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bibdate = "Wed Oct 13 11:14:08 2010",
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note = "Reprinted in \cite[\S 2.4]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
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;GI9articlefparith.bibJ:1930:RPRbR. A. J.Recent Publications: Reviews: em Standard Table of Square Roots, by L. M. MilneThomsonjAMERMATHMONTHLY376314314jun61930AMMYAE00029890 (print), 19300972 (electronic) OR 00029890 (print), 19300972 (electronic)00029890 OR 00029890Mon Jun 28 12:35:55 MDT 1999http://www.math.utah.edu/pub/tex/bib/fparith.bib; JST@ivision by Calculating Machine",
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bookfparith.bibCouffignal:1933:MCLL. CouffignalLes machines a calculer, leurs principes, leur evolution. (French) [Calculating machines, their principles, their evolution]GauthierVillarsParis, France5335351933Wed Oct 13 11:19:11 2010http://www.mIY #)+357E
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articlefparith.bibGarver:1932:QDNbRaymond GarverQuestions, Discussions, and Notes: a Square Root Method and Continued FractionsjAMERMATHMONTHLY399533535nov111932AMMYAE00029890 (print), 19300972 (electronic) OR 00029890 (print), 19300972 (electronic)00029890 OR 00029890Mon Jun 28 12:36:47 MDT 1999http://www.math.utah.eFcalculer, leurs principes, leur
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bibdate = "Wed Oct 13 11:19:11 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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}ath.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:19:11 ???Extracts reprinted in cite [ 3.2]Randell:1982:ODC. Translated by Mr. R. Basu.FrenchacknhfbL. CouffignalExtracts reprinted in \cite[\S 3.2]{Randell:1982:ODC}. Translated by Mr. R. Basu.Les machines {\`a} calculer, leurs principes, leur {\'e}volution. ({French}) [{Calculating} machines, their principles, their evolution]
@Book{Couffignal:1933:MCL,
author = "L. Couffignal",
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fjournal = "American Mathematical Monthly",
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}acknhfbhttp://www.jstor.org/page/journal/isis/about.htmlH. R. CalvertDecimal Division of Scales before the Metric System
@Article{Calvert:1936:DDS,
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@Article{Phillips:1936:BC,
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}n Durchfuhrung von
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howpublished = "German patent application Z23624.",
day = "11",
month = apr,
year = "1936",
bibdate = "Wed Oct 13 11:22:03 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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@Misc{Zuse:1936:VSD,
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title = "{Verfahren zur selbstt{\"a}tigen Durchfuhrung von
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[{Procedure} for automatic execution of calculations by
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Extracting a Square Root",
journal = jAMERMATHMONTHLY,
volume = "44",
number = "10",
pages = "644646",
month = dec,
year = "1937",
CODEN = "AMMYAE",
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ISSNL = "00029890",
bibdate = "Mon Jun 28 12:38:44 MDT 1999",
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acknowledgement = acknhfb,
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}ath.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1999.06.28 12:38:44 MDTAmerican Mathematical Monthlyacknhfbhttp://www.jstor.org/page/journal/amermathmont/about.htmlE. 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
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journal = jAMERMATHMONTHLY,
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}Xbolic Analysis of Relay and Switching Circuits",
type = "{Master of Science}",
school = "Department of Electrical Engineering, MIT",
address = "Cambridge, MA, USA",
pages = "72",
day = "10",
month = aug,
year = "1937",
bibdate = "Thu Nov 18 10:35:20 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Not submitted until 1940",
URL = "http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425.pdf",
acknowledgement = acknhfb,
authordates = "April 30, 1916February 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 twentyone and published
when he was twentytwo, is considered to be one of the
most important, if not the most important, master's
thesis of the twentieth century.''\par
Pages 5961 of the thesis are a section called
``Electric Adder to the Base Two'', and pages 6268,
``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.''",
}Zlished when he was twentytwo, is considered to be one of the most important, if not the most important, master's thesis of the twentieth century.''par Pages 5961 of the thesis are a section called ``Electric Adder to the Base Two'', and pages 6268, ``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.''acknhfbApril 30, 1916February 24, 2001Claude Elwood ShannonNot submitted until 1940A Symbolic Analysis of Relay and Switching Circuits
@MastersThesis{Shannon:1937:SAR,
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[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 twentyone and published
when he was twentytwo, is considered to be one of the
most important, if not the most important, master's
thesis of the twentieth century.''\par
Pages 5961 of the thesis are a section called
``Electric Adder to the Base Two'', and pages 6268,
``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.''",
}
}*}~Z #'E57=m;C]WsEe'ESarticlefparith.bibBenford:1938:LANFrank BenfordThe Law of Anomalous NumbersbCW '#7s/_1=m;=
=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 2010http://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 twentyone and pubY^s Numbers",
journal = jPROCAMERPHILSOC,
volume = "78",
number = "4",
pages = "551572",
month = mar,
year = "1938",
CODEN = "PAPCAA",
ISSN = "0003049X",
bibdate = "Thu Feb 15 16:28:28 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0003049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2G",
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 differen_t
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 lawhence 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 multidigit 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 affairsa.
The Law of Anomalous Numbers is thus a general
probability law of widespread application.",
acknowledgement = acknhfb,
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
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), 573585 (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.",
}cjPROCAMERPHILSOC784551572mar31938PAPCAA0003049X OR 0003049XThu Feb 15 16:28:28 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.02.15 16:28:28 ???http://links.jstor.org/sici?sici=0003049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2GIt 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 ind large groups, in good agreement with a distribution lawhence 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 multidigit 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 astroenomer 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.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), 573585 (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] fcontaining 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.acknhfbIt 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 gare without relationship are, when considered in large groups, in good agreement with a distribution lawhence 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 multidigit 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 gauhge 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 = jPROCAMERPHILSOC,
volume = "78",
number = "4",
pages = "551572",
month = mar,
year = "1938",
CODEN = "PAPCAA",
ISSN = "0003049X",
bibdate = "Thu Feb 15 16:28:28 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0003049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2G",
abstract = "It has been observed that the first pages of a table
of common logarithms show more wear than do the liast
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 lawhence the name ``Anomalous
Numbers.''\pajr
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 multidigit 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 lokng been
recognized as a common phenomenon in factual literature
and in the ordinary affairs of life. The wire gauge and
drill gauge of the mechanic, the magnitude scale of the
astronomer and the sensory response curves of the
psychologist are all particular examples of a
relationship that seems to extend to all human affairs.
The Law of Anomalous Numbers is thus a general
probability law of widespread application.",
acknowledgement = acknhfb,
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
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), 573585 (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.",
}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 = "GauthierVillars",
school = "Facult{\'e} des Sciences de Paris",
address = "Paris, France",
year = "1938",
bibdate = "Wed Oct 13 11:17:22 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Extracts reprinted in \cite[\S 2.7]{Randell:1982:ODC}.
Translated by Mr. R. Basu.",
acknowledgement = acknhfb,
language = "French",
}
+&+Lr
@Article{Ahmadifar:2015:NRN,
author = "H. Ahmadifar and G. Jaberipur",
title = "ASÇ9s
@Article{Akbarpour:2002:FCS,
author = "Behzad Akbarpour and Abdelkader Dekdouk and
}
@Article{Aiken:1964:PAC,
author = "H. H. Aiken",
title = "Proposed automatic calc:A
@Article{Aiken:1946:ASC,
author = "H. H. Aiken and G. M. Hopper",
title = "The {Azu
@Article{Ahmadi:2008:PFS,
author = "O. Ahmadi and D. Hankerson and F.
RodJ
@Article{Ahmad:1987:IDA,
author = "M. Ahmad",
title = "Implementable Decimal Aritx 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 = "GauthierVillars",
school = "Facult{\'e} des Sciences de Paris",
address = "Paris, France",
year = "1938",
bibdate = "Wed Oct 13 11:17:22 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Extracts reprinted in \cite[\S 2.7]{Randell:1982:ODC}.
Translated by Mr. R. Basu.",
acknowledgement = acknhfb,
language = "French",
}
hY #3'7G'=m;''/_ 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]GauthierVillarsFaculte des Sciences de ParisParis, France5515721938Wed Oct 13 11:17:22 2010http://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.FrenchacknhfbL. CouffignalExtracts reprinted in \cite[\S 2.7]{Randell:1982:ODC}. Translated by Mr. R. Basu.Sur l'analyse m{\'e}canique. Application aun Maitland) Wright",
title = "An Introduction to the Theory of Numbers",
publisher = pubOXFORD,
address = pubOXFORD:adr,
pages = "xvi + 403",
year = "1938",
LCCN = "QA241 .H28",
bibdate = "Fri Nov 30 06:49:15 2007",
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acknowledgement = acknhfb,
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DD9W#)]!)!=m;]Ibookfparith.bibHardy:1938:ITNG. H. (Godfrey Harold) Hardy and E. M. (Edward Maitland) WrightAn Introduction to the Theory of NumberspubOXFORDpubOXFORD:adrxvi + 4031938QA241 .H28Fri Nov 30 06:49:15 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.30 06:49:15 ???acknhfbG. H. (Godfrey Harold) Hardy and E. M. (Edward Maitland) WrightAn Introduction to the Theory of Numbers
@Book{Hardy:1938:ITN,
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Maitland) Wright",
title = "An Introduction to the Theory of Numbers",
publisher = pubOXFORD,
address = pubOXFORD:adr,
pages = "xvi + 403",
year = "1938",
LCCN = "QA241 .H28",
bibdate = "Fri Nov 30 06:49:15 2007",
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acknowledgement = acknhfb,
}sysis of Relay and Switching Circuits",
journal = jTRANSAMERINSTELECENG,
volume = "57",
number = "??",
pages = "713723",
month = dec,
year = "1938",
CODEN = "TAEEA5",
ISSN = "00963860",
bibdate = "Sat Nov 20 08:54:12 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www2.research.att.com/~njas/doc/shannonbio.html",
acknowledgement = acknhfb,
fjournal = "Transactions of the American Institute of Electrical
Engineers",
journalURL = "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 ... a
landmark in that it helped to change digital circuit
design from an art to a science.''",
} uster's thesis). In 1940, it received the Alfred Noble Prize of the combined engineering societies of the United States, an award given each year to a person not over thirty for a paper published in one of the journals of the participating societies. H. H. Goldstine cite Goldstine:1972:CPN called this work ``one of the most important master's theses ever written ... a landmark in that it helped to change digital circuit design from an art to a science.''acknhfbhttp://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 = jTRANSAMERINSTELECENG,
volume = "57",
number = "??",
pages = "713723",
month = dec,
year = "1938",
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ISSN = "00963860",
bibdate = "Sat Nov 20 08:54:12 2010",
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acknowledgement = acknhfb,
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journalURL = "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 ... a
landmark in that it helped to change digital circuit
design from an art to a science.''",
}
Y #/sA7=]; }/sUarticlefparith.bibShannon:1938:SARClaude E. ShannonA Symbolic Analysis of Relay and Switching CircuitsjTRANSAMERINSTELECENG57713723dec121938TAEEA500963860 OR 00963860Sat Nov 20 08:54:12 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www2.research.att.com/~njas/doc/shannonbio.html2010.11.20 08:54:12 ???Transactions of the American Institute of Electrical EngineersThis is Shannon's first published paper (his MatThe Artificial Arithmetick in Decimals of {Robert
Jager} ({London}, 1651)",
journal = jISIS,
volume = "31",
number = "1",
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http://www.jstor.org/stable/i302217;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/isis1930.bib",
URL = "http://www.jstor.org/stable/226014",
acknowledgement = acknhfb,
fjournal = "Isis",
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}!ficial Arithmetick in Decimals of {Robert Jager} ({London}, 1651)
@Article{Jager:1939:AAD,
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title = "The Artificial Arithmetick in Decimals of {Robert
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g!Y#)Q57E;QoQarticlefparith.bibJager:1939:AADRobert Jager and Boyd C. PattersonThe Artificial Arithmetick in Decimals of Robert Jager (London, 1651)jISIS3112531nov111939ISISA400211753 (print), 15456994 (electronic) OR 00211753 (print), 15456994 (electronic)00211753 OR 00211753Tue Jul 30 21:26:49 MDT 2013http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i302217; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/isis1930.bib2013.07.30 21:26:49 MDThttp://www.jstor.org/stable/226014Isisacknhfbhttp://www.jstor.org/page/journal/isis/about.htmlRobert Jager and Boyd C. PattersonThe Artixdecimal Arithmetic}}, by
George S. Terry}",
journal = jJRSTATSOC,
volume = "102",
number = "2",
pages = "299300",
month = "????",
year = "1939",
DOI = "http://dx.doi.org/10.2307/2980013",
bibdate = "Sat Jan 24 11:18:08 MST 2015",
bibsource = "http://www.jstor.org/stable/i349540;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jrssa1930.bib",
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}"tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/jrssa1930.bib2015.01.24 11:18:08 MSThttp://www.jstor.org/stable/2980013Journal of the Royal Statistical SocietyacknhfbM. G. K.Book Review: {{\booktitle{Duodecimal Arithmetic}}, by George S. Terry}
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title = "Book Review: {{\booktitle{Duodecimal Arithmetic}}, by
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^ ^7$X #%5=m;#+5}miscfparith.bibBush:1940:AMV. BushArithmetical Machine2993001940Wed Oct 13 11:37:32 2010http://ws#W !#1+/91'=m;_+g/qtechreportfparith.bibAtanasoff:~W"X ##
)OE#;S]articlefparith.bibK:1939:BRBdM. G. K.Book Review: booktitle Duodecimal Arithmetic, by George S. TerryjJRSTATSOC10222993001939http://dx.doi.org/10.2307/2980013Sat Jan 24 11:18:08 MST 2015http://www.jstor.org/stable/i349540; http://www.math.utah.edu/pub/{chine for the solution of large systems of
linear algebraic equations",
type = "Unpublished memorandum",
institution = "Iowa State College",
address = "Ames, IA, USA",
month = aug,
year = "1940",
bibdate = "Wed Oct 13 11:36:11 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.2]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
}#1940:CMSJ. V. AtanasoffComputing machine for the solution of large systems of linear algebraic equationsUnpublished memorandumIowa State CollegeAmes, IA, USA299300aug81940Wed Oct 13 11:36:11 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:36:11 ???Reprinted in cite [ 7.2]Randell:1982:ODC.acknhfbJ. V. AtanasoffReprinted in \cite[\S 7.2]{Randell:1982:ODC}.Computing machine for the solution of large systems of linear algebraic equations
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title = "Computing machine for the solution of large systems of
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type = "Unpublished memorandum",
institution = "Iowa State College",
address = "Ames, IA, USA",
month = aug,
year = "1940",
bibdate = "Wed Oct 13 11:36:11 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.2]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
}ished = "Vannevar Bush Papers, Container 18, Folder: Caldwell,
Samuel, 19391940",
year = "1940",
bibdate = "Wed Oct 13 11:37:32 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.3]{Randell:1982:ODC}.
Copyright interest in the unpublished writings of
Vannevar Bush has been dedicated to the public.",
acknowledgement = acknhfb,
}$ww.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.acknhfbVannevar Bush Papers, Container 18, Folder: Caldwell, Samuel, 19391940V. 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, 19391940",
year = "1940",
bibdate = "Wed Oct 13 11:37:32 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.3]{Randell:1982:ODC}.
Copyright interest in the unpublished writings of
Vannevar Bush has been dedicated to the public.",
acknowledgement = acknhfb,
}= "Unpublished memorandum",
institution = "Bell Telephone Laboratories",
address = "New York, NY, USA",
year = "1940",
bibdate = "Wed Oct 13 11:30:38 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.1]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
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w%U !#)'9C/=m;_'gtechreportfparith.bibStibitz:1940:CG. R. StibitzComputerUnpublished memorandumBell Telephone LaboratoriesNew York, NY, USA2993001940Wed Oct 13 11:30:38 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:30:38 ???Reprinted in cite [ 6.1]Randell:1982:ODC.acknhfbG. 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 = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.1]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
}of electrical data recording and reading
mechanism",
type = "{M.S.} thesis",
school = "Iowa State College",
address = "Ames, IA, USA",
pages = "32",
year = "1941",
bibdate = "Thu Nov 18 11:18:18 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
authordates = "19181963",
historicalnote = "From
http://www.lib.iastate.edu/arch/rgrp/5211.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 WisconsinMadison. He returned to
Iowa State in 1930 as Assistant Professor in
mathematics and physics and was promoted to Associate
Professor (1936). Atanasoff began developing concepts
for an electronic computing machine in 1937. It was
shortly thereafter that he, along with graduate student
Clifford Berry, started work on the world's first
electronic digital computer. The computer would later
be named the AtanasoffBerry 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 19671973. 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 AtanasoffBerry 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 oneofakind ABC
was destroyed in 1948, and most of its parts were lost.
Also cited in ``Charles W. Bradley Collection on the
ENIAC Trial, 19301966'', (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 50bit word.",
}&ard BerryDesign of electrical data recording and reading mechanismM.S. thesisIowa State CollegeAmes, IA, USA321941Thu Nov 18 11:18:18 2010http://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 oneofakind ABC was destroyed in 1948, and most of its parts were lost. Also cited in ``Charles W. Bradley Collection on the ENIAC Trial, 19301966'', (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 50bit word.acknhfb19181963Clifford 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 = "Ames, IA, USA",
pages = "32",
year = "1941",
bibdate = "Thu Nov 18 11:18:18 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
authordates = "19181963",
historicalnote = "From
http://www.lib.iastate.edu/arch/rgrp/5211.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 WisconsinMadison. He returned to
Iowa State in 1930 as Assistant Professor in
mathematics and physics and was promoted to Associate
Professor (1936). Atanasoff began developing concepts
for an electronic computing machine in 1937. It was
shortly thereafter that he, along with graduate student
Clifford Berry, started work on the world's first
electronic digital computer. The computer would later
be named the AtanasoffBerry 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 19671973. 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 AtanasoffBerry 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 oneofakind ABC
was destroyed in 1948, and most of its parts were lost.
