsack-sfoC. V. FreimanStatistical analysis of certain binary division algorithms
@Article{Freiman:1961:SAC,
author = "C. V. Freiman",
title = "Statistical analysis of certain binary division
algorithms",
journal = j-IRE-PROC,
volume = "49",
number = "1",
pages = "91--103",
month = jan,
year = "1961",
bibdate = "Mon Sep 16 16:12:21 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IRE Proceedings",
xxnote = "Check author name: I have found this paper cited both
as Freiman and as Frieman?? Hennessy and Patterson
\cite{Hennessy:2002:CAQ} have Freiman.",
}GC.
G. Brockus and R. J. Gonzalez and D. P. Rozenberg",
title = "Residue number systems for computers",
type = "{ASD} Technical Report",
number = "61-483",
institution = "Electronic Technology Laboratory, The University of
Michigan",
address = "Ann Arbor, MI, USA",
month = oct,
year = "1961",
bibdate = "Thu Nov 18 09:27:06 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txt",
abstract = "The purpose of the research performed under this
contract was to investigate the feasibility of residue
number systems in their applications to digital
computers. The problems of such an application are the
ones of magnitude determination, sign determination,
overflow, scaling, and division. These problems are not
H 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..",
}âJSH. L. Garner and R. F. Arnold and B. C. Benson and C. G. Brockus and R. J. Gonzalez and D. P. RozenbergResidue number systems for computersASD Technical Report61-483Electronic Technology Laboratory, The University of MichiganAnn Arbor, MI, USA91--103oct101961Thu Nov 18 09:27:06 2010https://www.math.utah.edu/pub/tex/bib/fparith.bib2010.11.18 09:27:06 ???http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txtThe 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,K 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.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 Lsupported by this contract, and led to the Ph.D..ack-nhfbThe 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.H. L. Garner Mand R. F. Arnold and B. C. Benson and C. G. Brockus and R. J. Gonzalez and D. P. RozenbergResidue number systems for computers
@TechReport{Garner:1961:RNS,
author = "H. L. Garner and R. F. Arnold and B. C. Benson and C.
G. Brockus and R. J. Gonzalez and D. P. Rozenberg",
title = "Residue number systems for computers",
type = "{ASD} Technical Report",
number = "61-483",
institution = "Electronic Technology Laboratory, The University of
Michigan",
address = "Ann Arbor, MI, USA",
month = oct,
year = "1961",
bibdate = "Thu Nov 18 09:27:06 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txt",
abstract = "The purpose of the research performed under this
contract was to investigate the feasibility of residue
number systems in their applications to digitNal
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..",
} journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "2",
pages = "87--88",
month = jun,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01939221",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=2;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also comment and reply
\cite{Amble:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=2&spage=87",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
}ãQparith.bibGarwick:1961:AFPJan V. GarwickThe Accuracy of Floating Point Computersj-NORDISK-TIDSKR-INFORM-BEHAND1287--88jun61961BITTEL, NBITABhttps://doi.org/10.1007/BF019392210006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)0006-3835 OR 00063835Wed Jan 4 18:52:07 MST 2006http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=2; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib2006.01.04 18:52:07 MSTSee also comment and reply cite Amble:1961:AFP,Garwick:1961:RAF.http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=2&spage=87floating-point accuracy; floating-point arithmeticack-nhfbhttp://link.springer.com/journal/10543Jan V. GarwickSee also comment and reply \cite{Amble:1961:AFP,Garwick:1961:RAF}.The Accuracy of Floating Point Computers
@Article{Garwick:1961:AFP,
author = "Jan V. Garwick",
title = "The Accuracy of Floating Point Computers",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "2",
pages = "87--88",
month = jun,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01939221",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=2;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also comment and reply
\cite{Amble:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=2&spage=87",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
}
ä‘ä!d] #-'AI)57=M;_qY'cK_articlefparith.bibGarwick:1961:RAFJ. V. GarwickReply to ``On the Accuracy of Floating Point Computers'' [BIT bf 1(3), 1961, pp. 220--221]j-NORDISK-TIDSKR-INFORM-BEHAND13222--2221961BITTEL, NBITAB0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)0006-3835 OR 00063835Mon Nov 16 14:36:22 1998https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib1998.11.16 14:36:22 ???See cite Garwick:1961:AFP,Amble:1961:AFP.floating-point accuracy; floating-point arithmeticack-nhfbhttp://link.springer.com/journal/10543J. VTXc^ #-)]I)Q57Cƒ;
IqY)]‘{articlefPAccuracy of Floating Point
Computers'' [BIT {\bf 1}(3), 1961, pp. 220--221]}",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "3",
pages = "222--222",
year = "1961",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon Nov 16 14:36:22 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Garwick:1961:AFP,Amble:1961:AFP}.",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
}ä. GarwickSee \cite{Garwick:1961:AFP,Amble:1961:AFP}.Reply to {``On the Accuracy of Floating Point Computers'' [BIT {\bf 1}(3), 1961, pp. 220--221]}
@Article{Garwick:1961:RAF,
author = "J. V. Garwick",
title = "Reply to {``On the Accuracy of Floating Point
Computers'' [BIT {\bf 1}(3), 1961, pp. 220--221]}",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "3",
pages = "222--222",
year = "1961",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon Nov 16 14:36:22 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Garwick:1961:AFP,Amble:1961:AFP}.",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
}ngs of the 1961 16th ACM national meeting}",
title = "Residue class error checking codes",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "132.101--132.104",
year = "1961",
DOI = "https://doi.org/10.1145/800029.808563",
bibdate = "Thu Aug 07 19:04:58 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Error checking codes based on residues have the
advantage over parity-based codes of monitoring
arithmetic as well as transmission operations. Codes
may be devised to detect burst-type errors, to correct
