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@Article{Murthy:1990:MPA,
author = "Narayan Murthy and Allen Stix",
title = "Multiple precision arithmetic: a programming
assignment in {CS2} applying linked lists",
journal = jSIGCSE,
volume = "22",
number = "1",
pages = "129133",
month = feb,
year = "1990",
CODEN = "SIGSD3",
DOI = "http://dx.doi.org/10.1145/319059.323431",
ISSN = "00978418",
ISSNL = "00978418",
bibdate = "Sat Nov 17 18:57:12 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/sigcse1990.bib",
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ÿ :ÿŒ8W #)1W57Eƒ;Qo1Ww articlefparith.bibSmith:1926:FGCDavid Eugene SmithThe First Great Commercial ArithmeticjISIS814149feb21926ISISA400211753 (print), 15456994 (electronic) OR 00211753 (print), 15456994 (electronic)00211753 OR 00211753Tue Jul 30 21:57:36 MDT 2013http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i211094; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/isis1920.bib2013.07.30 21:57:36 MDThttp://www.jstor.org/stable/223673Isisacknhfbhttp://www.jstor.org/page/journal/isis/about.htmlDavid Eugene SmithThe First Great Commercial Arithmetic
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acknowledgement = acknhfb,
fjournal = "Isis",
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;G%%Œarticlefparith.bibEscott:1937:QDNE. B. EscottQuestions, Discussions, and Notes: Rapid Method for Extracting a Square RootjAMERMATHMONTHLY4410644646dec121937AMMYAE00029890 (print), 19300972 (electronic) OR 00029890 (print), 19300972 (electronic)00029890 OR 00029890Mon Jun 28 12:38:44 MDT 1999http://www.math.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
Extracting a Square Root",
journal = jAMERMATHMONTHLY,
volume = "44",
number = "10",
pages = "644646",
month = dec,
year = "1937",
CODEN = "AMMYAE",
ISSN = "00029890 (print), 19300972 (electronic)",
ISSNL = "00029890",
bibdate = "Mon Jun 28 12:38:44 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",
}rith.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.''",
}
::CW '#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 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.''acknhfbApril 30, 1916February 24, 2001Claude Elwood ShannonNot submitted until 1940A Symbolic Analysis of Relay and Switching Circuits
@MastersThesis{Shannon:1937:SAR,
author = "Claude Elwood Shannon",
title = "A Symbolic Analysis of Relay and Switching Circuits",
type = "{Master of Science}",
school = "Department of Electrical Engineering, MIT",
address = "Cambridge, MA, USA",
pages = "72",
day = "10",
month = aug,
year = "1937",
bibdate = "Thu Nov 18 10:35:20 2010",
bibsource = "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.''",
}umbers 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.''\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 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",
journalURL = "http://www.jstor.org/journal/procamerphilsoci",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From \cite{Logan:1978:FDP}: ``Benford's paper was
published in 1938 in a journal of rather limited
circulation and not usually read by mathematicians. It
so happened that it was immediately followed in the
same issue by a physics paper which became of some
importance for secret nuclear work during World War II
[H. A. Bethe, M. E. Rose, and L. P. Smith, `The
Multiple Scattering of Electrons', Proc. Amer. Phil.
Soc. 78(4), 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.",
}
¤™
`qˆ4¤…Š
@Article{Bohlender:1992:PAF,
author = "G. Bohlender and D. Cordes and A. Kn{\"o}fel and U.
Kulisch and R. Lohner and W. V. Walter",
title = "Proposal for Accurate FloatingPoint Vector
Arithmetic",
journal = jMATHSCIENG,
volume = "189",
number = "??",
pages = "87104",
year = "1992",
CODEN = "MTSEAT",
ISSN = "00765392",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Mathematics in Science and Engineering",
}
p„c‰G
@Article{Bohlender:1988:IFA,
author = "Gerd Bohlender",
title = "Is floatingpoint arithmetic still adequate?",
journal = "Systems analysis and simulation",
volume = "46",
publisher = "AkademieVerlag",
address = "Berlin, Germany",
pages = "105108",
year = "1988",
MRclass = "68N15 (65G99)",
MRnumber = "976 389",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
xxjournal = "Math. Res.",
xxx = "I (Berlin, 1988)",
}éŒh™Q
@Article{Boggs:2004:MIP,
author = "Darrell Boggs and Aravindh Baktha and Jason Hawkins
and Deborah T. Marr and J. Alan Miller and Patrice
Roussel and Ronak Singhal and Bret Toll and K. S.
Venkatraman",
title = "The Microarchitecture of the {Intel{\reg}
Pentium{\reg} 4} Processor on 90nm Technology",
journal = jINTELTECHJ,
volume = "8",
number = "1",
pages = "17…g‹O
@Article{Bohlender:1982:ROA,
author = "G. Bohlender and K. Gr{\"u}ner and J. Wolff {von
Gudenberg}",
title = "{Realisierung einer optimalen Arithmetik} \toenglish
{Realization of Optimal Arithmetic} \endtoenglish",
journal = jELEKRECHENANLAGEN,
volume = "24",
number = "2",
pages = "6872",
month = apr,
year = "1982",
CODEN = "ELRAA4",
ISSN = "00135720",
bibdate = "Sat Feb 10 12:41:07 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Elektronische Rechenanlagen",
}R‡
@Article{Bohlender:1977:FPC,
author = "Gerd Bohlender",
title = "FloatingPoint Computation of Functions with Maximum
Accuracy",
journal = jIEEETRANSCOMPUT,
volume = "C26",
number = "7",
pages = "621632",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1977.1674894",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL …Š=
@Article{Bohannan:1982:MAP,
author = "J. W. Bohannan and D. J. Bradley and D. A. Kummer and
J. A. Saenz",
title = "Multiplication Algorithm for Packed {BCD} Numbers",
journal = jIBMTDB,
volume = "25",
number = "4",
pages = "2225",
month = sep,
year = "1982",
CODEN = "IBMTAA",
ISSN = "00188689",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "IBM Technical Disclosure Bulletin",
}Q$e 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] 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.acknhfbhttp://www.jstor.org/journal/procamerphilsociIt has been observed that the first pages of a table of common logarithms show more wear than do the last pages, indicating that more used numbers begin with the digit 1 than with the digit 9. A compilation of some 20,000 first digits taken from widely divergent sources shows that there is a logarithmic distribution of first digits when the numbers are composed of four or more digits. An analysis of the numbers from different sources shows that the numbers taken from unrelated subjects, such as a group of newspaper items, show a much better agreement with a logarithmic distribution than do numbers from mathematical tabulations or other formal data. There is here the peculiar fact that numbers that individually are without relationship are, when considered in large groups, in good agreement with a distribution 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 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 (print), 23269243 (electronic)",
ISSNL = "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 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.''\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 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",
journalURL = "http://www.jstor.org/journal/procamerphilsoci",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From \cite{Logan:1978:FDP}: ``Benford's paper was
published in 1938 in a journal of rather limited
circulation and not usually read by mathematicians. It
so happened that it was immediately followed in the
same issue by a physics paper which became of some
importance for secret nuclear work during World War II
[H. A. Bethe, M. E. Rose, and L. P. Smith, `The
Multiple Scattering of Electrons', Proc. Amer. Phil.
Soc. 78(4), 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.",
}
qqÓ[ #'E557=m;CŸ]WsŽEgŸe'EÌSarticlefparith.bibBenford:1938:LANFrank BenfordThe Law of Anomalous NumbersjPROCAMERPHILSOC784551572mar31938PAPCAA0003049X (print), 23269243 (electronic) OR 0003049X (print), 23269243 (electronic)0003049X 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 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 affairs. Th#
Y Y‡9W#)]!)!=m;]‡I£bookfparith.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,
author = "G. H. (Godfrey Harold) Hardy and E. M. (Edward
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title = "An Introduction to the Theory of Numbers",
publisher = pubOXFORD,
address = pubOXFORD:adr,
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}hY #3'ƒ7G'=m;''/ƒ_ phdthesisfparith.bibCouffignal:1938:AMAL. CouffignalSur l'analyse mecanique. Application aux machines a calculer et aux calculs de la mecanique celeste. (French) [On mechanical analysis. Application to calculating machines and to calculation in celestial mechanics]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 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]
@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",
} 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.''",
}
ùù” Y #/sA7=]; ‡}/s–Uarticlefparith.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 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.''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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http://www2.research.att.com/~njas/doc/shannonbio.html",
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.''",
}
¼ ¼ŠW"X ##
)OE‚#;S]Œarticlefparith.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/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}
@Article{K:1939:BRBd,
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title = "Book Review: {{\booktitle{Duodecimal 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",
URL = "http://www.jstor.org/stable/2980013",
acknowledgement = acknhfb,
fjournal = "Journal of the Royal Statistical Society",
}g!Y#)Q57Eƒ;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 Artificial Arithmetick in Decimals of {Robert Jager} ({London}, 1651)
@Article{Jager:1939:AAD,
author = "Robert Jager and Boyd C. Patterson",
title = "The Artificial Arithmetick in Decimals of {Robert
Jager} ({London}, 1651)",
journal = jISIS,
volume = "31",
number = "1",
pages = "2531",
month = nov,
year = "1939",
CODEN = "ISISA4",
ISSN = "00211753 (print), 15456994 (electronic)",
ISSNL = "00211753",
bibdate = "Tue Jul 30 21:26:49 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302217;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/isis1930.bib",
URL = "http://www.jstor.org/stable/226014",
acknowledgement = acknhfb,
fjournal = "Isis",
journalURL = "http://www.jstor.org/page/journal/isis/about.html",
}
fŠÐVf x&V '#)7#1'=m;‡!7³kmastersthesisfparith.bibBerry:1941:DEDClifford Edward 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 o†w%U !#)'9C/=m;_'g‡techreportfparith.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,
}‰7$X #%5=m;‚#‚+5ˆ}miscfparith.bibBush:1940:AMV. BushArithmetical Machine2993001940Wed Oct 13 11:37:32 2010http://www.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,
}ˆs#W !#1+/91'=m;_+g/ˆqtechreportfparith.bibAtanasoff: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
@TechReport{Atanasoff:1940:CMS,
author = "J. V. Atanasoff",
title = "Computing machine for the solution of large systems of
linear algebraic equations",
type = "Unpublished memorandum",
institution = "Iowa State College",
address = "Ames, IA, USA",
month = aug,
year = "1940",
bibdate = "Wed Oct 13 11:36:11 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.2]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
}
$F"
35Fmh–+¬W
@Article{Kaneko:1989:VRP,
author = "K. Kaneko and T. Okamoto and M. Nakajima and Y.
Nakakura and S. Gokita and J. Nishikawa and Y. Tanikawa
and H. Kadota",
title = "A {VLSI RISC} with 20{MFLOPS} peak, 64bit
floatingpoint unit",
journal = jIEEEJSOLIDSTATECIRCUITS,
volume = "24",
number = "5",
pages = "13311340",
month = oct,
year = "1989",
CODEN =
–‰/’_
@Article{Kaneko:1989:VRM,
author = "K. Kaneko and T. Okamoto and M. Nakajima and Y.
Nakakura and S. Gokita and J. Nishikawa and Y. Tanikawa
and H. Kadota",
title = "A {VLSI RISC} with {20MFLOPS} peak, 64bit
floatingpoint unit",
journal = jIEEEJSOLIDSTATECIRCUITS,
volume = "24",
number = "5",
pages = "13311340",
month = oct,
year = "1989",
CODEN =
“Ic
@Article{Karatsuba:1962:MMN,
author = "A. Karatsuba a sÁg
@Article{Kaplan:1999:JVA,
author = "Bonnie Kaplan",
title = "{John V. Atanasoff} (19031995) interview: {August
10, 1972}",
journal = "Computer Oral History Collection, Smithsonian
Institution Pr‡D
@Article{Kang:2006:SHS,
author = "J.Y. Kang and J.L. Gaudiot",
title = "A Simple HighSpeed Multiplier Design",
journal = jIEEETRANSCOMPUT,
volume = "55",
number = "10",
pages = "12531258",
month = oct,
year = "2006",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.2006.156",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Mon Jul 4 15:35:56 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/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1683756",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}Õ‹R—%
@Article{Kaneko:1973:LRE,
author = "Toyohisa Kaneko and Bede Liu",
title = "On Local Roundoff Errors in FloatingPoint
Arithmetic",
journal = jJACM,
volume = "20",
number = "3",
pages = "391398",
month = jul,
year = "1973",
CODEN = "JACOAH",
DOI = "http://doi.acm.org/10.1145/321765.321771",
ISSN = "00045411 (print), 1557735X (electronic)",
ISSNL = "000Éˆ
@Article{Kaneko:1973:LCO,
author = "T. Kaneko",
title = "Limitcycle oscillations in floatingpoint digital
filters",
journal = jIEEETRANSAUDIOELECTROACOUST,
volume = "21",
number = "2",
pages = "100106",
month = apr,
year = "1973",
CODEN = "ITADAS",
ISSN = "00189278",
ISSNL = "00189278",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "http:/Çˆ}‘{
@Article{Kanani:1973:NCS,
author = "Dhirubhai V. Kanani and Kenneth H. O'Keefe",
title = "A Note on ConditionalSum Addition for Base $2$
Systems",
journal = jIEEETRANSCOMPUT,
volume = "C22",
number = "6",
pages = "626626",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1973.5009117",
ISSN = "00189340 (print), 15579956 (eleÅ"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.",
}&neofakind 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.",
}
: W¡:ˆd)X!#/k +m_kg ˆQtechreportfparith.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,
}‰3(V !#'K7=m;_'g‰]techreportfparith.bibMauchly:1942:UHSJ. W. MauchlyThe use of high speed vacuum tube devices for 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}.",
acknowledgement = acknhfb,
}&'W #1/i/57Eƒ;SkW/iŽ]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.tandfonline.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",
ISSN = "01621459 (print), 1537274X (electronic)",
ISSNL = "01621459",
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",
}
0
’0”_+Y#/IuQ57=m;
„ysW„yIu”?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 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",
}Šk*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 12:36:57 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",
} "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",
}+
B ŒBŽGW !#3UA=‚ ;_‚ugY‘utechreportfparith.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}
@TechReport{vonNeumann:1945:FDR,
author = "John von Neumann",
title = "First Draft of a Report on the {EDVAC}",
institution = "University of Pennsylvania",
day = "30",
month = jun,
year = "1945",
bibdate = "Mon Jun 06 19:17:03 2005",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.",
acknowledgement = 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}.",
}Œq,Y#)GQ57=m;
sWGŽ'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.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",
CODEN = "NATUAS",
DOI = "http://dx.doi.org/10.1038/155052a0",
ISSN = "00280836 (print), 14764687 (electronic)",
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",
}n \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}.",
}
xix‡n0U #+!917=m;_=!g9ˆ[articlefparith.bibCesareo:1946:RIO. CesareoThe Relay InterpolatorjBELLLABSRECORD234574601946BLRCAB00058564 OR 00058564Wed Oct 13 11:31:47 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:31:47 ???Reprinted in cite [ 6.2]Randell:1982:ODC.Bell Laboratories RecordacknhfbO. CesareoReprinted in \cite[\S 6.2]{Randell:1982:ODC}.The Relay Interpolator
@Article{Cesareo:1946:RI,
author = "O. Cesareo",
title = "The Relay Interpolator",
journal = jBELLLABSRECORD,
volume = "23",
number = "??",
pages = "457460",
year = "1946",
CODEN = "BLRCAB",
ISSN = "00058564",
bibdate = "Wed Oct 13 11:31:47 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.2]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
fjournal = "Bell Laboratories Record",
}«/]!#)13;=„q;‚Y•U‚i1®]techreportfparith.bibBurks:1946:PDLArthur W. Burks and Herman H. Goldstine and John von NeumannPreliminary discussion of the logical design of an electronic computing instrumentinstINSTADVSTUDYinstINSTADVSTUDY:adr4228jun61946Wed Oct 13 08:17:48 2004ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.bib; ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib; ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/arith.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2004.10.13 08:17:48 ???Report to the U.S. Army Ordnance Department. Reprinted in cite [pp.~221259]Swartzlander:1976:CDD, cite [ 8.3]Randell:1982:ODC, and cite [pp.~97146]Aspray:1987:PJNDiscusses floatingpoint versus fixedpoint computation, and concludes that floatingpoint is probably not justifiable. They wrote:par ``There appear to be two major purposes in a `floating' decimal point system both of which arise from the fact that the number of digits in a word is a constant fixed by design considerations for each particular machine. The first of these purposes is to retain in a sum or product as many significant digits as possible and the second of these is to free the human operator from the burden of estimating and inserting into a problem `scale factors'  multipl5‰m.V#)Ee%E7=m;_EgiŠAarticlefparith.bibAiken:1946:ASCH. H. Aiken and G. M. HopperThe Automatic Sequence Controlled CalculatorjELECTRENG65384391, 449454, 5225281946ELENAC00959197 OR 00959197Wed Oct 13 11:26:29 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:26:29 ???Reprinted in cite [ 5.2]Randell:1982:ODC.Electrical Engineering (American Institute of Electrical Engineers)acknhfbH. H. Aiken and G. M. HopperReprinted in \cite[\S 5.2]{Randell:1982:ODC}.The {Automatic Sequence Controlled Calculator}
@Article{Aiken:1946:ASC,
author = "H. H. Aiken and G. M. Hopper",
title = "The {Automatic Sequence Controlled Calculator}",
journal = jELECTRENG,
volume = "65",
number = "??",
pages = "384391, 449454, 522528",
year = "1946",
CODEN = "ELENAC",
ISSN = "00959197",
bibdate = "Wed Oct 13 11:26:29 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.2]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
fjournal = "Electrical Engineering (American Institute of
Electrical Engineers)",
}p://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/arith.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Report to the U.S. Army Ordnance Department. Reprinted
in \cite[pp.~221259]{Swartzlander:1976:CDD}, \cite[\S
8.3]{Randell:1982:ODC}, and
\cite[pp.~97146]{Aspray:1987:PJN}",
acknowledgement = acknhfb,
remark = "Discusses floatingpoint versus fixedpoint
computation, and concludes that floatingpoint is
probably not justifiable. They wrote:\par
``There appear to be two major purposes in a `floating'
decimal point system both of which arise from the fact
that the number of digits in a word is a constant fixed
by design considerations for each particular machine.