Also cited in ``Charles W. Bradley Collection on the
ENIAC Trial, 19301966'', (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 50bit word.",
}
q&'W #1/i/57E;SkW/i]articlefparith.bibLancaster:1942:MMEOtis E. LancasterMachine Method for the Extraction of Cube RootjJAMSTATASSOC37217112115mar31942JSTNAL01621459 (print), 1537274X (electronic) OR 01621459 (print), 1537274X (electronic)01621459 OR 01621459Wed Jan 25 08:05:24 MST 2012http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314096; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib2012.01.25 08:05:24 MSThttp://www.jstor.org/stable/2279437Journal of the American Statistical Associationacknhfbhttp://www.tandfx&V '#)7#1'=m;!7kmastersthesisfparith.bibBerry:1941:DEDClifford Edwd for the Extraction of Cube Root",
journal = jJAMSTATASSOC,
volume = "37",
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pages = "112115",
month = mar,
year = "1942",
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bibdate = "Wed Jan 25 08:05:24 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314096;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
URL = "http://www.jstor.org/stable/2279437",
acknowledgement = acknhfb,
fjournal = "Journal of the American Statistical Association",
journalURL = "http://www.tandfonline.com/loi/uasa20",
}'
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@Article{Alam:1993:RTO,
author = "M. S. Alam and M. A. Karim",
title = "RealTime'O
@Article{AlTwaijry:1998:TSE,
author = "H. A. AlTwaijry and M. J. Flynn",
title = 3e5
@Article{AlTwaijry:1998:SPB,
author = "H. A. AlTwaijry and S. F. Oberman and S. T. Fu an3a
@Article{AlMouhamed:1995:ELF,
author = "Mayez AlMouhamed and Lubomir Bic",
title = 
@Article{Akleylek:2012:MRR,
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title = Q8
@Article{Akishita:2001:FSS,
author = "Toru Akishita",
title = "Fast Simultaneous 9qc
@Article{AlMohy:2012:MAB,
author = "Awad H. AlMohy",
title = "A more accurate {Q;>}
@Article{Alexander:1977:SRR,
author = "V. L. Alexander",
title = "Square Root Rou#G
@Article{Aldous:2010:WCO,
author = "David Aldous and Tung Phan",
title = "When CaMonline.com/loi/uasa20Otis E. LancasterMachine Method for the Extraction of Cube Root
@Article{Lancaster:1942:MME,
author = "Otis E. Lancaster",
title = "Machine Method for the Extraction of Cube Root",
journal = jJAMSTATASSOC,
volume = "37",
number = "217",
pages = "112115",
month = mar,
year = "1942",
CODEN = "JSTNAL",
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bibdate = "Wed Jan 25 08:05:24 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314096;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
URL = "http://www.jstor.org/stable/2279437",
acknowledgement = acknhfb,
fjournal = "Journal of the American Statistical Association",
journalURL = "http://www.tandfonline.com/loi/uasa20",
}speed vacuum tube devices for
calculating",
type = "Privately circulated memorandum",
institution = "Moore School of Electrical Engineering, University of
Pennsylvania",
address = "Philadelphia, PA, USA",
month = aug,
year = "1942",
bibdate = "Wed Oct 13 11:52:54 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.6]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
}(calculatingPrivately circulated memorandumMoore School of Electrical Engineering, University of PennsylvaniaPhiladelphia, PA, USA112115aug81942Wed Oct 13 11:52:54 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:52:54 ???Reprinted in cite [ 7.6]Randell:1982:ODC.acknhfbJ. W. MauchlyReprinted in \cite[\S 7.6]{Randell:1982:ODC}.The use of high speed vacuum tube devices for calculating
@TechReport{Mauchly:1942:UHS,
author = "J. W. Mauchly",
title = "The use of high speed vacuum tube devices for
calculating",
type = "Privately circulated memorandum",
institution = "Moore School of Electrical Engineering, University of
Pennsylvania",
address = "Philadelphia, PA, USA",
month = aug,
year = "1942",
bibdate = "Wed Oct 13 11:52:54 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.6]{Randell:1982:ODC}.",
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]B]k*Y #//357E
;G/marticlefparith.bibCrawford:1943:DNSW. S. H. CrawfordDiscussions and Notes: Square Roots from a Table of CosinesjAMERMATHMONTHLY503190191mar31943AMMYAE00029890 (print), 19300972 (electronic) OR 00029890 (print), 19300972 (electronic)00029890 OR 00029890Mon Jun 28 12:36:d)X!#/k +m_kg Qtechreportfpar3(V !#'K7=m;_'g]techreportfparith.bibMauchly:1942:UHSJ. W. MauchlyThe use of high speed vacuum tube devices for
title = "Report on Electronic Predictors for AntiAircraft Fire
Control",
institution = "Research Laboratories, R. C. A. Manufacturing Company,
Inc.",
address = "Camden, NJ, USA",
month = apr,
year = "1942",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.4]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
})ith.bibRajchman:1942:REPJ. A. Rajchman and G. A. Morton and A. W. VanceReport on Electronic Predictors for AntiAircraft Fire ControlResearch Laboratories, R. C. A. Manufacturing Company, Inc.Camden, NJ, USA112115apr41942http://www.math.utah.edu/pub/tex/bib/fparith.bibReprinted in cite [ 7.4]Randell:1982:ODC.acknhfbJ. A. Rajchman and G. A. Morton and A. W. VanceReprinted in \cite[\S 7.4]{Randell:1982:ODC}.Report on Electronic Predictors for AntiAircraft Fire Control
@TechReport{Rajchman:1942:REP,
author = "J. A. Rajchman and G. A. Morton and A. W. Vance",
title = "Report on Electronic Predictors for AntiAircraft Fire
Control",
institution = "Research Laboratories, R. C. A. Manufacturing Company,
Inc.",
address = "Camden, NJ, USA",
month = apr,
year = "1942",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.4]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
}d Notes: Square Roots from a Table of
Cosines",
journal = jAMERMATHMONTHLY,
volume = "50",
number = "3",
pages = "190191",
month = mar,
year = "1943",
CODEN = "AMMYAE",
ISSN = "00029890 (print), 19300972 (electronic)",
ISSNL = "00029890",
bibdate = "Mon Jun 28 12:36:57 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = acknhfb,
fjournal = "American Mathematical Monthly",
journalURL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}*57 MDT 1999http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1999.06.28 12:36:57 MDTAmerican Mathematical Monthlyacknhfbhttp://www.jstor.org/page/journal/amermathmont/about.htmlW. S. H. CrawfordDiscussions and Notes: Square Roots from a Table of Cosines
@Article{Crawford:1943:DNS,
author = "W. S. H. Crawford",
title = "Discussions and Notes: Square Roots from a Table of
Cosines",
journal = jAMERMATHMONTHLY,
volume = "50",
number = "3",
pages = "190191",
month = mar,
year = "1943",
CODEN = "AMMYAE",
ISSN = "00029890 (print), 19300972 (electronic)",
ISSNL = "00029890",
bibdate = "Mon Jun 28 12:36:57 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = acknhfb,
fjournal = "American Mathematical Monthly",
journalURL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}ignificant Figures of Numbers in Statistical Tables",
journal = jNATURE,
volume = "154",
number = "3921",
pages = "800801",
day = "23",
month = dec,
year = "1944",
CODEN = "NATUAS",
DOI = "http://dx.doi.org/10.1038/154800a0",
ISSN = "00280836 (print), 14764687 (electronic)",
ISSNL = "00280836",
bibdate = "Sun Sep 18 11:57:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf",
abstract = "A rough qualitative explanation of this fact can
easily be given. If we consider tables in which the
entries become rarer the larger they are, we can draw
the obvious conclusion that in any interval, say,
between 10 and 99, or 10,000 and 99,999, there are more
entries on the small side than on the large side.",
acknowledgement = acknhfb,
fjournal = "Nature",
journalURL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}+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 Lawacknhfbhttp://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
@Article{Goudsmit:1944:SFN,
author = "S. A. Goudsmit and W. H. Furry",
title = "Significant Figures of Numbers in Statistical Tables",
journal = jNATURE,
volume = "154",
number = "3921",
pages = "800801",
day = "23",
month = dec,
year = "1944",
CODEN = "NATUAS",
DOI = "http://dx.doi.org/10.1038/154800a0",
ISSN = "00280836 (print), 14764687 (electronic)",
ISSNL = "00280836",
bibdate = "Sun Sep 18 11:57:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf",
abstract = "A rough qualitative explanation of this fact can
easily be given. If we consider tables in which the
entries become rarer the larger they are, we can draw
the obvious conclusion that in any interval, say,
between 10 and 99, or 10,000 and 99,999, there are more
entries on the small side than on the large side.",
acknowledgement = acknhfb,
fjournal = "Nature",
journalURL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
_+Y#/IuQ57=m;
ysWyIu?articlefparith.bibGoudsmit:1944:SFNS. A. Goudsmit and W. H. FurrySignificant Figures of Numbers in Statistical TablesjNATURE154392180080123dec121944NATUAShttp://dx.doi.org/10.1038/154800a000280836 (print), 14764687 (electronic) OR 00280836 (print), 14764687 (electronic)00280836 OR 00280836Sun Sep 18 11:57:19 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib2011.09.18 11:57:19 ???http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdfA rough qualitative explanation of this fact can easily be given. If ibution of Numbers and Distribution of
Significant Figures",
journal = jNATURE,
volume = "155",
number = "??",
pages = "5253",
day = "13",
month = jan,
year = "1945",
CODEN = "NATUAS",
DOI = "http://dx.doi.org/10.1038/155052a0",
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ISSNL = "00280836",
bibdate = "Sun Sep 18 11:51:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf",
acknowledgement = acknhfb,
fjournal = "Nature",
journalURL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
},com/nature/archive/W. H. Furry and Henry HurwitzDistribution of Numbers and 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 = jNATURE,
volume = "155",
number = "??",
pages = "5253",
day = "13",
month = jan,
year = "1945",
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DOI = "http://dx.doi.org/10.1038/155052a0",
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bibdate = "Sun Sep 18 11:51:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf",
acknowledgement = acknhfb,
fjournal = "Nature",
journalURL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
q,Y#)GQ57=m;
sWG'articlefparith.bibFurry:1945:DNDW. H. Furry and Henry HurwitzDistribution of Numbers and Distribution of Significant FiguresjNATURE155525313jan11945NATUAShttp://dx.doi.org/10.1038/155052a000280836 (print), 14764687 (electronic) OR 00280836 (print), 14764687 (electronic)00280836 OR 00280836Sun Sep 18 11:51:37 2011http://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 Lawacknhfbhttp://www.nature.EDVAC}",
institution = "University of Pennsylvania",
day = "30",
month = jun,
year = "1945",
bibdate = "Mon Jun 06 19:17:03 2005",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
remark = "This is the report that got von Neumann's name
associated with the serial, storedprogram, 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 W670ORD4926. Reprinted in
\cite[pp.~177246]{Stern:1981:EUA},
\cite[pp.~399413]{Randell:1982:ODC},
\cite{vonNeumann:1993:FDR}, and
\cite{Laplante:1996:GPC}.",
}{EDVAC}",
institution = "University of Pennsylvania",
day = "30",
month = jun,
year = "1945",
bibdate = "Mon Jun 06 19:17:03 2005",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
remark = "This is the report that got von Neumann's name
associated with the serial, storedprogram, 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 W670ORD4926. Reprinted in
\cite[pp.~177246]{Stern:1981:EUA},
\cite[pp.~399413]{Randell:1982:ODC},
\cite{vonNeumann:1993:FDR}, and
\cite{Laplante:1996:GPC}.",
}
GW !#3UA= ;_ugYutechreportfparith.bibvonNeumann:1945:FDRJohn von NeumannFirst Draft of a Report on the EDVACUniversity of Pennsylvania525330jun61945Mon Jun 06 19:17:03 2005ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib; http://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, storedprogram, general purpose, digital architecture upon which 99.99% of all computers today are based.acknhfbJohn von NeumannReprinted in \cite[\S 8.2]{Randell:1982:ODC}.First Draft of a Report on the {EDVAC}
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bibdate = "Thu Nov 8 14:49:46 2007",
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booktitle = "Proceedings of the AIEEIRE '51: Papers and
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pages = "3540",
month = feb,
year = "1952",
CODEN = "????",
DOI = "http://dx.doi.org/10.2307/2986591",
ISSN = "14669404",
ISSNL = "14669404",
bibdate = "Thu Jan 22 18:10:18 MST 2015",
bibsource = "http://www.jstor.org/stable/i349863;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jrssd1950.bib",
URL = "http://www.jstor.org/stable/2986591",
acknowledgement = acknhfb,
fjournal = "The Incorporated Statistician",
journalURL = "http://www.jstor.org/journals/14669404.html",
}Irssd1950.bib2015.01.22 18:10:18 MSThttp://www.jstor.org/stable/2986591The Incorporated Statisticianacknhfbhttp://www.jstor.org/journals/14669404.htmlR. L. MichaelsonBinary Arithmetic
@Article{Michaelson:1952:BA,
author = "R. L. Michaelson",
title = "Binary Arithmetic",
journal = jINCSTAT,
volume = "3",
number = "1",
pages = "3540",
month = feb,
year = "1952",
CODEN = "????",
DOI = "http://dx.doi.org/10.2307/2986591",
ISSN = "14669404",
ISSNL = "14669404",
bibdate = "Thu Jan 22 18:10:18 MST 2015",
bibsource = "http://www.jstor.org/stable/i349863;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jrssd1950.bib",
URL = "http://www.jstor.org/stable/2986591",
acknowledgement = acknhfb,
fjournal = "The Incorporated Statistician",
journalURL = "http://www.jstor.org/journals/14669404.html",
}abilized Electronic Multiplier",
journal = jTRANSIREPROFGROUPELECCOMPUT,
volume = "EC1",
number = "??",
pages = "5259",
month = dec,
year = "1952",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Jul 15 15:20:53 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = acknhfb,
fjournal = "Transactions of the I.R.E. Professional Group on
Electronic Computers",
}JREPROFGROUPELECCOMPUTEC15259dec121952Fri Jul 15 15:20:53 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.15 15:20:53 ???Transactions of the I.R.E. Professional Group on Electronic ComputersacknhfbC. D. Morrill and R. V. BaumA Stabilized Electronic Multiplier
@Article{Morrill:1952:SEM,
author = "C. D. Morrill and R. V. Baum",
title = "A Stabilized Electronic Multiplier",
journal = jTRANSIREPROFGROUPELECCOMPUT,
volume = "EC1",
number = "??",
pages = "5259",
month = dec,
year = "1952",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Jul 15 15:20:53 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = acknhfb,
fjournal = "Transactions of the I.R.E. Professional Group on
Electronic Computers",
}Review of Electronic Digital Computers. Joint
{AIEEIRE} Computer Confer ence. {1012 December
1951}",
title = "The {IBM} cardprogrammed electronic calculator",
publisher = "American Institute of Electrical Engineers",
address = "New York, NY, USA",
pages = "3036",
year = "1952",
bibdate = "Wed Oct 13 11:28:45 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.4]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
}K28:45 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:28:45 ???Reprinted in cite [ 5.4]Randell:1982:ODC.acknhfbJ. W. Sheldon and L. TatumReview of Electronic Digital Computers. Joint {AIEEIRE} Computer Confer ence. {1012 December 1951}Reprinted in \cite[\S 5.4]{Randell:1982:ODC}.The {IBM} cardprogrammed electronic calculator
@InProceedings{Sheldon:1952:ICP,
author = "J. W. Sheldon and L. Tatum",
booktitle = "Review of Electronic Digital Computers. Joint
{AIEEIRE} Computer Confer ence. {1012 December
1951}",
title = "The {IBM} cardprogrammed electronic calculator",
publisher = "American Institute of Electrical Engineers",
address = "New York, NY, USA",
pages = "3036",
year = "1952",
bibdate = "Wed Oct 13 11:28:45 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.4]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
}
yKW'#AQga/=m;_AYgkIinproceedingsfparith.bibSheldon:1952:ICPJ. W. Sheldon and L. TatumReview of Electronic Digital Computers. Joint AIEEIRE Computer Confer ence. 1012 December 1951The IBM cardprogrammed electronic calculatorAmerican Institute of Electrical EngineersNew York, NY, USA30361952Wed Oct 13 11:n: Type 701 and Associated
Equipment",
publisher = pubIBM,
address = pubIBM:adr,
pages = "103",
year = "1953",
bibdate = "Wed Sep 14 23:17:49 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}L
**%MY #+%I57=m;'1e%MMarticlefparith.bibBackus:1954:ISSJ. W. BackusThe IBM 701 Speedcoding SystemjJACM114LW #%+#=m;/7bookfparith.bibIBM:1953:POTIBM CorporationPrinciples of Operation: Type 701 and Associated EquipmentpubIBMpubIBM:adr1031953Wed Sep 14 23:17:49 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.14 23:17:49 ???acknhfb{IBM Corporation}Principles of Operation: Type 701 and Associated Equipment
@Book{IBM:1953:POT,
author = "{IBM Corporation}",
title = "Principles of Operation: Type 701 and Associated
Equipment",
publisher = pubIBM,
address = pubIBM:adr,
pages = "103",
year = "1953",
bibdate = "Wed Sep 14 23:17:49 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}ing} System",
journal = jJACM,
volume = "1",
number = "1",
pages = "46",
month = jan,
year = "1954",
CODEN = "JACOAH",
ISSN = "00045411 (print), 1557735X (electronic)",
ISSNL = "00045411",
bibdate = "Fri Nov 04 00:18:27 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://community.computerhistory.org/scc/projects/FORTRAN/paper/p4backus.pdf",
abstract = "The IBM 701 Speedcoding System is a set of
instructions which causes the 701 to behave like a
threeaddress floating point calculator. Let us call
this the Speedcoding calculator. In addition to
operating in floating point, this Speedcoding
calculator has extremely convenient means for getting
information into the machine and for printing results;
it has an extensive set of operations to make the job
of programming as easy as possible. Speedcoding also
provides automatic address modification, flexible
tracing, convenient use of auxiliary storage, and
builtin checking.",
acknowledgement = acknhfb,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}M
++&Lr
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tFkcG
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author = "Mark Birman and Allen Samuels and George Chu and Chuk
]:4:8v(<y
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>h>i={
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author = "O. Amble and Jan V. Garwick",
title = "On the Accuracy of Floating Point Computers {[BIT {\bf
1}(2), 1961, pp. 8788]} OE4i
@Article{Alt:1979:SRD,
author = "H. Alt",
title = "Square Rooting Is as Difficult as Multiplication",
journal = jCOMPUTING,
volume = "21",
numbez
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author = "A. AbuElHaija and A. Peterson",
title = "okH<MkJB
@/
@Article{Arango:1966:FCP,
author = sn]
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author = "C. Ashton",
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3v/pa
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title = "Effects of input +%2e
@Article{Antelo:2012:GEI,
author = "Elisardo Antelo and David Hough and Paolo Ienne",
tiQI
@Article{Anonymous:2002:AIVf,
author = "Anonymous",
title = "Author index volume W #1[;a7E;][articlefparith.bibRothstein:1959:RBNJerome RothsteinResidues of Binary Numbers Modulo ThreejIRETRANSELECCOMPUTEC82229229jun61959IRELAOhttp://dx.doi.org/10.1109/TEC.1959.521952903679950 OR 03679950Thu Jul 14 15:56:45 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomputomputation of Square Roots Without
Using Division",
journal = jCACM,
volume = "2",
number = "11",
pages = "2324",
month = nov,
year = "1959",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Wed Jul 14 15:48:24 MDT 2004",
bibsource = "http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Sarafyan59;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See comments \cite{Traub:1960:CNM}.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Sarafyan59",
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}Division
@Article{Sarafyan:1959:NMC,
author = "Diran Sarafyan",
title = "A New Method of Computation of Square Roots Without
Using Division",
journal = jCACM,
volume = "2",
number = "11",
pages = "2324",
month = nov,
year = "1959",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
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bibdate = "Wed Jul 14 15:48:24 MDT 2004",
bibsource = "http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Sarafyan59;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See comments \cite{Traub:1960:CNM}.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Sarafyan59",