single errors in a binary arithmetic operation, to
correct burst errors and finally to correct any
single-digit error in a decimal operation.",
acknowledgement = ack-nhfb,
keywords = "decimal arithmetic",
}åWlass error checking codespub-ACMpub-ACM:adr132.101--132.1041961https://doi.org/10.1145/800029.808563Thu Aug 07 19:04:58 2008https://www.math.utah.edu/pub/tex/bib/fparith.bib2008.08.07 19:04:58 ???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.decimal arithmeticack-nhfbError 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.D. S. Henderson{Proceedings of the 1961 16th ACM national meeting}Residue class error checking codes
@InProceedings{Henderson:1961:RCE,
author = "D. S. Henderson",
booktitle = "{Proceedings of the 1961 16th ACM national meeting}",
title = "Residue class error checking codes",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "132.101--132.104",
year = "1961",
DOI = "https://doi.org/10.1145/800029.808563",
bibdate = "Thu Aug 07 19:04:58 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Error checking codes based on residues have the
advantage over parity-based codes of monitoring
arithmetic as well as transmission operations. Codes
may be devised to detect burst-type errors, to correct
single errors in a binary arithmetic operation, to
correct burst errors and finally to correct any
single-digit error in a decimal operation.",
acknowledgement = ack-nhfb,
keywords = "decimal arithmetic",
}
î)îŒ/f\#+A_;]7Ee;]
A_earticlefparith.bibKettel:1961:AAME. Kettel and W. SchneiderAn Accurate Analog Multiplier and Dividerj-IRE-TRANS-ELEC-COMPUTEC-102269--272jun61961IRELAOhttps://doi.org/10.1109/TEC.1961.52191980367-9950 OR 03679950Thu Jul 14 14:45:03 MDT 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:03 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219198IRE Transactions on Electronic CompZ‘Ge[ '#1+oQ#-W=o;…?1…?+sQinproceedingsfparith.bibHenderson:1961:RCED. S. HendersonProceedings of the 1961 16th ACM national meetingResidue cVrate Analog Multiplier and Divider",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "2",
pages = "269--272",
month = jun,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219198",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:03 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219198",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}æutersack-nhfbhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885E. Kettel and W. SchneiderAn Accurate Analog Multiplier and Divider
@Article{Kettel:1961:AAM,
author = "E. Kettel and W. Schneider",
title = "An Accurate Analog Multiplier and Divider",
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DOI = "https://doi.org/10.1109/TEC.1961.5219198",
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bibdate = "Thu Jul 14 14:45:03 MDT 2011",
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}nary number system''}",
journal = j-CACM,
volume = "4",
number = "8",
pages = "355--355",
month = aug,
year = "1961",
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bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
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note = "See \cite{Knuth:1960:INS}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
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}ç
úgÔ§†Œ!
@Article{Rump:1986:SER,
author = "Siegfried M. Rump",
title = "{Sichere ErgebnissÆ†Œ%
@Article{Rump:1991:CAI,
author = "Siegfried M. Rump",
title = "A Class of Arbitra*|’/¤_
@Article{Rump:2001:RPS,
author = "Siegfried M. Rump",
title = "Rigorous and PortaDY’s¥g
@Article{Rump:2008:AFPa,
author = "Siegfried M. Rump and Takeshi Ogita and Shin'ichi
V™A³
@Article{Rump:2008:AFPb,
author = "Siegfried M. Rump and Takeshi Ogita and Shin'ichi
Oishi",
title = "Accurate Floating-Point Summation. {Part II}: Sign,
V˜ š
@Article{Rump:2009:CPS,
author = "Siegfried M. Rump and Paul Zimmermann and Sylvie Boldo
XÌ‘^£=
@Article{Rump:2009:UFA,
author = "Siegfried M. Rump",
title = "Ultimately Fast Accurate Summation",
journal = j-SIAM-J-SCI-COMP,
volume = "31",
number = "5",
pages = "3466--350XÒmath.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib1996.01.09 07:10:22 ???See cite Knuth:1960:INS.Communications of the ACMack-nhfbhttps://dl.acm.org/loi/cacmDonald E. KnuthSee \cite{Knuth:1960:INS}.Errata: {``An imaginary number system''}
@Article{Knuth:1961:EIN,
author = "Donald E. Knuth",
title = "Errata: {``An imaginary number system''}",
journal = j-CACM,
volume = "4",
number = "8",
pages = "355--355",
month = aug,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Jan 09 07:10:22 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1960:INS}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
nnŒ#h\#-EO;]7Ee;]
ES_articlefparith.bibKovatch:1961:HEAG. Kovatch and W. E. MeserveThe Hall-Effect Analog Multiplierj-IRE-TRANS-ELEC-COMPUTEC-103512--515sep91961IRELAOhttps://doi.org/10.1109/TEC.1961.52192400367-9950 OR 03679950Thu Jul 14 14:45:04 MDT 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:04 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219240IRE Transactions on Electron`ŠWg[ #)+Y57=W;=?C+A]‹[articlefparith.bibKnuth:1961:EINDonald E. KnuthErrata: ``An imaginary number system''j-CACM48355--355aug81961CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Tue Jan 09 07:10:22 1996https://www.]{Hall-Effect} Analog Multiplier",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "3",
pages = "512--515",
month = sep,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219240",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219240",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}èic Computersack-nhfbhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885G. Kovatch and W. E. MeserveThe {Hall-Effect} Analog Multiplier
@Article{Kovatch:1961:HEA,
author = "G. Kovatch and W. E. Meserve",
title = "The {Hall-Effect} Analog Multiplier",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "3",
pages = "512--515",
month = sep,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219240",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219240",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}ques for High-Speed Carry-Propagation in
Binary Arithmetic Units",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "4",
pages = "691--698",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219274",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219274",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}éM. Lehman and N. BurlaSkip Techniques for High-Speed Carry-Propagation in Binary Arithmetic Units
@Article{Lehman:1961:STH,
author = "M. Lehman and N. Burla",