The first of these purposes is to retain in a sum or
product as many significant digits as possible and the
second of these is to free the human operator from the
burden of estimating and inserting into a problem
`scale factors'  multiplicative constants which
serve to keep numbers within the limits of the
machine.\par
There is, of course, no denying the fact that human
time is consumed in arranging for the introduction of
suitable scale factors. We only argue that the time so
consumed is a very small percentage of the total time
we will spend in preparing an interesting problem for
our machine. The first advantage of the floating point
is, we feel, somewhat illusory. In order to have such a
floating point, one must waste memory capacity which
could otherwise be used for carrying more digits per
word. It would therefore seem to us not at all clear
whether the modest advantages of a floating binary
point offset the loss of memory capacity and the
increased complexity of the arithmetic and control
circuits.''",
}/icative constants which serve to keep numbers within the limits of the machine.par There is, of course, no denying the fact that human time is consumed in arranging for the introduction of suitable scale factors. We only argue that the time so consumed is a very small percentage of the total time we will spend in preparing an interesting problem for our machine. The first advantage of the floating point is, we feel, somewhat illusory. In order to have such a floating point, one must waste memory capacity which could otherwise be used for carrying more digits per word. It would therefore seem to us not at all clear whether the modest advantages of a floating binary point offset the loss of memory capacity and the increased complexity of the arithmetic and control circuits.''acknhfbArthur W. Burks and Herman H. Goldstine and John von NeumannReport to the U.S. Army Ordnance Department. Reprinted in \cite[pp.~221259]{Swartzlander:1976:CDD}, \cite[\S 8.3]{Randell:1982:ODC}, and \cite[pp.~97146]{Aspray:1987:PJN}Preliminary discussion of the logical design of an electronic computing instrument
@TechReport{Burks:1946:PDL,
author = "Arthur W. Burks and Herman H. Goldstine and John von
Neumann",
title = "Preliminary discussion of the logical design of an
electronic computing instrument",
institution = instINSTADVSTUDY,
address = instINSTADVSTUDY:adr,
pages = "42",
day = "28",
month = jun,
year = "1946",
bibdate = "Wed Oct 13 08:17:48 2004",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/arith.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Report to the U.S. Army Ordnance Department. Reprinted
in \cite[pp.~221259]{Swartzlander:1976:CDD}, \cite[\S
8.3]{Randell:1982:ODC}, and
\cite[pp.~97146]{Aspray:1987:PJN}",
acknowledgement = acknhfb,
remark = "Discusses floatingpoint versus fixedpoint
computation, and concludes that floatingpoint is
probably not justifiable. They wrote:\par
``There appear to be two major purposes in a `floating'
decimal point system both of which arise from the fact
that the number of digits in a word is a constant fixed
by design considerations for each particular machine.
The first of these purposes is to retain in a sum or
product as many significant digits as possible and the
second of these is to free the human operator from the
burden of estimating and inserting into a problem
`scale factors'  multiplicative constants which
serve to keep numbers within the limits of the
machine.\par
There is, of course, no denying the fact that human
time is consumed in arranging for the introduction of
suitable scale factors. We only argue that the time so
consumed is a very small percentage of the total time
we will spend in preparing an interesting problem for
our machine. The first advantage of the floating point
is, we feel, somewhat illusory. In order to have such a
floating point, one must waste memory capacity which
could otherwise be used for carrying more digits per
word. It would therefore seem to us not at all clear
whether the modest advantages of a floating binary
point offset the loss of memory capacity and the
increased complexity of the arithmetic and control
circuits.''",
}

'jIç‡Ž1
@InProceedings{Ercegovac:1989:FRD,
author = "M. D. Ercegovac and T. Lang",
title = "Onthefly rounding for division and square root",
†;Œw
@InProceedings{Ercegovac:1989:FSC,
author = "Milo{\v{s}} D. Ercegovac and Algirdas Avi{\v{z}}ienis
and Earl Swartzlander",
title = "Foreword: {9th Symposium on Computer Arithmetic
(ARITH9)}",
crossref = "Ercegovac:1989:PSC",
pages = "vv",
year = "1989",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsellab.com/arithmetic/arith9/papers/ARITH9_contents.pdf;
http://www.acsellab.com/arithmetic/arith9/papers/ARITH9_foreword.pdf;
http://www.acsellab.com/arithmetic/arith9/papers/ARITH9_preface.pdf",
acknowledgement = acknhfb,
keywords = "ARITH9",
}‹‡Ž1
@InProceedings{Ercegovac:1989:FRD,
author = "M. D. Ercegovac and T. Lang",
title = "Onthefly rounding for division and square root",
crossref = "Ercegovac:1989:PSC",
pages = "169173",
year = "1989",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsellab.com/arithmetic/arith9/papers/ARITH9_Ercegovac_rounding.pdf",
acknowledgement = acknhfb,
keywords = "ARITH9",
summary = "In division and square root implementation based on
digitrecurrence algorithms, the result is obtained in
digitserial form, from most significant digit to least
significant. To reduce the complexity of the
resultdigit selection and to allow the \ldots{}",
}Š„!ˆC
@InProceedings{Ercegovac:1988:LAD,
author = "M. D. Ercegovac and T. Lang",
title = "OnLine Arithmetic: a Design Methodology and
Applications in Digital Signal Processing",
crossref = "Brodersen:1988:VSP",
volume = "3",
pages = "252263",
year = "1988",
bibdate = "Fri Dec 08 10:42:22 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[6677]{Swartzlander:1990:CAb}.",
acknowledgement = acknhfb,
}Šm•[
@InProceedings{Ercegovac:1987:LSC,
author = "Milo{\v{s}} D. Ercegovac and Tomas Lang",
title = "OnLine Scheme for Computing Rotation Factors",
crossref = "Irwin:1987:PSC",
pages = "196203",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsellab.com/arithmetic/arith8/papers/ARITH8_Ercegovac_Lang.pdf",
abstract = "An intç‡hQ
@InProceedings{Ercegovac:1985:DAP,
author = "M. D. Ercegovac and T. Lang",
title = "A Division Algorithm with Prediction of Quotient
Digits",
crossref = "Hwang:1985:PSC",
pages = "5156",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsellab.com/arithmetic/arith7/papers/ARITH7_Ercegovac_Lang.pdf",
abstract = "A division algorithm with a simple selection of
quotient digits including prediction is possible if the
divisor is restricted to a suitable range. The
condition that the divisor must satisfy to have the
quotient digit $ q_{i + 1} $ predicted while computing
$ R_{i + 1} $ are determined. Some implementation
considerations are also given.",
acknowledgement = acknhfb,
keywords = "ARITH7",
}”
!Ã!‹2W#1S}K7E
;_o=SgŒarticlefparith.bibGoldstine:1946:ENIH. H. Goldstine and Adele GoldstineThe Electronic Numerical Integrator and Computer (ENIAC)jMATHTABLESOTHERAIDSCOMPUT21597110jul71946MTTCAS08916837 OR 08916837Tue Oct 13 08:44:19 MDT 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:44:19 MDTReprinted in cite [ 7.7]Randell:1982:ODC.Mathematical Tables and Other Aids to Computationacknhfbhttp://www.ams.org/mcom/H. H. Goldstine and Adele GoldstineReprinted in \cite[\S 7.7]{Randell:1982:ODC}.The {Electronic Numerical Integrator and Computer (ENIAC)}
@Article{Goldstine:1946:ENI,
author = "H. H. Goldstine and Adele Goldstine",
title = "The {Electronic Numerical Integrator and Computer
(ENIAC)}",
journal = jMATHTABLESOTHERAIDSCOMPUT,
volume = "2",
number = "15",
pages = "97110",
month = jul,
year = "1946",
CODEN = "MTTCAS",
ISSN = "08916837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
note = "Reprinted in \cite[\S 7.7]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journalURL = "http://www.ams.org/mcom/",
}Ž:1Y!#+Cƒ;=m;'C/ƒŽ#techreportfparith.bibDreyer:1946:REMH.J. Dreyer and A. WaltherDer Rechenautomat Ipm. Entwicklung Mathematischer Instrumente in Deutschland 1939 bis 1945. (German) [The Ipm Calculator. The development of mathematical instruments in Germany 19391945]BerichtA3Institut fur Praktische Mathematik, Technische HochschuleDarmstadt, West Germany45746019aug81946Wed Oct 13 11:20:15 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:20:15 ???Reprinted in cite [ 3.3]Randell:1982:ODC. Translated by Mr. and Mrs. P. JonesGermanacknhfbH.J. Dreyer and A. WaltherReprinted in \cite[\S 3.3]{Randell:1982:ODC}. Translated by Mr. and Mrs. P. Jones{Der Rechenautomat Ipm. Entwicklung Mathematischer Instrumente in Deutschland 1939 bis 1945}. ({German}) [{The} {Ipm} Calculator. {The} development of mathematical instruments in {Germany} 19391945]
@TechReport{Dreyer:1946:REM,
author = "H.J. Dreyer and A. Walther",
title = "{Der Rechenautomat Ipm. Entwicklung Mathematischer
Instrumente in Deutschland 1939 bis 1945}. ({German})
[{The} {Ipm} Calculator. {The} development of
mathematical instruments in {Germany} 19391945]",
type = "{Bericht}",
number = "A3",
institution = "Institut f{\"u}r Praktische Mathematik, Technische
Hochschule",
address = "Darmstadt, West Germany",
day = "19",
month = aug,
year = "1946",
bibdate = "Wed Oct 13 11:20:15 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 3.3]{Randell:1982:ODC}.
Translated by Mr. and Mrs. P. Jones",
acknowledgement = acknhfb,
language = "German",
}
ú‡\4U #'917=m;_=g9ˆKarticlefparith.bibJuley:1947:BCJ. JuleyThe Ballistic ComputerjBELLLABSRECORD24591947BLRCAB00058564 OR 00058564Wed Oct 13 11:32:38 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:32:38 ???Reprinted in cite [ 6.3]Randell:1982:ODC.Bell Laboratories RecordacknhfbJ. JuleyReprinted in \cite[\S 6.3]{Randell:1982:ODC}.The Ballistic Computer
@Article{Juley:1947:BC,
author = "J. Juley",
title = "The Ballistic Computer",
journal = jBELLLABSRECORD,
volume = "24",
number = "??",
pages = "59",
year = "1947",
CODEN = "BLRCAB",
ISSN = "00058564",
bibdate = "Wed Oct 13 11:32:38 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.3]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
fjournal = "Bell Laboratories Record",
}3Y!#1]3;=m;„;]„Ctechreportfparith.bibGoldstine:1947:PCPHerman H. Goldstine and John von NeumannPlanning and coding of problems for an electronic computing instrumentTechnical report1instINSTADVSTUDYinstINSTADVSTUDY:adr691apr41947Wed Jun 01 17:41:33 2005http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.06.01 17:41:33 ???Report prepared for U.S. Army Ordnance Department under contract W36034OKD7481. Reprinted in cite [80151]Taub:1963:JNCa. Knuth cite [p.~278]Knuth:1997:SA cites pp.~142151 of this report as the first published treatment of doubleprecision arithmetic on digital computers.acknhfbHerman H. Goldstine and John von NeumannReport prepared for U.S. Army Ordnance Department under contract W36034OKD7481. Reprinted in \cite[80151]{Taub:1963:JNCa}. Knuth \cite[p.~278]{Knuth:1997:SA} cites pp.~142151 of this report as the first published treatment of doubleprecision arithmetic on digital computers.Planning and coding of problems for an electronic computing instrument
@TechReport{Goldstine:1947:PCP,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument",
type = "Technical report",
number = "1",
institution = instINSTADVSTUDY,
address = instINSTADVSTUDY:adr,
pages = "69",
day = "1",
month = apr,
year = "1947",
bibdate = "Wed Jun 01 17:41:33 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Report prepared for U.S. Army Ordnance Department
under contract W36034OKD7481. Reprinted in
\cite[80151]{Taub:1963:JNCa}. Knuth
\cite[p.~278]{Knuth:1997:SA} cites pp.~142151 of this
report as the first published treatment of
doubleprecision arithmetic on digital computers.",
acknowledgement = acknhfb,
}
©•
9J [©‡jU
@Article{Reid:1979:FMF,
author = "John Reid",
title = "Functions for Manipulating FloatingPoint Numbers",
journal = jSIGNUM,
volume = "14",
number = "4",
pages = "1113",
month = dec,
year = "1979",
CODEN = "SNEWD6",
ISSN = "01635778 (print), 15580237 (electronic)",
ISSNL = "01635778",
bibdate = "Tue Apr 12 07:50:08 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbiblio.txt;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb # " and " # acknj,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Computer Sci. and Systems Div., AERE, Harwell, UK",
fjournal = "ACM SIGNUM Newsletter",
keywords = "complex numbers; digital arithmetic; floating;
FORTRAN; point arithmetic; portability; precision",
treatment = "P Practical",
}b‡D
@Article{Redinbo:1979:FFA,
author = "G. R. Redinbo",
title = "Finite Field Arithmetic on an Array Processor",
journal = jIEEETRANSCOMPUT,
volume = "C28",
number = "7",
pages = "461471",
month = jul,
year = "1979",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1979.1675390",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Mon Jul 11 06:49:39 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/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675390",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}aŠ"”E
@Article{ReidGreen:2002:TEA,
author = "Keith S. ReidGreen",
title = "Three early algorithms: [{Bresenham}'s linedrawing
algorithm; a squareroot algorithm; {Machin}'s
algorithm: computation of $ \pi $ ]",
journal = jIEEEANNHISTCOMPUT,
volume = "24",
number = "4",
pages = "1013",
month = oct,
year = "2002",
CODEN = "IAHCEX",
DOI = "http://dx.doi.org/10‰’5
@Article{Rehmer:1987:DIM,
author = "Karl Rehmer",
title = "Development and Implementation of the {Magnavox}
Generic {Ada} Basic Mathematics Package",
journal = jSIGADALETTERS,
volume = "7",
number = "3",
pages = "7383",
month = may # "\slash " # jun,
year = "1987",
CODEN = "AALEE5",
ISSN = "0736721X",
ISSNL = "0736721X",
bibdate = "Thu Sep 28 07:33:23 MDT :…E‹
@Article{Rees:1991:RRA,
author = "Jonathan Rees and William Clinger and others",
title = "The revised$^4$ report on the algorithmic language
{Scheme}",
journal = "ACM SIGPLAN Lisp Pointers",
volume = "4",
number = "3",
pages = "155",
month = jul # "\slash " # sep,
year = "1991",
bibdate = "Wed Jan 29 16:50:56 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
remark = "From \cite{Steele:2004:RHP}: ``the result [of a
binarytodecimal conversion] is expressed using the
minimum number of digits\ldots{}''",
}
0
l ³lŒD6W #/)[57Eƒ;Qo)_Ž
articlefparith.bibRicheson:1947:FAPA. W. RichesonThe First Arithmetic Printed in EnglishjISIS37124756may51947ISISA400211753 (print), 15456994 (electronic) OR 00211753 (print), 15456994 (electronic)00211753 OR 00211753Tue Jul 30 21:27:09 MDT 2013http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i302230; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/isis1940.bib2013.07.30 21:27:09 MDThttp://www.jstor.org/stable/226161Isisacknhfbhttp://www.jstor.org/page/journal/isis/about.htmlA. W. RichesonThe First Arithmetic Printed in {English}
@Article{Richeson:1947:FAP,
author = "A. W. Richeson",
title = "The First Arithmetic Printed in {English}",
journal = jISIS,
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MRreviewer = "E. Bodewig",
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in \cite[v.~5, pp.~479557]{Taub:1961:JNC}.",
ZMnumber = "0031.31402",
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fjournal = "Bulletin of the American Mathematical Society",
kwds = "nla, linear system, rounding error",
referred = "[Markov1999a].",
remark = "This may be the first journal publication about the
use of doubleprecision arithmetic on computers, used
for the accumulation of inner products and matrix
products. On pp.~10351038, the authors show that when
the sum of $m$ products of two $s$digit numbers is
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digits only after the final sum is complete, then the
rounding error is essentially one unit in the last
place, instead of $m$ times that value. Cited in
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}7
DD—97Y#3]g!!571!;m;Gg‡m!]Ogš3Oarticlefparith.bibvonNeumann:1947:NIMJohn von Neumann and Herman H. GoldstineNumerical Inverting of Matrices of High OrderjBULLAMS531110211099nov111947BAMOAD00029904 (print), 1936881X (electronic) OR 00029904 (print), 1936881X (electronic)00029904 OR 0002990465.0XMR0024235 (9,471b)E. BodewigThu Nov 8 14:49:36 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.08 14:49:36 ???See cite Goldstine:1951:NIM for Part II. Reprinted in cite [v.~5, pp.~479557]Taub:1961:JNC.Bulletin of the American Mathematical SocietyThis may be the first journal publication about the use of doubleprecision arithmetic on computers, used for the accumulation of inner products and matrix products. On pp.~10351038, the authors show that when the sum of $m$ products of two $s$digit numbers is accumulated in precision $ 2 s $, with rounding to $s$ digits only after the final sum is complete, then the rounding error is essentially one unit in the last place, instead of $m$ times that value. Cited in cite Sterbenz:1974:FPC.0031.31402acknhfbJohn von Neumann and Herman H. GoldstineSee \cite{Goldstine:1951:NIM} for Part II. Reprinted in \cite[v.~5, pp.~479557]{Taub:1961:JNC}.Numerical Inverting of Matrices of High Order
@Article{vonNeumann:1947:NIM,
author = "John von Neumann and Herman H. Goldstine",
title = "Numerical Inverting of Matrices of High Order",
journal = jBULLAMS,
volume = "53",
number = "11",
pages = "10211099",
month = nov,
year = "1947",
CODEN = "BAMOAD",
ISSN = "00029904 (print), 1936881X (electronic)",
ISSNL = "00029904",
MRclass = "65.0X",
MRnumber = "MR0024235 (9,471b)",
MRreviewer = "E. Bodewig",
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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in \cite[v.~5, pp.~479557]{Taub:1961:JNC}.",
ZMnumber = "0031.31402",
acknowledgement = acknhfb # " and " # ackjg,
fjournal = "Bulletin of the American Mathematical Society",
kwds = "nla, linear system, rounding error",
referred = "[Markov1999a].",
remark = "This may be the first journal publication about the
use of doubleprecision arithmetic on computers, used
for the accumulation of inner products and matrix
products. On pp.~10351038, the authors show that when
the sum of $m$ products of two $s$digit numbers is
accumulated in precision $ 2 s $, with rounding to $s$
digits only after the final sum is complete, then the
rounding error is essentially one unit in the last
place, instead of $m$ times that value. Cited in
\cite{Sterbenz:1974:FPC}.",
}
iÔG
(Xi‰2’e
@Article{Clenshaw:1986:UAR,
author = "C. W. Clenshaw and F. W. J. Olver",
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month = dec,
year = "1986",
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ISSNL aŠA•
@Article{Clenshaw:1986:GEL,
author = "C. W. Clenshaw and Daniel W. Lozier and F. W. J. Olver
and P. R. Turner",
title = "Generalized Exponential and Logarithmic Functions",
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volume = "12",
number = "56",
pages = "10911101",
month = sep # "\slash " # dec,
year = "1986",
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IS_…Š
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author = "W. K. Clarkson",
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fjournal = "Communications of the ACM",
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}³†R%
@Article{Clarke:1999:VSD,
author = "Edmund M. Clarke and Steven M. German and Xudong
Zhao",
title = "Verifying the {SRT} Division Algorithm Using Theorem
Proving Techniques",