XMLdata = "ftp://ftp.informatik.unitrier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sarafyan59",
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dY #/)57E;O?c)Suarticlefparith.bibSarafyan:1959:NMCDiran SarafyanA New Method of Computation of Square Roots Without Using DivisionjCACM2112324nov111959CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Wed Jul 14 15:48:24 MDT 2004http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Sarafyan59; http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2004.07.14 15:48:24 MDTSee comments cite Traub:1960:CNM.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Diran SarafyanSee comments \cite{Traub:1960:CNM}.A New Method of Computation of Square Roots Without Using Translator Compiler of the {IBM FORTRAN
Automatic Coding System}",
journal = jCACM,
volume = "2",
number = "2",
pages = "921",
month = feb,
year = "1959",
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}idan:1959:ATC,
author = "Peter B. Sheridan",
title = "The Arithmetic Translator Compiler of the {IBM FORTRAN
Automatic Coding System}",
journal = jCACM,
volume = "2",
number = "2",
pages = "921",
month = feb,
year = "1959",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
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bibdate = "Wed Jul 14 15:48:22 MDT 2004",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
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articlefparith.bibSheridan:1959:ATCPeter B. SheridanThe Arithmetic Translator Compiler of the IBM FORTRAN Automatic Coding SystemjCACM22921feb21959CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Wed Jul 14 15:48:22 MDT 2004http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Sheridan59; http://ei.cs.vt.edu/~cs4304/bibliography.html; http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2004.07.14 15:48:22 MDTCommunications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Peter B. SheridanThe Arithmetic Translator Compiler of the {IBM FORTRAN Automatic Coding System}
@Article{Sher root of a complex number",
journal = jCOMPJ,
volume = "2",
number = "2",
pages = "8989",
month = jul,
year = "1959",
CODEN = "CMPJA6",
DOI = "http://dx.doi.org/10.1093/comjnl/2.2.89",
ISSN = "00104620 (print), 14602067 (electronic)",
ISSNL = "00104620",
bibdate = "Fri Sep 29 08:55:11 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/020089.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/tiff/89.tif",
acknowledgement = acknhfb,
fjournal = "The Computer Journal",
journalURL = "http://comjnl.oxfordjournals.org/",
}acheyOn taking the square root of a complex number
@Article{Strachey:1959:TSR,
author = "C. Strachey",
title = "On taking the square root of a complex number",
journal = jCOMPJ,
volume = "2",
number = "2",
pages = "8989",
month = jul,
year = "1959",
CODEN = "CMPJA6",
DOI = "http://dx.doi.org/10.1093/comjnl/2.2.89",
ISSN = "00104620 (print), 14602067 (electronic)",
ISSNL = "00104620",
bibdate = "Fri Sep 29 08:55:11 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/020089.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/tiff/89.tif",
acknowledgement = acknhfb,
fjournal = "The Computer Journal",
journalURL = "http://comjnl.oxfordjournals.org/",
}
_X #/#g[57Em;E5O#g!articlefparith.bibStrachey:1959:TSRC. StracheyOn taking the square root of a complex numberjCOMPJ228989jul71959CMPJA6http://dx.doi.org/10.1093/comjnl/2.2.8900104620 (print), 14602067 (electronic) OR 00104620 (print), 14602067 (electronic)00104620 OR 00104620Fri Sep 29 08:55:11 MDT 2000http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/2000.09.29 08:55:11 MDThttp://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.tifThe Computer Journalacknhfbhttp://comjnl.oxfordjournals.org/C. Str with Fixed Decimal Precision, of a
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journal = jCACM,
volume = "2",
number = "7",
pages = "2727",
month = jul,
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bibdate = "Mon Jan 22 07:25:37 MST 2001",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
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acknowledgement = acknj,
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}Taranto:1959:BCF,
author = "Donald Taranto",
title = "Binary Conversion, with Fixed Decimal Precision, of a
Decimal Fraction",
journal = jCACM,
volume = "2",
number = "7",
pages = "2727",
month = jul,
year = "1959",
CODEN = "CACMA2",
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bibdate = "Mon Jan 22 07:25:37 MST 2001",
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acknowledgement = acknj,
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TV #+%e;7;K;]%i]articlefparith.b܍kY #)57EK;?Oc)articlefparith.bibTaranto:1959:BCFDonald TarantoBinary Conversion, with Fixed Decimal Precision, of a Decimal FractionjCACM272727jul71959CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Mon Jan 22 07:25:37 MST 2001ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Taranto59; http://www.math.utah.edu/pub/tex/bib/fparith.bib2001.01.22 07:25:37 MSTCommunications of the ACMdecimal floatingpoint arithmeticacknjhttp://portal.acm.org/browse_dl.cfm?idx=J79Donald TarantoBinary Conversion, with Fixed Decimal Precision, of a Decimal Fraction
@Article{etric Computing Technique",
journal = jIRETRANSELECCOMPUT,
volume = "EC8",
number = "5",
pages = "330334",
month = sep,
year = "1959",
CODEN = "IRELAO",
ISSN = "03679950",
bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "IRE Transactions on Electronic Computers",
}ibVolder:1959:CTCJ. E. VolderThe CORDIC Trigonometric Computing TechniquejIRETRANSELECCOMPUTEC85330334sep91959IRELAO03679950 OR 03679950Thu Sep 1 10:15:31 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:31 ???IRE Transactions on Electronic ComputersacknjJ. E. VolderThe {CORDIC} Trigonometric Computing Technique
@Article{Volder:1959:CTC,
author = "J. E. Volder",
title = "The {CORDIC} Trigonometric Computing Technique",
journal = jIRETRANSELECCOMPUT,
volume = "EC8",
number = "5",
pages = "330334",
month = sep,
year = "1959",
CODEN = "IRELAO",
ISSN = "03679950",
bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "IRE Transactions on Electronic Computers",
}ytical Iterative Processes",
journal = jCOMPJ,
volume = "1",
number = "4",
pages = "163167",
month = jan,
year = "1959",
CODEN = "CMPJA6",
ISSN = "00104620 (print), 14602067 (electronic)",
ISSNL = "00104620",
bibdate = "Fri Sep 29 08:55:07 MDT 2000",
bibsource = "Compiler/semantics.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/010163.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/163.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/164.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/165.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/166.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/167.tif",
acknowledgement = acknhfb,
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txK
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YY #+%57E5;??c%Ccarticlefparith.bibErcoli:1960:LEEPaolo ErcoliLetter to the Editor: Errors Due to Overflow in Arithmetic OperationsjCACM312A9A9dec121960CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Fri Nov 25 18:19:29 MST 2005http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:29 MSTSee cite Ercoli:1957:EDO.Communications of the ACMacknhfbhttp://porion Process for Digital
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(August 1961), 355 \cite{Knuth:1961:EIN}. See
\cite{Nadler:1961:DSR} for extension to division and
square root.",
abstract = "For centuries the decimal number system reigned
supreme, except, perhaps, among the Mayan Indians,
until the advent of digital computers brought the
binary and octal systems into the limelight. This paper
introduces another number system which may prove useful
for manipulating complex numbers on machines.",
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abstract = "For centuries the decimal number system reigned
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abstract = "Three types of floatingpoint arithmetics with error
control are discussed and compared with conventional
floatingpoint arithmetic. General multiplication and
division shift criteria are derived (for any base) for
Metropolisstyle arithmetics. The limitations and most
suitable range of application for each arithmetic are
discussed.",
acknowledgement = acknhfb,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
reviewer = "C. B. Haselgrove",
xxmonth = "none",
xxnumber = "none",
}e discussed and compared with conventional floatingpoint arithmetic. General multiplication and division shift criteria are derived (for any base) for Metropolisstyle arithmetics. The limitations and most suitable range of application for each arithmetic are discussed.Journal of the ACMCited in cite Sterbenz:1974:FPC.acknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401C. B. HaselgroveThree types of floatingpoint arithmetics with error control are discussed and compared with conventional floatingpoint arithmetic. General multiplication and division shift criteria are derived (for any base) for Metropolisstyle arithmetics. The limitations and most suitable range of application for each arithmetic are discussed.W. G. WadeyFloatingPoint Arithmetics
@Article{Wadey:1960:FA,
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abstract = "Three types of floatingpoint arithmetics with error
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floatingpoint arithmetic. General multiplication and
division shift criteria are derived (for any base) for
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acknowledgement = acknhfb,
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T T@W #1+e!577=;7U+emarticlefparith.bibWilkinson:1960:EAFJ. H. WilkinsonError Analysis of FloatingPoint ComputationjNUMMATH2319340dec121960NUMMA70029599X (print), 09453245 (electronic) OR 0029599X (print), 09453245 (electronic)0029599X OR 0029599X65.00MR0116477 (22 \#7264)C. B. HaselgroveFri May 14 17:18:08 2010http://www.math.utah.edu/pub/bibnet/authors/w/wilkinsonjameshaP,X #'#A57'=m;)1Me)#A
articlefparith.bibWadey:1960:FAW. G. WadeyFloatingPoint ArithmeticsjJACM72129139apr41960JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 0004541165.00 (68.00)22\#6090Fri Dec 08 14:44:46 1995http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 14:44:46 ???Three types of floatingpoint arithmetics with error control arof FloatingPoint Computation",
journal = jNUMMATH,
volume = "2",
pages = "319340",
month = dec,
year = "1960",
CODEN = "NUMMA7",
ISSN = "0029599X (print), 09453245 (electronic)",
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MRclass = "65.00",
MRnumber = "MR0116477 (22 \#7264)",
MRreviewer = "C. B. Haselgrove",
bibdate = "Fri May 14 17:18:08 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinsonjameshardy.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Numerische Mathematik",
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DOI = "http://dx.doi.org/10.1007/BF01933434",
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bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=00063835&volume=1&issue=3;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
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note = "See \cite{Garwick:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=1&issue=3&spage=220",
acknowledgement = acknhfb,
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number = "16",
institution = "National Physical Laboratory",
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year = "1961",
bibdate = "Fri Aug 20 10:05:25 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
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OO/U !#1==E[=m;M= techreportfparith.bibAnonymous:1961:MCMAnonymousModern Computing MethodsNotes on Applied Science16National Physical LaboratoryHer Majesty's Stationery Office, London2202221961Fri Aug 20 10:05:25 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.08.20 10:05:25 ???Cited in cite Sterbenz:1974:FPC.acknhfbAnonymousModern Computing Methods
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@Article{Boldo:2011:EAE,
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@Article{Boldo:2011:FVN,
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@Article{Boley:1995:FPF,
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@Article{Bomar:1995:RNA,
author = "B. W. Bomar and L. M. Smith and R. D. Joseph",
title U
@Article{Brakefield:1972:OFP,
author = "James C. Brakefield",
title 7
@Article{Boldo:2009:KAC,
author = "S. Boldo",
title = "{Kahan}'s Algorithm for a Kwo
@Article{Boldo:2009:FVA,
author = "S. Boldo and M. Daumas and RenCang Li",
title = KF
@Article{Bollen:1984:NSD,
author = "J. A. M. Bollen",
title = "Numerical Stabilitwo
@Article{Boldo:2008:EFC,
author = "Sylvie Boldo and Guillaume Melquiond",
title = "Emulation of a {FMA} aJ219227IRE Transactions on Electronic ComputersacknhfbAlgirdas Avi{\v{z}}ienisSignedDigit Number Representations for Fast Parallel Arithmetic
@Article{Avizienis:1961:SDN,
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Arithmetic",
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10Y #11
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volume = "EC10",
number = "1",
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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, analogtoresidue conversion, logical
design of the arithmetic units, residuetoanalog
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 = acknhfb,
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}igation include sampling, analogtoresidue conversion, logical design of the arithmetic units, residuetoanalog 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 ComputersacknhfbA system design for a digital correlator based on the application of the residue number system for computation is presented. Areas of investigation include sampling, analogtoresidue conversion, logical design of the arithmetic units, residuetoanalog 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 resul.t 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.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
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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, analogtoresidue conversion, logical
design of the arithmetic units, residuetoanalog
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
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=!2V #/)c57=m;?c)carticlefparith.bibClarkson:1961:DMIW. K. ClarksonA Divisionless Method of Inte1/1Y #+5{;a7E;=]=5{7articlefparith.bibCheney:1961:DCBPhilip Warren CheneyA Digital Correlator Based on the Residue Number SystemjIRETRANSELECCOMPUTEC1016370mar31961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.521915403679950 OR 03679950Thu Jul 14 14:45:02 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://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 invest,thod of Integer Conversion",
journal = jCACM,
volume = "4",
number = "7",
pages = "315316",
month = jul,
year = "1961",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Thu Sep 08 08:14:59 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
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}ger ConversionjCACM47315316jul71961CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Thu Sep 08 08:14:59 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.08 08:14:59 ???Communications of the ACMacknjhttp://portal.acm.org/browse_dl.cfm?idx=J79W. K. ClarksonA Divisionless Method of Integer Conversion
@Article{Clarkson:1961:DMI,
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title = "A Divisionless Method of Integer Conversion",
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}Multiple Precision Arithmetic",
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bibdate = "Thu Sep 15 18:36:06 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
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@Article{Cox:1961:NMP,
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title = "A Note on Multiple Precision Arithmetic",
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RR4Y #'%];a7E;]%]articlefparith.bibCroy:1961:RTMJohn E. CroyRapid Technique of Manual or Machine BinarytoDecimal Integer Conversion Using Decimal Radix ArithmeticjIRETRANSELECCOMPUTEC104777777dec121961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.521928603679950 OR 03679950Thu Jul 14 14:45:05 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://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 Computersackn63W#%A[57=K;?cA[articlefparith.bibCox:1961:NMPA. G. Cox and H. A. LutherA Note on Multiple Precision ArithmeticjCACM48353aug81961CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (3al or Machine BinarytoDecimal
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bibdate = "Thu Jul 14 14:45:05 MDT 2011",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
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}hfbJohn E. CroyRapid Technique of Manual or Machine BinarytoDecimal Integer Conversion Using Decimal Radix Arithmetic
@Article{Croy:1961:RTM,
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title = "Rapid Technique of Manual or Machine BinarytoDecimal
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}s of certain binary division
algorithms",
journal = jIREPROC,
volume = "49",
number = "1",
pages = "91103",
month = jan,
year = "1961",
bibdate = "Mon Sep 16 16:12:21 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acksfo # " and " # acknhfb,
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.",
}bibFreiman:1961:SACC. V. FreimanStatistical analysis of certain binary division algorithmsjIREPROC49191103jan11961Mon Sep 16 16:12:21 2002http://www.math.utah.edu/pub/tex/bib/fparith.bib2002.09.16 16:12:21 ???IRE ProceedingsacksfoC. 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 = jIREPROC,
volume = "49",
number = "1",
pages = "91103",
month = jan,
year = "1961",
bibdate = "Mon Sep 16 16:12:21 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acksfo # " and " # acknhfb,
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.",
}
T7Z #)]I)U57C;
IqY)]{articlefpariDg6\!#+[U51=m;#yy[Uw
techreportfparith.bibGarner:1961:=[5W #'!=m;+'
articlefparith.8;C.
G. Brockus and R. J. Gonzalez and D. P. Rozenberg",
title = "Residue number systems for computers",
type = "{ASD} Technical Report",
number = "61483",
institution = "Electronic Technology Laboratory, The University of
Michigan",
address = "Ann Arbor, MI, USA",
month = oct,
year = "1961",
bibdate = "Thu Nov 18 09:27:06 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txt",
abstract = "The purpose of the research performed under this
contract was to investigate the feasibility of residue
number systems in their applications to digital
computers. The problems of such an application are the
ones of magnitude determination, sign determination,
overflow, scaling, and division. These problems are not
< independent, but are found to be quite interrelated. A
theoretical treatment of residue number systems is
given which lays the foundation for a unified study of
the complete problem. Treatments of an organizational
nature are given which deal with multiplication,
division, and scaling. The matter of correlating the
theoretical and organizational studies to physical
realizations involving networks is treated also. The
question of whether the residue number system can be
successfully applied to general purpose computers is
still an open one. Their application to special purpose
machines is considered both feasible and practical.",
acknowledgement = acknhfb,
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..",
}>RNSH. 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 Report61483Electronic Technology Laboratory, The University of MichiganAnn Arbor, MI, USA91103oct101961Thu Nov 18 09:27:06 2010http://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?, 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@ supported by this contract, and led to the Ph.D..acknhfbThe 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. GarnerA and 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.
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title = "Residue number systems for computers",
type = "{ASD} Technical Report",
number = "61483",
institution = "Electronic Technology Laboratory, The University of
Michigan",
address = "Ann Arbor, MI, USA",
month = oct,
year = "1961",
bibdate = "Thu Nov 18 09:27:06 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txt",
abstract = "The purpose of the research performed under this
contract was to investigate the feasibility of residue
number systems in their applications to digitBal
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 = acknhfb,
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.