title = "Skip Techniques for High-Speed Carry-Propagation in
Binary Arithmetic Units",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "4",
pages = "691--698",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219274",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219274",
acknowledgement = ack-nhfb,
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}
WWi^#+9#;]7Ee;]
9#ŽCarticlefparith.bibLehman:1961:STHM. Lehman and N. BurlaSkip Techniques for High-Speed Carry-Propagation in Binary Arithmetic Unitsj-IRE-TRANS-ELEC-COMPUTEC-104691--698dec121961IRELAOhttps://doi.org/10.1109/TEC.1961.52192740367-9950 OR 03679950Thu Jul 14 14:45:04 MDT 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:04 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219274IRE Transactions on Electronic Computersack-nhfbhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885bhmetic in binary computers",
journal = j-IRE-PROC,
volume = "49",
number = "??",
pages = "67--91",
month = jan,
year = "1961",
bibdate = "Sat May 18 14:34:55 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite{Swartzlander:1976:CDD}.",
acknowledgement = ack-nhfb,
fjournal = "IRE Proceedings",
}ê
!!‡[jY #1+_!=o;]++a_ˆ!articlefparith.bibMacSorley:1961:HSAO. L. MacSorleyHigh-speed arithmetic in binary computersj-IRE-PROC4967--91jan11961Sat May 18 14:34:55 2002https://www.math.utah.edu/pub/tex/bib/fparith.bib2002.05.18 14:34:55 ???Reprinted in cite Swartzlander:1976:CDD.IRE Proceedingsack-nhfbO. L. MacSorleyReprinted in \cite{Swartzlander:1976:CDD}.High-speed arithmetic in binary 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 = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite{Swartzlander:1976:CDD}.",
acknowledgement = ack-nhfb,
fjournal = "IRE Proceedings",
}he calculator: and other seminal writings",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xxxviii + 400",
year = "1961",
ISBN = "0-486-24691-4 (paperback)",
ISBN-13 = "978-0-486-24691-8 (paperback)",
LCCN = "QA75 .C52 1961",
bibdate = "Sat Jan 12 22:30:15 MST 2013",
bibsource = "clio-db.cc.columbia.edu:7090/Voyager;
https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$7.95",
acknowledgement = ack-nhfb,
subject = "Calculators; Babbage, Charles",
subject-dates = "Charles Babbage (26 December 1791--18 October 1871)",
tableofcontents = "Chapters from Passages from the life of a
philosopher \\
Selections from Babbage's calculating engines \\
Appendix of miscellaneous papers",
}ëhback) OR 0486246914 (paperback)978-0-486-24691-8 (paperback) OR 9780486246918 (paperback)QA75 .C52 1961Sat Jan 12 22:30:15 MST 2013clio-db.cc.columbia.edu:7090/Voyager; https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib; https://www.math.utah.edu/pub/tex/bib/adabooks.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib2013.01.12 22:30:15 MSTCalculators; Babbage, CharlesChapters from Passages from the life of a philosopher Selections from Babbage's calculating engines Appendix of miscellaneous papersack-nhfbCharles Babbage (26 December 1791--18 October 1871)Philip Morrison and Emily Morrison{Charles Babbage} on the principles and development of the calculator: and other seminal writingsChapters from Passages from the life of a philosopher \\ Selections from Babbage's calculating engines \\ Appendix of miscellaneous papers
@Book{Morrison:1961:CBP,
editor = "Philip Morrison and Emily Morrison",
title = "{Charles Babbage} on the principles and development of
the calculator: and other seminal writings",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xxxviii + 400",
year = "1961",
ISBN = "0-486-24691-4 (paperback)",
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bibdate = "Sat Jan 12 22:30:15 MST 2013",
bibsource = "clio-db.cc.columbia.edu:7090/Voyager;
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https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$7.95",
acknowledgement = ack-nhfb,
subject = "Calculators; Babbage, Charles",
subject-dates = "Charles Babbage (26 December 1791--18 October 1871)",
tableofcontents = "Chapters from Passages from the life of a
philosopher \\
Selections from Babbage's calculating engines \\
Appendix of miscellaneous papers",
}
ºº’6k_#/QK''s)Eƒ+;G‚sQO‚!’Y¶bookfparith.bibMorrison:1961:CBPPhilip Morrison and Emily MorrisonCharles Babbage on the principles and development of the calculator: and other seminal writingspub-DOVERpub-DOVER:adrxxxviii + 40019610-486-24691-4 (papergroot in the quater-imaginary
number system",
journal = j-CACM,
volume = "4",
number = "4",
pages = "192--193",
month = apr,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.99",
MRnumber = "23\#B555",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1960:INS}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions",
ZMreviewer = "C. B. Haselgrove",
}ì-imaginary number system
@Article{Nadler:1961:DSR,
author = "Morton Nadler",
title = "Division and square root in the quater-imaginary
number system",
journal = j-CACM,
volume = "4",
number = "4",
pages = "192--193",
month = apr,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.99",
MRnumber = "23\#B555",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1960:INS}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions",
ZMreviewer = "C. B. Haselgrove",
}
dl] #+' 57E‚9;=?MC'A Uarticlefparith.bibNadler:1961:DSRMorton NadlerDivision and square root in the quater-imaginary number systemj-CACM44192--193apr41961CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 0001078265.9923\#B555Fri Nov 25 18:19:32 MST 2005http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:32 MSTSee cite Knuth:1960:INS.Communications of the ACM$sqrt (x)$; elementary functionsack-nhfbhttps://dl.acm.org/loi/cacmMorton NadlerSee \cite{Knuth:1960:INS}.Division and square root in the quaterknion of First Significant Digits",
journal = j-ANN-MATH-STAT,
volume = "32",
number = "4",
pages = "1223--1230",
month = dec,
year = "1961",
CODEN = "AASTAD",
ISSN = "0003-4851 (print), 2168-8990 (electronic)",
ISSN-L = "0003-4851",
bibdate = "Thu Feb 15 15:07:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0003-4851%28196112%2932%3A4%3C1223%3AOTDOFS%3E2.0.CO%3B2-T",
abstract = "It has been noticed by astute observers that well used
tables of logarithms are invariably dirtier at the
front than at the back. Upon reflection one is led to
inquire whether there are more physical constants with
low order first significant digits than high. Actual
counts by Benford [2] show that not only is this the
case but that it seems to be an empirical otruth that
whenever one has a large body of physical data,
Farmer's Almanac, Census Reports, Chemical Rubber
Handbook, etc., the proportion of these data with first