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http://www.wkap.nl/oasis.htm/194806",
acknowledgement = acknhfb,
fjournal = "Formal Methods in System Design",
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MRclass = "65G05",
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@Article{Clenshaw:1963:ASF,
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k
»°kˆB:V !#)'S7)1=‚Q;'S‰3techreportfparith.bibTukey:1948:NSRJohn W. TukeyA note on the squareroot iterationSRG Memorandum report10instPRINCETONinstPRINCETON:adr181948Tue May 15 08:00:09 2012http://www.math.utah.edu/pub/bibnet/authors/t/tukeyjohnw.bib; http://www.math.utah.edu/pub/tex/bib/elefunt.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2012.05.15 08:00:09 ???acknhfbJohn W. TukeyA note on the squareroot iteration
@TechReport{Tukey:1948:NSR,
author = "John W. Tukey",
title = "A note on the squareroot iteration",
type = "SRG Memorandum report",
number = "10",
institution = instPRINCETON,
address = instPRINCETON:adr,
pages = "18",
year = "1948",
bibdate = "Tue May 15 08:00:09 2012",
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http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
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}ˆ9U #)%?'7=m;_9%g?ˆ articlefparith.bibEckert:1948:ECW. J. EckertElectrons and computationjSCIMONTHLY675315323nov111948SCMOAA00963771 OR 00963771Wed Oct 13 11:27:40 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:27:40 ???Reprinted in cite [ 5.3]Randell:1982:ODC.The Scientific MonthlyacknhfbW. J. EckertReprinted in \cite[\S 5.3]{Randell:1982:ODC}.Electrons and computation
@Article{Eckert:1948:EC,
author = "W. J. Eckert",
title = "Electrons and computation",
journal = jSCIMONTHLY,
volume = "67",
number = "5",
pages = "315323",
month = nov,
year = "1948",
CODEN = "SCMOAA",
ISSN = "00963771",
bibdate = "Wed Oct 13 11:27:40 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.3]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
fjournal = "The Scientific Monthly",
}ŠB8V #'%uK7E
;_o=%g}‹U
articlefparith.bibAlt:1948:BTLaFranz L. AltA Bell Telephone Laboratories' Computing MachineIjMATHTABLESOTHERAIDSCOMPUT321113jan11948MTTCAS08916837 OR 08916837Tue Oct 13 08:44:19 MDT 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:44:19 MDTReprinted in cite [ 6.4]Randell:1982:ODC.Mathematical Tables and Other Aids to Computationacknhfbhttp://www.ams.org/mcom/Franz L. AltReprinted in \cite[\S 6.4]{Randell:1982:ODC}.A {Bell Telephone Laboratories}' Computing Machine{I}
@Article{Alt:1948:BTLa,
author = "Franz L. Alt",
title = "A {Bell Telephone Laboratories}' Computing
Machine{I}",
journal = jMATHTABLESOTHERAIDSCOMPUT,
volume = "3",
number = "21",
pages = "113",
month = jan,
year = "1948",
CODEN = "MTTCAS",
ISSN = "08916837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
note = "Reprinted in \cite[\S 6.4]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journalURL = "http://www.ams.org/mcom/",
} 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/a/turingalanmathison.bib;
http://www.math.utah.edu/pub/bibnet/subjects/accstabnumalg2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/accstabnumalg.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite{Turing:1992:PM} with summary and
notes (including corrections)",
URL = "http://turing.ecs.soton.ac.uk/browse.php/B/18",
ZMnumber = "0033.28501",
acknowledgement = acknhfb,
fjournal = "Quarterly Journal of Mechanics and Applied
Mathematics",
mynote = "The notes are not very good. They mainly correct
errors and fill in the gaps of derivations. Much better
would have been higher level comments from a numerical
analyst, e.g. on where Turing's ideas/predictions were
wrong.",
};
™‰yW #+%
97=m;M%
ˆiarticlefparith.bibHuskey:1949:PCPH. D. HuskeyOn the Precision of a Certain Procedure of Numerical IntegrationjJRESNATLBURSTAND4257621949JRNBAG00910635 OR 00910635Fri Aug 20 09:32:34 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.08.20 09:32:34 ???Cited in cite Sterbenz:1974:FPC.acknhfbH. D. HuskeyOn the Precision of a Certain Procedure of Numerical Integration
@Article{Huskey:1949:PCP,
author = "H. D. Huskey",
title = "On the Precision of a Certain Procedure of Numerical
Integration",
journal = jJRESNATLBURSTAND,
volume = "42",
number = "??",
pages = "5762",
year = "1949",
CODEN = "JRNBAG",
ISSN = "00910635",
bibdate = "Fri Aug 20 09:32:34 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}‡}=W #S{=m;SˆIarticlefparith.bibHartree:1949:NSRDouglas R. (Douglas Rayner) HartreeNote On Systematic Roundoff Errors in Numerical IntegrationJournal of Research of the National Bureau of Standards4262??1949Wed Feb 14 19:07:37 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.02.14 19:07:37 ???acknhfbDouglas R. (Douglas Rayner) HartreeNote On Systematic Roundoff Errors in Numerical Integration
@Article{Hartree:1949:NSR,
author = "Douglas R. (Douglas Rayner) Hartree",
title = "Note On Systematic Roundoff Errors in Numerical
Integration",
journal = "Journal of Research of the National Bureau of
Standards",
volume = "42",
number = "??",
pages = "62??",
month = "????",
year = "1949",
bibdate = "Wed Feb 14 19:07:37 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}
Çö ‰SBW '#+'7;Q'=m;_';g?‰Uinproceedingsfparith.bibWorsley:1950:EDB. H. WorsleyReport of a Conference on High Speed Automatic Calculating Machines, 2225 June 1949The EDSAC demonstrationUniversity Mathematical LaboratoryCambridge, UK1216jan11950Wed Oct 13 11:39:09 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:39:09 ???Reprinted in cite [ 8.6]Randell:1982:ODC.acknhfbB. H. WorsleyReport of a Conference on High Speed Automatic Calculating Machines, {2225 June 1949}Reprinted in \cite[\S 8.6]{Randell:1982:ODC}.The {EDSAC} demonstration
@InProceedings{Worsley:1950:ED,
author = "B. H. Worsley",
booktitle = "Report of a Conference on High Speed Automatic
Calculating Machines, {2225 June 1949}",
title = "The {EDSAC} demonstration",
publisher = "University Mathematical Laboratory",
address = "Cambridge, UK",
pages = "1216",
month = jan,
year = "1950",
bibdate = "Wed Oct 13 11:39:09 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.6]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
}‰NAW'#'C7Q'=m;_C;g#‰Oinproceedingsfparith.bibWilkes:1950:EM. V. Wilkes and W. RenwickReport of a Conference on High Speed Automatic Calculating Machines, 2225 June 1949The EDSACUniversity Mathematical LaboratoryCambridge, UK911jan11950Wed Oct 13 12:00:41 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 12:00:41 ???Reprinted in cite [ 8.5]Randell:1982:ODC.acknhfbM. V. Wilkes and W. Renwick{Report of a Conference on High Speed Automatic Calculating Machines, 2225 June 1949}Reprinted in \cite[\S 8.5]{Randell:1982:ODC}.The {EDSAC}
@InProceedings{Wilkes:1950:E,
author = "M. V. Wilkes and W. Renwick",
booktitle = "{Report of a Conference on High Speed Automatic
Calculating Machines, 2225 June 1949}",
title = "The {EDSAC}",
publisher = "University Mathematical Laboratory",
address = "Cambridge, UK",
pages = "911",
month = jan,
year = "1950",
bibdate = "Wed Oct 13 12:00:41 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.5]{Randell:1982:ODC}.",
acknowledgement = acknhfb,
}Œ6@W #1E+3!E%;„I5EŽÐbookfparith.bibStifler:1950:HSCW. W. Stifler, Jr.Highspeed computing devicespubMCGRAWHILLpubMCGRAWHILL:adrxiii + 4511950QA75 .E5Fri Aug 20 10:18:44 MDT 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2010.08.20 10:18:44 MDTSupervised by Charles Brown Tompkins and C. H. Wakelin, Engineering Research Associates. The contents of this volume were first assembled in the form of a report to the Office of Naval Research, prepared under a provision of contract N6ONR240, Task 1. Cited in cite Sterbenz:1974:FPC.computersacknhfbW. W. {Stifler, Jr.}Highspeed computing devices
@Book{Stifler:1950:HSC,
editor = "W. W. {Stifler, Jr.}",
title = "Highspeed computing devices",
publisher = pubMCGRAWHILL,
address = pubMCGRAWHILL:adr,
pages = "xiii + 451",
year = "1950",
LCCN = "QA75 .E5",
bibdate = "Fri Aug 20 10:18:44 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = acknhfb,
remark = "Supervised by Charles Brown Tompkins and C. H.
Wakelin, Engineering Research Associates. The contents
of this volume were first assembled in the form of a
report to the Office of Naval Research, prepared under
a provision of contract N6ONR240, Task 1. Cited in
\cite{Sterbenz:1974:FPC}.",
subject = "computers",
}
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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,
}‰>KW#EQQ=a;EQŠearticlefparith.bibMorrill:1952:SEMC. D. Morrill and R. V. BaumA Stabilized Electronic MultiplierjTRANSIREPROFGROUPELECCOMPUTEC15259dec121952Fri 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;
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acknowledgement = acknhfb,
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}‹JV #1/!O77E‚#;SGc/articlefparith.bibMichaelson:1952:BAR. L. MichaelsonBinary ArithmeticjINCSTAT313540feb21952http://dx.doi.org/10.2307/298659114669404 OR 1466940414669404 OR 14669404Thu Jan 22 18:10:18 MST 2015http://www.jstor.org/stable/i349863; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/jrssd1950.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,
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:â:™%NY #+%I57=m;'‰1e‰%M—Marticlefparith.bibBackus:1954:ISSJ. W. BackusThe IBM 701 Speedcoding SystemjJACM1146jan11954JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 00045411Fri Nov 04 00:18:27 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.11.04 00:18:27 ???http://community.computerhistory.org/scc/projects/FORTRAN/paper/p4backus.pdfThe 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.Journal of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401The 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.J. W. BackusThe {IBM 701 Speedcoding} System
@Article{Backus:1954:ISS,
author = "J. W. Backus",
title = "The {IBM 701 Speedcoding} System",
journal = jJACM,
volume = "1",
number = "1",
pages = "46",
month = jan,
year = "1954",
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ISSN = "00045411 (print), 1557735X (electronic)",
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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",
}†MW #%+#=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,
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title = "Principles of Operation: Type 701 and Associated
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publisher = pubIBM,
address = pubIBM:adr,
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acknowledgement = acknhfb,
}",
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",
}Nnd coding manual  Datatron
operation manual  Central computer handbook 
Paper tape system handbook  Card converter Model 500
handbook  Magnetic tape system handbook 
Cardatron system handbook  Model 560 DATAFILE
handbook  Control console and consolette handbook
 Floating point control unit handbook  External
switching unit handbook  Tape preparation unit
handbook.",
}O
W²WŒXPX#?WQ=a;‚[?[ŽEarticlefparith.bibFreeman:1954:TSAH. Freeman and E. ParsonsTimeSharing Analog Multiplier (TSAM)jTRANSIREPROFGROUPELECCOMPUTEC311117mar31954Fri 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 ComputersCited in US Patent 3,043,516 (10 July 1962): Time Summing Device for Division, Multiplication, Root Taking and Interpolation, by Harold W. Abbott and Vernon P. Mathis.acknhfbH. Freeman and E. ParsonsTimeSharing Analog Multiplier ({TSAM})
@Article{Freeman:1954:TSA,
author = "H. Freeman and E. Parsons",
title = "TimeSharing Analog Multiplier ({TSAM})",
journal = jTRANSIREPROFGROUPELECCOMPUT,
volume = "EC3",
number = "1",
pages = "1117",
month = mar,
year = "1954",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Jul 15 15:20:53 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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acknowledgement = acknhfb,
fjournal = "Transactions of the I.R.E. Professional Group on
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remark = "Cited in US Patent 3,043,516 (10 July 1962): Time
Summing Device for Division, Multiplication, Root
Taking and Interpolation, by Harold W. Abbott and
Vernon P. Mathis.",
}ŽKOV #/Q1%/Em;3†WU1
manualfparith.bibBurroughs:1954:DHBurroughs Corporation. ElectroDataDatatron handbooksThe DivisionPasadena, CA, USA461954Sat Feb 24 15:01:45 MST 1996http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MST12 volumes in 1.Datatron (Computer)Datatron programming and coding manual  Datatron operation manual  Central computer handbook  Paper tape system handbook  Card converter Model 500 handbook  Magnetic tape system handbook  Cardatron system handbook  Model 560 DATAFILE handbook  Control console and consolette handbook  Floating point control unit handbook  External switching unit handbook  Tape preparation unit handbook.acknhfb{Burroughs Corporation. ElectroData}12 volumes in 1.Datatron handbooks
@Manual{Burroughs:1954:DH,
author = "{Burroughs Corporation. ElectroData}",
title = "Datatron handbooks",
organization = "The Division",
address = "Pasadena, CA, USA",
year = "1954",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "12 volumes in 1.",
acknowledgement = acknhfb,
keywords = "Datatron (Computer)",
remark = "Datatron programming and coding manual  Datatron
operation manual  Central computer handbook 
Paper tape system handbook  Card converter Model 500
handbook  Magnetic tape system handbook 
Cardatron system handbook  Model 560 DATAFILE
handbook  Control console and consolette handbook
 Floating point control unit handbook  External
switching unit handbook  Tape preparation unit
handbook.",
}
ÂÓäõ±l›Y
@Article{Ercegovac:2007:CSR,
author = "Milo{\v{s}} D. Ercegovac and JeanMichel Muller",
title = "Complex Square Root with Operand Prescaling",
journal = jJVLSISIGNALPROC,
volume = "49",
number = "1",
pages = "1930",
month = oct,
year = "2007",
CODEN = "JVSPED",
DOI = "http://dx.doi.org/10.1007/s1126500600292",
ISSN = "09225773",
ISSNL = "09225773",
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Some Elementary Functions Using Small Multipliers",
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month = jul,
year = "2000",
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author = "Milo{\v{s}} D. Ercegovac and Laurent Imbert and David
W. Matula and JeanMichel Muller and Guoheng Wei",
title = "Improving {Goldschmidt} Division, Square Root, and
Square Root Reciprocal",
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volume = "49",
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@Article{Ercegovac:1994:VHR,
author = "M. D. Ercegovac and T. Lang and P. Montuschi",
title = "VeryHigh Radix Division with Prescaling and Selection
by Rounding",
journal = jIEEETRANSCOMPUT,
volume = "43",
number = "8",
pages = "909918",
month = aug,
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ISSN = "00189340 (print), 155799ÃŸ
@Article{Ercegovac:1992:FRC,
author = "M. D. Ercegovac and T. Lang",
title = "Onthefly rounding [computing arithmetic]",
journal = jIEEETRANSCOMPUT,
volume = "41",
number = "12",
pages = "14971503",
month = dec,
year = "1992",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.214659",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdaóŽœ;
@Article{Ercegovac:1991:MPM,
author = "Milo{\v{s}} D. Ercegovac and Tomas Lang",
title = "Module to perform multiplication, division, and square
root in systolic arrays for matrix computations",
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volume = "11",
number = "3",
pages = "212221",
month = mar,
year = "1991",
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@Article{Ercoli:1957:EDO,
author = "Paolo Ercoli and Roberto Vacca",
title = "Errors Due to Overflow in Arithmetic Operations
Particularly as Regards {FINAC} Electronic Computer",
journal = jJACM,
volume = "4",
number = "4",
pages = "450455",
month = oct,
year = "1957",
CODEN = "JACOAH",
ISSN = "00045411 (print), 1557735X (electronic)",
ISSNL = "00045411",
bibdate = "Thu Dec 08 09:28:48 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See letter \cite{Ercoli:1960:LEE}.",
acknowledgement = acknhfb,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
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}d
ÑGÑ‰;SV#)g[;7=a;]g[Š'articlefparith.bibMayer:1954:ODFM. A. Mayer and B. M. Gordon and R. N. NicolaAn operational digital feedback dividerjIRETRANSELECCOMPUTEC311720mar31954IRELAO03679950 OR 03679950Sun Jul 17 09:52:58 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.17 09:52:58 ???IRE Transactions on Electronic ComputersacknhfbM. A. Mayer and B. M. Gordon and R. N. NicolaAn operational digital feedback divider
@Article{Mayer:1954:ODF,
author = "M. A. Mayer and B. M. Gordon and R. N. Nicola",
title = "An operational digital feedback divider",
journal = jIRETRANSELECCOMPUT,
volume = "EC3",
number = "1",
pages = "1720",
month = mar,
year = "1954",
CODEN = "IRELAO",
ISSN = "03679950",
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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acknowledgement = acknhfb,
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}‰5RW#+AQQ=a;AQŠ]articlefparith.bibKovach:1954:AMUL. D. Kovach and W. ComleyAn Analog Multiplier Using ThyritejTRANSIREPROFGROUPELECCOMPUTEC324245jun61954Sun Jul 17 09:57:13 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.17 09:57:13 ???Transactions of the I.R.E. Professional Group on Electronic ComputersacknhfbL. D. Kovach and W. ComleyAn Analog Multiplier Using Thyrite
@Article{Kovach:1954:AMU,
author = "L. D. Kovach and W. Comley",
title = "An Analog Multiplier Using Thyrite",
journal = jTRANSIREPROFGROUPELECCOMPUT,
volume = "EC3",
number = "2",
pages = "4245",
month = jun,
year = "1954",
CODEN = "????",
ISSN = "????",
bibdate = "Sun Jul 17 09:57:13 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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acknowledgement = acknhfb,
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;yŠ9
articlefparith.bibGorn:1954:AACSaul GornThe Automatic Analysis and Control of Computing ErrorsjJSIAM226981jun61954JSIMAV03684245 (print), 1095712X (electronic) OR 03684245 (print), 1095712X (electronic)Thu Oct 15 18:16:06 MDT 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.15 18:16:06 MDTJournal of the Society for Industrial and Applied MathematicsacknhfbSaul GornThe Automatic Analysis and Control of Computing Errors
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author = "Saul Gorn",
title = "The Automatic Analysis and Control of Computing
Errors",
journal = jJSIAM,
volume = "2",
number = "2",
pages = "6981",
month = jun,
year = "1954",
CODEN = "JSIMAV",
ISSN = "03684245 (print), 1095712X (electronic)",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = acknhfb,
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®
È,®Š{VX#+wM#E%;M!wMŒ bookfparith.bibEckert:1955:FFSW. J. (Wallace John) Eckert and Rebecca Bradley JonesFaster, faster; a simple description of a giant electronic calculator and the problems it solvespubIBMpubIBM:adr1601955QA76 .E25Fri Aug 20 08:57:56 MDT 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2010.08.20 08:57:56 MDTCited in cite Sterbenz:1974:FPC.Computersacknhfb19021971W. J. (Wallace John) Eckert and Rebecca Bradley JonesFaster, faster; a simple description of a giant electronic calculator and the problems it solves
@Book{Eckert:1955:FFS,