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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 = jNORDISKTIDSKRINFORMBEHAND,
volume = "1",
number = "2",
pages = "8788",
month = jun,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "http://dx.doi.org/10.1007/BF01939221",
ISSN = "00063835 (print), 15729125 (electronic)",
ISSNL = "00063835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=00063835&volume=1&issue=2;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also comment and reply
\cite{Amble:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=1&issue=2&spage=87",
acknowledgement = acknhfb,
journalURL = "http://link.springer.com/journal/10543",
keywords = "floatingpoint accuracy; floatingpoint arithmetic",
}Eth.bibGarwick:1961:AFPJan V. GarwickThe Accuracy of Floating Point ComputersjNORDISKTIDSKRINFORMBEHAND128788jun61961BITTEL, NBITABhttp://dx.doi.org/10.1007/BF0193922100063835 (print), 15729125 (electronic) OR 00063835 (print), 15729125 (electronic)00063835 OR 00063835Wed Jan 4 18:52:07 MST 2006http://springerlink.metapress.com/openurl.asp?genre=issue&issn=00063835&volume=1&issue=2; http://www.math.utah.edu/pub/tex/bib/bit.bib; http://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=00063835&volume=1&issue=2&spage=87floatingpoint accuracy; floatingpoint arithmeticacknhfbhttp://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",
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note = "See also comment and reply
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URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=1&issue=2&spage=87",
acknowledgement = acknhfb,
journalURL = "http://link.springer.com/journal/10543",
keywords = "floatingpoint accuracy; floatingpoint arithmetic",
}Accuracy of Floating Point
Computers'' [BIT {\bf 1}(3), 1961, pp. 220221]}",
journal = jNORDISKTIDSKRINFORMBEHAND,
volume = "1",
number = "3",
pages = "222222",
year = "1961",
CODEN = "BITTEL, NBITAB",
ISSN = "00063835 (print), 15729125 (electronic)",
ISSNL = "00063835",
bibdate = "Mon Nov 16 14:36:22 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Garwick:1961:AFP,Amble:1961:AFP}.",
acknowledgement = acknhfb,
journalURL = "http://link.springer.com/journal/10543",
keywords = "floatingpoint accuracy; floatingpoint arithmetic",
} V. GarwickSee \cite{Garwick:1961:AFP,Amble:1961:AFP}.Reply to {``On the Accuracy of Floating Point Computers'' [BIT {\bf 1}(3), 1961, pp. 220221]}
@Article{Garwick:1961:RAF,
author = "J. V. Garwick",
title = "Reply to {``On the Accuracy of Floating Point
Computers'' [BIT {\bf 1}(3), 1961, pp. 220221]}",
journal = jNORDISKTIDSKRINFORMBEHAND,
volume = "1",
number = "3",
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bibdate = "Mon Nov 16 14:36:22 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Garwick:1961:AFP,Amble:1961:AFP}.",
acknowledgement = acknhfb,
journalURL = "http://link.springer.com/journal/10543",
keywords = "floatingpoint accuracy; floatingpoint arithmetic",
}
[G9W '#1+oQ#]=m;?1?+sQinproceedingsfparith.bibHenderson:1961:RCED. S. HendersonProceedings of the 1961 16th ACM national meetingResidue classK8Y #'AI)57=I;_qY'cK[articlefparith.bibGarwick:1961:RAFJ. V. GarwickReply to ``On the Accuracy of Floating Point Computers'' [BIT bf 1(3), 1961, pp. 220221]jNORDISKTIDSKRINFORMBEHAND132222221961BITTEL, NBITAB00063835 (print), 15729125 (electronic) OR 00063835 (print), 15729125 (electronic)00063835 OR 00063835Mon Nov 16 14:36:22 1998http://www.math.utah.edu/pub/tex/bib/bit.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1998.11.16 14:36:22 ???See cite Garwick:1961:AFP,Amble:1961:AFP.floatingpoint accuracy; floatingpoint arithmeticacknhfbhttp://link.springer.com/journal/10543J.Gngs of the 1961 16th ACM national meeting}",
title = "Residue class error checking codes",
publisher = pubACM,
address = pubACM:adr,
pages = "132.101132.104",
year = "1961",
DOI = "http://doi.acm.org/10.1145/800029.808563",
bibdate = "Thu Aug 07 19:04:58 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Error checking codes based on residues have the
advantage over paritybased codes of monitoring
arithmetic as well as transmission operations. Codes
may be devised to detect bursttype errors, to correct
single errors in a binary arithmetic operation, to
correct burst errors and finally to correct any
singledigit error in a decimal operation.",
acknowledgement = acknhfb,
keywords = "decimal arithmetic",
}
+&L+r:u
@Book{Seife:2000:ZBD,
author = "Charles Seife",
title = "Zero: The Biography of a9f^=
@Book{Sites:1992:AAR,
editor = "Richard L. Sites and Richard Witek and others",
title = 'eE
@Book{Siewiorek:1991:AST,
author = "Daniel P. Siewiorek and Philip John {Koopman, Jr.}",
$jU
@Book{Shauman:1979:OMA,
author = "Aleksandr Mikhailovich Shauman",
title = "Osnov+
@Book{Shannon:1993:CES,
author = "Claude Elwood Shannon and N. J. A. (Neil James
*6%K
@Book{Scott:1985:CNS,
author = "Norman R. Scott",
title = "Computer Number System%
@Book{Scott:1968:OET,
author = "Th{\'e}odore G. Scott",
title = "Ordinateurs {\'ep%
@Book{Schmid:1983:DC,
author = "Hermann Schmid",
title = "Decimal Computation",
5
@Book{Schmid:1978:EDS,
author = "Hermann Schmid",
title = "{Elektronische Dezimal(L error checking codespubACMpubACM:adr132.101132.1041961http://doi.acm.org/10.1145/800029.808563Thu Aug 07 19:04:58 2008http://www.math.utah.edu/pub/tex/bib/fparith.bib2008.08.07 19:04:58 ???Error checking codes based on residues have the advantage over paritybased codes of monitoring arithmetic as well as transmission operations. Codes may be devised to detect bursttype errors, to correct single errors in a binary arithmetic operation, to correct burst errors and finally to correct any singledigit error in a decimal operation.decimal arithmeticacknhfbError checking codes based on residues have the advantage over paritybased codes of monitoring arithmetic as well as transmission operations. Codes may be devised to detect bursttype errors, to correct single errors in a binary arithmetic operation, to correct burst errors and finally to correct any singledigit 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 = pubACM,
address = pubACM:adr,
pages = "132.101132.104",
year = "1961",
DOI = "http://doi.acm.org/10.1145/800029.808563",
bibdate = "Thu Aug 07 19:04:58 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Error checking codes based on residues have the
advantage over paritybased codes of monitoring
arithmetic as well as transmission operations. Codes
may be devised to detect bursttype errors, to correct
single errors in a binary arithmetic operation, to
correct burst errors and finally to correct any
singledigit error in a decimal operation.",
acknowledgement = acknhfb,
keywords = "decimal arithmetic",
}rate Analog Multiplier and Divider",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "2",
pages = "269272",
month = jun,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219198",
ISSN = "03679950",
bibdate = "Thu Jul 14 14:45:03 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219198",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}3 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219198IRE Transactions on Electronic ComputersacknhfbE. 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",
journal = jIRETRANSELECCOMPUT,
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o;W #)+Y57=S;=?c+A]warticlefparith.bibKnuth:1961:EINDonald E. KnuthErrata: ``An imaginary number system''jCACM48355355aug81961CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Tue Jan 09 07:10:22 1996http://www.math.utah.edu/pub/tex/bib/cacQ`:W#+A_;a7E;]A_articlefparith.bibKettel:1961:AAME. Kettel and W. SchneiderAn Accurate Analog Multiplier and DividerjIRETRANSELECCOMPUTEC102269272jun61961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.521919803679950 OR 03679950Thu Jul 14 14:45:03 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:0Nnary number system''}",
journal = jCACM,
volume = "4",
number = "8",
pages = "355355",
month = aug,
year = "1961",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Tue Jan 09 07:10:22 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1960:INS}.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}m1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.01.09 07:10:22 ???See cite Knuth:1960:INS.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Donald 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 = jCACM,
volume = "4",
number = "8",
pages = "355355",
month = aug,
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bibdate = "Tue Jan 09 07:10:22 1996",
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note = "See \cite{Knuth:1960:INS}.",
acknowledgement = acknhfb,
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}{HallEffect} Analog Multiplier",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "3",
pages = "512515",
month = sep,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219240",
ISSN = "03679950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219240",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}14:45:04 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219240IRE Transactions on Electronic ComputersacknhfbG. Kovatch and W. E. MeserveThe {HallEffect} Analog Multiplier
@Article{Kovatch:1961:HEA,
author = "G. Kovatch and W. E. Meserve",
title = "The {HallEffect} Analog Multiplier",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "3",
pages = "512515",
month = sep,
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bibdate = "Thu Jul 14 14:45:04 MDT 2011",
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acknowledgement = acknhfb,
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}
TU #1+_!=m;]++a_articlefparith.bibMacSorley:1961:HSAO. L. MacSorleyHighspeed arithmetic in binary computersjIREPROC496791jan11961Sat May 18 14:34:55 2002http://www.math.utah.edu/pub/tex/bib/fparith.bib2002.05.18 14:34:55 ???Reprinted in cite Swartzlander:1976:CDD.IRE ProceedingsacknhfbO. L. MacSorleyReprinted in \cite{Swartzlander:1976:CDD}.Highspeed arithmetic in binary computers
@Article{MacSorley:1961:HSA,
author = "O. L. MacSorley",
title = "Highspeed arithmetic in binary computers",
journal = jIREPROC,
volume = "49",
number = "??",
pages = "6791",
month = jan,
year = "1961",
bibdate = "Sat May 18 14:34:55 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite{Swartzlander:1976:CDD}.",
acknowledgement = acknhfb,
fjournal = "IRE Proceedings",
}root in the quaterimaginary
number system",
journal = jCACM,
volume = "4",
number = "4",
pages = "192193",
month = apr,
year = "1961",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
MRclass = "65.99",
MRnumber = "23\#B555",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1960:INS}.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$\sqrt(x)$; elementary functions",
ZMreviewer = "C. B. Haselgrove",
}ber system
@Article{Nadler:1961:DSR,
author = "Morton Nadler",
title = "Division and square root in the quaterimaginary
number system",
journal = jCACM,
volume = "4",
number = "4",
pages = "192193",
month = apr,
year = "1961",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
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MRnumber = "23\#B555",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1960:INS}.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
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ZMreviewer = "C. B. Haselgrove",
}
?Y #+' 57E5;=?Mc'A qarticlefparith.bibNadler:1961:DSRMorton NadlerDivision and square root in the quaterimaginary number systemjCACM44192193apr41961CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 0001078265.9923\#B555Fri Nov 25 18:19:32 MST 2005http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:32 MSTSee cite Knuth:1960:INS.Communications of the ACM$sqrt (x)$; elementary functionsacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Morton NadlerSee \cite{Knuth:1960:INS}.Division and square root in the quaterimaginary num[^ "12231230",
month = dec,
year = "1961",
CODEN = "AASTAD",
ISSN = "00034851",
bibdate = "Thu Feb 15 15:07:57 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=00034851%28196112%2932%3A4%3C1223%3AOTDOFS%3E2.0.CO%3B2T",
abstract = "It has been noticed by astute observers that well used
tables of logarithms are invariably dirtier at the
front than at the back. Upon reflection one is led to
inquire whether there are more physical constants with
low order first significant digits than high. Actual
counts by Benford [2] show that not only is this the
case but that it seems to be an empirical truth that
whenever one has a large body of physical data,
Farmer's Almanac, Census Reports, Chemical Rubber
Handbook, etc., the proportion_ of these data with first
significant digit $n$ or less is approximately $
\log_{10}(n + 1) $. Any reader formerly unaware of this
``peculiarity'' will find an actual sampling experiment
wondrously tantalizing. Thus, for example,
approximately $ 0.7 $ of the physical constants in the
Chemical Rubber Handbook begin with $4$ or less ($
\log_{10}(4 + 1) = 0.699 $ ). This is to be contrasted
with the widespread intuitive evaluation $ 4 / 9 $
ths.",
acknowledgement = acknhfb,
fjournal = "Annals of Mathematical Statistics",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From p. 1223: ``\ldots{} the proportion of these data
with first significant digit $n$ or less is
approximately $ \log_{10}(n + 1) $.''\par
\ldots{} ``The only distribution for first significant
digits which is invariant under scale change of the
underlying distribution is $ \log_{10}(n + 1) $.
Contrary to suspicion this is a nontrivial
mathematical result, for the variable $n$ is
discrete.''.\par
From p. 1230: ``The foregoing results bear on questions
of roundoff 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}.",
}
+Lr&+)U
@Article{Shannon:1938:SAR,
author = "Claude E. Shannon",
title = "A Symbolic Analr<y
@Article{Shanks:1962:CD,
author = "Daniel Shanks and John W. {Wrench, Jr.}",
title = fM
@Article{Shaham:1972:NDA,
author = "Z. Shaham and Z. Riesel",
title = "A Note on 2/
@Article{Shah:1985:PHS,
author = "A. Shah and M. SidAhmed and G. Jullien",
title = !C
@Article{Sharp:1993:PRN,
author = "W. E. Sharp and Carter Bays",
title = "A porta*9W/
@Article{Shaeffer:1991:HEP,
author = "D. L. Shaeffer and J. R. Kimbrough and S. M. Denton
$^=
@Article{Seznec:1992:OFC,
author = "A. Seznec and K. Courtel",
title = "{OPAC}: a'^m[
@Article{Shand:1991:HSL,
author = "M. Shand and P. Bertin and J. Vuillemin",
title = $9
@Article{Shary:1999:OEG,
author = "S. P. Shary",
title = "Outer Estimation of Gen7b. Upon reflection one is led to inquire whether there are more physical constants with low order first significant digits than high. Actual counts by Benford [2] show that not only is this the case but that it seems to be an empirical truth that whenever one has a large body of physical data, Farmer's Almanac, Census Reports, Chemical Rubber Handbook, etc., the proportion of these data with first significant digit $n$ or less is approximately $ log _10(n + 1) $. Any reader formerly unaware of this ``peculiarity'' will find an actual sampling experiment wondrously tantalizing. Thus, for example, approximately $ 0.7 $ of the physical constants in the Chemical Rubber Handbook begin with $4$ or less ($ log _10(4 + 1) = 0.699 $ ). This is to be contrasted with the widespread intuitive evaluation $ 4 / 9 $ ths.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(nc + 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 nontrivial mathematical result, for the variable $n$ is discrete.''.par From p. 1230: ``The foregoing results bear on questions of roundoff 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.acknhfbIt 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 dlow order first significant digits than high. Actual counts by Benford [2] show that not only is this the case but that it seems to be an empirical truth that whenever one has a large body of physical data, Farmer's Almanac, Census Reports, Chemical Rubber Handbook, etc., the proportion of these data with first significant digit $n$ or less is approximately $ \log_{10}(n + 1) $. Any reader formerly unaware of this ``peculiarity'' will find an actual sampling experiment wondrously tantalizing. Thus, for example, approximately $ 0.7 $ of the physical constants in the Chemical Rubber Handbook begin with $4$ or less ($ \log_{10}(4 + 1) = 0.699 $ ). This is to be contrasted with the widespread intuitive evaluation $ 4 / 9 $ ths.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 = jANNMATHSTAT,
volume = "32",
number = "4",
pages = e "12231230",
month = dec,
year = "1961",
CODEN = "AASTAD",
ISSN = "00034851",
bibdate = "Thu Feb 15 15:07:57 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=00034851%28196112%2932%3A4%3C1223%3AOTDOFS%3E2.0.CO%3B2T",
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 proportifon 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 = acknhfb,
fjournal = "Annals of Mathematical Statistics",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From p. 1223: ``\ldots{} the proportion of these data
with first significant digit $n$ or less is
approximately $ \log_{10}(n + 1) $.''\par
\ldots{} ``The only distribution for first significant
digits which is invariant under scale change of the
underlying distribution is $ \log_{10}(n + 1) $.
Contrary to suspicion this is a nontrivial
mathematical result, for the variable $n$ is
discrete.''.\par
From p. 1230: ``The foregoing results bear on questions
of roundoff 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}.",
}
JJmAV #3'C57=m;?c'Cuarticlefparith.bibRabinowiti@Y #k+!7=m;CmOs7uk5articlefparith.bibPinkham:1961:DFSRoger S. PinkhamOn the Distribution of First Significant DigitsjANNMATHSTAT32412231230dec121961AASTAD00034851 OR 00034851Thu Feb 15 15:07:57 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.02.15 15:07:57 ???http://links.jstor.org/sici?sici=00034851%28196112%2932%3A4%3C1223%3AOTDOFS%3E2.0.CO%3B2TIt has been noticed by astute observers that well used tables of logarithms are invariably dirtier at the front than at the backaon Division",
journal = jCACM,
volume = "4",
number = "2",
pages = "9898",
month = feb,
year = "1961",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Thu Sep 08 00:29:25 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}z:1961:MPDP. RabinowitzMultiplePrecision DivisionjCACM429898feb21961CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Thu Sep 08 00:29:25 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.08 00:29:25 ???Communications of the ACMacknjhttp://portal.acm.org/browse_dl.cfm?idx=J79P. RabinowitzMultiplePrecision Division
@Article{Rabinowitz:1961:MPD,
author = "P. Rabinowitz",
title = "MultiplePrecision Division",
journal = jCACM,
volume = "4",
number = "2",
pages = "9898",
month = feb,
year = "1961",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Thu Sep 08 00:29:25 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
} Time for Synchronous Binary
Division",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "2",
pages = "169174",
month = jun,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219186",
ISSN = "03679950",
bibdate = "Thu Jul 14 14:45:03 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219186",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219186IRE Transactions on Electronic ComputersacknhfbRoy 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 = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "2",
pages = "169174",
month = jun,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219186",
ISSN = "03679950",
bibdate = "Thu Jul 14 14:45:03 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219186",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
EE+CY #1)'57Ek;A=)M articlefparith.bibSpielberg:1961:ECFKurt SpielbergEfficient Continued Fraction Approximations To Elementary FunctionsjMATHCOMPUT1576409417oct101961MCMPAF00255718 (print), 10886842 (electronic) OR 00255718 (print), 10886842 (electronic)00255718 OR 00255718Tue Oct 13 08:06:19 MDT 1998ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; httpnxBW #){;a7E;]){?articlefparith.bibSaltman:1961:RCTRoy G. SaltmanReducing Computing Time for Synchronous Binary DivisionjIRETRANSELECCOMPUTEC102169174jun61961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.521918603679950 OR 03679950Thu Jul 14 14:45:03 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:03 MDThttp://ieeexplorekued Fraction Approximations To
Elementary Functions",
journal = jMATHCOMPUT,
volume = "15",
number = "76",
pages = "409417",
month = oct,
year = "1961",
CODEN = "MCMPAF",
ISSN = "00255718 (print), 10886842 (electronic)",
ISSNL = "00255718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = acknj # " and " # acknhfb,
fjournal = "Mathematics of Computation",
journalURL = "http://www.ams.org/mcom/",
}://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:06:19 MDTMathematics of Computationacknjhttp://www.ams.org/mcom/Kurt SpielbergEfficient Continued Fraction Approximations To Elementary Functions
@Article{Spielberg:1961:ECF,
author = "Kurt Spielberg",
title = "Efficient Continued Fraction Approximations To
Elementary Functions",
journal = jMATHCOMPUT,
volume = "15",
number = "76",
pages = "409417",
month = oct,
year = "1961",
CODEN = "MCMPAF",
ISSN = "00255718 (print), 10886842 (electronic)",
ISSNL = "00255718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = acknj # " and " # acknhfb,
fjournal = "Mathematics of Computation",
journalURL = "http://www.ams.org/mcom/",
}Power Series in Terms of
Polynomials, Rational Approximations and Continued
Fractions",
journal = jJACM,
volume = "8",
number = "4",
pages = "613627",
month = oct,
year = "1961",
CODEN = "JACOAH",
ISSN = "00045411 (print), 1557735X (electronic)",
ISSNL = "00045411",
bibdate = "Sat Dec 09 14:01:44 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}x/bib/fparith.bib1995.12.09 14:01:44 ???Journal of the ACMacknjhttp://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,
author = "K. Spielberg",
title = "Representation of Power Series in Terms of
Polynomials, Rational Approximations and Continued
Fractions",
journal = jJACM,
volume = "8",
number = "4",
pages = "613627",
month = oct,
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CODEN = "JACOAH",
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bibdate = "Sat Dec 09 14:01:44 1995",
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acknowledgement = acknj,
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journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
EX #'!O%1%=m;M!MSEbookfparith.bibTaub:1961:JNCA. H. TaubJohn von Neumann: Collected WorkspubPERGAMONpubPERGAMON:adr??? (vol. 1), 568 (vol. 2), 574 (vol. 3), 516 (vol. 4), ??? (vol. 5), ??? (vol. 6)1961s\DY #1%[57=K;1e%[Garticlefparith.bibSpielberg:1961:RPSK. SpielbergRepresentation of Power Series in Terms of Polynomials, Rational Approximations and Continued FractionsjJACM84613627oct101961JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 00045411Sat Dec 09 14:01:44 1995ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tepd Works",
publisher = pubPERGAMON,
address = pubPERGAMON:adr,
pages = "??? (vol. 1), 568 (vol. 2), 574 (vol. 3), 516 (vol.
4), ??? (vol. 5), ??? (vol. 6)",
year = "19611963",
LCCN = "????",
bibdate = "Wed Jun 01 16:58:29 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Six volumes. Volume I: Logic, Theory of Sets and
Quantum Mechanics (1961); Volume II: Operators, Ergodic
Theory and Almost Periodic Functions in a Group (1961);
Volume III: Rings of Operators (1961); Volume IV:
Continuous Geometry and Other Topics (1962); Volume V:
Design of Computers, Theory of Automata and Numerical
Analysis (1963); Volume VI: Theory of Games,
Astrophysics, Hydrodynamics and Meteorology (1963).",
acknowledgement = acknhfb,
}t  1963Wed Jun 01 16:58:29 2005http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.06.01 16:58:29 ???Six volumes. Volume I: Logic, Theory of Sets and Quantum Mechanics (1961); Volume II: Operators, Ergodic Theory and Almost Periodic Functions in a Group (1961); Volume III: Rings of Operators (1961); Volume IV: Continuous Geometry and Other Topics (1962); Volume V: Design of Computers, Theory of Automata and Numerical Analysis (1963); Volume VI: Theory of Games, Astrophysics, Hydrodynamics and Meteorology (1963).acknhfbA. H. TaubSix volumes. Volume I: Logic, Theory of Sets and Quantum Mechanics (1961); Volume II: Operators, Ergodic Theory and Almost Periodic Functions in a Group (1961); Volume III: Rings of Operators (1961); Volume IV: Continuous Geometry and Other Topics (1962); Volume V: Design of Computers, Theory of Automata and Numerical Analysis (1963); Volume VI: Theory of Games, Astrophysics, Hydrodynamics and Meteorology (1963).{John von Neumann}: Collected Works
@Book{Taub:1961:JNC,
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title = "{John von Neumann}: Collected Works",
publisher = pubPERGAMON,
address = pubPERGAMON:adr,
pages = "??? (vol. 1), 568 (vol. 2), 574 (vol. 3), 516 (vol.