significant digit $n$ or less is approximately $
\log_{10}(n + 1) $. Any reader formerly unaware of this
``peculiarity'' will find an actual sampling experiment
wondrously tantalizing. Thus, for example,
approximately $ 0.7 $ of the physical constants in the
Chemical Rubber Handbook begin with $4$ or less ($
\log_{10}(4 + 1) = 0.699 $). This is to be contrasted
with the widespread intuitive evaluation $ 4 / 9 $
ths.",
acknowledgement = ack-nhfb,
fjournal = "Annals of Mathematical Statistics",
journal-URL = "http://projecteuclid.org/all/euclid.aoms/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = p "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}.",
}írhow 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.Annals of Mathematical StatisticsBenford's Law; Law of Anomalous Numbers; Zipf's LawFrom 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) $.s 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.ack-nhfbhttp://projecteuclid.org/all/euclid.aoms/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 tseems 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.Roger S. PinkhamOn the Distribution of First Significant Digits
@Article{Pinkham:1961:DFS,
author = "Roger S. Pinkham",
title = "On the Distribution of First Significant Digits",
journal = j-ANN-MATH-STAT,
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pages = "1223--1230",
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bibdate = "Thu Feb 15 15:07:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
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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 digivt $n$ or less is approximately $
\log_{10}(n + 1) $. Any reader formerly unaware of this
``peculiarity'' will find an actual sampling experiment
wondrously tantalizing. Thus, for example,
approximately $ 0.7 $ of the physical constants in the
Chemical Rubber Handbook begin with $4$ or less ($
\log_{10}(4 + 1) = 0.699 $). This is to be contrasted
with the widespread intuitive evaluation $ 4 / 9 $
ths.",
acknowledgement = ack-nhfb,
fjournal = "Annals of Mathematical Statistics",
journal-URL = "http://projecteuclid.org/all/euclid.aoms/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From p. 1223: ``\ldots{} the proportion of these data
with first significant digit $n$ or less is
approximately $ \log_{10}(n + 1) $.''\par
\ldots{} ``The only distribution for first significant
digits which is invariant under scale change of the
underlying distribution is $ \log_{10}(n + 1) $.
Contrary to suspicion this is a non-trivial
mathematical result, for the variable $n$ is
discrete.''.\par
From p. 1230: ``The foregoing results bear on questions
of round-off in computing machines. Since $ d(u v) = u
d v + v d u $, the error resulting from multiplying two
rounded numbers will be governed primarily by the first
significant digits of the two numbers being multiplied.
Now the distribution of first significant digits,
favoring as it does low order digits, tends to produce
less error than would be the case if first significant
digits were uniform as has sometimes been
assumed.''\par
Cited in \cite{Sterbenz:1974:FPC}.",
}
ÆÆ¶m^ #--k+!57=o;CŽkOsŽ7_Žs-kµ-articlefparith.bibPinkham:1961:DFSRoger S. PinkhamOn the Distribution of First Significant Digitsj-ANN-MATH-STAT3241223--1230dec121961AASTAD0003-4851 (print), 2168-8990 (electronic) OR 00034851 (print), 21688990 (electronic)0003-4851 OR 00034851Thu Feb 15 15:07:57 2007https://www.math.utah.edu/pub/tex/bib/fparith.bib2007.02.15 15:07:57 ???http://links.jstor.org/sici?sici=0003-4851%28196112%2932%3A4%3C1223%3AOTDOFS%3E2.0.CO%3B2-TIt 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] sqcision Division",
journal = j-CACM,
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bibdate = "Thu Sep 08 00:29:25 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
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https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
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acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}î1994.09.08 00:29:25 ???Communications of the ACMack-njhttps://dl.acm.org/loi/cacmPhilip RabinowitzMultiple-Precision Division
@Article{Rabinowitz:1961:MPD,
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ÅÅŒ/n[ #3/CW57=ƒ;?C/CŽarticlefparith.bibRabinowitz:1961:MPDPhilip RabinowitzMultiple-Precision Divisionj-CACM4298--98feb21961CACMA2https://doi.org/10.1145/366105.3661710001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Thu Sep 08 00:29:25 1994ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fparith.biby Time for Synchronous Binary
Division",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "2",
pages = "169--174",
month = jun,
year = "1961",
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bibdate = "Thu Jul 14 14:45:03 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219186",
acknowledgement = ack-nhfb,
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}ïeeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885Roy G. SaltmanReducing Computing Time for Synchronous Binary Division
@Article{Saltman:1961:RCT,
author = "Roy G. Saltman",
title = "Reducing Computing Time for Synchronous Binary
Division",
journal = j-IRE-TRANS-ELEC-COMPUT,
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articlefparith.bibSaltman:1961:RCTRoy G. SaltmanReducing Computing Time for Synchronous Binary Divisionj-IRE-TRANS-ELEC-COMPUTEC-102169--174jun61961IRELAOhttps://doi.org/10.1109/TEC.1961.52191860367-9950 OR 03679950Thu Jul 14 14:45:03 MDT 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:03 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219186IRE Transactions on Electronic Computersack-nhfbhttps://i|ued Fraction Approximations To
Elementary Functions",
journal = j-MATH-COMPUT,
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CODEN = "MCMPAF",
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bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
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acknowledgement = ack-nj # " and " # ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}ðTOR database1998.10.13 08:06:19 MDTMathematics of Computationack-njMath. Comput.http://www.ams.org/mcom/Kurt SpielbergEfficient Continued Fraction Approximations To Elementary Functions