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}‰UV#/IM%57=m;IMIM‰{articlefparith.bibCrockett:1955:GMMJ. B. Crockett and H. ChernoffGradient Methods of MaximizationjPACJMATH533501955PJMAAI00308730 (print), 19455844 (electronic) OR 00308730 (print), 19455844 (electronic)00308730 OR 00308730Fri Aug 20 08:54:24 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.08.20 08:54:24 ???Pacific Journal of MathematicsCited in cite Sterbenz:1974:FPC.acknhfbJ. B. Crockett and H. ChernoffGradient Methods of Maximization
@Article{Crockett:1955:GMM,
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title = "Gradient Methods of Maximization",
journal = jPACJMATH,
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acknowledgement = acknhfb,
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remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}Š5TX #%57=m;1Oe%‹=articlefparith.bibMoshman:1954:GPRJack MoshmanThe Generation of PseudoRandom Numbers on a Decimal CalculatorjJACM128891apr41954JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 00045411Fri Nov 04 00:18:27 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.11.04 00:18:27 ???Journal of the ACMdecimal floatingpoint arithmeticacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401Jack MoshmanThe Generation of PseudoRandom Numbers on a Decimal Calculator
@Article{Moshman:1954:GPR,
author = "Jack Moshman",
title = "The Generation of PseudoRandom Numbers on a Decimal
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journal = jJACM,
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pages = "8891",
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year = "1954",
CODEN = "JACOAH",
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bibdate = "Fri Nov 04 00:18:27 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",
keywords = "decimal floatingpoint arithmetic",
}
n¾×nŠfYX #1W57=m;1e1W‹articlefparith.bibParsons:1955:SDCFrances L. ParsonsA Simple DeskCalculator Method for Checking Binary Results of Digital Computer Arithmetic OperationsjJACM23205207jul71955JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 00045411Wed Nov 09 01:00:34 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.11.09 01:00:34 ???Journal of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401Frances L. ParsonsA Simple DeskCalculator Method for Checking Binary Results of Digital Computer Arithmetic Operations
@Article{Parsons:1955:SDC,
author = "Frances L. Parsons",
title = "A Simple DeskCalculator Method for Checking Binary
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journal = jJACM,
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number = "3",
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month = jul,
year = "1955",
CODEN = "JACOAH",
ISSN = "00045411 (print), 1557735X (electronic)",
ISSNL = "00045411",
bibdate = "Wed Nov 09 01:00:34 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",
}‡dXV #/)=)7;K;9)=‰articlefparith.bibLenaerts:1955:ASRE. H. LenaertsAutomatic Square RootingjELECTRONENG27287289jul71955ELEGAP00134902 OR 00134902Thu Sep 1 10:15:41 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:41 ???Electronic EngineeringacknjE. H. LenaertsAutomatic Square Rooting
@Article{Lenaerts:1955:ASR,
author = "E. H. Lenaerts",
title = "Automatic Square Rooting",
journal = jELECTRONENG,
volume = "27",
number = "??",
pages = "287289",
month = jul,
year = "1955",
CODEN = "ELEGAP",
ISSN = "00134902",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
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acknowledgement = acknj,
fjournal = "Electronic Engineering",
}ˆ?WX#/U'/!=K;Uˆ_Ñbookfparith.bibHastings:1955:ADCCecil B. Hastings, Jr. and Jeanne T. Hayward and James P. Wong, Jr.Approximations for Digital ComputerspubPRINCETONpubPRINCETON:adrviii + 2011955QA76 .H33Mon Sep 30 14:51:50 1996ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.09.30 14:51:50 ???acknjCecil B. {Hastings, Jr.} and Jeanne T. Hayward and James P. {Wong, Jr.}Approximations for Digital Computers
@Book{Hastings:1955:ADC,
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James P. {Wong, Jr.}",
title = "Approximations for Digital Computers",
publisher = pubPRINCETON,
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year = "1955",
LCCN = "QA76 .H33",
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ÓÃÓ¢_X #)?57=m;Ž1OqeŽ)Gžgarticlefparith.bibPerkins:1956:EPCRobert PerkinsEASIAC, A PseudoComputerjJACM326572apr41956JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 00045411Fri Nov 04 23:46:26 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.11.04 23:46:26 ???One of the primary functions of the MIDAC installation at the University of Michigan is the instru\ŠJ^W #//A;a7Ea;]/AŒ articlefparith.bibLilamand:1956:TDMM. Lejet LilamandA TimeDivision MultiplierjIRETRANSELECCOMPUTEC512634mar31956IRELAOhttp://dx.doi.org/10.1109/TEC.1956.521978903679950 OR 03679950Thu Jun 30 15:46:18 MDT 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.06.30 15:46:18 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219789IRE Transactions on Electronic ComputersacknhfbM. Lejet LilamandA TimeDivision Multiplier
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}‰m]W #3AQ+3E%;u1AQŠ}bookfparith.bibHildebrand:1956:INAFrancis Begnaud HildebrandIntroduction to numerical analysispubMCGRAWHILLpubMCGRAWHILL:adr5111956QA300 .H5Fri Aug 20 09:19:58 MDT 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2010.08.20 09:19:58 MDTInternational series in pure and applied mathematicsSee also second edition cite Hildebrand:1974:INA,Hildebrand:1987:INA.Numerical analysisacknhfbFrancis Begnaud HildebrandIntroduction to numerical analysis
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author = "Francis Begnaud Hildebrand",
title = "Introduction to numerical analysis",
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address = pubMCGRAWHILL:adr,
pages = "511",
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remark = "See also second edition
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subject = "Numerical analysis",
}ib",
abstract = "One of the primary functions of the MIDAC installation
at the University of Michigan is the instruction of
beginners in the various aspects of digital machine use
including programming and coding. \ldots{} In
conducting these courses it was soon found to be
extremely difficult, in five or six instruction
periods, to bring a complete newcomer up to the point
where he can code and check out on MIDAC anything more
than a rather trivial routine. As might be expected the
difficulty centers around problems of scaling,
instruction modification and binary representation.
\ldots{} To alleviate these problems it was decided
that a new computer was needed: one designed to make
programming easier. At the cost of some of MIDAC's
speed and capacity plus two or three manmonths of
programming time EASIAC, the EASy Instruction Automatic
Computer, was realized as a translationinterpretation
program in MIDAC.",
acknowledgement = acknhfb,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "decimal floatingpoint arithmetic",
remark = "Early example of a decimal floatingpoint machine.",
}_ction of beginners in the various aspects of digital machine use including programming and coding. ldots In conducting these courses it was soon found to be extremely difficult, in five or six instruction periods, to bring a complete newcomer up to the point where he can code and check out on MIDAC anything more than a rather trivial routine. As might be expected the difficulty centers around problems of scaling, instruction modification and binary representation. ldots To alleviate these problems it was decided that a new computer was needed: one designed to make programming easier. At the cost of some of MIDAC's speed and capacity plus two or three manmonths of programming time EASIAC, the EASy Instruction Automatic Computer, was realized as a translationinterpretation program in MIDAC.Journal of the ACMdecimal floatingpoint arithmeticEarly example of a decimal floatingpoint machine.acknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401One of the primary functions of the MIDAC installation at the University of Michigan is the instruction of beginners in the various aspects of digital machine use including programming and coding. \ldots{} In conducting these courses it was soon found to be extremely difficult, in five or six instruction periods, to bring a complete newcomer up to the point where he can code and check out on MIDAC anything more than a rather trivial routine. As might be expected the difficulty centers around problems of scaling, instruction modification and binary representation. \ldots{} To alleviate these problems it was decided that a new computer was needed: one designed to make programming easier. At the cost of some of MIDAC's speed and capacity plus two or three manmonths of programming time EASIAC, the EASy Instruction Automatic Computer, was realized as a translationinterpretation program in MIDAC.Robert Perkins{EASIAC}, {A} PseudoComputer
@Article{Perkins:1956:EPC,
author = "Robert Perkins",
title = "{EASIAC}, {A} PseudoComputer",
journal = jJACM,
volume = "3",
number = "2",
pages = "6572",
month = apr,
year = "1956",
CODEN = "JACOAH",
ISSN = "00045411 (print), 1557735X (electronic)",
ISSNL = "00045411",
bibdate = "Fri Nov 04 23:46:26 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "One of the primary functions of the MIDAC installation
at the University of Michigan is the instruction of
beginners in the various aspects of digital machine use
including programming and coding. \ldots{} In
conducting these courses it was soon found to be
extremely difficult, in five or six instruction
periods, to bring a complete newcomer up to the point
where he can code and check out on MIDAC anything more
than a rather trivial routine. As might be expected the
difficulty centers around problems of scaling,
instruction modification and binary representation.
\ldots{} To alleviate these problems it was decided
that a new computer was needed: one designed to make
programming easier. At the cost of some of MIDAC's
speed and capacity plus two or three manmonths of
programming time EASIAC, the EASy Instruction Automatic
Computer, was realized as a translationinterpretation
program in MIDAC.",
acknowledgement = acknhfb,
fjournal = "Journal of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "decimal floatingpoint arithmetic",
remark = "Early example of a decimal floatingpoint machine.",
}
F`FŒbY#+k;a7Ea;]k%articlefparith.bibSydnor:1956:AMSR. L. Sydnor and T. R. O'Meara and J. StrathmanAnalog Multipliers and Squarers Using a Multigrid ModulatorjIRETRANSELECCOMPUTEC528285jun61956IRELAOhttp://dx.doi.org/10.1109/TEC.1956.521980403679950 OR 03679950Thu Jun 30 15:46:21 MDT 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.06.30 15:46:21 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219804IRE Transactions on Electronic ComputersacknhfbR. L. Sydnor and T. R. O'Meara and J. StrathmanAnalog Multipliers and Squarers Using a Multigrid Modulator
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author = "R. L. Sydnor and T. R. O'Meara and J. Strathman",
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llm\ #+%oU57Eƒ;‚†w['†w%o'
articlefparith.bibMurphy:1957:PIAR. W. MurphyA PositiveInteger Arithmetic for Data ProcessingjIBMJRD12158170apr41957IBMJAEhttp://dx.doi.org/10.1147/rd.12.015800188646 (print), 21518556 (electronic) OR 00188646 (print), 21518556 (electronic)00188646 OR 0018864668.0X18,939dTue Sep 11 15:35:33 MDT 2012http://ieeexplore.ieee.org/servlet/opac?punumber=5288520; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib; http://www.research.ibm.com/journal/2012.09.11 15:35:33 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392735; http://www.research.ibm.com/journal/rd/012/ibmrd0102G.pdfIt is hypothesized that positive numbers suffice for the expression of quantities in accounting. New arithmetic operations are devised that yield nonnegative results in computation, and the applicability of these operations to data processing is studied. These operations permit a wide variety of functions to be computed with fewer and less complex steps and imply the feasibility of constructing less complex dataprocessing machines.IBM Journal of Research and Developmentacknhfbhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520C. C. GotliebIt is hypothesized that positive numbers suffice for the expression of quantities in accounting. New arithmetic operations are devised that yield nonnegative results in computation, and the applicability of these operations to data processing is studied. These operations permit a wide variety of functions to be computed with fewer and less complex steps and imply the feasibility of constructing less complex dataprocessing machines.R. W. MurphyA PositiveInteger Arithmetic for Data Processing
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title = "A PositiveInteger Arithmetic for Data Processing",
journal = jIBMJRD,
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abstract = "It is hypothesized that positive numbers suffice for
the expression of quantities in accounting. New
arithmetic operations are devised that yield
nonnegative results in computation, and the
applicability of these operations to data processing is
studied. These operations permit a wide variety of
functions to be computed with fewer and less complex
steps and imply the feasibility of constructing less
complex dataprocessing machines.",
acknowledgement = acknhfb,
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<<‡]pU #)#E;7=m;]'#Eˆarticlefparith.bibWadel:1957:NBNL. B. WadelNegative base number systemsjIRETRANSELECCOMPUTEC6123??jun61957IRELAO03679950 OR 03679950Thu Nov 06 05:53:55 2014http://www.math.utah.edu/pub/tex/bib/fparith.bib2014.11.06 05:53:55 ???IRE Transactions on Electronic Computersnegative baseacknhfbL. B. WadelNegative base number systems
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}poZ !#++‚u/Em;‚E7‚+‚mtechreportfparith.bibTaylor:1957:CCAW. Bruce TaylorCOIN (CompileInterpreter): an automatic programming, fixed and floatingpoint library of subroutines for the ERA 1103 computerOperations Research Office, Johns Hopkins UniversityBethesda, MD, USA431957Sat Feb 24 15:01:45 MST 1996http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MSTStaff paper / Johns Hopkins University, Operations Research Office; OROSP32 Staff paper (Johns Hopkins University. Operations Research Office); OROSP32.Military art and science  Data processing.; Military research  Data processing.Cover title. ``Operating under contract with the Department of the Army.'' ``Project COMPLAB.'' ``October 1957.'' OROSP32acknhfbW. Bruce Taylor{COIN} (CompileInterpreter): an automatic programming, fixed and floatingpoint library of subroutines for the {ERA} 1103 computer
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}‡nnW #+/Y=m;'/ˆAarticlefparith.bibPawlak:1957:UENZ. PawlakUse of expansions with a negative basis in the arithmometer of a digital computerBull. Acad. Pol. Sci., Ser. Sci. Tech.52322361957Thu Nov 06 05:56:32 2014http://www.math.utah.edu/pub/tex/bib/fparith.bib2014.11.06 05:56:32 ???negative baseacknhfbZ. PawlakUse of expansions with a negative basis in the arithmometer of a digital computer
@Article{Pawlak:1957:UEN,
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volume = "5",
number = "??",
pages = "232236",
month = "????",
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bibdate = "Thu Nov 06 05:56:32 2014",
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392687;
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abstract = "An experimental 50megacycle arithmetic unit has been
built which performs a repetitive multiplication
program and checks the results for errors. The unit
uses pulse circuitry which has been developed to
perform digital operations at a 50megacycle
pulserepetition rate. This paper describes the
arithmetic system and the circuits which perform the
required functions. These circuits include a full
binary adder, a phaselocked frequency divider which
provides a 3.125megacycle secondary timing source, a
reshaping and retiming circuit using germanium diodes
and capacitive storage, a highspeed shift register, a
highspeed indicator register, and a binary word
generator.\par
Various novel features of a digital system operating at
these high speeds are described. These include the use
of coaxial delay lines for the distribution of signals
and as storage elements, and the use of secondary
emission tubes in amplifier and multivibrator
circuits.\par
In a 50megacycle system the interdependence of the
space and time dimensions is marked, and although this
introduces problems which are not ordinarily
encountered in computing systems, it may be used
advantageously to provide features such as the
variablephase clock system used in the arithmetic
unit.\par
The performance and reliability of the arithmetic unit
are discussed as well as the reliability of the
components and circuits which make up the system.
Although the techniques and circuitry discussed here
have been applied only to a relatively simple
arithmetic unit, it is felt that they could be useful
in a variety of highspeed computing and measurements
applications.",
acknowledgement = acknhfb,
bookURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
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}q used advantageously to provide features such as the variablephase clock system used in the arithmetic unit.\par The performance and reliability of the arithmetic unit are discussed as well as the reliability of the components and circuits which make up the system. Although the techniques and circuitry discussed here have been applied only to a relatively simple arithmetic unit, it is felt that they could be useful in a variety of highspeed computing and measurements applications.R. M. Walker and D. E. Rosenheim and P. A. Lewis and A. G. AndersonAn Experimental 50Megacycle Arithmetic Unit
@Article{Walker:1957:EMA,
author = "R. M. Walker and D. E. Rosenheim and P. A. Lewis and
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title = "An Experimental 50Megacycle Arithmetic Unit",
journal = jIBMJRD,
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abstract = "An experimental 50megacycle arithmetic unit has been
built which performs a repetitive multiplication
program and checks the results for errors. The unit
uses pulse circuitry which has been developed to
perform digital operations at a 50megacycle
pulserepetition rate. This paper describes the
arithmetic system and the circuits which perform the
required functions. These circuits include a full
binary adder, a phaselocked frequency divider which
provides a 3.125megacycle secondary timing source, a
reshaping and retiming circuit using germanium diodes
and capacitive storage, a highspeed shift register, a
highspeed indicator register, and a binary word
generator.\par
Various novel features of a digital system operating at
these high speeds are described. These include the use
of coaxial delay lines for the distribution of signals
and as storage elements, and the use of secondary
emission tubes in amplifier and multivibrator
circuits.\par
In a 50megacycle system the interdependence of the
space and time dimensions is marked, and although this
introduces problems which are not ordinarily
encountered in computing systems, it may be used
advantageously to provide features such as the
variablephase clock system used in the arithmetic
unit.\par
The performance and reliability of the arithmetic unit
are discussed as well as the reliability of the
components and circuits which make up the system.