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bibdate = "Wed Jun 01 16:58:29 2005",
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note = "Six volumes. Volume I: Logic, Theory of Sets and
Quantum Mechanics (1961); Volume II: Operators, Ergodic
Theory and Almost Periodic Functions in a Group (1961);
Volume III: Rings of Operators (1961); Volume IV:
Continuous Geometry and Other Topics (1962); Volume V:
Design of Computers, Theory of Automata and Numerical
Analysis (1963); Volume VI: Theory of Games,
Astrophysics, Hydrodynamics and Meteorology (1963).",
acknowledgement = acknhfb,
}Square Root Expansions for the Inverse Cosine
and Inverse Hyperbolic Cosine",
journal = jMATHCOMPUT,
volume = "15",
number = "76",
pages = "399403",
month = oct,
year = "1961",
CODEN = "MCMPAF",
ISSN = "00255718 (print), 10886842 (electronic)",
ISSNL = "00255718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = acknhfb,
fjournal = "Mathematics of Computation",
journalURL = "http://www.ams.org/mcom/",
}ue Oct 13 08:06:19 MDT 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:06:19 MDTMathematics of Computationacknhfbhttp://www.ams.org/mcom/Henry C. {Thacher, Jr.}Iterated Square Root Expansions for the Inverse Cosine and Inverse Hyperbolic Cosine
@Article{Thacher:1961:ISR,
author = "Henry C. {Thacher, Jr.}",
title = "Iterated Square Root Expansions for the Inverse Cosine
and Inverse Hyperbolic Cosine",
journal = jMATHCOMPUT,
volume = "15",
number = "76",
pages = "399403",
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sFY #75'57E
;A=;5Warticlefparith.bibThacher:1961:ISRHenry C. Thacher, Jr.Iterated Square Root Expansions for the Inverse Cosine and Inverse Hyperbolic CosinejMATHCOMPUT1576399403oct101961MCMPAF00255718 (print), 10886842 (electronic) OR 00255718 (print), 10886842 (electronic)00255718 OR 00255718TvyDomestic Electronic Digital
Computing Systems",
type = "Report",
number = "1115",
institution = "Ballistic Research Laboratories",
address = "Aberdeen Proving Ground, MD, USA",
pages = "1131",
month = mar,
year = "1961",
bibdate = "Fri Nov 28 19:37:51 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Based on the results of a third survey, the
engineering and programming characteristics of two
hundred twentytwo 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 = ackmfc # " and " # acknhfb,
}{ 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.ackmfcBased on the results of a third survey, the engineering and programming characteristics of two hundred twentytwo 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.Martin H. WeikA Third Survey of Domestic Electronic Digital Computing Systems
@TechReport{Weik:1961:TSD,
author = "Martin H. Weik",
title = "A Third Survey of Domestic Electronic Digital
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abstract = "Based on the results of a third survey, the
engineering and programming characteristics of two
hundred twentytwo different electronic digital
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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 = ackmfc # " and " # acknhfb,
}
bb
GY !#')KM=m;]])atechreportfparith.bibWeik:1961:TSDMartin H. WeikA Third Survey of Domestic Electronic Digital Computing SystemsReport1115Ballistic Research LaboratoriesAberdeen Proving Ground, MD, USA1131mar31961Fri Nov 28 19:37:51 2003http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 19:37:51 ???Based on the results of a third survey, the engineering and programming characteristics of two hundred twentytwo different electronic digital computing systems are given. The data are presented from the point of view of application, numerical and arithmetic characteristics, input,zlgorithm for Rapid Binary Division",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "4",
pages = "662670",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219271",
ISSN = "03679950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219271",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}4 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219271IRE Transactions on Electronic ComputersacknhfbJ. B. Wilson and R. S. LedleyAn Algorithm for Rapid Binary Division
@Article{Wilson:1961:ARB,
author = "J. B. Wilson and R. S. Ledley",
title = "An Algorithm for Rapid Binary Division",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "4",
pages = "662670",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219271",
ISSN = "03679950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219271",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
aHW#+GY;a7E;]GY articlefparith.bibWilson:1961:ARBJ. B. Wilson and R. S. LedleyAn Algorithm for Rapid Binary DivisionjIRETRANSELECCOMPUTEC104662670dec121961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.521927103679950 OR 03679950Thu Jul 14 14:45:04 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:0niac III} Arithmetic System",
crossref = "AFIPS:1962:APS",
pages = "192202",
year = "1962",
bibdate = "Wed Feb 14 17:14:21 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}
OIU '#3M)=m;Qcinproceedingsfparith.bibAshenhurst:1962:MIAR. L. AshenhurstThe Maniac III Arithmetic SystemAFIPS:1962:APS1922021962Wed Feb 14 17:14:21 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.02.14 17:14:21 ???acknhfbR. 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 = "192202",
year = "1962",
bibdate = "Wed Feb 14 17:14:21 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}r system: {Project Stretch}",
publisher = pubMCGRAWHILL,
address = pubMCGRAWHILL:adr,
pages = "xvii + 322",
year = "1962",
LCCN = "1876",
bibdate = "Fri Nov 19 10:02:31 MST 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/t/tukeyjohnw.bib;
http://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
library.ox.ac.uk:210/ADVANCE",
note = "This important book is the primary description of the
influential IBM 7030 Stretch computer, written by its
architects.",
URL = "http://edthelen.org/comphist/IBM7030PlanningMcJones.pdf",
acknowledgement = acknhfb,
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 floatingpoint 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 ndigit operand
that is not preshifted is extended with n zeros, so as
to provide the extra positions to which the preshifted
operand can be added. Any operand or result that is
shifted left to be normalized requires a corresponding
number of zeros to be shifted in at the right. Both
sets of zeros tend to produce numbers smaller in
absolute value than they would have been if more digits
had been carried. In the noisy mode these numbers are
simply extended with 1 s instead of zeros (1 s in a
binary machine, 9s in a decimal machine). 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 noisymode 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 builtin 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 noisymode 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 fixedpoint arithmetic. In other words, the
contention is not that normalized FLP arithmetic is
more prone to significance loss than equivalent
fixedpoint 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 fixedpoint arithmetic; multiplication and
division do not handle it at all correctly by means of
leading zeros. (In particular, fixedpoint
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 fixedpoint operands do
give correct significance indications, the use of other
operations and of builtin scaling loops frequently
destroys entirely the leadingzeros method of counting
significance.)''",
subject = "Computer architecture",
tableofcontents = "Foreword v \\
Preface vii \\
1. Project Stretch 1 \\
[by W. Buchholz] \\
2. Architectural Philosophy 5 \\
[by F. P. Brooks, Jr.] \\
2.1. The Two Objectives of Project Stretch 5 \\
2.2. Resources 6 \\
2.3. Guiding Principles 7 \\
2.4. Contemporary Trends in Computer Architecture 10
\\
2.5. Hindsight 15 \\
3. System Summary of IBM 7030 17 \\
[by W. Buchholz] \\
3.1. System Organization 17 \\
3.2. Memory Units 17 \\
3.3. Index Memory 19 \\
3.4. Special Registers 19 \\
3.5. Input and Output Facilities 19 \\
3.6. Highspeed Disk Units 20 \\
3.7. Central Processing Unit 20 \\
3.8. Instruction Controls 21 \\
3.9. Indexarithmetic Unit 21 \\
3.10. Instruction Lookahead 21 \\
3.11. Arithmetic Unit 22 \\
3.12. Instruction Set 24 \\
3.13. Data Arithmetic 24 \\
3.14. Radixconversion Operations 27 \\
3.15. Connective Operations 27 \\
3.16. Indexarithmetic Operations 27 \\
3.17. Branching Operations 28 \\
3.18. Transmission Operations 28 \\
3.19. InputOutput 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. Taperecording Convention 71 \\
6.15. Cardpunching Convention 71 \\
6.16. List of 7030 Character Set 72 \\
7. Variablefieldlength Operation 75 \\
[by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
\\
7.1. Introduction 75 \\
7.2. Addressing of Variablefieldlength 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. Radixconversion Operation 87 \\
7.13. Logical Connectives of Two Variables 87 \\
7.14. Connective Operations 89 \\
8. Floatingpoint Operation 92 \\
[by S. G. Campbell] \\
General Discussion \\
8.1. Problems of Fixedpoint Arithmetic 92 \\
8.2. Floatingpoint Arithmetic 94 \\
8.3. Normalization 97 \\
8.4. Floatingpoint Singularities 98 \\
8.5. Range and Precision 99 \\
8.6. Roundoff Error 100 \\
8.7. Significance Checks 101 \\
8.8. Forms of Floatingpoint Arithmetic 103 \\
8.9. Structure of Floatingpoint Data 104 \\
Floatingpoint Features of the 7030 \\
8.10. Floatingpoint Instruction Format 106 \\
8.11. Floatingpoint Data Formats 106 \\
8.12. Singular Floatingpoint Numbers 108 \\
8.13. Indicators 112 \\
8.14. Universal Accumulator 113 \\
8.15. Fraction Arithmetic 114 \\
8.16. Floatingpointarithmetic Operations 114 \\
8.17. Fixedpoint Arithmetic Using Unnormalized \\
Floatingpoint Operations 118 \\
8.18. Special Functions and Forms of Arithmetic 119 \\
8.19. Multipleprecision 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 Singleaddress 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. Programinterrupt System 136 \\
10.6. Components of the Programinterrupt System 137
\\
10.7. Examples of Programinterrupt 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. Recordhandling Applications 172 \\
11.14. File Maintenance 175 \\
11.15. Subroutine Control 177 \\
11.16. Conclusion 178 \\
12. InputOutput Control 179 \\
[by W. Buchholz] \\
12.1. A Generalized Approach to Connecting \\
InputOutput and External Storage 179 \\
12.2. InputOutput 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 InputOutput 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 Lookahead Unit 228 \\
[by R. S. Balance, J. Cocke, and H. G. Kolsky] \\
15.1. General Description 228 \\
15.2. Timingsimulation Program 230 \\
15.3. Description of the Lookahead Unit 238 \\
15.4. Forwarding 240 \\
15.5. Counter Sequences 241 \\
15.6. Recovery after Interrupt 246 \\
15.7. A Lookback at the Lookahead 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 Setup Mode 258 \\
17.3. Bytesequence Formation 259 \\
17.4. Pattern Selection 260 \\
17.5. Transformation Facilities 261 \\
17.6. Statistical Aids 263 \\
17.7. The BYTEBYBYTE Instruction 263 \\
17.8. Monitoring for Special Conditions 264 \\
17.9. Instruction Set 265 \\
17.10. Collating Operations 266 \\
17.11. Table Lookup Operations 267 \\
17.12. Example 267 \\
Appendix A. Summary Data 273 \\
A.1. List of the Larger IBM Storedprogram 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. Cuberoot Extraction 296 \\
B.3. Matrix Multiplication 298 \\
B.4. Conversion of Decimal Numbers to a \\
Floatingpoint Normalized Vector 299 \\
B.5. Editing a Typed Message 301 \\
B.6. Transposition of a Large Bit Matrix 303 \\
Index 305",
}k 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 floatingpoint 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 ndigit operand that is not preshifted is extended with n zeros, so as to provide the extra positions to which the preshifted operand can be added. Any operand or result that is shifted left to be normalized requires a corresponding number of zeros to be shifted in at the right. Both sets of zeros tend to produce numbers smaller in absolute value than they would have been if more digits had been carried. In the noisy mode these numbers are simply extended with 1 s instead of zeros (1 s in a binary machine, 9s in a decimal machine). 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 noisymode 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 builtin 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 noisymode 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 fixedpoint arithmetic. In other words, the contention is not that normalized FLP arithmetic is more prone to significance loss than equivalent fixedpoint 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 fixedpoint arithmetic; multiplication and division do not handle it at all correctly by means of leading zeros. (In particular, fixedpoint 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 fixedpoint operands do give correct significance indications, the use of other operations and of builtin scaling loops frequently destroys entirely the leadingzeros 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. Highspeed Disk Units 20 3.7. Central Processing Unit 20 3.8. Instruction Controls 21 3.9. Indexarithmetic Unit 21 3.10. Instruction Lookahead 21 3.11. Arithmetic Unit 22 3.12. Instruction Set 24 3.13. Data Arithmetic 24 3.14. Radixconversion Operations 27 3.15. Connective Operations 27 3.16. Indexarithmetic Operations 27 3.17. Branching Operations 28 3.18. Transmission Operations 28 3.19. InputOutput 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. Taperecording Convention 71 6.15. Cardpunching Convention 71 6.16. List of 7030 Character Set 72 7. Variablefieldlength Operation 75 [by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz] 7.1. Introduction 75 7.2. Addressing of Variablefieldlength 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. Radixconversion Operation 87 7.13. Logical Connectives of Two Variables 87 7.14. Connective Operations 89 8. Floatingpoint Operation 92 [by S. G. Campbell] General Discussion 8.1. Problems of Fixedpoint Arithmetic 92 8.2. Floatingpoint Arithmetic 94 8.3. Normalization 97 8.4. Floatingpoint Singularities 98 8.5. Range and Precision 99 8.6. Roundoff Error 100 8.7. Significance Checks 101 8.8. Forms of Floatingpoint Arithmetic 103 8.9. Structure of Floatingpoint Data 104 Floatingpoint Features of the 7030 8.10. Floatingpoint Instruction Format 106 8.11. Floatingpoint Data Formats 106 8.12. Singular Floatingpoint Numbers 108 8.13. Indicators 112 8.14. Universal Accumulator 113 8.15. Fraction Arithmetic 114 8.16. Floatingpointarithmetic Operations 114 8.17. Fixedpoint Arithmetic Using Unnormalized Floatingpoint Operations 118 8.18. Special Functions and Forms of Arithmetic 119 8.19. Multipleprecision 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 Singleaddress 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. Programinterrupt System 136 10.6. Components of the Programinterrupt System 137 10.7. Examples of Programinterrupt 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. Recordhandling Applications 172 11.14. File Maintenance 175 11.15. Subroutine Control 177 11.16. Conclusion 178 12. InputOutput Control 179 [by W. Buchholz] 12.1. A Generalized Approach to Connecting InputOutput and External Storage 179 12.2. InputOutput 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 InputOutput 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 Lookahead Unit 228 [by R. S. Balance, J. Cocke, and H. G. Kolsky] 15.1. General Description 228 15.2. Timingsimulation Program 230 15.3. Description of the Lookahead Unit 238 15.4. Forwarding 240 15.5. Counter Sequences 241 15.6. Recovery after Interrupt 246 15.7. A Lookback at the Lookahead 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 Setup Mode 258 17.3. Bytesequence Formation 259 17.4. Pattern Selection 260 17.5. Transformation Facilities 261 17.6. Statistical Aids 263 17.7. The BYTEBYBYTE Instruction 263 17.8. Monitoring for Special Conditions 264 17.9. Instruction Set 265 17.10. Collating Operations 266 17.11. Table Lookup Operations 267 17.12. Example 267 Appendix A. Summary Data 273 A.1. List of the Larger IBM Storedprogram 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. Cuberoot Extraction 296 B.3. Matrix Multiplication 298 B.4. Conversion of Decimal Numbers to a Floatingpoint Normalized Vector 299 B.5. Editing a Typed Message 301 B.6. Transposition of a Large Bit Matrix 303 Index 305acknhfbWerner BuchholzThis important book is the primary description of the influential IBM 7030 Stretch computer, written by its architects.Planning a computer system: {Project Stretch}
@Book{Buchholz:1962:PCS,
editor = "Werner Buchholz",
title = "Planning a computer system: {Project Stretch}",
publisher = pubMCGRAWHILL,
address = pubMCGRAWHILL:adr,
pages = "xvii + 322",
year = "1962",
LCCN = "1876",
bibdate = "Fri Nov 19 10:02:31 MST 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/t/tukeyjohnw.bib;
http://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
library.ox.ac.uk:210/ADVANCE",
note = "This important book is the primary description of the
influential IBM 7030 Stretch computer, written by its
architects.",
URL = "http://edthelen.org/comphist/IBM7030PlanningMcJones.pdf",
acknowledgement = acknhfb,
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 floatingpoint 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 ndigit operand
that is not preshifted is extended with n zeros, so as
to provide the extra positions to which the preshifted
operand can be added. Any operand or result that is
shifted left to be normalized requires a corresponding
number of zeros to be shifted in at the right. Both
sets of zeros tend to produce numbers smaller in
absolute value than they would have been if more digits
had been carried. In the noisy mode these numbers are
simply extended with 1 s instead of zeros (1 s in a
binary machine, 9s in a decimal machine). 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 noisymode 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 builtin 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 noisymode 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 fixedpoint arithmetic. In other words, the
contention is not that normalized FLP arithmetic is
more prone to significance loss than equivalent
fixedpoint 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 fixedpoint arithmetic; multiplication and
division do not handle it at all correctly by means of
leading zeros. (In particular, fixedpoint
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 fixedpoint operands do
give correct significance indications, the use of other
operations and of builtin scaling loops frequently
destroys entirely the leadingzeros method of counting
significance.)''",
subject = "Computer architecture",
tableofcontents = "Foreword v \\
Preface vii \\
1. Project Stretch 1 \\
[by W. Buchholz] \\
2. Architectural Philosophy 5 \\
[by F. P. Brooks, Jr.] \\
2.1. The Two Objectives of Project Stretch 5 \\
2.2. Resources 6 \\
2.3. Guiding Principles 7 \\
2.4. Contemporary Trends in Computer Architecture 10
\\
2.5. Hindsight 15 \\
3. System Summary of IBM 7030 17 \\
[by W. Buchholz] \\
3.1. System Organization 17 \\
3.2. Memory Units 17 \\
3.3. Index Memory 19 \\
3.4. Special Registers 19 \\
3.5. Input and Output Facilities 19 \\
3.6. Highspeed Disk Units 20 \\
3.7. Central Processing Unit 20 \\
3.8. Instruction Controls 21 \\
3.9. Indexarithmetic Unit 21 \\
3.10. Instruction Lookahead 21 \\
3.11. Arithmetic Unit 22 \\
3.12. Instruction Set 24 \\
3.13. Data Arithmetic 24 \\
3.14. Radixconversion Operations 27 \\
3.15. Connective Operations 27 \\
3.16. Indexarithmetic Operations 27 \\
3.17. Branching Operations 28 \\
3.18. Transmission Operations 28 \\
3.19. InputOutput 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. Taperecording Convention 71 \\
6.15. Cardpunching Convention 71 \\
6.16. List of 7030 Character Set 72 \\
7. Variablefieldlength Operation 75 \\
[by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
\\
7.1. Introduction 75 \\
7.2. Addressing of Variablefieldlength 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. Radixconversion Operation 87 \\
7.13. Logical Connectives of Two Variables 87 \\
7.14. Connective Operations 89 \\
8. Floatingpoint Operation 92 \\
[by S. G. Campbell] \\
General Discussion \\
8.1. Problems of Fixedpoint Arithmetic 92 \\
8.2. Floatingpoint Arithmetic 94 \\
8.3. Normalization 97 \\
8.4. Floatingpoint Singularities 98 \\
8.5. Range and Precision 99 \\
8.6. Roundoff Error 100 \\
8.7. Significance Checks 101 \\
8.8. Forms of Floatingpoint Arithmetic 103 \\
8.9. Structure of Floatingpoint Data 104 \\
Floatingpoint Features of the 7030 \\
8.10. Floatingpoint Instruction Format 106 \\
8.11. Floatingpoint Data Formats 106 \\
8.12. Singular Floatingpoint Numbers 108 \\
8.13. Indicators 112 \\
8.14. Universal Accumulator 113 \\
8.15. Fraction Arithmetic 114 \\
8.16. Floatingpointarithmetic Operations 114 \\
8.17. Fixedpoint Arithmetic Using Unnormalized \\
Floatingpoint Operations 118 \\
8.18. Special Functions and Forms of Arithmetic 119 \\
8.19. Multipleprecision 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 Singleaddress 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. Programinterrupt System 136 \\
10.6. Components of the Programinterrupt System 137
\\
10.7. Examples of Programinterrupt 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. Recordhandling Applications 172 \\
11.14. File Maintenance 175 \\
11.15. Subroutine Control 177 \\
11.16. Conclusion 178 \\
12. InputOutput Control 179 \\
[by W. Buchholz] \\
12.1. A Generalized Approach to Connecting \\
InputOutput and External Storage 179 \\
12.2. InputOutput 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 InputOutput 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 Lookahead Unit 228 \\
[by R. S. Balance, J. Cocke, and H. G. Kolsky] \\
15.1. General Description 228 \\
15.2. Timingsimulation Program 230 \\
15.3. Description of the Lookahead Unit 238 \\
15.4. Forwarding 240 \\
15.5. Counter Sequences 241 \\
15.6. Recovery after Interrupt 246 \\
15.7. A Lookback at the Lookahead 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 Setup Mode 258 \\
17.3. Bytesequence Formation 259 \\
17.4. Pattern Selection 260 \\
17.5. Transformation Facilities 261 \\
17.6. Statistical Aids 263 \\
17.7. The BYTEBYBYTE Instruction 263 \\
17.8. Monitoring for Special Conditions 264 \\
17.9. Instruction Set 265 \\
17.10. Collating Operations 266 \\
17.11. Table Lookup Operations 267 \\
17.12. Example 267 \\
Appendix A. Summary Data 273 \\
A.1. List of the Larger IBM Storedprogram 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. Cuberoot Extraction 296 \\
B.3. Matrix Multiplication 298 \\
B.4. Conversion of Decimal Numbers to a \\
Floatingpoint Normalized Vector 299 \\
B.5. Editing a Typed Message 301 \\
B.6. Transposition of a Large Bit Matrix 303 \\
Index 305",
}