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&&‹bq] #1%[57=M;1e%[ŒIarticlefparith.bibSpielberg:1961:RPSK. SpielbergRepresentation of Power Series in Terms of Polynomials, Rational Approximations and Continued Fractionsj-J-ACM84613--627oct101961JACOAH0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)0004-5411 OR 00045411Sat Dec 09 14:01:44 1995ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex‚‹`p] #1)'57Em;A'=) articlefparith.bibSpielberg:1961:ECFKurt SpielbergEfficient Continued Fraction Approximations To Elementary Functionsj-MATH-COMPUT1576409--417oct101961MCMPAF0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)0025-5718 OR 00255718Tue Oct 13 08:06:19 MDT 1998ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSPower Series in Terms of
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bibdate = "Sat Dec 09 14:01:44 1995",
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https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}ñ/bib/fparith.bib1995.12.09 14:01:44 ???Journal of the ACMack-njhttp://portal.acm.org/browse_dl.cfm?idx=J401K. SpielbergRepresentation of Power Series in Terms of Polynomials, Rational Approximations and Continued Fractions
@Article{Spielberg:1961:RPS,
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}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",
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ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
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fjournal = "Mathematics of Computation",
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++˜rßL¹&“‡F
@Article{Ullah:2021:AOA,
author = "S. Ullah and H. Schmidl and S. S. Sahoo and S. Rehman
r*‡n]
@Article{Ulman:1983:SDI,
author = "Z. D. Ulman",
title = "Sign Detection and Impl†aC
@Article{Ulman:1998:HPF,
author = "Zenon D. Ulman and Maciej Czyzak",
title = "Hi<±‡bE
@Article{Um:2001:OAC,
author = "Junhyung Um and Taewhan Kim",
title = "An optimalDÂ>š}
@Article{Umemura:1991:FNL,
author = "K. Umemura",
title = "Floating-point number *îŒ|™y
@Article{Umemura:1991:FPN,
author = "Kyoji Umemura",
title = "Floating-point Numb*ô‡Z5
@Article{Unguru:1989:BRB,
author = "Sabetai Unguru",
title = "Book Review: {{\boo$ý;ºw
@Article{Upton:1994:RAH,
author = "Michael Upton and Thomas Huff and Trevor Mudge and
3ó‡Q#
@Article{Upton:1998:RH,
author = "Graham Upton",
title = "Rounding halves",
jou<´Z=ZË<Ãˆ;w
@Article{Ballard:2014:CLB,
author = "G. Ballard and E. Carson and J. Demmel and M. Hoemmena
£ˆ#G
@Article{Bankas:2015:NMA,
author = "Edem Kwedzo Bankas and Kazeem Alagbe Gbolagade",
titb;<ý…L‹
@Article{Barany:1988:FEI,
author = "T. E. Barany",
title = "Fast evaluation of in 0b<†A
@Article{Barlow:1985:PEA,
author = "J. L. Barlow and E. H. Bareiss",
title = "Pro’ªÔ
@Article{Barrett:1989:FMA,
author = "Geoff Barrett",
title = "Formal methods appl"_GÕ…q‹e
@Article{Barrow:1924:QDD,
author = "D. F. Barrow",
title = "Questions and DiscussAedu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:06:19 MDTMathematics of Computationack-nhfbMath. Comput.http://www.ams.org/mcom/Henry C. {Thacher, Jr.}Iterated Square Root Expansions for the Inverse Cosine and Inverse Hyperbolic Cosine
@Article{Thacher:1961:ISR,
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title = "Iterated Square Root Expansions for the Inverse Cosine
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bibdate = "Tue Oct 13 08:06:19 MDT 1998",
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acknowledgement = ack-nhfb,
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fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
LL‹(r] #-75'57E;A'=;5Œarticlefparith.bibThacher:1961:ISRHenry C. Thacher, Jr.Iterated Square Root Expansions for the Inverse Cosine and Inverse Hyperbolic Cosinej-MATH-COMPUT1576399--403oct101961MCMPAF0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)0025-5718 OR 00255718Tue Oct 13 08:06:19 MDT 1998https://www.math.utah.†‰Domestic Electronic Digital
Computing Systems",
type = "Report",
number = "1115",
institution = "Ballistic Research Laboratories",
address = "Aberdeen Proving Ground, MD, USA",
pages = "1131",
month = mar,
year = "1961",
bibdate = "Fri Nov 28 19:37:51 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Based on the results of a third survey, the
engineering and programming characteristics of two
hundred twenty-two different electronic digital
computing systems are given. The data are presented
from the point of view of application, numerical and
arithmetic characteristics, input, output and storage
systems, construction and checking features, power,
space, weight, and site preparation and personnel
requirements, production records, cost and rental
rates, sale and lease policy, reliability, operating
experience, and time availability, engineering
modifications and improvements and other related
topics. An analysis of the survey data, fifteen
comparative tables, a discussion of trends, a revised
bibliography, and a complete glossary of computer
engineering and programming terminology are included.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}ó‹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.ack-mfcBased 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, reliŒability, 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.Martin H. WeikA Third Survey of Domestic Electronic Digital Computing Systems
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journal = j-IRE-TRANS-ELEC-COMPUT,
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@Article{Wilson:1961:ARB,
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}
ÄÄŒ0t\#+GY;]7Ee;]
GYe articlefparith.bibWilson:1961:ARBJ. B. Wilson and R. S. LedleyAn Algorithm for Rapid Binary Divisionj-IRE-TRANS-ELEC-COMPUTEC-104662--670dec121961IRELAOhttps://doi.org/10.1109/TEC.1961.52192710367-9950 OR 03679950Thu Jul 14 14:45:04 MDT 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:04 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219271IRE Transactions on Electronic Compniac III} Arithmetic System",
crossref = "AFIPS:1962:APS",
pages = "192--202",
year = "1962",
bibdate = "Wed Feb 14 17:14:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}õ
''…UuY '#3-M)=o;-Q…einproceedingsfparith.bibAshenhurst:1962:MIAR. L. AshenhurstThe Maniac III Arithmetic SystemAFIPS:1962:APS192--2021962Wed Feb 14 17:14:21 2007https://www.math.utah.edu/pub/tex/bib/fparith.bib2007.02.14 17:14:21 ???ack-nhfbR. L. AshenhurstThe {Maniac III} Arithmetic System
@InProceedings{Ashenhurst:1962:MIA,
author = "R. L. Ashenhurst",
title = "The {Maniac III} Arithmetic System",
crossref = "AFIPS:1962:APS",
pages = "192--202",
year = "1962",
bibdate = "Wed Feb 14 17:14:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}”r System: {Project Stretch}",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xvii + 322",
year = "1962",
LCCN = "1876",
bibdate = "Fri Nov 19 10:02:31 MST 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
library.ox.ac.uk:210/ADVANCE",