Although the techniques and circuitry discussed here
have been applied only to a relatively simple
arithmetic unit, it is felt that they could be useful
in a variety of highspeed computing and measurements
applications.",
acknowledgement = acknhfb,
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^^½q^#+eU57Eƒ;‚™S[™Ye¶Yarticlefparith.bibWalker:1957:EMAR. M. Walker and D. E. Rosenheim and P. A. Lewis and A. G. AndersonAn Experimental 50Megacycle Arithmetic UnitjIBMJRD13257278jul71957IBMJAEhttp://dx.doi.org/10.1147/rd.13.025700188646 (print), 21518556 (electronic) OR 00188646 (print), 21518556 (electronic)00188646 OR 00188646Tue Sep 11 15:35:35 MDT 2012http://ieeexplore.ieee.org/servlet/opac?punumber=5288520; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib; http://www.research.ibm.com/journal/2012.09.11 15:35:35 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392687; http://www.research.ibm.com/journal/rd/013/ibmrd0103H.pdfAn experimental 50megacycle arithmetic unit has been built which performs a repetitive multiplication program and checks the results for errors. The unit uses pulse circuitry which has been developed to perform digital operations at a 50megacycle pulserepetition rate. This paper describes the arithmetic system and the circuits which perform the required functions. These circuits include a full binary adder, a phaselocked frequency divider which provides a 3.125megacycle secondary timing source, a reshaping and retiming circuit using germanium diodes and capacitive storage, a highspeed shift register, a highspeed indicator register, and a binary word generator.par Various novel features of a digital system operating at these high speeds are described. These include the use of coaxial delay lines for the distribution of signals and as storage elements, and the use of secondary emission tubes in amplifier and multivibrator circuits.par In a 50megacycle system the interdependence of the space and time dimensions is marked, and although this introduces problems which are not ordinarily encountered in computing systems, it may be used advantageously to provide features such as the variablephase clock system used in the arithmetic unit.par The performance and reliability of the arithmetic unit are discussed as well as the reliability of the components and circuits which make up the system. Although the techniques and circuitry discussed here have been applied only to a relatively simple arithmetic unit, it is felt that they could be useful in a variety of highspeed computing and measurements applications.IBM Journal of Research and Developmentacknhfbhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520An experimental 50megacycle arithmetic unit has been built which performs a repetitive multiplication program and checks the results for errors. The unit uses pulse circuitry which has been developed to perform digital operations at a 50megacycle pulserepetition rate. This paper describes the arithmetic system and the circuits which perform the required functions. These circuits include a full binary adder, a phaselocked frequency divider which provides a 3.125megacycle secondary timing source, a reshaping and retiming circuit using germanium diodes and capacitive storage, a highspeed shift register, a highspeed indicator register, and a binary word generator.\par Various novel features of a digital system operating at these high speeds are described. These include the use of coaxial delay lines for the distribution of signals and as storage elements, and the use of secondary emission tubes in amplifier and multivibrator circuits.\par In a 50megacycle system the interdependence of the space and time dimensions is marked, and although this introduces problems which are not ordinarily encountered in computing systems, it may bel
Š tW #)+e57=K;?c+e‹
articlefparith.bibBemer:1958:MMSRobert W. BemerA Machine Method for SquareRoot ComputationjCACM1167jan11958CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Thu Sep 15 18:35:46 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.15 18:35:46 ???Communications of the ACMacknjhttp://portal.acm.org/browse_dl.cfm?idx=J79Robert W. BemerA Machine Method for SquareRoot Computation
@Article{Bemer:1958:MMS,
author = "Robert W. Bemer",
title = "A Machine Method for SquareRoot Computation",
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number = "1",
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ISSN = "00010782 (print), 15577317 (electronic)",
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bibdate = "Thu Sep 15 18:35:46 1994",
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}ˆ_sV !#1U+1Em;eUŠtechreportfparith.bibAnonymous:1958:ARMAnonymousAnalysis and research memorandum 294AR Memo294 (AD 207929)Massachusetts Institute of Technology, Naval Supersonic LaboratoryCambridge, MA, USA723oct101958Sat Feb 24 15:01:45 MST 1996http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MSTError functions.; Floatingpoint arithmetic.acknhfbAnonymousAnalysis and research memorandum 294
@TechReport{Anonymous:1958:ARM,
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address = "Cambridge, MA, USA",
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bibdate = "Sat Feb 24 15:01:45 MST 1996",
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acknowledgement = acknhfb,
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@Article{Weibel:1957:EAM,
author = "Erich S. Weibel",
title = "An Electronic Analog Multiplier Using Carriers",
journal = jIRETRANSELECCOMPUT,
volume = "EC6",
number = "1",
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bibdate = "Thu Jun 30 16:07:23 MDT 2011",
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MRclass = "94A15 (68A20)",
MRnumber = "50 16105",
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author = "Tien Chi Chen",
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ISSNL = "00188646",
MRclass = "65D20",
MRnumber = "49i„ˆ)
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author = "Tien Chi Chen",
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Mendell and R. Nair and C. D. Wait and T. J. C. Ward
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floatingpoint unit for {Blue Gene/L}",
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articlefparith.bibDelury:1958:CANDaniel B. DeluryComputation with Approximate NumbersjMATHTEACH51521530nov11195800255769 OR 00255769Fri Nov 28 11:47:47 2003http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 11:47:47 ???The Mathematics TeacheracknhfbDaniel B. DeluryComputation with Approximate Numbers
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author = "Daniel B. Delury",
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year = "1958",
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‰iarticlefparith.bibCouleur:1958:BBDJ. F. CouleurBIDEC  A BinarytoDecimal or DecimaltoBinary ConverterjIRETRANSELECCOMPUTEC73133161958IRELAO03679950 OR 03679950Fri Nov 28 16:28:12 2003http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 16:28:12 ???IRE Transactions on Electronic Computersdecimal floatingpoint arithmeticackmfcJ. F. Couleur{BIDEC}  {A} BinarytoDecimal or DecimaltoBinary Converter
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ÂÂ–:Y #++U57Ek;†'?Oc†'+U–carticlefparith.bibSisson:1958:IDRRoger L. SissonAn Improved Decimal Redundancy CheckjCACM151012may51958CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Mon Jan 22 07:22:12 MST 2001http://dblp.unitrier.de/db/journals/cacm/cacm1.html#Sisson58; http://www.math.utah.edu/pub/tex/bib/fparith.bib2001.01.22 07:22:12 MSTAs more emphasis is placed on improving the accuracy of data fed into automatic computing systems, more emphasis will be placed on redundancy checking of predictable fields within the input. Two systems (at least) of checking a field of decimal digits have been proposed. In both of these it is assumed that the field to be checked is all numeric and that the redundancy must be of only one digit.Communications of the ACMdecimal floatingpoint arithmeticacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79As more emphasis is placed on improving the accuracy of data fed into automatic computing systems, more emphasis will be placed on redundancy checking of predictable fields within the input. Two systems (at least) of checking a field of decimal digits have been proposed. In both of these it is assumed that the field to be checked is all numeric and that the redundancy must be of only one digit.Roger L. SissonAn Improved Decimal Redundancy Check
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00—LY#3eY577+={;†3q!e†3eY—articlefparith.bibAshenhurst:1959:UFPRobert L. Ashenhurst and Nicholas MetropolisUnnormalized Floating Point ArithmeticjJACM63415428jul71959JACOAH00045411 (print), 1557735X (electronic) OR 00045411 (print), 1557735X (electronic)00045411 OR 0004541168.00MR0105833 (21 \#4568)H. H. GoldstineFri Dec 08 13:06:24 1995http://www.math.utah.edu/pub/bibnet/authors/m/metropolisnicholas.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 13:06:24 ???Algorithms for floating point computer arithmetic are described, in which fractional parts are not subject to the usual normalization convention. These algorithms give results in a form which furnishes some indication of their degree of precision. An analysis of onestage error propagation is developed for each operation; a suggested statistical model for longrun error propagation is also set forth.Journal of the Association for Computing Machinery0121.12102acknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401Algorithms for floating point computer arithmetic are described, in which fractional parts are not subject to the usual normalization convention. These algorithms give results in a form which furnishes some indication of their degree of precision. An analysis of onestage error propagation is developed for each operation; a suggested statistical model for longrun error propagation is also set forth.Robert L. Ashenhurst and Nicholas MetropolisUnnormalized Floating Point Arithmetic
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author = "Robert L. Ashenhurst and Nicholas Metropolis",
title = "Unnormalized Floating Point Arithmetic",
journal = jJACM,
volume = "6",
number = "3",
pages = "415428",
month = jul,
year = "1959",
CODEN = "JACOAH",
ISSN = "00045411 (print), 1557735X (electronic)",
ISSNL = "00045411",
MRclass = "68.00",
MRnumber = "MR0105833 (21 \#4568)",
MRreviewer = "H. H. Goldstine",
bibdate = "Fri Dec 08 13:06:24 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolisnicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0121.12102",
abstract = "Algorithms for floating point computer arithmetic are
described, in which fractional parts are not subject to
the usual normalization convention. These algorithms
give results in a form which furnishes some indication
of their degree of precision. An analysis of onestage
error propagation is developed for each operation; a
suggested statistical model for longrun error
propagation is also set forth.",
acknowledgement = acknhfb,
fjournal = "Journal of the Association for Computing Machinery",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
} bibsource = "http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Buchholz59;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "decimal floatingpoint arithmetic",
oldlabel = "Buchholz59",
XMLdata = "ftp://ftp.informatik.unitrier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Buchholz59",
xxnote = "Check author first name: article has W. Buchholz; I
think it should be Werner, not Wilfried.",
}„
ð÷ðŒW #'c57E‚;?c1cŽ!articlefparith.bibCarr:1959:EAFJohn W. Carr IIIError Analysis in Floating Point ArithmeticjCACM251015may51959CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Wed Jul 14 15:48:23 MDT 2004http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Carr59a; http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2004.07.14 15:48:23 MDTCommunications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79John W. {Carr III}Error Analysis in Floating Point Arithmetic
@Article{Carr:1959:EAF,
author = "John W. {Carr III}",
title = "Error Analysis in Floating Point Arithmetic",
journal = jCACM,
volume = "2",
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pages = "1015",
month = may,
year = "1959",
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ISSNL = "00010782",
bibdate = "Wed Jul 14 15:48:23 MDT 2004",
bibsource = "http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Carr59a;
http://portal.acm.org/;
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acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Carr59a",
XMLdata = "ftp://ftp.informatik.unitrier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Carr59a",
}ŽY #//57Eo;?Oc/‘ articlefparith.bibBuchholz:1959:FFCWilfried BuchholzFingers or Fists? (The Choice of Decimal or Binary Representation)jCACM2123111959CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Mon Jan 22 06:28:45 MST 2001http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Buchholz59; http://www.math.utah.edu/pub/tex/bib/fparith.bib2001.01.22 06:28:45 MSTCommunications of the ACMdecimal floatingpoint arithmeticacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Wilfried BuchholzFingers or Fists? (The Choice of Decimal or Binary Representation)
@Article{Buchholz:1959:FFC,
author = "Wilfried Buchholz",
title = "Fingers or Fists? (The Choice of Decimal or Binary
Representation)",
journal = jCACM,
volume = "2",
number = "12",
pages = "311",
month = "????",
year = "1959",
CODEN = "CACMA2",
ISSN = "00010782 (print), 15577317 (electronic)",
ISSNL = "00010782",
bibdate = "Mon Jan 22 06:28:45 MST 2001",
bibsource = "http://dblp.unitrier.de/db/journals/cacm/cacm2.html#Buchholz59;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "decimal floatingpoint arithmetic",
oldlabel = "Buchholz59",
XMLdata = "ftp://ftp.informatik.unitrier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Buchholz59",
xxnote = "Check author first name: article has W. Buchholz; I
think it should be Werner, not Wilfried.",
}
0ˆ*U #'U;7=m;]O'Y‰?articlefparith.bibDaggett:1959:DBCD. H. DaggettDecimalBinary Conversions in CORDICjIRETRANSELECCOMPUTEC85335339sep91959IRELAO03679950 OR 03679950Thu Sep 08 08:14:00 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.08 08:14:00 ???IRE Transactions on Electronic Computersdecimal floatingpoint arithmeticacknjD. H. DaggettDecimalBinary Conversions in {CORDIC}
@Article{Daggett:1959:DBC,
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volume = "EC8",
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}LW %#%ym9'!=%;!‚;{1my!9Ž[incollectionfparith.bibCarr:1959:PCJohn W. Carr IIIEugene M. Grabbe and Simon Ramo and Dean E. WooldridgeHandbook of Automation, Computation, and ControlProgramming and CodingpubWILEYpubWILEY:adr10151959TJ213 .G72Fri Aug 20 08:41:16 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2010.08.20 08:41:16 ???Chapter 2.19581961: Volume 1. Control fundamentals. Volume 2. Computers and data processing. Volume 3. Systems and components. Cited in cite Sterbenz:1974:FPC.automation; mathematics; computers; operations researchacknhfbJohn W. {Carr III}Handbook of Automation, Computation, and ControlEugene M. Grabbe and Simon Ramo and Dean E. WooldridgeChapter 2.Programming and Coding
@InCollection{Carr:1959:PC,
author = "John W. {Carr III}",
editor = "Eugene M. Grabbe and Simon Ramo and Dean E.
Wooldridge",
booktitle = "Handbook of Automation, Computation, and Control",
title = "Programming and Coding",
publisher = pubWILEY,
address = pubWILEY:adr,
year = "1959",
LCCN = "TJ213 .G72",
bibdate = "Fri Aug 20 08:41:16 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "Chapter 2.",
acknowledgement = acknhfb,
bookpages = "????",
remark = "19581961: Volume 1. Control fundamentals. Volume 2.
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components. Cited in \cite{Sterbenz:1974:FPC}.",
subject = "automation; mathematics; computers; operations
research",
}
êû
‡!ŽE
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L“I
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author = "Luigi Dadda",
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È £ÈWW #)!57Eƒ1;?c!articlefparith.bibGurzi:1960:HSMFred GurziA HighSpeed Multiplication Process for Digital ComputersjCACM34241245apr41960CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Fri Nov 25 18:19:26 MST 2005http://dblp.unitrier.de/db/journals/cacm/cacm3.html#Gurzi60; http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:26 MSTCommunications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Fred GurziA HighSpeed Multiplication Process for Digital Computers
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@TechReport{Jensen:1960:CIF,
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institution = "Massachusetts Institute of Technology, Lincoln
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address = "Lexington, MA, USA",
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note = "Errata, {\sl Commun\i\ca\tions of the ACM\/ \bf 4}
(August 1961), 355 \cite{Knuth:1961:EIN}. See
\cite{Nadler:1961:DSR} for extension to division and
square root.",
abstract = "For centuries the decimal number system reigned
supreme, except, perhaps, among the Mayan Indians,
until the advent of digital computers brought the
binary and octal systems into the limelight. This paper
introduces another number system which may prove useful
for manipulating complex numbers on machines.",
acknowledgement = acknhfb,
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((T,Y #)#S57Eƒ1;C?c#GW‘karticlefparith.bibTraub:1960:CNMJ. F. TraubComments on a recent paper [``A New Method of Computation of Square Roots Without Using Division'']jCACM328686feb21960CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Fri Nov 25 18:19:25 MST 2005http://dblp.unitrier.de/db/journals/cacm/cacm3.html#Traub60; http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:25 MSTSee cite Sarafyan:1959:NMC.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79J. F. TraubSee \cite{Sarafyan:1959:NMC}.Comments on a recent paper [{``A New Method of Computation of Square Roots Without Using Division''}]
@Article{Traub:1960:CNM,
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}‘Q/Z#)C#I)U57C‚;cKqYCg’{articlefparith.bibAmble:1961:AFPO. Amble and Jan V. GarwickOn the Accuracy of Floating Point Computers [BIT bf 1(2), 1961, pp. 8788]jNORDISKTIDSKRINFORMBEHAND13220222sep91961BITTEL, NBITABhttp://dx.doi.org/10.1007/BF0193343400063835 (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=3; 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 cite Garwick:1961:AFP,Garwick:1961:RAF.http://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=1&issue=3&spage=220floatingpoint accuracy; floatingpoint arithmeticacknhfbhttp://link.springer.com/journal/10543O. Amble and Jan V. GarwickSee \cite{Garwick:1961:AFP,Garwick:1961:RAF}.On the Accuracy of Floating Point Computers {[BIT {\bf 1}(2), 1961, pp. 8788]}
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iarticlefparith.bibAvizienis:1961:SDNAlgirdas AvizienisSignedDigit Number Representations for Fast Parallel ArithmeticjIRETRANSELECCOMPUTEC103389400sep91961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.521922703679950 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 14:45:04 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219227IRE Transactions on Electronic ComputersacknhfbAlgirdas Avi{\v{z}}ienisSignedDigit Number Representations for Fast Parallel Arithmetic
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include sampling, analogtoresidue conversion, logical
design of the arithmetic units, residuetoanalog
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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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fjournal = "IRE Transactions on Electronic Computers",
}²
MM/2Y #+5{;a7E‚;Š=]Š=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 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.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 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.Philip Warren CheneyA Digital Correlator Based on the Residue Number System
@Article{Cheney:1961:DCB,
author = "Philip Warren Cheney",
title = "A Digital Correlator Based on the Residue Number
System",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "1",
pages = "6370",
month = mar,
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http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219154",
abstract = "A system design for a digital correlator based on the
application of the residue number system for
computation is presented. Areas of investigation
include sampling, 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,
fjournal = "IRE Transactions on Electronic Computers",
}
B[BŠ4W#%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 (electronic)00010782 OR 00010782Thu Sep 15 18:36:06 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.15 18:36:06 ???Communications of the ACMacknjhttp://portal.acm.org/browse_dl.cfm?idx=J79A. G. Cox and H. A. LutherA Note on Multiple Precision Arithmetic
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{ˆ[6W #'!=m;+'‹
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@Article{Freiman:1961:SAC,
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xxnote = "Check author name: I have found this paper cited both
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@Article{Croy:1961:RTM,
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keywords = "theory",
subject = "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation",
}wÇ…2Še
@Article{Dunham:1989:PAH,
author = "C. B. Dunham",
title = "Perturbation Analysis of {Horner}'s Method for Nice
Cases",
journal = jSIGNUM,
volume = "24",
number = "2 and 3",
pages = "89",
month = apr # "/" # jul,
year = "1989",
CODEN = "SNEWD6",
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ISSNL = "01635778",
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fjournal = "ACM SIGNUM Newsletter",
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author = "Fred W. Dorr and Cleve B. Moler",
title =
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author = "Iain S. Duff and Jacques Laminie and Alain Lichnewsky
ak…*ŠU
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author = "U. Dutta and D. Bhattacharya and A. D. Sarma",
title = "Implementation of Multibyte Floating Point Arithmetic
in 8bit Microprocessor",
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volume = "17",
number = "3",
pages = "104113",
month = sep,
year = "1986",
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@Article{Dvir:2010:HRT,
author = "Zeev Dvir and Amir Shpilka and Amir Yehudayoff",
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month = "????",
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fjournal = "SIAM Journal on Computing",
journalURL = "http://epubs.siam.org/sicomp",
}Ak‹#–G
@Article{Duprat:1988:HPE,
author = "Jean Duprat and JeanMichel Muller",
title = "Hardwired polynomial evaluation",
journal = jJPARDISTCOMP,
volume = "5",
number = "3",
pages = "291309",
month = jun,
year = "1988",
CODEN = "JPDCER",
ISSN = "07437315 (print), 10960848 (electronic)",
ISSNL = "07437315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex ›ibdate = "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..",
}·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. Garner 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.