nn!KV %#/)+c=+3%=%;M)g+=incollectionfparith.bibCampbell:1962:FPOS. G. CampbellWerner BuchholzPlanning lJ\ #/+c+3!E{;{C7%+{geSbookfparith.bibBuchholz:1962:PCSWerner BuchholzPlanning a computer system: Project StretchpubMCGRAWHILLpubMCGRAWHILL:adrxvii + 32219621876Fri Nov 19 10:02:31 MST 2010http://www.math.utah.edu/pub/bibnet/authors/t/tukeyjohnw.bib; http://www.math.utah.edu/pub/tex/bib/annhistcomput.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib; library.ox.ac.uk:210/ADVANCE2010.11.19 10:02:31 MSTThis important book is the primary description of the influential IBM 7030 Stretch computer, written by its architects.http://edthelen.org/comphist/IBM7030PlanningMcJones.pdfThe text of the booolz",
booktitle = "Planning a Computer System: {Project Stretch}",
title = "FloatingPoint Operation",
publisher = pubMCGRAWHILL,
address = pubMCGRAWHILL:adr,
pages = "92121",
year = "1962",
LCCN = "QA76.8.I2 I5",
bibdate = "Wed Feb 14 17:24:27 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = acknhfb,
bookpages = "322",
subject = "IBM 7030 (Computer); IBM Stretch",
}
50V5
@InProceedings{Krithivasan:2004:SPM,
author = "S. Krithivasan and M. J. Schulte and J. GloB=
@InProceedings{Krueger:2004:DLI,
author = "S. D. Krueger and P.M. Seidel",
booktitle = B F
@InProceedings{Kubosawa:1992:BFP,
author = "H. Kubosawa and A. Katsuno and H. Takahashi an&[7
@InProceedings{Krithivasan:2003:MAM,
author = "S. Krithivasan and M. J. Schulte",
title ?N
@InProceedings{Krishnan:2001:PEM,
author = "Shankar Krishnan and Mark Foskey and Tim Culve:؉hQ
@InProceedings{Krishnan:1989:ESA,
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booktitle = "International m[
@InProceedings{Krishnan:1989:CBN,
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@InProceedings{Krishnan:1988:SCR,
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} "Logarithmic and Exponential Function Evaluation in a
Variable Structure Digital Computer",
journal = jIRETRANSELECCOMPUT,
volume = "EC11",
number = "2",
pages = "155164",
month = apr,
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with floatingpoint computers",
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pages = "7",
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author = "J. Descloux",
title = "Remarks on errors in first order iterative processes
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bibdate = "Sat Feb 24 15:01:45 MST 1996",
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uMZ !#/#1+Em;Yy/#1#techreportfparith.bibDescloux:1962:REFJ. DesclouxRemarks on errors in first order iterative processes with floatingpoint computersUniversity of Illinois Graduate College, Digital Computer LaboratoryUrbana, IL, USA71962Sat Feb 24 15:01:45 MST 1996http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MSTReport / University of Illinois, Digital Computer Laboratory; no. 113 Report (University of Illinois (UrbanaChampaign campus). Digital Computer Laboratory); no. 113.Electronic digital computers.; Numerical calculations.Supported by: National Science Foundation under grant G16489. ``March 22, 1962.''acknhfbJ. DesclouxRemarks on errors in first order eshold Realization of Arithmetic Circuits",
journal = jIRETRANSELECCOMPUT,
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@Article{Ercegovac:1988:LSC,
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title =R%
@Article{Ercegovac:1990:FMC,
author = "M. D. Ercegovac and T. Lang",
title = "Fas ʏ
@Article{Ercegovac:1992:FRC,
author = "M. D. Ercegovac and T. Lang",
title = "On&;
@Article{Ercegovac:1991:MPM,
author = "Milo{\v{s}} D. Ercegovac and Tomas Lang",
title =#XH
@Article{Ercegovac:1990:RSR,
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title = "Rad ͆:u
@Article{Ercegovac:1987:FCR,
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title = "On6m
@Article{Ercegovac:1973:REC,
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title = "Radixu0a
@Article{Ercegovac:1984:LAO,
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@Article{Ercegovac:1990:SRD,
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title = "Sim ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219366IRE Transactions on Electronic ComputersacknhfbM. A. Fischler and E. A. PoeThreshold Realization of Arithmetic Circuits
@Article{Fischler:1962:TRA,
author = "M. A. Fischler and E. A. Poe",
title = "Threshold Realization of Arithmetic Circuits",
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sNW#/Ee;a7E;]Ee%articlefparith.bibFischler:1962:TRAM. A. Fischler and E. A. PoeThreshold Realization of Arithmetic CircuitsjIRETRANSELECCOMPUTEC112287288apr41962IRELAOhttp://dx.doi.org/10.1109/TEC.1962.521936603679950 OR 03679950Thu Jul 14 09:11:50 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 09:11:50 MDThttp://r representation for use with
algorithmic languages",
journal = jCACM,
volume = "5",
number = "3",
pages = "160161",
month = mar,
year = "1962",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
MRclass = "68.00",
MRnumber = "26\#4506",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Algorithmic languages, such as ALGOL, make provision
for two types of numbers, real and integer, which are
usually implemented on the computer by means of
floatingpoint and fixedpoint 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
fixedpoint numbers is not a proper subset of the set
of floatingpoint 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, fixedpoint addition or
floatingpoint addition.",
acknowledgement = acknhfb,
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} of fixedpoint numbers is not a proper subset of the set of floatingpoint 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, fixedpoint addition or floatingpoint addition.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79R. 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 floatingpoint and fixedpoint 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 fixedpoint numbers is not a proper subset of the set of floatingpoint 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, fixedpoint addition or floatingpoint addition.A. A. GrauOn a floatingpoint number representation for use with algorithmic languages
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abstract = "Algorithmic languages, such as ALGOL, make provision
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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
fixedpoint numbers is not a proper subset of the set
of floatingpoint 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, fixedpoint addition or
floatingpoint addition.",
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XOZ #'!%57;m;c?cw!%articlefparith.bibGrau:1962:FNRA. A. GrauOn a floatingpoint number representation for use with algorithmic languagesjCACM53160161mar31962CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 0001078268.0026\#4506Fri Dec 8 08:24:14 1995http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 08:24:14 ???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 floatingpoint and fixedpoint 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 setlving Linear Simultaneous Equations
Using the Residue Number System",
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}s on Electronic ComputersacknhfbRonald M. GuffinA Computer for Solving Linear Simultaneous Equations Using the Residue Number System
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yQV #Ii+3!E%;uMmIiibookfparith.bibHamming:1962:NMSR. W. (Richard Wesley) HammingNumerical methods for scientists and engineerspubMCGRAWHILLpubMCGRAWHILL:adr4111962QA297 .H28Fri Aug 2ɌUPY #+5;a7E;]5{
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}ng Point Feature on the {IBM Type 1620}",
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@Article{Jones:1962:FPF,
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qUW #)#W57;K;?c#Warticlefparith.bibKnuth:1962:EPCD. E. KnuthEvaluation of Polynomials By ComputerjCACM512595599dec121962CACMA200010782 (print), 15577317 (electronic) OR ԍ_TW#'g;a75%E;]gCarticlefparith.bibKeir:1962:DODY. A. Keir and P. W. Cheney and M. TannenbaumDivision and overflow detection in residue number systemsjIRETRANSELECCOMPUTEC114501507aug81962IRELAOhttp://dx.doi.org/10.1109/TEC.1962.521938903679950 OR 0367995068.00MR0150990 (27 \#976)N. H. ChoksyThu Jul 14 09:11:51 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://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 ComputersacknhfbY. A. Keir and P. W. Cheney and M. TannenbaumDivision and overflow dels By Computer",
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@Article{Pezaris:1971:NBB,
author = "S. D. Pezaris",
title = "A 40ns 17Bit by 1a00010782 (print), 15577317 (electronic)00010782 OR 00010782Thu Sep 1 10:15:40 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:40 ???Communications of the ACMacknjhttp://portal.acm.org/browse_dl.cfm?idx=J79D. E. KnuthEvaluation of Polynomials By Computer
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}dware Conversion of Decimal
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HuH!XX #1+A;7=a;]+I articlefparith.bibMacSorley:1962:RBAO. L. MacSorleyReview: booktitle An Algorithm for Rapid Binary Division, by J. B. Wilson and R. S. LedleyjIRETRANSELECCOMPUTEC113420420jun61962IRELAO03679950 OR ۊWV #)#o57=m;?Oc#o/articlefparith.bibLynch:1962:WBDW. C. LynchOn a WiredIn BinarytoDecimal Conversion SchemejCACM53159159mar31962CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 155773يbVX #'!57=m;?Oc!yarticlefparith.bibLake:1962:LEHG. T. LakeLetter to the Editor: Hardware Conversion of Decimal and Binary NumbersjCACM59468469sep91962CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Fri Nov 28 18:16:30 20Decimal Conversion Scheme",
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}'h.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 08:10:44 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038037A particular set of unnormalized arithmetic operations termed ``basic'' are described, in the context of the University of Chicago Maniac III Computer. Each basic operation involves three operand words and generates two result words, all in unnormalized floating point format. The use of these operations in the implementation of multiprecision arithmetic is explained; in particular, it is demonstrated that multiprecision division can be effected in a nontentative manner with their aid.IEEE Transactions on Electronic ComputersCited in cite Sterbenz:1974:FPC.0124.07910acknhfbA particular set of unnormalized arithmetic operations termed ``basic'' are described, in the context of the University of Chicago Maniac III Computer. Each basic operation involves three operand words and generates two result words, all in unnormalized floating point format. The use of these operations in the impl(ementation of multiprecision arithmetic is explained; in particular, it is demonstrated that multiprecision division can be effected in a nontentative manner with their aid.N. Metropolis and R. L. AshenhurstBasic Operations in an Unnormalized Arithmetic System
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@Article{Svoboda:1963:AD,
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mvU '#1+e3;m;/+e5inproceedingsfparith.bibWilkinson:1963:PSAJ. H. WilkinsonPlane rotations in floatingpoint arithmeticMetropolis:1963:PFS185198196365.3528\#1744Fri Dec 8 08:24:14 1995http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 08:24:14 ???acknhfbA. S. HouseholderJ. H. WilkinsonPlane rotations in floatingpoint arithmetic
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acknowledgement = acknj,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
mwU #11Y!=m;M1Y5bookfparith.bibWilkinson:1963:REAJames H. WilkinsonRounding Errors in Algebraic ProcessespubPHpubPH:adrvi + 1611963QA76.5 .W53 1964Thu Sep 08 13:29:45 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.08 13:29:45 ???Cited in cite Sterbenz:1974:FPC.acknjJames H. WilkinsonRounding Errors in Algebraic Processes
@Book{Wilkinson:1963:REA,
author = "James H. Wilkinson",
title = "Rounding Errors in Algebraic Processes",
publisher = pubPH,
address = pubPH:adr,
pages = "vi + 161",
year = "1963",
LCCN = "QA76.5 .W53 1964",
bibdate = "Thu Sep 08 13:29:45 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}ulating machine",
journal = jIEEESPECTRUM,
volume = "1",
number = "??",
pages = "6269",
month = aug,
year = "1964",
CODEN = "IEESAM",
ISSN = "00189235 (print), 19399340 (electronic)",
ISSNL = "00189235",
bibdate = "Wed Oct 13 11:16:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
note = "Previously unpublished memorandum. Reprinted in
\cite[\S 5.1]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
fjournal = "IEEE Spectrum",
remark = "This article does not appear in the IEEE Xplore
database, and that source lists only volume 1, number
1, for 1964. I found multiple references to this paper
as the August 1964 issue, so perhaps IEEE Xplore is
missing early journal issues??",
}title = "Proposed automatic calculating machine",
journal = jIEEESPECTRUM,
volume = "1",
number = "??",
pages = "6269",
month = aug,
year = "1964",
CODEN = "IEESAM",
ISSN = "00189235 (print), 19399340 (electronic)",
ISSNL = "00189235",
bibdate = "Wed Oct 13 11:16:56 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
note = "Previously unpublished memorandum. Reprinted in
\cite[\S 5.1]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
fjournal = "IEEE Spectrum",
remark = "This article does not appear in the IEEE Xplore
database, and that source lists only volume 1, number
1, for 1964. I found multiple references to this paper
as the August 1964 issue, so perhaps IEEE Xplore is
missing early journal issues??",
}
""RxZ #)#Y+57=O;%'k#Y}articlefparith.bibAiken:1964:PACH. H. AikenProposed automatic calculating machinejIEEESPECTRUM16269aug81964IEESAM00189235 (print), 19399340 (electronic) OR 00189235 (print), 19399340 (electronic)00189235 OR 00189235Wed Oct 13 11:16:56 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/master.bib2010.10.13 11:16:56 ???Previously unpublished memorandum. Reprinted in cite [ 5.1]Randell:1982:ODC.IEEE SpectrumThis article does not appear in the IEEE Xplore database, and that source lists only volume 1, number 1, for 1964. I found multiple references to this paper as the August 1964 issue, so perhaps IEEE Xplore is missing early journal issues??acknhfbH. H. AikenPreviously unpublished memorandum. Reprinted in \cite[\S 5.1]{Randell:1982:ODC}.Proposed automatic calculating machine
@Article{Aiken:1964:PAC,
author = "H. H. Aiken",
;ing point interpretive system:
for the {RPC 4000 General Precision} electronic
computer",
organization = "General Precision, Inc.",
address = "West Lafayette, IN, USA",
pages = "45",
year = "1964",
bibdate = "Mon May 06 10:24:31 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
keywords = "Electronic digital computers  Programming.; Purdue
University School of Electrical Engineering; RPC 4000
(Computer)",
remark = "Program no. H102.0",
}x/bib/fparith.bib2002.05.06 10:24:31 ???Electronic digital computers  Programming.; Purdue University School of Electrical Engineering; RPC 4000 (Computer)Program no. H102.0acknhfbAnonymous{PINT}: {Purdue} floating point interpretive system: for the {RPC 4000 General Precision} electronic computer
@Manual{Anonymous:1964:PPF,
author = "Anonymous",
title = "{PINT}: {Purdue} floating point interpretive system:
for the {RPC 4000 General Precision} electronic
computer",
organization = "General Precision, Inc.",
address = "West Lafayette, IN, USA",
pages = "45",
year = "1964",
bibdate = "Mon May 06 10:24:31 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
keywords = "Electronic digital computers  Programming.; Purdue
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::_V '#/=U9KEm;E=U9mastersthesisfparG{[#'U_57E;;?c;U_'articlefparith.bibBaer:1964:MPARobert M. Baer and Martin G. RedlichMultipleprecision arithmetic and the exact calculation of the $ 3  j $, $ 6  j $ and $ 9  j $ symbolsjCACM711657659nov111964CACMA200010782 (pD0zV #3i57=m;1ei!articlefparith.bibAshenhurst:1964:FEUR. L. AshenhurstFunction Evaluation in Unnormalized AritARyX #1[;;=m;y3g'manualfparith.bibAnonymous:1964:PPFAnonymousPINT: Purdue floating point interpretive system: for the RPC 4000 General Precision electronic computerGeneral Precision, Inc.West Lafayette, IN, USA451964Mon May 06 10:24:31 2002http://www.math.utah.edu/pub/te>uation in Unnormalized Arithmetic",
journal = jJACM,
volume = "11",
number = "2",
pages = "168187",
month = apr,
year = "1964",
CODEN = "JACOAH",
ISSN = "00045411 (print), 1557735X (electronic)",
ISSNL = "00045411",
bibdate = "Thu Nov 03 22:33:52 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}hmeticjJACM112168187apr41964JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 00045411Thu Nov 03 22:33:52 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.11.03 22:33:52 ???Journal of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401R. L. AshenhurstFunction Evaluation in Unnormalized Arithmetic
@Article{Ashenhurst:1964:FEU,
author = "R. L. Ashenhurst",
title = "Function Evaluation in Unnormalized Arithmetic",
journal = jJACM,
volume = "11",
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pages = "168187",
month = apr,
year = "1964",
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journal = jCACM,
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bibsource = "http://portal.acm.org/;
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abstract = "Described in this paper is a system of generalpurpose
multipleprecision fixedpoint routines and their use
in subroutines which calculate exactly the
quantummechanical 3j, 6j and 9j symbols of large
arguments.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
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&Lr+>}
@Article{Capps:1988:OAL,
author = "C. David Capps and R. Aaron Falk and Theodore L.
ш*U
@Article{Cappa:1973:AIA,
author = "M. Cappa and V. C. Hamacher",
title = "An Augmi(Q
@Article{Capocelli:1988:EVN,
author = "R. M. Capocelli and R. Giancarlo",
title = ÇiS
@Article{Cantor:1962:LEF,
author = "D. Cantor and G. Estrin and R. Turn",
title = K
@Article{Calvetti:1991:REF,
author = "Daniela Calvetti",
title = "Roundoff error "={
@Article{Campbell:1986:SS,
author = "R. A. Campbell",
title = "In Search of a SinH
@Article{Campbell:1986:NSR,
author = "R. A. Campbell",
title = "{NS32000} Square ~
@Article{Calvert:1936:DDS,
author = "H. R. Calvert",
title = "Decimal Division ofM
@Article{Callahan:1988:EII,
author = "D. Callahan and J. Cocke and K. Kennedy",
title = Erint), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 0001078265.2531\#865Mon Oct 24 09:33:02 MDT 2005http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.10.24 09:33:02 MDTDescribed in this paper is a system of generalpurpose multipleprecision fixedpoint routines and their use in subroutines which calculate exactly the quantummechanical 3j, 6j and 9j symbols of large arguments.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Described in this paper is a system of generalpurpose multipleprecision fixedpoint routines and their use in subroutines which calculate exactly the quantummechanical 3j, 6j and 9j symbols of large arguments.Robert M. Baer and Martin G. RedlichMultipleprecision arithmetic and the exact calculation of the $ 3  j $, $ 6  j $ and $ 9  j $ symbols
@Article{Baer:1964:MPA,
author = "Robert M. Baer and Martin G. Redlich",
title = "Multipleprecision arithmetic and the exact
calculation of the $ 3  j $, $ 6  j $ and $ 9  j $
symbols",
journal = jCACM,
volume = "7",
number = "11",
pages = "657659",
month = nov,
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bibdate = "Mon Oct 24 09:33:02 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Described in this paper is a system of generalpurpose
multipleprecision fixedpoint routines and their use
in subroutines which calculate exactly the
quantummechanical 3j, 6j and 9j symbols of large
arguments.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
} study of floating point arithmetic",
type = "Thesis ({M.S. in Math.})",
school = "Georgia Institute of Technology",
address = "Atlanta, GA, USA",
pages = "51",
year = "1964",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
keywords = "Electronic digital computers.; Number theory.;
Numerical calculations  Computer programs.",
}ith.bibBookhart:1964:SFPThomas Woodward BookhartA study of floating point arithmeticThesis (M.S. in Math.)Georgia Institute of TechnologyAtlanta, GA, USA511964Sat Feb 24 15:01:45 MST 1996http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MSTElectronic digital computers.; Number theory.; Numerical calculations  Computer programs.acknhfbThomas Woodward BookhartA study of floating point arithmetic
@MastersThesis{Bookhart:1964:SFP,
author = "Thomas Woodward Bookhart",
title = "A study of floating point arithmetic",
type = "Thesis ({M.S. in Math.})",
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pages = "51",
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bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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} some general modes of
arithmetic",
journal = jCACM,
volume = "7",
number = "2",
pages = "119127",
month = feb,
year = "1964",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
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bibdate = "Mon Oct 24 09:33:00 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An interpretive programming package is described for
computation with operands which may be real, complex,
single or double precision, or real multiple precision.
It also performs operations on matrices formed from
these elements. A simple language structure is used to
describe the computation.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}J10782 (print), 15577317 (electronic)00010782 OR 00010782Mon Oct 24 09:33:00 MDT 2005http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.10.24 09:33:00 MDTAn interpretive programming package is described for computation with operands which may be real, complex, single or double precision, or real multiple precision. It also performs operations on matrices formed from these elements. A simple language structure is used to describe the computation.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79An interpretive programming package is described for computation with operands which may be real, complex, single or double precision, or real multiple precision. It also performs operations on matrices formed from these elements. A simple language structure is used to describe the computation.R. A. BrookerA programming package for some general modes of arithmetic
@Article{Brooker:1964:PPS,
author = "R. A. Brooker",
title = "A programming package for some general modes of
arithmetic",
journal = jCACM,
volume = "7",
number = "2",
pages = "119127",
month = feb,
year = "1964",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Mon Oct 24 09:33:00 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An interpretive programming package is described for
computation with operands which may be real, complex,
single or double precision, or real multiple precision.