note = "This important book is the primary description of the
influential IBM 7030 Stretch computer, written by its
architects.",
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 wou–ld 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 ---
where—as 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 occur™red 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 \\
š [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 œ\\
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. Ržound-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. BuchhoŸlz] \\
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 T echniques 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 Se£quences 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-sequen¤ce 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",
}ö
-štá¹&-“Ñ@¢
@Book{Feijen:1990:BOB,
editor = "W. H. J. Feijen and A. J. M. van Gasteren and David
za‡Ž3
@Book{Ercegovac:1985:DSH,
author = "Milo{\v{s}} D. Ercegovac and Tom{\'a}s Lang",
title „L‰
@Book{Ercegovac:1994:DSR,
author = "Milo{\v{s}} D. (Dragutin) Ercegovac and Tomas Lang",
1äŒp™a
@Book{Ercegovac:2004:DA,
author = "Milo{\v{s}} Dragutin Ercegovac and Tom{\'a}s Lang",
tK9‘J£
@Book{Esmay:2017:HNS,
author = "Gabriel Esmay",
title = "The History of Number Systems",
publisher = "Teacher Created Materials",
address = "Huntington Beach, CA",
pages = f¤…A‹
@Book{Evanczuk:1984:MSS,
editor = "Stephen Evanczuk",
booktitle = "Microprocessor sysy”G©
@Book{Farquhar:1994:MPH,
author = "Erin Farquhar and Philip Bruce",
title = "The 1ôƒW‡/
@Book{Fike:1968:CEM,
author = "C. T. Fike",
title = "Computer Evaluation of Mathe±§ntial IBM 7030 Stretch computer, written by its architects.http://ed-thelen.org/comp-hist/IBM-7030-Planning-McJones.pdfThe 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 dªo 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.)''Computer architectureForeword 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. Relationsh®ip 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 A¯pproach 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 Des°cription 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 2±66 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 305ack-nhfbWerner BuchholzThis important book is the primary description of the influential IBM 7030 Stretch computer, written by its architects.Planning a Computer System: {Project Stretch}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 \\ ²2.4. 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 3³9 \\ 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-leng´th 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. Univerµsal 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 Inter·ruptions 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 a¸fter 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 ¹Data 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
@Book{Buchholz:1962:PCS,
editor = "Werner Buchholz",
title = "Planning a Computer System: {Project Stretch}",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xvii + 322",
year = "1962",
LCCN = "1876",
bibdate = "Fri Nov 19 10:02:31 MST 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utºah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
library.ox.ac.uk:210/ADVANCE",
note = "This important book is the primary description of the
influential IBM 7030 Stretch computer, written by its
architects.",
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 ¼no 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
l½oss 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
¾ 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 meth¿od 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 ÀUnit 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
\\
Á 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.Â 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 \\
Ã 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-poÄint 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 1Å27 \\
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 Æ155 \\
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 ReadÇing 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
È 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 ÉTransfer 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",
}
®a®‰'wZ %#/)+c=+3%=';M)g+=Šincollectionfparith.bibCampbell:1962:FPOS. G. CampbellWerner BuchholzPlanning a Ì‚¤va #/+c+3!E„y;{µE7ñ%+{gü‚–Sbookfparith.bibBuchholz:1962:PCSWerner BuchholzPlanning a Computer System: Project Stretchpub-MCGRAW-HILLpub-MCGRAW-HILL:adrxvii + 32219621876Fri Nov 19 10:02:31 MST 2010https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib; https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib; library.ox.ac.uk:210/ADVANCE2010.11.19 10:02:31 MSTThis important book is the primary description of the influe¦olz",
booktitle = "Planning a Computer System: {Project Stretch}",
title = "Floating-Point Operation",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
bookpages = "322",
pages = "92--121",
year = "1962",
LCCN = "QA76.8.I2 I5",
bibdate = "Wed Feb 14 17:24:27 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "IBM 7030 (Computer); IBM Stretch",
}÷Computer System: Project StretchFloating-Point Operationpub-MCGRAW-HILLpub-MCGRAW-HILL:adr92--1211962QA76.8.I2 I5Wed Feb 14 17:24:27 2007https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2007.02.14 17:24:27 ???IBM 7030 (Computer); IBM Stretchack-nhfb322S. G. CampbellPlanning a Computer System: {Project Stretch}Werner BuchholzFloating-Point Operation
@InCollection{Campbell:1962:FPO,
author = "S. G. Campbell",
editor = "Werner Buchholz",
booktitle = "Planning a Computer System: {Project Stretch}",
title = "Floating-Point Operation",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
bookpages = "322",
pages = "92--121",
year = "1962",
LCCN = "QA76.8.I2 I5",
bibdate = "Wed Feb 14 17:24:27 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "IBM 7030 (Computer); IBM Stretch",
} "Logarithmic and Exponential Function Evaluation in a
Variable Structure Digital Computer",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "2",
pages = "155--164",
month = apr,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219348",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:49 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219348",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}øor: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,
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journal = j-IRE-TRANS-ELEC-COMPUT,
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month = apr,