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..",
}
°g7\!#+[U51=m;#Žy‹Žy[Uw
techreportfparith.bibGarner:1961: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. ³= "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",
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¨9Y #'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. 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",
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",
}T8Z #)]I)U57C‚;
IqY)]‘{articlefparith.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",
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",
}
²# èù.ñ#Ô…t‹i
@Article{Goodman:1990:SMR,
author = "R. H. Goodman",
† Œ
@Article{Goodman:1985:REF,
author = "R. H. Goodman and A. Feldstein and J. Bustoz",
title = "Relative error in floatingpoint multiplication",
journal = jCOMPUTING,
volume = "35",
number = "2",
pages = "127139",
year = "1985",
CODEN = "CMPTA2",
ISSN = "0010485X (print), 14365057 (electronic)",
ISSNL = "0010485X",
MRclass = "65G05",
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bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journalURL = "http://link.springer.com/journal/607",
reviewer = "Luciano Biasini",
}‡Ž
@Article{Goodman:1977:EGD,
author = "R. Goodman and A. Feldstein",
title = "Effect of Guard Digits and Normalization Options on
Floating Point Multiplication",
journal = jCOMPUTING,
volume = "18",
number = "2",
pages = "93106",
month = "????",
year = "1977",
CODEN = "CMPTA2",
ISSN = "0010485X (print), 14365057 (electronic)",
ISSNL = "0010485X",
MRclass = "65G05",
MRnumber = "55 11596",
bibdate = "Fri Dec 08 12:02:42 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journalURL = "http://link.springer.com/journal/607",
reviewer = "N. N. Abdelmalek",
}¥Ge
@Article{Goodrich:1982:VEP,
author = "J. L. Goodrich",
ˆp‘a
@Article{Goodman:1976:REF,
author = "Richard Goodman",
title = "On roundoff error in fixedpoint multiplication",
journal = jBIT,
volume = "16",
number = "1",
pages = "4151",
month = mar,
year = "1976",
CODEN = "BITTEL, NBITAB",
DOI = "http://dx.doi.org/10.1007/BF01940776",
ISSN = "00063835 (print), 15729125 (electronic)",
ISSNL = "00063835",
bibdate = "Wed JanÓ†Œ
@Article{Goodman:1976:EGD,
author = "R. Goodman and A. Feldstein",
title = "Effect of Guard Digits and Normalization Options on
Floating Point Multiplication",
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volume = "18",
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month = "????",
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bibdate = "Fri Jun 21 11:25:02 MDT 2013",
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http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
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fjournal = "SIAM Review",
journalURL = "http://epubs.siam.org/sirev",
}e†
Œ
@Article{Goodman:1978:ITD,
author = "R. Goodman and J. Bustoz and A. Feldstein",
title = "Improved Trailing Digits Estimates Applied to Optimal
Computer Arithmetic",
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volume = "20",
number = "3",
pages = "625625",
month = "????",
year = "1978",
CODEN = "SIREAD",
ISSN = "00361445 (print), 10957200 (electronic)",
ISSNL = "00361445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
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fjournal = "SIAM Review",
journalURL = "http://epubs.siam.org/sirev",
}ý.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",
}º
Q5Q‹`;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 14:45:03 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,
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",
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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=5219198",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}‘G:W '#1+oQ#]=m;…?1…?+sQinproceedingsfparith.bibHenderson:1961:RCED. S. HendersonProceedings of the 1961 16th ACM national meetingResidue class 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",
}
µ
µ‹T=W#EO;a7E‚;]ESarticlefparith.bibKovatch:1961:HEAG. Kovatch and W. E. MeserveThe HallEffect Analog MultiplierjIRETRANSELECCOMPUTEC103512515sep91961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.521924003679950 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 14:45:04 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,
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",
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219240",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}ŠoY#+9#;a7E‚;]9#uarticlefparith.bibLehman:1961:STHM. Lehman and N. BurlaSkip Techniques for HighSpeed CarryPropagation in Binary Arithmetic UnitsjIRETRANSELECCOMPUTEC104691698dec121961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.521927403679950 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 14:45:04 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219274IRE Transactions on Electronic ComputersacknhfbM. Lehman and N. BurlaSkip Techniques for HighSpeed CarryPropagation in Binary Arithmetic Units
@Article{Lehman:1961:STH,
author = "M. Lehman and N. Burla",
title = "Skip Techniques for HighSpeed CarryPropagation in
Binary Arithmetic Units",
journal = jIRETRANSELECCOMPUT,
volume = "EC10",
number = "4",
pages = "691698",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219274",
ISSN = "03679950",
bibdate = "Thu Jul 14 14:45:04 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",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219274",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}date = "Fri Nov 25 18:19:32 MST 2005",
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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",
}À
»É
Ìíz
ÆÉ
3…/Š_
@Article{Rodrigues:1981:HEM,
author = "M. R. D. Rodrigues and J. H. P. Zurawski and J. B.
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month = jul,
year = "1981",
CODEN = "IPETD3",
ISSN = "01437062",
bibdate = "Thu Sep 1 10:15:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "IEE proceedings, E: Computers and digital techniques",
}.†qc
@Article{Robertson:1979:VPA,
author = "D. A. Robertson",
title = "Variable precision arithmetic on {CDC 6000\slash 7000}
machines",
journal = jSPE,
volume = "9",
number = "3",
pages = "247248",
month = mar,
year = "1979",
CODEN = "SPEXBL",
DOI = "http://dx.doi.org/10.1002/spe.4380090310",
ISSN = "00380644 (print), 1097024X (electronic)",
ISSNL = "00380644",
bibdate = "Wed Sep 10 12:36:39 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/spe.bib",
acknowledgement = acknhfb,
fjournal = "Software  Practice and Experience",
journalURL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097024X",
onlinedate = "27 Oct 2006",
}f‡];
@Article{Robertson:1973:SIC,
author = "James E. Robertson and Kishor S. Trivedi",
title = "The status of investigations into computer hardware
design based on the use of continued fractions",
journal = jIEEETRANSCOMPUT,
volume = "C22",
number = "6",
pages = "555560",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1973.5009106",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Thu Nov 8 14:50:24 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsellab.com/arithmetic/arith2/papers/ARITH2_Robertson.pdf",
acknowledgement = acknhfb,
fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH2; continued fractions",
}±G›
@Article{Robertson:1970:CBM,
author = "J. E. Robertson",
title = "The Correspondence Between Methods of Digital Division
and Multiplier Recoding Procedures",
journal = jIEEETRANSCOMPUT,
volume = "C19",
number = "8",
pages = "692701",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1970.223018",
ISSN = "00189340 (print), 1557
@Article{Robertson:1958:NCDb,
author = "James E. Robertson",
title = "A New Class of Digital Division Methods",
journal = jIRETRANSELECCOMPUT,
volume = "EC7",
number = "3",
pages = "218222",
month = „8ˆq
@Article{Robison:1983:USF,
author = "A. D. Robison",
title = "Use Squares for Fast Multiplication",
journal = jEDN,
volume = "28",
number = "21",
pages = "263, 267",
month = oct,
year = "1983",
CODEN = "EDNSBH",
ISSN = "00127515, 03646637",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "EDN",
}û
@Y #+' 57E‚5;=?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 number 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)",
ISSNL = "00010782",
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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",
keywords = "$\sqrt(x)$; elementary functions",
ZMreviewer = "C. B. Haselgrove",
}/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}.",
}Ástants 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.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 = "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}.",
}
f×fˆmBV #3'C57=m;?c'C‰uarticlefparith.bibRabinowitz: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",
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ISSN = "00010782 (print), 15577317 (electronic)",
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bibdate = "Thu Sep 08 00:29:25 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
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}´AY #k+!7=m;CŽmOsŽ7Žuk³5articlefparith.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 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.Annals of Mathematical StatisticsBenford's Law; Law of Anomalous Numbers; Zipf's LawFrom p. 1223: ``ldots the proportion of these data with first significant digit $n$ or less is approximately $ log _10(n + 1) $.''par ldots ``The only distribution for first significant digits which is invariant under scale change of the underlying distribution is $ log _10(n + 1) $. 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 conÁ
U
U‹+DY #1)'57Ek;A=)ŒM 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; http://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,
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acknowledgement = acknj # " and " # acknhfb,
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}‹xCW #){;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://ieeexplore.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,
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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",
}
ä……3 ‘¢ä…Š
@Book{Couffignal:1933:MCL,
author …Š
@Book{Couffignal:1933:MCL,
auth„]‰;
@Book{Cardenas:1972:CS,
editor = "Alfonso F. Cardenas and Leon Presser and Miguel A.
Marin",
booktitle = "Computer Science",
title = "Computer Science",
publisher = pubWILEYINTERSCIENCE,
address = pubWILEYINTERSCIENCE:adr,
pages = "xii + 522",
year = "1972",
ISBN = "0471134686",
ISBN13 = "9780471134688",
LCCN = "QA76.5 .C365; TK7885 .C178c",
bibdate = "Sat Nov 29 11:09:31 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
}O_
@Book{Cody:1980:SME,
author = "W. J. Cody and W. Waite",
title = "Software Manual for the Elementary Functions",
publisher = pubPH,
address = pubPH:adr,
pages = "x + 269",
year = "1980",
ISBN = "0138220646",
ISBN13 = "9780138220648",
LCCN = "Q†m[
@Book{Carey:1989:PSM,
editor = "Graham F. Carey",
booktitle = "Parallel supercomputing: methods, algorithms and
applications",
title = "Parallel supercomputing: methods, algorithms and
applications",
publisher = pubWILEY,
address = pubWILEY:adr,
pages = "x + 287",
year = "1989",
ISBN = "0471924369",
ISBN13 = "9780471924364",
LCCN = "M89.E02452; QA76.6",
bibdate = "Mon Jan 2 15:42:42 MST 2006",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/d/duffiains.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
library.ox.ac.uk:210/ADVANCE",
series = "Wiley series in parallel computing",
acknowledgement = acknhfb,
subject = "Parallel programming (Computer science)",
}tŒl™Y
@Book{ChaitinChatelin:1996:LFP,
author = "Fran{\c{c}}oise ChaitinChatelin and Val{\'e}rie
Frayss{\'e}",
title = "Lectures on Finite Precision Computations",
publisher = pubSIAM,
address = pubSIAM:adr,
pages = "xv + 235",
year = "1996",
ISBN = "0898713587",
ISBN13 = "9780898713589",
LCCN = "QA297 .C417 1996",
bibdate = "Wed Nov 16 14:38:30 MST 2005",
bibsource = "httf„u‰k
@Book{Cavanagh:1984:DCA,
author = "Joseph J. F. Cavanagh",
title = "Digital Computer Arithmetic: Design and
Implementation",
publisher = pubWILEY,
address = pubWILEY:adr,
pages = "xi + 468",
year = "1984",
ISBN = "0070102821",
ISBN13 = "9780070102828",
LCCN = "QA76.9.C62 C38 1984",
bibdate = "Sat May 18 14:16:35 2002",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$21.95",
acknowledgement = acknj,
}&„ˆ
@Book{Catanzaro:1991:STP,
editor = "Ben J. Catanzaro",
title = "The {SPARC} Technical Papers",
publisher = pubSV,
address = pubSV:adr,
pages = "xvi + 501",
year = "1991",
ISBN = "0387976345, 3540976345",
ISBN13 = "9780387976341, 9783540976349",
LCCN = "QA76.9.A73 S65 1991",
bibdate = "Wed Feb 9 01:57:02 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
} ¯Š3‚”e
@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;Ë
’
FX #'!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)1961  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,
editor = "A. H. Taub",
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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year = "19611963",
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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,
}‹\EY #1%[57=K;1e%[ŒGarticlefparith.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/tex/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,
year = "1961",
CODEN = "JACOAH",
ISSN = "00045411 (print), 1557735X (electronic)",
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bibdate = "Sat Dec 09 14:01:44 1995",
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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 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,
}Æ
‰
‰ŠsGY #75'57E
;A=;5‹Warticlefparith.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 00255718Tue 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
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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
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
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acknowledgement = ackmfc # " and " # acknhfb,
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HY !#')KM=m;Œ]Œ])™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, 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
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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
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H·‰!LV %#/)+c=+3%=%;M)g+=Šincollectionfparith.bibCampbell:1962:FPOS. G. CampbellWerner BuchholzPlanning a Computer System: Project StretchFloatingPoint OperationpubMCGRAWHILLpubMCGRAWHILL:adr921211962QA76.8.I2 I5Wed Feb 14 17:24:27 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2007.02.14 17:24:27 ???IBM 7030 (Computer); IBM Stretchacknhfb322S. G. CampbellPlanning a Computer System: {Project Stretch}Werner BuchholzFloatingPoint Operation
@InCollection{Campbell:1962:FPO,
author = "S. G. Campbell",
editor = "Werner Buchholz",
booktitle = "Planning a Computer System: {Project Stretch}",
title = "FloatingPoint Operation",
publisher = pubMCGRAWHILL,
address = pubMCGRAWHILL:adr,
pages = "92121",
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}älK\ #/+c+3!Eƒ{;{µC7ñ%+{g‚”eSbookfparith.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 architÐ…OJU '#3M)=m;Q…cinproceedingsfparith.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
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title = "The {Maniac III} Arithmetic System",
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}‹aIW#+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 14:45:04 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,
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title = "An Algorithm for Rapid Binary Division",
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volume = "EC10",
number = "4",
pages = "662670",
month = dec,
year = "1961",
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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/;
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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
Í 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 \Î\
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 \\
Ï 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",
}ËÑects.http://edthelen.org/comphist/IBM7030PlanningMcJones.pdfThe text of the book is in the public domain, with the permission of the author in 2003. See cite MacKenzie:1991:IAL for a remark about the noisy mode for 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. InstrÒuction 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 ÓInstructions 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 detailÔ 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
destÕroys 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 SiÖgns 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",
}
æßæuNZ !#/#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 iterative processes with floatingpoint computers
@TechReport{Descloux:1962:REF,
author = "J. Descloux",
title = "Remarks on errors in first order iterative processes
with floatingpoint computers",
institution = "University of Illinois Graduate College, Digital
Computer Laboratory",
address = "Urbana, IL, USA",
pages = "7",
year = "1962",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Report / University of Illinois, Digital Computer
Laboratory; no. 113 Report (University of Illinois
(UrbanaChampaign campus). Digital Computer
Laboratory); no. 113.",
acknowledgement = acknhfb,
keywords = "Electronic digital computers.; Numerical
calculations.",
remark = "Supported by: National Science Foundation under grant
G16489. ``March 22, 1962.''",
}ŽMY#+S=;a7E‚y;]S=S
articlefparith.bibCantor:1962:LEFD. Cantor and G. Estrin and R. TurnLogarithmic and Exponential Function Evaluation in a Variable Structure Digital ComputerjIRETRANSELECCOMPUTEC112155164apr41962IRELAOhttp://dx.doi.org/10.1109/TEC.1962.521934803679950 OR 03679950Thu Jul 14 09:11:49 MDT 2011ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; 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 09:11:49 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219348IRE Transactions on Electronic ComputersacknjD. Cantor and G. Estrin and R. TurnLogarithmic and Exponential Function Evaluation in a Variable Structure Digital Computer
@Article{Cantor:1962:LEF,
author = "D. Cantor and G. Estrin and R. Turn",
title = "Logarithmic and Exponential Function Evaluation in a
Variable Structure Digital Computer",
journal = jIRETRANSELECCOMPUT,
volume = "EC11",
number = "2",
pages = "155164",
month = apr,
year = "1962",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1962.5219348",
ISSN = "03679950",
bibdate = "Thu Jul 14 09:11:49 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
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=5219348",
acknowledgement = acknj # "\slash " # acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
‹sOW#/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://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",
journal = jIRETRANSELECCOMPUT,
volume = "EC11",
number = "2",
pages = "287288",
month = apr,
year = "1962",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1962.5219366",
ISSN = "03679950",
bibdate = "Thu Jul 14 09:11:50 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=5219366",
acknowledgement = acknhfb,
fjournal = "IRE Transactions on Electronic Computers",
}6",
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,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
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¤¤žXPZ #'!%57;m;‹c?c‹w!%œarticlefparith.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 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.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
@Article{Grau:1962:FNR,
author = "A. A. Grau",
title = "On a floatingpoint number 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)",
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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,
fjournal = "Communications of the ACM",
journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
reviewer = "R. L. Ashenhurst",
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ª §ª‰yRV #Ii+3!E%;uMmIiŠibookfparith.bibHamming:1962:NMSR. W. (Richard Wesley) HammingNumerical methods for scientists and engineerspubMCGRAWHILLpubMCGRAWHILL:adr4111962QA297 .H28Fri Aug 20 09:12:08 MDT 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2010.08.20 09:12:08 MDTInternational series in pure and applied mathematicsCited in cite Sterbenz:1974:FPC.Numerical analysis; Electronic digital computersacknhfbR. W. (Richard Wesley) HammingNumerical methods for scientists and engineers
@Book{Hamming:1962:NMS,
author = "R. W. (Richard Wesley) Hamming",
title = "Numerical methods for scientists and engineers",
publisher = pubMCGRAWHILL,
address = pubMCGRAWHILL:adr,
pages = "411",
year = "1962",
LCCN = "QA297 .H28",
bibdate = "Fri Aug 20 09:12:08 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "International series in pure and applied mathematics",
acknowledgement = acknhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
subject = "Numerical analysis; Electronic digital computers",
}ŒUQY #+5;a7E‚;]5{
articlefparith.bibGuffin:1962:CSLRonald M. GuffinA Computer for Solving Linear Simultaneous Equations Using the Residue Number SystemjIRETRANSELECCOMPUTEC112164173apr41962IRELAOhttp://dx.doi.org/10.1109/TEC.1962.521934903679950 OR 03679950Thu Jul 14 09:11:49 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 09:11:49 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219349IRE Transactions on Electronic ComputersacknhfbRonald M. GuffinA Computer for Solving Linear Simultaneous Equations Using the Residue Number System
@Article{Guffin:1962:CSL,
author = "Ronald M. Guffin",
title = "A Computer for Solving Linear Simultaneous Equations
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¡ª‡sTU#1?m7=m;A?mˆcarticlefparith.bibKaratsuba:1962:MMNA. Karatsuba and Y. OfmanMultiplication of multidigit numbers on automatajDOKLAKADNAUK1452932941962DANKAS00023264 OR 00023264Tue Jul 05 10:35:11 2005http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.07.05 10:35:11 ???Doklady Akademii nauk SSSRacknhfbA. Karatsuba and Y. OfmanMultiplication of multidigit numbers on automata
@Article{Karatsuba:1962:MMN,
author = "A. Karatsuba and Y. Ofman",
title = "Multiplication of multidigit numbers on automata",
journal = jDOKLAKADNAUK,
volume = "145",
number = "??",
pages = "293294",
month = "????",
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}Š[SV#)Ec7=m;OO‚Eg‹{articlefparith.bibJones:1962:FPFF. B. Jones and A. W. WymoreFloating Point Feature on the IBM Type 1620jIBMTDB05624346may51962IBMTAA00188689 OR 00188689Fri Nov 28 11:26:02 2003http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 11:26:02 ???IBM Technical Disclosure Bulletindecimal floatingpoint arithmeticThe IBM 1620 normalized variableprecision arithmetic provides up to 100 decimal digits with an exponent range of $ pm 99 $.acknhfbF. B. Jones and A. W. WymoreFloating Point Feature on the {IBM Type 1620}
@Article{Jones:1962:FPF,
author = "F. B. Jones and A. W. Wymore",
title = "Floating Point Feature on the {IBM Type 1620}",
journal = jIBMTDB,
volume = "0562",
pages = "4346",
month = may,
year = "1962",
CODEN = "IBMTAA",
ISSN = "00188689",
bibdate = "Fri Nov 28 11:26:02 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
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keywords = "decimal floatingpoint arithmetic",
remark = "The IBM 1620 normalized variableprecision arithmetic
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range of $ \pm 99 $.",
}
( (‰qVW #)#W57;K;?c#WŠarticlefparith.bibKnuth:1962:EPCD. E. KnuthEvaluation of Polynomials By ComputerjCACM512595599dec121962CACMA200010782 (print), 15577317 (electronic) OR 00010782 (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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journal = jCACM,
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}_UW#'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 detection in residue number systems
@Article{Keir:1962:DOD,
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title = "Division and overflow detection in residue number
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219389",
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month = jan,
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volume = "EC12",
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Florent de Dinechin and ClaudePierre Jeannerod and
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keywords = "decimal floatingpoint arithmetic",
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month = sep,
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author = "N. Metropolis",
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ZMnumber = "0128.36301",
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fjournal = "Numerische Mathematik",
journalURL = "http://link.springer.com/journal/211",
}5†U+
@Article{Metropolis:1965:BAU,
author = "N. Metropolis",
title = "Berichtigung: {Algorithms} in unnormalized arithmetic.