It also performs operations on matrices formed from
these elements. A simple language structure is used to
describe the computation.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
ZZY #'+g]57;O;A?_cA/kkarticlefparith.bibCody:1964:DPSW. J. Cody, Jr.DoublePrecision Square Root for the CDC3600jCACM712715718dec121964CACMA2http://doi.acm.org/10.1145/355588.36512200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Thu Sep 1 10:15:43 1994ftp://garbo.uwasa.fi/pc/doP`~X #177=m;Ou;# manualfparith.bibBurroughs:1964:BBIBurroughs CorporationBurroughs B5500 Information Processing Systems Reference ManualBurroughs CorporatioM}[ #'57E;[?c['S articlefparith.bibBrooker:1964:PPSR. A. BrookerA programming package for some general modes of arithmeticjCACM72119127feb21964CACMA200010782 (print), 15577317 (electronic) OR 000Ihs B5500} Information Processing Systems
Reference Manual",
organization = "Burroughs Corporation",
address = "Detroit, MI, USA",
year = "1964",
bibdate = "Wed Nov 22 21:15:11 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
keywords = "decimal floatingpoint arithmetic",
remark = "The B5500 uses a decimal integer or fixedpoint
coefficient of 21 or 22 digits, with an exponent range
of $ \pm 63 $.",
}nDetroit, MI, USA1191271964Wed Nov 22 21:15:11 2006http://www.math.utah.edu/pub/tex/bib/fparith.bib2006.11.22 21:15:11 ???decimal floatingpoint arithmeticThe B5500 uses a decimal integer or fixedpoint coefficient of 21 or 22 digits, with an exponent range of $ pm 63 $.acknhfb{Burroughs Corporation}{Burroughs B5500} Information Processing Systems Reference Manual
@Manual{Burroughs:1964:BBI,
author = "{Burroughs Corporation}",
title = "{Burroughs B5500} Information Processing Systems
Reference Manual",
organization = "Burroughs Corporation",
address = "Detroit, MI, USA",
year = "1964",
bibdate = "Wed Nov 22 21:15:11 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
keywords = "decimal floatingpoint arithmetic",
remark = "The B5500 uses a decimal integer or fixedpoint
coefficient of 21 or 22 digits, with an exponent range
of $ \pm 63 $.",
}Oquare Root for the {CDC3600}",
journal = jCACM,
volume = "7",
number = "12",
pages = "715718",
month = dec,
year = "1964",
CODEN = "CACMA2",
DOI = "http://doi.acm.org/10.1145/355588.365122",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/bibnet/authors/c/codywilliamj.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In January of 1960, the late Hans J. Maehly completed
a summary of approximations to the elementary functions
for the CDC1604 computer. The approximations and
techniques suggested by Maehly are equally applicable
to the second large computer in the CDC line, the 3600.
Unlike the 1604, however, the 3600 has builtin
doubleprecision floatingpoint arithmetic. The present
work, largely inspired by the successes of Maehly and
his associates, concerns the extension of one of
Maehly's ideas to a doubleprecision subroutine for the
3600.",
acknowledgement = acknj,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$sqrt(x)$; CDC 3600; elementary functions",
}Qcsoft/fpbibl18.zip; http://www.math.utah.edu/pub/bibnet/authors/c/codywilliamj.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:43 ???In January of 1960, the late Hans J. Maehly completed a summary of approximations to the elementary functions for the CDC1604 computer. The approximations and techniques suggested by Maehly are equally applicable to the second large computer in the CDC line, the 3600. Unlike the 1604, however, the 3600 has builtin doubleprecision floatingpoint arithmetic. The present work, largely inspired by the successes of Maehly and his associates, concerns the extension of one of Maehly's ideas to a doubleprecision subroutine for the 3600.Communications of the ACM$sqrt(x)$; CDC 3600; elementary functionsacknjhttp://portal.acm.org/browse_dl.cfm?idx=J79In January of 1960, the late Hans J. Maehly completed a summary of approximations to the elementary functions for the CDC1604 computer. The approximations and techniques suggested by Maehly are equally applicRable to the second large computer in the CDC line, the 3600. Unlike the 1604, however, the 3600 has builtin doubleprecision floatingpoint arithmetic. The present work, largely inspired by the successes of Maehly and his associates, concerns the extension of one of Maehly's ideas to a doubleprecision subroutine for the 3600.W. J. {Cody, Jr.}DoublePrecision Square Root for the {CDC3600}
@Article{Cody:1964:DPS,
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title = "DoublePrecision Square Root for the {CDC3600}",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In January of 1960, the late Hans J. Maehly completed
a summary of approximations to the elementary functions
for the CDC1604 computer. The approximations and
techniques suggested by Maehly are equally applicable
to the second large computer in the CDC line, the 3600.
Unlike the 1604, however, the 3600 has builtin
doubleprecision floatingpoint arithmetic. The present
work, largely inspired by the successes of Maehly and
his associates, concerns the extension of one of
Maehly's ideas to a doubleprecision subroutine for the
3600.",
acknowledgement = acknj,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$sqrt(x)$; CDC 3600; elementary functions",
}BuiltIn Square Root Method",
journal = jIEEETRANSELECCOMPUT,
volume = "EC13",
number = "2",
pages = "156157",
month = apr,
year = "1964",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1964.263791",
ISSN = "03677508",
bibdate = "Thu Jul 14 06:56:59 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038119",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}7.14 06:56:59 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038119IEEE Transactions on Electronic ComputersacknhfbD. CowgillLogic Equations for a BuiltIn Square Root Method
@Article{Cowgill:1964:LEB,
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title = "Logic Equations for a BuiltIn Square Root Method",
journal = jIEEETRANSELECCOMPUT,
volume = "EC13",
number = "2",
pages = "156157",
month = apr,
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'e}V '#5/['1;m;/[mmastersthesisfparY6W ##G!57=K;7UGaarticlefparith.bibEve:1964:EPJ. EveThe Evaluation of PolynomialsjNUMMATH617211964NUMMA7002959WMW #!o=a7E;_!o
articlefparith.bibCowgill:1964:LEBD. CowgillLogic Equations for a BuiltIn Square Root MethodjIEEETRANSELECCOMPUTEC132156157apr41964IEECA8http://dx.doi.org/10.1109/PGEC.1964.26379103677508 OR 03677508Thu Jul 14 06:56:59 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.0T
journal = jNUMMATH,
volume = "6",
pages = "1721",
year = "1964",
CODEN = "NUMMA7",
ISSN = "0029599X (print), 09453245 (electronic)",
ISSNL = "0029599X",
bibdate = "Fri Sep 16 10:21:47 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
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acknowledgement = acknj,
fjournal = "Numerische Mathematik",
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xxmonth = "(none)",
xxnumber = "(none)",
}9X (print), 09453245 (electronic) OR 0029599X (print), 09453245 (electronic)0029599X OR 0029599XFri Sep 16 10:21:47 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.16 10:21:47 ???Numerische Mathematikacknjhttp://link.springer.com/journal/211J. EveThe Evaluation of Polynomials
@Article{Eve:1964:EP,
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title = "The Evaluation of Polynomials",
journal = jNUMMATH,
volume = "6",
pages = "1721",
year = "1964",
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ISSN = "0029599X (print), 09453245 (electronic)",
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7/Y #+%i57E;E?McE%iGarticlefparith0Z #)=97EU;__) articlefparith.bibMerrill:1964:IDCRoy D. MerrillImproving Digital Computer Performance Using Residue Number TheoryjIEEETRANSELECCOMPUTEC13293101apr41964IEECA8http://dx.doi.org/10.1109/PGEC.1964.263777; http://dx.doi.org/10.1109/PGEC.1964.26377603677508 OR 03677508Thu Jul 14 06:56:58 MDT 2011http://ieeexplore.ieee.org/; http://www.computer.y}
X#1[;'Em;%M[?bookfparith.bibMcCracken:1964:NMFDaniel D. McCracken and William S. DornNumerical methods and FORTRAN programming, with applications in engineering and sciencepubWILuxComputer Performance Using Residue
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keywords = "residue arithmetic; residue number system",
summary = "Residue arithmetic has the interesting characteristic
that in multiplication, addition and subtraction any
digit in the result is dependent only on its two
corresponding operand digits. Consequently, for these
operations, residue arithmetic is \ldots{}",
}zorg/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 06:56:58 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038105; http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4038099IEEE Transactions on Electronic Computersresidue arithmetic; residue number systemacknhfbRoy D. MerrillImproving Digital Computer Performance Using Residue Number Theory
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CC9W '#';'97Em;?gmastersthesisfparith.bibMoss:1964:RDCGeorge Joseph Moss, Jr.Recording digital counter with floating point output formatThesis (M.S.)University of MarylandCollege Park, MD, USA1551964Sat Feb 24 15:01:45 MST 1996http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MSTacknhfbGeorge Joseph {Moss, Jr.}Recording digital counter with floating point output format
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cV #'%I!+=K;%IIbookfparith.bibRice:1964:AFVJohn R. RiceThe Approximation of Functions1pubAWpubAW:adrvarious1964QA221 .R5 V.12Fri Dec 08 13:02:52 1995ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 13:02:52 ???acknjJohn R. RiceThe Approximation of Functions
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journal = jCACM,
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r&L];
@InProceedings{Ohhashi:1985:HSC,
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title = "HighSpeed Computation of Unary Functions",
crossref = "Hwang:1985:PSC",
pages = "8285",
year = B
@InProceedings{Ohlsson:1983:MML,
author = "Lennart Ohlsson and Bertil Svensson",
title =dE
@InProceedings{Oh:2005:FPS,
author = "H.J. Oh and S. M. Mueller and C. Jacobi and K. D.
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author = "R. L. Ashenhurst",
editor = "L. B. Rall",
booktitle = "Error in digital computation",
title = "Techniques for automatic error monitoring and
control",
publisher = pubWILEY,
address = pubWILEY:adr,
pages = "4359",
year = "1965",
bibdate = "Tue Oct 9 09:42:56 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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volume = "EC14",
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month = jun,
year = "1965",
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} 06:26:33 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038457IEEE Transactions on Electronic ComputersacknhfbA. J. AtrubinA OneDimensional RealTime Iterative Multiplier
@Article{Atrubin:1965:ODR,
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title = "A OneDimensional RealTime Iterative Multiplier",
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bibdate = "Thu Sep 8 08:20:53 1994",
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}7 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Thu Sep 8 08:20:53 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.08 08:20:53 ???Communications of the ACMacknjhttp://portal.acm.org/browse_dl.cfm?idx=J79B. I. BlumAn Extended Arithmetic Package
@Article{Blum:1965:EAP,
author = "B. I. Blum",
title = "An Extended Arithmetic Package",
journal = jCACM,
volume = "8",
number = "5",
pages = "318320",
month = may,
year = "1965",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
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bibdate = "Thu Sep 8 08:20:53 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
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acknowledgement = acknj,
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}tle = "Computation of the Base Two Logarithm of Binary
Numbers",
journal = jIEEETRANSELECCOMPUT,
volume = "EC14",
number = "6",
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month = dec,
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DOI = "http://dx.doi.org/10.1109/PGEC.1965.264080",
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bibsource = "http://www.computer.org/tc/;
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}lectronic ComputersacknhfbM. Combet and H. {Van Zonneveld} and L. VerbeekComputation of the Base Two Logarithm of Binary Numbers
@Article{Combet:1965:CBT,
author = "M. Combet and H. {Van Zonneveld} and L. Verbeek",
title = "Computation of the Base Two Logarithm of Binary
Numbers",
journal = jIEEETRANSELECCOMPUT,
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acknowledgement = acknhfb,
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]W#+g{=a7E;_k{articlefparith.bibCombet:1965:CBTM. Combet and H. Van Zonneveld and L. VerbeekComputation of the Base Two Logarithm of Binary NumbersjIEEETRANSELECCOMPUTEC146863867dec121965IEECA8http://dx.doi.org/10.1109/PGEC.1965.26408003677508 OR 03677508Thu Jul 14 06:26:41 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 06:26:41 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038605IEEE Transactions on Eel Multipliers",
journal = jALTAFREQ,
volume = "34",
number = "??",
pages = "349356",
month = mar,
year = "1965",
CODEN = "ALFRAJ",
ISSN = "00026557",
ISSNL = "00026557",
bibdate = "Fri Nov 09 10:47:42 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[pages
118225]{Swartzlander:1990:CAa}.",
URL = "http://en.wikipedia.org/wiki/Dadda_multiplier;
http://en.wikipedia.org/wiki/luigi_dadda",
acknowledgement = acknhfb,
authordates = "29 April 192326 October 2012",
fjournal = "Alta frequenza",
remark = "According to an ARITH'21 conference attendee, this is
a recommended article for understanding the Wallace and
Dadda multipliers.",
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@Article{Dadda:1965:SSP,
author = "Luigi Dadda",
title = "Some Schemes for Parallel Multipliers",
journal = jALTAFREQ,
volume = "34",
number = "??",
pages = "349356",
month = mar,
year = "1965",
CODEN = "ALFRAJ",
ISSN = "00026557",
ISSNL = "00026557",
bibdate = "Fri Nov 09 10:47:42 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[pages
118225]{Swartzlander:1990:CAa}.",
URL = "http://en.wikipedia.org/wiki/Dadda_multiplier;
http://en.wikipedia.org/wiki/luigi_dadda",
acknowledgement = acknhfb,
authordates = "29 April 192326 October 2012",
fjournal = "Alta frequenza",
remark = "According to an ARITH'21 conference attendee, this is
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}
`X #)#W#77=m;};)
I#WIarticlefparith.bibDadda:1965:SSPLuigi DaddaSome Schemes for Parallel MultipliersjALTAFREQ34349356mar31965ALFRAJ00026557 OR 0002655700026557 OR 00026557Fri Nov 09 10:47:42 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.09 10:47:42 ???Reprinted in cite [pages 118225]Swartzlander:1990:CAa.http://en.wikipedia.org/wiki/Dadda_multiplier; http://en.wikipedia.org/wiki/luigi_daddaAlta frequenzaAccording to an ARITH'21 conference attendee, this is a recommended article for understanding the Wallace and Dadda multipliers.acknhfb29 April 192326 October 2012Luigi DaddaReprinted in \cite[pages 118225]{Swartzlander:1990:CAa}.Some Scof a Diode Squarer by Applying the
Criterion of Square Root of the Integral of Per Cent
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volume = "EC14",
number = "3",
pages = "456463",
month = jun,
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} Applying the Criterion of Square Root of the Integral of Per Cent Error Squared
@Article{Deiters:1965:ODD,
author = "Robert M. Deiters",
title = "Optimum Design of a Diode Squarer by Applying the
Criterion of Square Root of the Integral of Per Cent
Error Squared",
journal = jIEEETRANSELECCOMPUT,
volume = "EC14",
number = "3",
pages = "456463",
month = jun,
year = "1965",
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DOI = "http://dx.doi.org/10.1109/PGEC.1965.264153",
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bibdate = "Thu Jul 14 06:26:34 MDT 2011",
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038465",
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fjournal = "IEEE Transactions on Electronic Computers",
}
%%OY #/u=a7E;_/uearticlefparith.bibDeiters:1965:ODDRobert M. DeitersOptimum Design of a Diode Squarer by Applying the Criterion of Square Root of the Integral of Per Cent Error SquaredjIEEETRANSELECCOMPUTEC143456463jun61965IEECA8http://dx.doi.org/10.1109/PGEC.1965.26415303677508 OR 03677508Thu Jul 14 06:26:34 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 06:26:34 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038465IEEE Transactions on Electronic ComputersacknhfbRobert M. DeitersOptimum Design of a Diode Squarer by of {Boolean} Functions",
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volume = "8",
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journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
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sjb = "Commenting on \cite{Mano:1965:PSB}.",
}
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journal = jCACM,
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http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Recently M. Morris Mano presented a method for
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of arithmetic and conditional transfer operations in a
decimal computer lacking builtin logical
instructions.",
acknowledgement = acknhfb,
checked = "19940407",
fjournal = "Communications of the ACM",
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QQY #')a57E);3?Yc3)e7articlefparith.bibDodd:1965:RSBGeorge G. DoddRemarks on Simulation of Boolean FunctionsjCACM88517517aug81965CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Fri Nov 25 18:20:01 MST 2005ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib; http://www.acm.org/pubs/cor",
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crossref = "Alt:1965:AC",
volume = "6",
pages = "131194",
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?"Y #+%=a7EU;__%#articlefparith=!U %#+%G#=m;%Gm@incollectionfparith.bibGarner:1965:NSAH. L. GarnerNumber systems and arithmeticAlt:1965:AC61311941965Sat May 18 14:18:19 2002http://www.math.utah.edu/pub/tex/bib/fparith.bib2002.05.18 14:18:19 ???acknhfbH. L. GarnerNumber systems and arithmetic
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}".bibGarner:1965:RIDH. L. GarnerR6522 Improving Digital Computer Performance Using Residue Number TheoryjIEEETRANSELECCOMPUTEC142277277apr41965IEECA8http://dx.doi.org/10.1109/PGEC.1965.26397503677508 OR 03677508Thu Jul 14 06:26:23 MDT 2011http://ieeexplore.ieee.org/; http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 06:26:23 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038430; http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4038385IEEE Transactions on Electronic Computersresidue arithmetic; residue number systemacknhfbH. L. Garner{R6522} Improving Digital Computer Performance Using Residue Number Theory
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http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038535",
acknowledgement = acknhfb,
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}#anscomput.bib2011.07.14 06:26:40 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038535IEEE Transactions on Electronic ComputersacknhfbD. Hammel{R6554} The Logic of Computer Arithmetic
@Article{Hammel:1965:RLC,
author = "D. Hammel",
title = "{R6554} The Logic of Computer Arithmetic",
journal = jIEEETRANSELECCOMPUT,
volume = "EC14",
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FGF[&[ #))57=a;?c)qarticlefparH%Z#I=a7E ;_'Icarticlefparith.bibHamming:1965:NLBR. W. Hamming and W. L. MammelA Note on the Location of the Binary Point in a Computin&$Y #/++O57E;S'c/7Carticlefparith.bibHammer:1965:BRBaPreston C. HammerBook Review: booktitle Experimenta#W #+[=a7E;__yarticlefparith.bibHammel:1965:RLCD. HammelR6554 The Logic of Computer ArithmeticjIEEETRANSELECCOMPUTEC144670670aug81965IEECA8http://dx.doi.org/10.1109/PGEC.1965.26403103677508 OR 03677508Thu Jul 14 06:26:40 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetrd Computing and Mathematics}} by N. C.
Metropolis; A. H. Taub; John Todd; C. B. Tompkins}",
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}$l Arithmetic, High Speed Computing and Mathematics by N. C. Metropolis; A. H. Taub; John Todd; C. B. TompkinsjTECHNOMETRICS718282feb21965TCMTA2http://dx.doi.org/10.2307/126613900401706 (print), 15372723 (electronic) OR 00401706 (print), 15372723 (electronic)00401706 OR 00401706Sat Jun 21 13:17:45 MDT 2014http://www.jstor.org/journals/00401706.html; http://www.jstor.org/stable/i254241; http://www.math.utah.edu/pub/bibnet/authors/m/metropolisnicholas.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/technometrics1960.bib2014.06.21 13:17:45 MDThttp://www.jstor.org/stable/1266139Technometricsacknhfbhttp://www.jstor.org/journals/00401706.htmlPreston C. HammerBook Review: {{\booktitle{Experimental Arithmetic, High Speed Computing and Mathematics}} by N. C. Metropolis; A. H. Taub; John Todd; C. B. Tompkins}
@Article{Hammer:1965:BRBa,
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title = "Book Review: {{\booktitle{Experimental Arithmetic,
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journal = jTECHNOMETRICS,
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bibsource = "http://www.jstor.org/journals/00401706.html;
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http://www.math.utah.edu/pub/bibnet/authors/m/metropolisnicholas.bib;
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}Note on the Location of the Binary Point in a
Computing Machine",
journal = jIEEETRANSELECCOMPUT,
volume = "EC14",
number = "2",
pages = "260261",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1965.264258",
ISSN = "03677508",
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038414",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Electronic Computers",
remark = "The authors consider the lowlevel multiplication
circuit efficiency of placing the binary point before
or after the first bit. If the leading bit is equally
likely to be a 0 or a 1, then their analysis shows that
it is better to place the point before the leading bit.