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CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219366",
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bibdate = "Thu Jul 14 09:11:50 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219366",
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@Article{Grehan:1988:FPCb,
author = "R. Grehan",
title = "Floating-Point Without µ„f‰M
@Article{Grehan:1989:FPR,
author = "R. Grehan",
title = "Floating-Point Revisited#5ˆz‘u
@Article{Griffin:1991:REA,
author = "C. Griffin and P. Rao and F. Taylor",
title = "Roundoff error analy)6‰K“
@Article{Griffiths:1981:BDC,
author = "L. K. Griffiths",
title = "Binary-to-Decimal Conversion",
journal = j-IBM-TDB,
volume = "24",
number = "1A",
pages = î…s‹g
@Article{Groeger:1989:DRG,
author = "Detlef Gr{\"o}ger",
title = "{Zur Division m#=Žœ
@Article{Gross:1985:SIF,
author = "Thomas Gross",
title = "Software implementatio5„a‰C
@Article{Grosse:1987:UCB,
author = "Eric Grosse and Cleve Moler",
title = "Underfœ‡\9
@Article{Grossschadl:2001:BSU,
author = "J. Gro{\ss}sch{\"a}dl",
title = "A Bit-SC1bhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885M. A. Fischler and E. A. PoeThreshold Realization of Arithmetic Circuits
@Article{Fischler:1962:TRA,
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journal = j-IRE-TRANS-ELEC-COMPUT,
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Eesarticlefparith.bibFischler:1962:TRAM. A. Fischler and E. A. PoeThreshold Realization of Arithmetic Circuitsj-IRE-TRANS-ELEC-COMPUTEC-112287--288apr41962IRELAOhttps://doi.org/10.1109/TEC.1962.52193660367-9950 OR 03679950Thu Jul 14 09:11:50 MDT 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 09:11:50 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219366IRE Transactions on Electronic Computersack-nhfÕmputation of rational approximations to
continuous functions",
journal = j-CACM,
volume = "5",
number = "7",
pages = "401--403",
month = jul,
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CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/368273.368578",
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ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:39 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\abs(x)$; $\cos(x)$; $\Gamma(1+x)$; $\sin(x)$;
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functions",
}ûÙfparith.bibFraser:1962:CRAW. Fraser and J. F. HartOn the computation of rational approximations to continuous functionsj-CACM57401--403jul71962CACMA2https://doi.org/10.1145/368273.3685780001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Fri Nov 25 18:19:39 MST 2005http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:39 MSTCommunications of the ACM$abs (x)$; $cos (x)$; $Gamma (1+x)$; $sin (x)$; elementary functions; Remes algorithm; special functionsack-nhfbhttps://dl.acm.org/loi/cacmW. Fraser and J. F. HartOn the computation of rational approximations to continuous functions
@Article{Fraser:1962:CRA,
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}Ûr representation for use with
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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.",
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}üÝ 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.Communications of the ACMack-nhfbhttps://dl.acm.org/loi/cacmR. L. AshenhurstAlgorithmic 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. FurthermoreÞ, 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.A. A. GrauOn a floating-point number representation for use with algorithmic languages
@Article{Grau:1962:FNR,
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abstract = "Algorithmic languages, such as ALGOL, make provision
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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,
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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",
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bibdate = "Thu Jul 14 09:11:49 MDT 2011",
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}ý M. GuffinA Computer for Solving Linear Simultaneous Equations Using the Residue Number System
@Article{Guffin:1962:CSL,
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title = "A Computer for Solving Linear Simultaneous Equations
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bibdate = "Fri Aug 20 09:12:08 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
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}ÿal Disclosure Bulletindecimal floating-point arithmeticThe IBM 1620 normalized variable-precision arithmetic provides up to 100 decimal digits with an exponent range of $ pm 99 $.ack-nhfbF. B. Jones and A. W. WymoreFloating Point Feature on the {IBM Type 1620}
@Article{Jones:1962:FPF,
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journal = j-DOKL-AKAD-NAUK,
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number = "??",
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year = "1962",
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@Article{Karatsuba:1962:MMN,
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bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219389",
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ÆÆŽ.‚\#'g;]75%Ee;]
garticlefparith.bibKeir:1962:DODY. A. Keir and P. W. Cheney and M. TannenbaumDivision and overflow detection in residue number systemsj-IRE-TRANS-ELEC-COMPUTEC-114501--507aug81962IRELAOhttps://doi.org/10.1109/TEC.1962.52193890367-9950 OR 0367995068.00MR0150990 (27 \#976)N. H. ChoksyThu Jul 14 09:11:51 MDT 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 09:11:51 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219389IRE Transactions on Electronic Computersack-nhfbhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885Y. A. Keir and P. W. Cheney and M. TannenbaumDivision and overflow detection in residue number systems
@Artiëc in {COBOL}",
journal = j-CACM,
volume = "5",
number = "5",
pages = "269--271",
month = may,
year = "1962",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/367710.367739",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:38 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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journal-URL = "https://dl.acm.org/loi/cacm",
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@Article{Lu:1997:SMK,
author = "Chung-Chin Lu",
title = "A search of minimal key :L‡2Že
@Article{Lu:2015:REP,
author = "Xin Lu and Shufang Xu",
title = "Rounding errors c>†o_
@Article{Lu:2021:EDN,
author = "Jinming Lu and Chao Fang and Mingyang Xu and Jun Lin
qÊ‡Ž?