{I}. {Recurrence} relations",
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booktitle = "{Digitale Informationswandler}",
title = "{Entwicklungslinien einer Rechenger{\"a}teEntwicklung
von der Mechanik zur Elektronik}. ({German}) [Lines of
development of computing equipment development from
mechanics to electronics]",
publisher = "Vieweg \& Sohn, GmbH",
address = "Braunschweig, West Germany",
pages = "508532",
year = "1962",
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note = "Reprinted in \cite[\S 4.3]{Randell:1982:ODC}.
Translated by Mr. and Mrs. P. Jones.",
acknowledgement = acknhfb,
language = "German",
}ŽnbX #'wI)U57C‚;KMY{=articlefparith.bibWynn:1962:AAPP. WynnAn Arsenal of ALGOL Procedures for Complex ArithmeticjNORDISKTIDSKRINFORMBEHAND24232255dec121962BITTEL, NBITABhttp://dx.doi.org/10.1007/BF0194017100063835 (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=2&issue=4; 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 MSThttp://www.springerlink.com/openurl.asp?genre=article&issn=00063835&volume=2&issue=4&spage=232Cited in cite Sterbenz:1974:FPC.acknhfbhttp://link.springer.com/journal/10543P. WynnAn Arsenal of {ALGOL} Procedures for Complex Arithmetic
@Article{Wynn:1962:AAP,
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i ¿iŠReW#/iQ!57=K;7UiU‹Oarticlefparith.bibClenshaw:1963:ASFC. W. Clenshaw and G. F. Miller and M. WoodgerAlgorithms for Special Functions IjNUMMATH44034191963NUMMA70029599X (print), 09453245 (electronic) OR 0029599X (print), 09453245 (electronic)0029599X OR 0029599XFri Sep 16 10:21:31 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.16 10:21:31 ???Numerische Mathematikacknjhttp://link.springer.com/journal/211C. W. Clenshaw and G. F. Miller and M. WoodgerAlgorithms for Special Functions {I}
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}Œ=dY #)#57E‚5;?cc#iarticlefparith.bibBemer:1963:NRTR. W. BemerA Note on Range Transformations for Square Root and LogarithmjCACM66306307jun61963CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Fri Nov 25 18:19:47 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 18:19:47 MSTCommunications of the ACM$log (x)$; $sqrt (x)$; elementary functionsacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79R. W. BemerA Note on Range Transformations for Square Root and Logarithm
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author = "R. W. Bemer",
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articlefparith.bibDescloux:1963:NREJ. DesclouxNote on the RoundOff Errors in Iterative ProcessesjMATHCOMPUT17811827jan11963MCMPAF00255718 (print), 10886842 (electronic) OR 00255718 (print), 10886842 (electronic)00255718 OR 00255718Tue 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/J. DesclouxNote on the RoundOff Errors in Iterative Processes
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author = "J. Descloux",
title = "Note on the RoundOff Errors in Iterative Processes",
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volume = "17",
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year = "1963",
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}‹sfW#'?m=a7E‚;_?m# articlefparith.bibDaly:1963:HSAW. G. Daly and J. F. KruyA HighSpeed Arithmetic Unit Using Tunnel DiodesjIEEETRANSELECCOMPUTEC125503511oct101963IEECA8http://dx.doi.org/10.1109/PGEC.1963.26364403677508 OR 03677508Thu Jul 14 08:10:42 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 08:10:42 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037964IEEE Transactions on Electronic ComputersacknhfbW. G. Daly and J. F. KruyA HighSpeed Arithmetic Unit Using Tunnel Diodes
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author = "W. G. Daly and J. F. Kruy",
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bibdate = "Thu Jul 14 08:10:42 MDT 2011",
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author = "Warren E. {Ferguson, Jr.}",
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number = "7",
pages = "3841",
month = jul,
year = "1991",
CODEN = "IEESAM",
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fjournal = "IEEE Spectrum",
keywords = "floatingpoint arithmetic",
remark = "Contains performancecomparison tables for Cyrix,
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chips.",
} Íˆ<y
@Article{Fettweis:1972:CBM,
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pages = "486491",
month = sep,
year = "1972",
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bip‡ti
@Article{Ferro:1986:DTF,
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http://wwiˆ)
@Article{Ferrari:1969:CDM,
author = "D. Ferrari",
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Multiplier''}",
journal = jIEEETRANSCOMPUT,
volume = "C18",
number = "10",
pages = "960960",
month = oct,
year = "1969",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1969.222555",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL =¾Ž7œo
@Article{Ferrari:1967:DMU,
author = "Domenico Ferrari",
title = "A Division Method Using a Parallel Multiplier",
journal = jIEEETRANSELECCOMPUT,
volume = "EC16",
number = "2",
pages = "224226",
month = apr,
year = "1967",
CODEN = "IEECA8",
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@Article{Ferguson:1984:SFP,
author = "Kenneth M. Ferguson",
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@Article{Ferguson:1984:SFP,
author = "Kenneth M. Ferguson",
title = "{Savage} floatingpoint benchmark deficiencies of in
{16BST}",
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fjournal = "Dr. Dobb's Journal of Software Tools",
}5”K©
@Article{Fernandez:2003:FPA,
author = "Jos{\'e}Jes{\'u}s Fern{\'a}ndez and Inmaculada
Garc{\'\i}a and Ester M. Garz{\'o}n",
title = "Floating point arithmetic teaching for computational
science",
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volume = "19",
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pages = "13211334",
month = nov,
year = "2003",
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º Ÿº‰aiW #+%K57;K;?c%KŠuarticlefparith.bibEisman:1963:PERS. H. EismanPolynomial Evaluation RevisitedjCACM67384385jul71963CACMA200010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Thu Sep 1 10:15:41 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:41 ???Communications of the ACMacknjhttp://portal.acm.org/browse_dl.cfm?idx=J79S. H. EismanPolynomial Evaluation Revisited
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}Œ]hW #13}=a7E‚;_G3}Ž3articlefparith.bibDietmeyer:1963:CPNDonald L. DietmeyerConversion from Positive to Negative and Imaginary RadixjIEEETRANSELECCOMPUTEC1212022feb21963IEECA8http://dx.doi.org/10.1109/PGEC.1963.26339103677508 OR 03677508Thu Jul 14 08:10:36 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 08:10:36 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037765IEEE Transactions on Electronic Computersimaginary base; negative baseacknhfbDonald L. DietmeyerConversion from Positive to Negative and Imaginary Radix
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title = "Conversion from Positive to Negative and Imaginary
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bibdate = "Thu Jul 14 08:10:36 MDT 2011",
bibsource = "http://www.computer.org/tc/;
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acknowledgement = acknhfb,
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ÄwÖ‹lW#)7ƒ[=m;!7ƒ‹articlefparith.bibGeier:1963:ACDA. Geier and I. SturzThe approximate calculation of a definite integral with automatic choice of integration steps (intervals). The program for the computer $ rm MECIPTI $ in a floating point regime. (Romanian)An. Univ. Timisoara Ser. Sti. Mat.Fiz.1133139196368.0030\#3588Fri Dec 08 13:52:47 1995http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 13:52:47 ???acknhfbR. N. GossA. Geier and I. SturzThe approximate calculation of a definite integral with automatic choice of integration steps (intervals). The program for the computer {$ {\rm MECIPTI} $} in a floating point regime. (Romanian)
@Article{Geier:1963:ACD,
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@Book{Flores:1963:LCA,
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title = "The Logic of Computer Arithmetic",
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address = pubPH:adr,
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}Š8jY #%57=K;5O‹Karticlefparith.bibEve:1963:SAIJ. EveStarting approximation for the iterative calculation of square rootsjCOMPJ62742761963CMPJA600104620 (print), 14602067 (electronic) OR 00104620 (print), 14602067 (electronic)00104620 OR 00104620Thu Sep 15 18:37:30 1994ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.15 18:37:30 ???The Computer Journalacknjhttp://comjnl.oxfordjournals.org/J. EveStarting approximation for the iterative calculation of square roots
@Article{Eve:1963:SAI,
author = "J. Eve",
title = "Starting approximation for the iterative calculation
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journal = jCOMPJ,
volume = "6",
pages = "274276",
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ISSN = "00104620 (print), 14602067 (electronic)",
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@Book{DEC:1976:DHM,
author = "{Digital Equipment Corporation}",
title = "{DECsystem}10\slash 20 Hardware Manual",
publisher = pubDP,
address = pubDP:adr,
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month = mar,
year¬Ø
@Book{Copeland:2005:ATA,
editor = "B. Jack Copeland",
booktitle = "{Alan Turing}'s {Automatic Computing Engine}: the
master codebreaker's struggle to build the modern
computer",
title = "{Alan Turing}'s {Automatic Computing Engine}: the
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computer",
publisher = pubOXFORD,
address = pubOXFORD:adr,
pages = "xx + 553",
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@Book{DEC:1977:VAH,
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LCCN = "QA76.8 .V12D5 B 2 829 348",
bibdate = "Thu Sep 15 18:50:55 1994",
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}š„=ˆ{
@Book{DEC:1976:DHM,
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month = mar,
year = "1976",
bibdate = "Fri Dec 08 13:03:19 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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Laboratory Operating Note 75, November 1976.",
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}^…%ŠK
@Book{Cowell:1984:SDM,
editor = "Wayne R. Cowell",
booktitle = "Sources and Development of Mathematical Software",
title = "Sources and Development of Mathematical Software",
publisher = pubPH,
address = pubPH:adr,
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LCCN = "QA76.95 .S68 1984",
bibdate = "Tue Dec 14 22:44:45 1993",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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acknowledgement = acknhfb,
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@Book{Couffignal:1933:MCL,
author = "L. Couffignal",
title = "Les machines {\`a} calculer, leurs principes, leur
{\'e}volution. ({French}) [{Calculating} machines,
their principles, their evolution]",
publisher = "GauthierVillars",
address = "Paris, France",
year = "1933",
bibdate = "Wed Oct 13 11:19:11 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Extracts reprinted in \cite[\S 3.2]{Randell:1982:ODC}.
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acknowledgement = acknhfb,
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}„/ˆ_
@Book{Cody:1980:SME,
author = "W. J. Cody and W. Waite",
title = "Software Manual for the Elementary Functions",
publisher = pubPH,
address = pubPH:adr,
pages = "x + 269",
year = "1980",
ISBN = "0138220646",
ISBN13 = "9780138220648",
LCCN = "QA331 .C635 1980",
bibdate = "Thu Sep 1 10:12:51 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
}‚
¤
“¤ (9‚&šM
@Article{Hegland:1994:SSP,
author = ‰’9
@Article{He:2001:UAA,
author = "Yun He and Chris H. Q. Ding",
title = "Using Accurate Arithmetics to Improve Numerical
Reproducibility and Stability in Parallel
Applications",
journal = jJSUPERCOMPUTING,
volume = "18",
number = "3",
pages = "259277",
month = mar,
year = "2001",
CODEN = "JOSUED",
DOI = "http://dx.doi.org/10.1023/A:1008153532043",
ISSN = ý‹n—]
@Article{Hayes:2001:TB,
author = "Brian Hayes",
title = "Third Base",
journal = jAMSCI,
volume = "89",
number = "6",
pages = "490495",
month = nov # "\slash " # dec,
year = "2001",
CODEN = "AMSCAC",
ISSN = "00030996 (print), 15452786 (electronic)",
ISSNL = "00030996",
bibdate = "Tue Nov 08 08:06:17 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib"û…5Šk
@Article{Hecker:1996:LGF,
author = "Chris Hecker",
title = "Let's get to the (floating) point",
journal = "Game Developer",
volume = "2",
number = "??",
pages = "1924",
month = feb # "\slash " # mar,
year = "1996",
ISSN = "1073922X",
bibdate = "Fri Jan 06 07:46:23 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "accurate floatingpoint summation; splitting of
floatingpoint numbers into high and low parts",
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acknowledgement = acknhfb,
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*ˆ
@Article{Heath:1986:NRD,
author = "J. Heath",
title = "A note on {``Realization of digital filters using
inputscaled floatingpoint arithmetic''}",
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volume = "34",
number = "4",
pages = "995995",
month = aug,
year = "1986",
CODEN = "IETABA",
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bibdate = "Sat Jul 16 08:40:53 MDT 2005",
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author = "J. Heath and H. {Nagle, Jr.} and S. Shiva",
title = "Realization of digital filters using inputscaled
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volume = "27",
number = "5",
pages = "469477",
month = oct,
year = "1979",
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number = "1",
pages = "115116",
month = mar,
year = "1980",
CODEN = "BITTEL, NBITAB",
DOI = "http://dx.doi.org/10.1007/BF01933594",
ISSN = "00063835 (print), 15729125 (electronic)",
ISSNL = "00063835",
MRclass = "6804 (65G10)",
MRnumber = "81gF…x‹q
@Article{Haviland:1980:CAP,
author = "G. L. Haviland and A. A. Tuszynski",
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journal = jIEEETRANSCOMPUT,
volume = "C29",
number = "2",
pages = "6879",
month = feb,
year = "1980",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1980.1675529",
ISSN = "00189340 (print), 15579956 (electronic)",
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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abstract = "The 7090 at NYU has been modified to include a
``Significance Mode'' of operation which is intended to
facilitate the identification of significant bits in
the results of floatingpoint arithmetic operations.
The manner in which floatingpoint arithmetic is
handled in this mode is discussed. Several numerical
experiments using this mode are described and
comparisons are made with the ordinary ``normalized
mode.'' Examples include power series evaluation,
linear equations solution, determinant evaluation and
matrix inversion.",
acknowledgement = acknhfb,
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™wmY #1'g[57E‚5;ˆ1?cˆ1'g˜Marticlefparith.bibGoldstein:1963:SADMax GoldsteinSignificance arithmetic on a digital computerjCACM63111117mar31963CACMA2http://dx.doi.org/10.1145/366274.36633900010782 (print), 15577317 (electronic) OR 00010782 (print), 15577317 (electronic)00010782 OR 00010782Fri Nov 25 18:19:45 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 18:19:45 MSTThe 7090 at NYU has been modified to include a ``Significance Mode'' of operation which is intended to facilitate the identification of significant bits in the results of floatingpoint arithmetic operations. The manner in which floatingpoint arithmetic is handled in this mode is discussed. Several numerical experiments using this mode are described and comparisons are made with the ordinary ``normalized mode.'' Examples include power series evaluation, linear equations solution, determinant evaluation and matrix inversion.Communications of the ACMacknhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79The 7090 at NYU has been modified to include a ``Significance Mode'' of operation which is intended to facilitate the identification of significant bits in the results of floatingpoint arithmetic operations. The manner in which floatingpoint arithmetic is handled in this mode is discussed. Several numerical experiments using this mode are described and comparisons are made with the ordinary ``normalized mode.'' Examples include power series evaluation, linear equations solution, determinant evaluation and matrix inversion.Max GoldsteinSignificance arithmetic on a digital computer
@Article{Goldstein:1963:SAD,
author = "Max Goldstein",
title = "Significance arithmetic on a digital computer",
journal = jCACM,
volume = "6",
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abstract = "The 7090 at NYU has been modified to include a
``Significance Mode'' of operation which is intended to
facilitate the identification of significant bits in
the results of floatingpoint arithmetic operations.