However, they report that a more likely distribution is
logarithmic (as predicted by Benford's Law, although
the Newcomb / Benford work is neither mentioned nor
cited), in which case there is no advantage for either
choice of placement of the binary point. The conclude
that it would be humane to place it after the leading
digit, by analogy with how people learn decimal
arithmetic.",
}%
?e7]B
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voag MachinejIEEETRANSELECCOMPUTEC142260261apr41965IEECA8http://dx.doi.org/10.1109/PGEC.1965.26425803677508 OR 03677508Thu Jul 14 06:26:22 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/benfordslaw.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 06:26:22 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038414IEEE Transactions on Electronic ComputersThe authors consider the lowlevel multiplication circuit efficiency of placing the binary point before or after the first bit. If the leading bit is equally likely to be a 0 or a 1, then their analysis shows that it is better to place the point before the leading bit. However, they report that a more likely distribution is logarithmic (as predicted by Benford's Law, although the Newcomb / Benford work is neither mentioned nor cited), in which case there is no advantage for either choice of placement of the binary point. The conclude that it would be humane to place it after the leading digit, by analogy with how people learn decimal arithmetic.acknhfbR. W. Hamming and W. L. MammelA Note on the Location of the Binary Point in a Computing Machine
@Article{Hamming:1965:NLB,
author = "R. W. Hamming and W. L. Mammel",
title = "A Note on the Location of the Binary Point in a
Computing Machine",
journal = jIEEETRANSELECCOMPUT,
volume = "EC14",
number = "2",
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month = apr,
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bibdate = "Thu Jul 14 06:26:22 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/benfordslaw.bib;
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038414",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Electronic Computers",
remark = "The authors consider the lowlevel multiplication
circuit efficiency of placing the binary point before
or after the first bit. If the leading bit is equally
likely to be a 0 or a 1, then their analysis shows that
it is better to place the point before the leading bit.
However, they report that a more likely distribution is
logarithmic (as predicted by Benford's Law, although
the Newcomb / Benford work is neither mentioned nor
cited), in which case there is no advantage for either
choice of placement of the binary point. The conclude
that it would be humane to place it after the leading
digit, by analogy with how people learn decimal
arithmetic.",
}sion FloatingPoint Arithmetic
with 132Bit Numbers",
journal = jCACM,
volume = "8",
number = "3",
pages = "175177",
month = mar,
year = "1965",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
MRclass = "68.00",
MRnumber = "30\#2707",
bibdate = "Fri Dec 08 14:32:51 1995",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In a recent paper, Gregory and Raney described a
technique for doubleprecision floatingpoint
arithmetic. A similar technique can be developed for
tripleprecision floatingpoint arithmetic and its is
the purpose of this note to describe this technique.
Only the multiplication and the division algorithms are
described, since the additionsubtraction algorithm can
be obtained by a trivial modification of the algorithm
in Gregory's and Raney's paper.",
acknowledgement = acknhfb,
checked = "19940404",
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}&ith.bibIkebe:1965:NTPYasuhiko IkebeNote on TriplePrecision FloatingPoint Arithmetic with 132Bit NumbersjCACM83175177mar31965CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 0001078268.0030\#2707Fri Dec 08 14:32:51 1995ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 14:32:51 ???In a recent paper, Gregory and Raney described a technique for doubleprecision floatingpoint arithmetic. A similar technique can be developed for tripleprecision floatingpoint arithmetic and its is the purpose of this note to describe this technique. Only the multiplication and the division algorithms are described, since the additionsubtraction algorithm can be obtained by a trivial modification of the algorithm in Gregory's and Raney's paper.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79In a recent paper, Gregory and Raney described a technique for doubleprecision floatingpoint arithmetic. A similar technique can be developed for tripleprecision floatingpoint arithmetic and its is the purpose of this note to describe this technique. Only the multiplication and the division algorithms are described, since the additionsubtraction algorithm can be obtained by a trivial modification of the algorithm in Gregory's and Raney's paper.Yasuhiko IkebeNote on TriplePrecision FloatingPoint Arithmetic with 132Bit Numbers
@Article{Ikebe:1965:NTP,
author = "Yasuhiko Ikebe",
title = "Note on TriplePrecision FloatingPoint Arithmetic
with 132Bit Numbers",
journal = jCACM,
volume = "8",
number = "3",
pages = "175177",
month = mar,
year = "1965",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
MRclass = "68.00",
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bibdate = "Fri Dec 08 14:32:51 1995",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In a recent paper, Gregory and Raney described a
technique for doubleprecision floatingpoint
arithmetic. A similar technique can be developed for
tripleprecision floatingpoint arithmetic and its is
the purpose of this note to describe this technique.
Only the multiplication and the division algorithms are
described, since the additionsubtraction algorithm can
be obtained by a trivial modification of the algorithm
in Gregory's and Raney's paper.",
acknowledgement = acknhfb,
checked = "19940404",
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}ration of Square Roots on a Computer with
Rapid Multiplication Compared with Division (in
{Technical Notes and Short Papers})",
journal = jMATHCOMPUT,
volume = "19",
number = "91",
pages = "497500",
month = jul,
year = "1965",
CODEN = "MCMPAF",
ISSN = "00255718 (print), 10886842 (electronic)",
ISSNL = "00255718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
garbo.uwasa.fi:/pc/docsoft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
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fjournal = "Mathematics of Computation",
journalURL = "http://www.ams.org/mcom/",
}'ication Compared with Division (in {Technical Notes and Short Papers})
@Article{James:1965:GSR,
author = "Wendy James and P. Jarratt",
title = "The Generation of Square Roots on a Computer with
Rapid Multiplication Compared with Division (in
{Technical Notes and Short Papers})",
journal = jMATHCOMPUT,
volume = "19",
number = "91",
pages = "497500",
month = jul,
year = "1965",
CODEN = "MCMPAF",
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bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
garbo.uwasa.fi:/pc/docsoft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
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acknowledgement = acknj # " and " # acknhfb,
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'Y#)A'57E?;A=Ayarticlefparith.bibJames:1965:GSRWendy James and P. JarrattThe Generation of Square Roots on a Computer with Rapid Multiplication Compared with Division (in Technical Notes and Short Papers)jMATHCOMPUT1991497500jul71965MCMPAF00255718 (print), 10886842 (electronic) OR 00255718 (print), 10886842 (electronic)00255718 OR 00255718Tue Oct 13 08:06:19 MDT 1998ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; garbo.uwasa.fi:/pc/docsoft/fpbiblio.txt; http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:06:19 MDTMathematics of Computationacknjhttp://www.ams.org/mcom/Wendy James and P. JarrattThe Generation of Square Roots on a Computer with Rapid Multiple Manual",
title = "The FloatingPoint Over\slash Underflow Trap Routine
{{\tt FPTRP}}",
publisher = "Institute of Computer Science, University of Toronto",
address = "Toronto, Ontario, Canada",
year = "1965",
LCCN = "????",
bibdate = "Wed Feb 14 19:11:11 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kahanwilliamm.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Section 4.1.",
acknowledgement = acknhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}(14 19:11:11 2007http://www.math.utah.edu/pub/bibnet/authors/k/kahanwilliamm.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.02.14 19:11:11 ???Section 4.1.Cited in cite Sterbenz:1974:FPC.acknhfbW. KahanProgrammer's Reference ManualSection 4.1.The FloatingPoint Over\slash Underflow Trap Routine {{\tt FPTRP}}
@InCollection{Kahan:1965:FPO,
author = "W. Kahan",
booktitle = "Programmer's Reference Manual",
title = "The FloatingPoint Over\slash Underflow Trap Routine
{{\tt FPTRP}}",
publisher = "Institute of Computer Science, University of Toronto",
address = "Toronto, Ontario, Canada",
year = "1965",
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bibdate = "Wed Feb 14 19:11:11 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kahanwilliamm.bib;
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7(W %#)Gu==s;%MG%incollectionfparith.bibKahan:1965:FPOW. KahanProgrammer's Reference ManualThe FloatingPoint Over / Underflow Trap Routine tt FPTRPInstitute of Computer Science, University of TorontoToronto, Ontario, Canada4975001965Wed Feb g Truncation Errors",
journal = jCACM,
volume = "8",
number = "1",
pages = "4040",
month = jan,
year = "1965",
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remark = "Gives summation error estimate formula `s = fl(a + b);
error = (a  s) + b', also discovered independently by
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})fm?idx=J79W. KahanFurther Remarks on Reducing Truncation Errors
@Article{Kahan:1965:FRR,
author = "W. Kahan",
title = "Further Remarks on Reducing Truncation Errors",
journal = jCACM,
volume = "8",
number = "1",
pages = "4040",
month = jan,
year = "1965",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Thu Sep 08 00:18:17 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
remark = "Gives summation error estimate formula `s = fl(a + b);
error = (a  s) + b', also discovered independently by
\cite{Moller:1965:QDP}. Extends Gill's earlier
fixedpoint result \cite{Gill:1951:PSS}. Cited in
\cite{Sterbenz:1974:FPC}.",
}
F"*V #+)y57=m;1Me)y5articlefparith.bibKanner:1965:NBCHerbert KannerNumber Base Conversion in Significant Digit ArithmeticjJACM122242246apr41965JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (e͍.)W #)g57=m;?Qcgarticlefparith.bibKahan:1965:FRRW. KahanFurther Remarks on Reducing Truncation ErrorsjCACM814040jan11965CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Thu Sep 08 00:18:17 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.08 00:18:17 ???Communications of the ACMGives summation error estimate formula `s = fl(a + b); error = (a  s) + b', also discovered independently by cite Moller:1965:QDP. Extends Gill's earlier fixedpoint result cite Gill:1951:PSS. Cited in cite Sterbenz:1974:FPC.acknjhttp://portal.acm.org/browse_dl.cion in Significant Digit
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@Article{Kanner:1965:NBC,
author = "Herbert Kanner",
title = "Number Base Conversion in Significant Digit
Arithmetic",
journal = jJACM,
volume = "12",
number = "2",
pages = "242246",
month = apr,
year = "1965",
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ISSN = "00045411 (print), 1557735X (electronic)",
ISSNL = "00045411",
bibdate = "Thu Nov 03 08:47:50 1994",
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fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}he DoublePrecision Square
Root Routine",
journal = jCACM,
volume = "8",
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pages = "202",
month = apr,
year = "1965",
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ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
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keywords = "$\sqrt(x)$; elementary functions; floatingpoint
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}+cknjhttp://portal.acm.org/browse_dl.cfm?idx=J79R. KingLetter to the {Editor}: On the DoublePrecision Square Root Routine
@Article{King:1965:LED,
author = "R. King",
title = "Letter to the {Editor}: On the DoublePrecision Square
Root Routine",
journal = jCACM,
volume = "8",
number = "4",
pages = "202",
month = apr,
year = "1965",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$\sqrt(x)$; elementary functions; floatingpoint
arithmetic",
}
T+Z #'57;1;?carticlefparith.bibKing:1965:LEDR. KingLetter to the Editor: On the DoublePrecision Square Root RoutinejCACM84202apr41965CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Thu Sep 1 10:15:43 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:43 ???Communications of the ACM$sqrt (x)$; elementary functions; floatingpoint arithmeticavideandCorrect Method for Variable Precision
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abstract = "Described in this paper is a divideandcorrect method
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Unlike the earlier methods of Stein and Pope, the
present method uses a suitably rounded form of the
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exact quotient character. It is believed that this
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@InProceedings{Seidel:2001:DFI,
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@InProceedings{Seidel:2001:BMR,
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@InProceedings{Schwarz:1995:RQC,
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@InProceedings{Schwarz:1999:GFPa,
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@InProceedings{Schwarz:2003:HID,
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@InProceedings{Seidel:1998:HSR,
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@InProceedings{Seidel:1998:HHL,
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727X~)
@Artiy
@Article{Price:1996:RA,
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@Article{Pritchard:1994:RAR,
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,)
@Article{Prince:1994:TFM,
author = "Timothy Prince",
title = "{{\tt float}}Preci,/
@Article{Prince:1990:GST,
author = "Timothy Prince",
title = "Generating Source F!Є;
@Article{Prince:1989:FTF,
author = "Timothy Prince",
title = "Float Trig Function\9
@Article{Prince:1984:SFP,
author = "Thomas Prince",
title = "{Savage} Floating Poܙ<y
@Article{Price:1995:PFF,
author = "Dick Price",
title = "{Pentium FDIV} Flaw  Lessons Learned",
journal = jIEEEMICRO,
volume = "15",
number = "2",
p/0. AshenhurstRadix Conversion in an Unnormalized Arithmetic System
@Article{Metropolis:1965:RCU,
author = "N. Metropolis and R. L. Ashenhurst",
title = "Radix Conversion in an Unnormalized Arithmetic
System",
journal = jMATHCOMPUT,
volume = "19",
number = "91",
pages = "435441",
month = jul,
year = "1965",
CODEN = "MCMPAF",
ISSN = "00255718 (print), 10886842 (electronic)",
ISSNL = "00255718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolisnicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
URL = "http://links.jstor.org/sici?sici=00255718%28196507%2919%3A91%3C435%3ARCIAUA%3E2.0.CO%3B2D",
ZMnumber = "0146.14607",
acknowledgement = acknhfb,
fjournal = "Mathematics of Computation",
journalURL = "http://www.ams.org/mcom/",
}
##Q6X#3Qw'57E;CA!=Qwarticlefparith.bibMetropolis:1965:RCUN. Metropolis and R. L. AshenhurstRadix Conversion in an Unnormalized Arithmetic SystemjMATHCOMPUT1991435441jul71965MCMPAF00255718 (print), 10886842 (electronic) OR 00255718 (print), 10886842 (electronic)00255718 OR 00255718Tue Oct 13 08:06:19 MDT 1998http://www.math.utah.edu/pub/bibnet/authors/m/metropolisnicholas.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:06:19 MDThttp://links.jstor.org/sici?sici=00255718%28196507%2919%3A91%3C435%3ARCIAUA%3E2.0.CO%3B2DMathematics of Computation0146.14607acknhfbhttp://www.ams.org/mcom/N. Metropolis and R. L",
journal = jIEEETRANSELECCOMPUT,
volume = "EC14",
number = "2",
pages = "181185",
month = apr,
year = "1965",
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ISSN = "03677508",
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fjournal = "IEEE Transactions on Electronic Computers",
}7.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 06:26:22 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038397IEEE Transactions on Electronic ComputersacknhfbGernot MetzeMinimal Square Rooting
@Article{Metze:1965:MSR,
author = "Gernot Metze",
title = "Minimal Square Rooting",
journal = jIEEETRANSELECCOMPUT,
volume = "EC14",
number = "2",
pages = "181185",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1965.263963",
ISSN = "03677508",
bibdate = "Thu Jul 14 06:26:22 MDT 2011",
bibsource = "http://www.computer.org/tc/;
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http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038397",
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fjournal = "IEEE Transactions on Electronic Computers",
}
v>9V #+!II)57=m;?Y'CI/articlefparith.bibMoller:1965:NQDOle MollerNote on Quasi DoublePrecisionjNORDISKTIDSKRINFORMBEHAND5425j8W #+%S!57=K;7U%W articlefparith.bibMiller:1965:ASFG. F. MillerAlgorithms for Special Functions IIjNUMMATH71941961965NUMMA70029599X (print), 09453245 (electronic)~7W #)%9=a7E;_%9Warticlefparith.bibMetze:1965:MSRGernot MetzeMinimal Square RootingjIEEETRANSELECCOMPUTEC142181185apr41965IEECA8http://dx.doi.org/10.1109/PGEC.1965.26396303677508 OR 03677508Thu Jul 14 06:26:22 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://wwwl Functions {II}",
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volume = "7",
pages = "194196",
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029599X (print), 09453245 (electronic)",
ISSNL = "0029599X",
bibdate = "Fri Sep 16 10:22:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Numerische Mathematik",
journalURL = "http://link.springer.com/journal/211",
xxmonth = "(none)",
xxnumber = "(none)",
}8 OR 0029599X (print), 09453245 (electronic)0029599X OR 0029599XFri Sep 16 10:22:10 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.16 10:22:10 ???Numerische Mathematikacknjhttp://link.springer.com/journal/211G. F. MillerAlgorithms for Special Functions {II}
@Article{Miller:1965:ASF,
author = "G. F. Miller",
title = "Algorithms for Special Functions {II}",
journal = jNUMMATH,
volume = "7",
pages = "194196",
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029599X (print), 09453245 (electronic)",
ISSNL = "0029599X",
bibdate = "Fri Sep 16 10:22:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Numerische Mathematik",
journalURL = "http://link.springer.com/journal/211",
xxmonth = "(none)",
xxnumber = "(none)",
}Precision",
journal = jNORDISKTIDSKRINFORMBEHAND,
volume = "5",
number = "4",
pages = "251255",
year = "1965",
CODEN = "BITTEL, NBITAB",
ISSN = "00063835 (print), 15729125 (electronic)",
ISSNL = "00063835",
bibdate = "Sat Nov 14 09:14:57 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Moller:1965:QDP}.",
acknowledgement = acknj # " and " # acknhfb,
journalURL = "http://link.springer.com/journal/10543",
}912551965BITTEL, NBITAB00063835 (print), 15729125 (electronic) OR 00063835 (print), 15729125 (electronic)00063835 OR 00063835Sat Nov 14 09:14:57 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib1998.11.14 09:14:57 ???See cite Moller:1965:QDP.acknjhttp://link.springer.com/journal/10543Ole M{\o}llerSee \cite{Moller:1965:QDP}.Note on Quasi DoublePrecision
@Article{Moller:1965:NQD,
author = "Ole M{\o}ller",
title = "Note on Quasi DoublePrecision",
journal = jNORDISKTIDSKRINFORMBEHAND,
volume = "5",
number = "4",
pages = "251255",
year = "1965",
CODEN = "BITTEL, NBITAB",
ISSN = "00063835 (print), 15729125 (electronic)",
ISSNL = "00063835",
bibdate = "Sat Nov 14 09:14:57 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Moller:1965:QDP}.",
acknowledgement = acknj # " and " # acknhfb,
journalURL = "http://link.springer.com/journal/10543",
}on in Floating Point Addition",
journal = jNORDISKTIDSKRINFORMBEHAND,
volume = "5",
number = "1",
pages = "3750",
month = mar,
year = "1965",
CODEN = "BITTEL, NBITAB",
DOI = "http://dx.doi.org/10.1007/BF01975722",
ISSN = "00063835 (print), 15729125 (electronic)",
ISSNL = "00063835",
MRclass = "65.80",
MRnumber = "31\#5359",
bibdate = "Wed Jan 4 18:52:08 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=00063835&volume=5&issue=1;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Moller:1965:NQD}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=5&issue=1&spage=37",
acknowledgement = acknj # " and " # acknhfb,
journalURL = "http://link.springer.com/journal/10543",
keywords = "accurate floatingpoint summation; floatingpoint
arithmetic; rounding errors",
remark = "Gives summation error estimate formula `s = fl(a + b);
error = (a  s) + b', also discovered independently by
\cite{Kahan:1965:FRR}. Extends Gill's earlier
fixedpoint result \cite{Gill:1951:PSS}.",
}:b2006.01.04 18:52:08 MSTSee also cite Moller:1965:NQD.http://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=5&issue=1&spage=37accurate floatingpoint summation; floatingpoint arithmetic; rounding errorsGives summation error estimate formula `s = fl(a + b); error = (a  s) + b', also discovered independently by cite Kahan:1965:FRR. Extends Gill's earlier fixedpoint result cite Gill:1951:PSS.acknjhttp://link.springer.com/journal/10543Ole M{\o}llerSee also \cite{Moller:1965:NQD}.Quasi DoublePrecision in Floating Point Addition
@Article{Moller:1965:QDP,
author = "Ole M{\o}ller",
title = "Quasi DoublePrecision in Floating Point Addition",
journal = jNORDISKTIDSKRINFORMBEHAND,
volume = "5",
number = "1",
pages = "3750",
month = mar,
year = "1965",
CODEN = "BITTEL, NBITAB",
DOI = "http://dx.doi.org/10.1007/BF01975722",
ISSN = "00063835 (print), 15729125 (electronic)",
ISSNL = "00063835",
MRclass = "65.80",
MRnumber = "31\#5359",
bibdate = "Wed Jan 4 18:52:08 MST 2006",
bibsource = "http://springerlink.metapress.com