@Article{Lucal:1959:AOD,
author = "Harold M. Lucal",
title = "Arithmetic Operatio¶„Y‰5
@Article{Ludgate:1909:PAM,
author = "P. E. Ludgate",
title = "On a proposed analy9
ž
@Article{Luk:1988:AAB,
author = "Franklin T. Luk and Haesun Park",
title = "An an!6…v‹m
@Article{Luke:1957:CLZ,
author = "Y. L. Luke",
title = "On the Computation of $ \‹ –
@Article{Luo:2000:API,
author = "Z. Luo and M. Martonosi",
title = "Accelerating AC†
@Article{Luo:2020:ADN,
author = "Y. Luo and S. Yu",
title = "Accelerating Deep Neoÿu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:38 MSTCommunications of the ACMack-nhfbhttps://dl.acm.org/loi/cacmO. KesnerFloating-point arithmetic in {COBOL}
@Article{Kesner:1962:FPA,
author = "O. Kesner",
title = "Floating-point arithmetic in {COBOL}",
journal = j-CACM,
volume = "5",
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https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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??‹5‚[ #+QW57E‚9;?CUŒkarticlefparith.bibKesner:1962:FPAO. KesnerFloating-point arithmetic in COBOLj-CACM55269--271may51962CACMA2https://doi.org/10.1145/367710.3677390001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Fri Nov 25 18:19:38 MST 2005http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edïòomials 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",
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bibdate = "Thu Dec 08 11:11:03 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
note = "See letter \cite{Knuth:1963:LEE}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "The author that Motzkin (1962) showed that Horner's
rule for polynomial evaluation may not be optimal, and
develops the idea further for arbitrary polynomials,
but also observes that the coefficients of the revised
polynomials may be difficult to find. He also asks
about, but does not answer, the question of error
analysis of the various methods.",
}ôte Knuth:1963:LEE.Communications of the ACMThe 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.ack-nhfbhttps://dl.acm.org/loi/cacmDonald E. KnuthSee letter \cite{Knuth:1963:LEE}.Evaluation of polynomials by computer
@Article{Knuth:1962:EPC,
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title = "Evaluation of polynomials by computer",
journal = j-CACM,
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https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
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note = "See letter \cite{Knuth:1963:LEE}.",
acknowledgement = ack-nhfb,
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about, but does not answer, the question of error
analysis of the various methods.",
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YY•‚\ #)+WW57'=ƒk;K?…EC+OW—articlefparith.bibKnuth:1962:EPCDonald E. KnuthEvaluation of polynomials by computerj-CACM512595--599dec121962CACMA2https://doi.org/10.1145/355580.3690740001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 0001078268.00 (12.00)27 \#970Thu Dec 08 11:11:03 2005http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; MathSciNet database2005.12.08 11:11:03 ???See letter ciódware Conversion of Decimal
and Binary Numbers",
journal = j-CACM,
volume = "5",
number = "9",
pages = "468--469",
month = sep,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 28 18:16:30 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
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journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "decimal floating-point arithmetic",
}00010782Fri Nov 28 18:16:30 2003https://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 18:16:30 ???Communications of the ACMdecimal floating-point arithmeticack-mfchttps://dl.acm.org/loi/cacmG. T. LakeLetter to the Editor: Hardware Conversion of Decimal and Binary Numbers
@Article{Lake:1962:LEH,
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title = "Letter to the Editor: Hardware Conversion of Decimal
and Binary Numbers",
journal = j-CACM,
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acknowledgement = ack-mfc # " and " # ack-nhfb,
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©¬©‰w‚Z #)#o57=o;?OC#o‹articlefparith.bibLynch:1962:WBDW. C. LynchOn a Wired-In Binary-to-Decimal Conversion Schemej-CACM53159--159mar31962CACMA20001-0782 (print), 1557-7317 (electroniúŠH‚\ #'!57=o;?OC!‹[articlefparith.bibLake:1962:LEHG. T. LakeLetter to the Editor: Hardware Conversion of Decimal and Binary Numbersj-CACM59468--469sep91962CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR ÷-Decimal Conversion Scheme",
journal = j-CACM,
volume = "5",
number = "3",
pages = "159--159",
month = mar,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 28 18:21:41 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "decimal floating-point arithmetic",
}c) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Fri Nov 28 18:21:41 2003https://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 18:21:41 ???Communications of the ACMdecimal floating-point arithmeticack-mfchttps://dl.acm.org/loi/cacmW. C. LynchOn a Wired-In Binary-to-Decimal Conversion Scheme
@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",
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month = mar,
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acknowledgement = ack-mfc # " and " # ack-nhfb,
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}tle{An Algorithm for Rapid Binary
Division}, by {J. B. Wilson and R. S. Ledley}",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "3",
pages = "420--420",
month = jun,
year = "1962",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Sat Jul 16 20:52:08 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}:52:08 ???IRE Transactions on Electronic Computersack-nhfbhttps://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885O. L. MacSorleyReview: \booktitle{An Algorithm for Rapid Binary Division}, by {J. B. Wilson and R. S. Ledley}
@Article{MacSorley:1962:RBA,
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acknowledgement = ack-nhfb,
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+IŒ7articlefparith.bibMacSorley:1962:RBAO. L. MacSorleyReview: booktitle An Algorithm for Rapid Binary Division, by J. B. Wilson and R. S. Ledleyj-IRE-TRANS-ELEC-COMPUTEC-113420--420jun61962IRELAO0367-9950 OR 03679950Sat Jul 16 20:52:08 2011https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.16 20ü,
journal = j-SIAM-REVIEW,
volume = "4",
number = "3",
pages = "256--256",
month = "????",
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CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1004066",
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ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:04:54 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/4/3;
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https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
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@Article{McGee:1962:BM,
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CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
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bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
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