The manner in which floatingpoint arithmetic is
handled in this mode is discussed. Several numerical
experiments using this mode are described and
comparisons are made with the ordinary ``normalized
mode.'' Examples include power series evaluation,
linear equations solution, determinant evaluation and
matrix inversion.",
acknowledgement = acknhfb,
fjournal = "Communications of the ACM",
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¡ Ë¡Œ&oY #+!=a7E‚;_!]articlefparith.bibLehman:1963:MABM. LehmanThe Minimization of Assimilations in Binary CarryStorage Arithmetic UnitsjIEEETRANSELECCOMPUTEC124409410aug81963IEECA8http://dx.doi.org/10.1109/PGEC.1963.26347903677508 OR 03677508Thu Jul 14 08:10:40 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 08:10:40 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037921IEEE Transactions on Electronic ComputersacknhfbM. LehmanThe Minimization of Assimilations in Binary CarryStorage Arithmetic Units
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}Œ1nY #93=a7E‚;_3iarticlefparith.bibKrishnamurthy:1963:CMDE. V. KrishnamurthyOn Computer Multiplication and Division Using Binary LogarithmsjIEEETRANSELECCOMPUTEC123319320jun61963IEECA8http://dx.doi.org/10.1109/PGEC.1963.26357203677508 OR 03677508Thu Jul 14 08:10:39 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 08:10:39 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037874IEEE Transactions on Electronic ComputersacknhfbE. V. KrishnamurthyOn Computer Multiplication and Division Using Binary Logarithms
@Article{Krishnamurthy:1963:CMD,
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ÜÜŠ4qX#1Y#'57=m;#CY#‹ articlefparith.bibLindamood:1963:MCOGeorge E. Lindamood and George ShapiroMagnitude comparison and overflow detection in modular arithmetic computersjSIAMREVIEW543423501963SIREAD00361445 (print), 10957200 (electronic) OR 00361445 (print), 10957200 (electronic)00361445 OR 00361445Wed Apr 29 18:26:14 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib1998.04.29 18:26:14 ???SIAM Reviewacknhfbhttp://epubs.siam.org/sirevGeorge E. Lindamood and George ShapiroMagnitude comparison and overflow detection in modular arithmetic computers
@Article{Lindamood:1963:MCO,
author = "George E. Lindamood and George Shapiro",
title = "Magnitude comparison and overflow detection in modular
arithmetic computers",
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month = "????",
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}hpY #+%=a7E‚U;ƒ__%‘marticlefparith.bibLehmer:1963:RDOD. H. LehmerR6317 Division and Overflow Detection in Residue Number SystemsjIEEETRANSELECCOMPUTEC1213637feb21963IEECA8http://dx.doi.org/10.1109/PGEC.1963.26349303677508 OR 03677508Thu Jul 14 08:10:36 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 08:10:36 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037786; http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4037754IEEE Transactions on Electronic Computersresidue arithmetic; residue number systemacknhfbD. H. Lehmer{R6317} Division and Overflow Detection in Residue Number Systems
@Article{Lehmer:1963:RDO,
author = "D. H. Lehmer",
title = "{R6317} Division and Overflow Detection in Residue
Number Systems",
journal = jIEEETRANSELECCOMPUT,
volume = "EC12",
number = "1",
pages = "3637",
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ZMnumber = "0124.07910",
abstract = "A particular set of unnormalized arithmetic operations
termed ``basic'' are described, in the context of the
University of Chicago Maniac III Computer. Each basic
operation involves three operand words and generates
two result words, all in unnormalized floating point
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ËËœ1rZ#3Qw=97Eƒ);‡a_M!‡aQw›s articlefparith.bibMetropolis:1963:BOUN. Metropolis and R. L. AshenhurstBasic Operations in an Unnormalized Arithmetic SystemjIEEETRANSELECCOMPUTEC126896904dec121963IEECA8http://dx.doi.org/10.1109/PGEC.1963.263593; http://dx.doi.org/10.1109/PGEC.1963.26359203677508 OR 03677508Thu Jul 14 08:10:44 MDT 2011http://www.computer.org/tc/; 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/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 implementation 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
@Article{Metropolis:1963:BOU,
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title = "Basic Operations in an Unnormalized Arithmetic
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038037",
ZMnumber = "0124.07910",
abstract = "A particular set of unnormalized arithmetic operations
termed ``basic'' are described, in the context of the
University of Chicago Maniac III Computer. Each basic
operation involves three operand words and generates
two result words, all in unnormalized floating point
format. The use of these operations in the
implementation of multiprecision arithmetic is
explained; in particular, it is demonstrated that
multiprecision division can be effected in a
nontentative manner with their aid.",
acknowledgement = acknhfb,
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ò#KtW#)E{#57E';;E{‘articlefparith.bibStern:1963:CSRT. E. Stern and R. M. LernerA circuit for the square root of the sum of the squaresjPROCIEEE514593596apr41963IEEPAD00189219 (print), 15582256 (electronic) OR 00189219 (print), 15582256 (electronic)00189219 OR 00189219Sat Jul 16 15:28:13 MDT 2005http://ieeexplore.ieee.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.07.16 15:28:13 MDTProceedings of the IEEEacknhfbhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5T. E. Stern and R. M. LernerA circuit for the square root of the sum of the squares
@Article{Stern:1963:CSR,
author = "T. E. Stern and R. M. Lerner",
title = "A circuit for the square root of the sum of the
squares",
journal = jPROCIEEE,
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bibdate = "Sat Jul 16 15:28:13 MDT 2005",
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summary = "A piecewiselinear network can produce an output
proportional to the square root of the sum of the
squares of a set of input voltages, using resistors and
diodes alone. The required relationship between
voltages can be represented by a multi \ldots{}",
}Š
sV#'o]+3)E%;mM;o]‹bookfparith.bibMood:1963:ITSAlexander McFarlane Mood and Franklin A. GraybillIntroduction to the theory of statisticspubMCGRAWHILLpubMCGRAWHILL:adrSecond4431963HA29 .M75 1963Fri Aug 20 10:02:03 MDT 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2010.08.20 10:02:03 MDTMcGrawHill series in probability and statisticsCited in cite Sterbenz:1974:FPC.Mathematical statisticsacknhfbAlexander McFarlane Mood and Franklin A. GraybillIntroduction to the theory of statistics
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author = "Alexander McFarlane Mood and Franklin A. Graybill",
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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series = "McGrawHill series in probability and statistics",
acknowledgement = acknhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
subject = "Mathematical statistics",
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bibsource = "http://ieeexplore.ieee.org/;
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acknowledgement = acknhfb,
fjournal = "Proceedings of the IEEE",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "A piecewiselinear network can produce an output
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squares of a set of input voltages, using resistors and
diodes alone. The required relationship between
voltages can be represented by a multi \ldots{}",
}ôp 29 08:55:45 MDT 2000",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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}õ
×
™ª¿×
3fw
ž
@Article{Tang:1990:AET,
author = "Ping Tak Peter Tang",
title ‡fM
@Article{Takagi:1998:PTL,
author = "N. Takagi",
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}k‡iS
@Article{Takagi:1992:RMM,
author = "N. Takagi",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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acknowledgement = acknhfb,
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journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
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ïˆz‘u
@Article{Takagi:1992:MMH,
author = "N. Takagi and S. Yajima",
title = "Modular multiplication hardware algorithms with a
redundant representation and their application to {RSA}
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pages = "887891",
month = jul,
year = "1992",
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‰†vm
@Article{Takagi:1991:RCM,
author = "N. Takagi and T. Asada and S. Yajima",
title = "Redundant {CORDIC} Methods with a Constant Scale
Factor for Sine and Cosine Computation",
journal = jIEEETRANSCOMPUT,
volume = "C40",
number = "9",
pages = "989995",
month = sep,
year = "1991",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.83660",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = "00189340",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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fjournal = "IEEE Transactions on Computers",
journalURL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
>ˆ$I
@Article{Takagi:1987:LED,
author = "Naofumi Takagi and Shuzo Yajima",
title = "OnLine ErrorDetectable HighSpeed Multiplier Using
Redundant Binary Representation and ThreeRail Logic",
journal = jIEEETRANSCOMPUT,
volume = "C36",
number = "11",
pages = "13101317",
month = nov,
year = "1987",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/TC.1987.5009470",
ISSN = R‘7#§`7¥š#†xq
@Article{Lucal:1959:2†hQ
@Article{Lorenz:1984:MIL,
author = "E. Lorenz and R. Sandau",
title = "{M{\"o}glichkeiten der Implementierung
leistungsf{\"a}higer Multiplikationsprogramme in
Mikrorechnersystemen} \toenglish {Possibilities of the
Implementation of Efficient Multiplication Instructions
in Microcomputer Systems} \endtoenglish",
journal = jNACHELEK,
volume = "34",
number = "8",
pages = "288290",
month = "????",
year = "1984",
CODEN = "NTELAP",
ISSN = "03234657",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknj,
fjournal = "Nachrichtentechnik Elektronik",
}I!…f‹M
@Article{Lowan:1960:PREa,
author = "Arnold N. Lowan",
title = "On the Propagation of RoundOff Errors in the
Numerical Integration of the Heat Equation",
journal = jMATHCOMPUT,
volume = "14",
number = "70",
pages = "139146",
month = apr,
year = "1960",
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/",
}¢®†Œ
@Article{LoÚ ºA
@Article{Lo:1994:RFP,
author = "JienChung Lo",
title = "Reliable FloatingPoint Arithmetic Algorithms for
ErrorCoded Operands",
journal = jIEEETRANSCOMPUT,
volume = "43",
number = "4",
pages = "400412",
month = apr,
year = "1994",
CODEN = "ITCOB4",
DOI = "http://dx.doi.org/10.1109/12.278479",
ISSN = "00189340 (print), 15579956 (electronic)",
ISSNL = ª†Œ
@Article{Lozier:1990:CPL,
author = "D. W. Lozier and F. W. J. Olver",
title = "Closure and Precision in LevelIndex Arithmetic",
journal = jSIAMJNUMERANAL,
volume = "27",
number = "5",
pages = "12951304",
month = oct,
year = "1990",
CODEN = "SJNAAM",
ISSN = "00361429 (print), 10957170 (electronic)",
ISSNL = "00361429",
MRclass = "6504 (65G05)",
MRnumber = "91f:65002",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = acknhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journalURL = "http://epubs.siam.org/sinum",
} L²“+¦W
@Article{Long:2014:SIF,
author = "Fan Long and Stelios SidiroglouDouskos and Deokhwan
Kim and Martin Rinard",
title = "Sound input f‡Ž5
@Article{Long:1970:LAS,
author = "C. T. Long and J. H. Jordan",
title = "A Limited Arithmetic on Simple Continued Fractions 
{II}",
journal = jFIBQUART,
volume = "8",
number = "2",
pages = "135157",
month = mar,
year = "1970",
CODEN = "FIBQAU",
ISSN = "00150517",
ISSNL = "00150517",
bibdate = "Thu Oct 20 18:05:25 MDT 2011",
bibsource = "http://www.fq.math.ca/82.html;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/82/long.pdf",
acknowledgement = acknhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journalURL = "http://www.fq.math.ca/",
}ù
®‡vU #+!?17;m;K!?ˆ= articlefparith.bibSvoboda:1963:ADA. SvobodaAn algorithm for divisionjINFPROCESSMACH925331963IPRMDD0373885X OR 0373885XThu Apr 2 08:38:35 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib1998.04.02 08:38:35 ???Information processing machinesacksfoA. SvobodaAn algorithm for division
@Article{Svoboda:1963:AD,
author = "A. Svoboda",
title = "An algorithm for division",
journal = jINFPROCESSMACH,
volume = "9",
number = "??",
pages = "2533",
month = "????",
year = "1963",
CODEN = "IPRMDD",
ISSN = "0373885X",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acksfo # " and " # acknhfb,
fjournal = "Information processing machines",
}”NuZ#+C157E‚K;‡5OC5–;articlefparith.bibStroud:1963:MPFA. H. Stroud and D. SecrestA multipleprecision floatingpoint interpretive program for the Control Data 1604jCOMPJ616266apr41963CMPJA600104620 (print), 14602067 (electronic) OR 00104620 (print), 14602067 (electronic)00104620 OR 00104620Fri Sep 29 08:55:45 MDT 2000ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/2000.09.29 08:55:45 MDThttp://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/060062.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/62.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/63.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/64.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/65.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/66.tifThe Computer Journalacknhfbhttp://comjnl.oxfordjournals.org/A. H. Stroud and D. SecrestA multipleprecision floatingpoint interpretive program for the {Control Data} 1604
@Article{Stroud:1963:MPF,
author = "A. H. Stroud and D. Secrest",
title = "A multipleprecision floatingpoint interpretive
program for the {Control Data} 1604",
journal = jCOMPJ,
volume = "6",
number = "1",
pages = "6266",
month = apr,
year = "1963",
CODEN = "CMPJA6",
ISSN = "00104620 (print), 14602067 (electronic)",
ISSNL = "00104620",
bibdate = "Fri Sep 29 08:55:45 MDT 2000",
bibsource = "ftp://garbo.uwasa.fi/pc/docsoft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/060062.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/62.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/63.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/64.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/65.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/66.tif",
acknowledgement = acknhfb # " and " # acknj,
fjournal = "The Computer Journal",
journalURL = "http://comjnl.oxfordjournals.org/",
}
H HRyZ #)#Y+57=O;%'ƒk#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",
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??",
}†mxU #11Y!=m;M1Y‡5§bookfparith.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}.",
}†mwU '#1+e3;m;/+e‡5inproceedingsfparith.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
@InProceedings{Wilkinson:1963:PSA,
author = "J. H. Wilkinson",
title = "Plane rotations in floatingpoint arithmetic",
crossref = "Metropolis:1963:PFS",
pages = "185198",
year = "1963",
MRclass = "65.35",
MRnumber = "28\#1744",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = acknhfb,
reviewer = "A. S. Householder",
}
¸É[Éf¿¸Žre
@Book{Muller:2006:EFA,
author = "JeanMichel Muller",
title = "Elementary functions: algorithms and implementation",
publisher = pubBIRKHAUSER,
address = pubBIRKHAUSER:adr,
edition = "Second",
pages = "xxii + 266",
year = "2006",
ISBN = "0817643729",
ISBN13 = "9780817643720",
LCCN = "QA331 .M866 2006",
bibdate = "Fri Jul 25 12:00:55 1997",
bibsource = "http://www.math.utah.edu/®y
@Book{Omondi:1994:CAS,
author = "Amos R. Omondi",
title = "Computer Arithmetic Systems: Algorithms, Architecture,
and Implementation",
publisher = pubPH,
address = pubPH:adr,
pages = "xvi + 520",
year = "1994",
ISBN = "0133343014",
ISBN13 = "9780133343014",
LCCN = "QA76.9.C62 O46 1994",
bibdate = "Sat Dec 09 11:5†W/
@Book{Muller:2010:HFP,
author = "JeanMichel Muller and Nicolas Brisebarre and Florent
de Dinechin and ClaudePierre Jeannerod and Vincent
Lef{\`e}vre and Guillaume Melquiond and Nathalie Revol
and Damien Stehl{\'e} and Serge Torres",
title = "Handbook of FloatingPoint Arithmetic",
publisher = pubBIRKHAUSERBOSTON,
address = pubBIRKHAUSERBOSTON:adr,
pages = "xxiii + 572",
year = "2010",
DOI = "http://dx.doi.org/10.1007/9780817647049",
ISBN = "081764704X",
ISBN13 = "9780817647049",
LCCN = "QA76.9.C62 H36 2010",
bibdate = "Thu Jan 27 16:18:58 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$90 (est.)",
acknowledgement = acknhfb,
}Y‡Ž5
@Book{Nelson:1991:SPM,
editor = "Greg Nelson",
title = "Systems Programming with {Modula3}",
publisher = pubPH,
address = pubPH:adr,
pages = "ix + 267",
year = "1991",
ISBN = "0135904641",
ISBN13 = "9780135904640",
LCCN = "QA76.66 .S87 1991",
bibdate = "Mon Sep 12 08:08:01 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "A description of the Modula 3 programming language by
the committee that designed it, with an entertaining
appendix on how various design decisions were made.
Section 3.4 describes three floatingpoint interfaces
that provide parameters of the underlying
floatingpoint system, access primitives, and exception
handling.",
acknowledgement = acknj,
}
…4Ši
@Book{Muller:1997:EFA,
author = "JeanMichel Muller",
title = "Elementary functions: algorithms and implementation",
publisher = pubBIRKHAUSER,
address = pubBIRKHAUSER:adr,
pages = "xv + 204",
year = "1997",
ISBN = "081763990X",
ISBN13 = "9780817639907",
LCCN = "QA331.M866 1997",
bibdate = "Fri Jul 25 12:00:55 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$59.95",
URL = "http://www.birkhauser.com/cgiwin/ISBN/081763990X;
http://www.enslyon.fr/~jmmuller/book_functions.html",
acknowledgement = acknhfb,
}
Ý“R§%
@Book{Mueller:2000:CAC,
author = "Silvia M. Mueller and Wolfgang J. Paul",
title = "Computer Architecture: Complexity and Correctness",
publisher = pubSV,
address = pubSV:adr,
pages = "xiii + 553",
year = "2000",
ISBN = "3540674810",
ISBN13 = "9783540674818",
LCCN = "QA76.9.A73 M845 2000",
bibdate = "Mon Mar 05 18:45:52 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.sbib/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??",
}ù