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@Article{J:1930:RPRb,
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title = "Large-Number Division by Calculating Machine",
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number = "6",
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bookfparith.bibCouffignal:1933:MCLL. CouffignalLes machines a calculer, leurs principes, leur evolution. (French) [Calculating machines, their principles, their evolution]Gauthier-VillarsParis, France533--5351933Wed Oct 13 11:19:11 2010http://www.m4Y #-)+357E
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articlefparith.bibGarver:1932:QDNbRaymond GarverQuestions, Discussions, and Notes: a Square Root Method and Continued Fractionsj-AMER-MATH-MONTHLY399533--535nov111932AMMYAE0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)0002-9890 OR 00029890Mon Jun 28 12:36:47 MDT 1999http://www.math.utah.e1calculer, leurs principes, leur
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fjournal = "American Mathematical Monthly",
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title = "{Verfahren zur selbstt{\"a}tigen Durchfuhrung von
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acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
rL&5kzu
@Article{Ahmadi:2008:PFS,
author = "O. Ahmadi and D. Hankerson and F.
RodI%
@Article{Aharony:2012:IFP,
author = "Merav Aharony and Emanuel Gofman and Elena Guralnik
P'A
@Article{Agrawal:1975:AAN,
author = "D. P. Agrawal",
title = "Arithmetic Algorith Q
@Article{Agrawal:1977:CNB,
author = "D. P. Agrawal",
title = "Comments on {``A Noo3g
@Article{Agrawal:1979:HSA,
author = "D. P. Agrawal",
title = "High-Speed Arithmet
Ǉwo
@Article{Agrawal:1980:NBA,
author = "D. P. Agrawal",
title = "On Negabinary-BinarI
@Article{Agrawal:1983:ICA,
author = "D. P. Agrawal and T. R. N. Rao",
title = "InZR%
@Article{Agrawal:1984:ACB,
author = "V. K. Agrawal and S. Murugesan",
title = "AlBm[
@Article{Ahmad:1972:ISH,
author = "M. Ahmad",
title = "Iterative schemes for highath.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1999.06.28 12:38:44 MDTAmerican Mathematical Monthlyack-nhfbhttp://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 = j-AMER-MATH-MONTHLY,
volume = "44",
number = "10",
pages = "644--646",
month = dec,
year = "1937",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:38:44 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}Dbolic Analysis of Relay and Switching Circuits",
type = "{Master of Science}",
school = "Department of Electrical Engineering, MIT",
address = "Cambridge, MA, USA",
pages = "72",
day = "10",
month = aug,
year = "1937",
bibdate = "Thu Nov 18 10:35:20 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Not submitted until 1940",
URL = "http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425.pdf",
acknowledgement = ack-nhfb,
author-dates = "April 30, 1916--February 24, 2001",
remark = "Smiley \cite[p. 91]{Smiley:2010:MWI} claims: ``He
[Shannon] also had the insight, like Atanasoff, that
the binary arithmetic that relay switches represented
would simplify information systems. His master's
thesis, written when he as twenty-one and published
when he was twenty-two, is considered to be one of the
most important, if not the most important, master's
thesis of the twentieth century.''\par
Pages 59--61 of the thesis are a section called
``Electric Adder to the Base Two'', and pages 62--68,
``A Factor Table Machine'', describe a machine that
will print a table of factors and primes of all the
integers from 1 to 100,000,000. Shannon notes on page
68: ``As to the practicality of such a device, it might
be said that J. P. Kulik spent 20 years in constructing
a table of primes up to 100,000,000 and when finished
it was found to contain so many errors that it was not
worth publishing. The machine described here could
probably be made to handle 5 numbers per second so that
the table would require only about 2 months to
construct.''",
}Flished when he was twenty-two, is considered to be one of the most important, if not the most important, master's thesis of the twentieth century.''par Pages 59--61 of the thesis are a section called ``Electric Adder to the Base Two'', and pages 62--68, ``A Factor Table Machine'', describe a machine that will print a table of factors and primes of all the integers from 1 to 100,000,000. Shannon notes on page 68: ``As to the practicality of such a device, it might be said that J. P. Kulik spent 20 years in constructing a table of primes up to 100,000,000 and when finished it was found to contain so many errors that it was not worth publishing. The machine described here could probably be made to handle 5 numbers per second so that the table would require only about 2 months to construct.''ack-nhfbApril 30, 1916--February 24, 2001Claude Elwood ShannonNot submitted until 1940A Symbolic Analysis of Relay and Switching Circuits
@MastersThesis{Shannon:1937:SAR,
author = "Claude Elwood Shannon",
title G= "A Symbolic Analysis of Relay and Switching Circuits",
type = "{Master of Science}",
school = "Department of Electrical Engineering, MIT",
address = "Cambridge, MA, USA",
pages = "72",
day = "10",
month = aug,
year = "1937",
bibdate = "Thu Nov 18 10:35:20 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Not submitted until 1940",
URL = "http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425.pdf",
acknowledgement = ack-nhfb,
author-dates = "April 30, 1916--February 24, 2001",
remark = "Smiley \cite[p. 91]{Smiley:2010:MWI} claims: ``He
[Shannon] also had the insight, like Atanasoff, that
the binary arithmetic that relay switches represented
would simplify information systems. His master's
thesis, written when he as twenty-one and published
when he was twenty-two, is considered to be one of the
most important, if not the most important, master's
thesis of the twentieth century.''\par
Pages 59--61 of the thesis are a section called
``Electric Adder to the Base Two'', and pages 62--68,
``A Factor Table Machine'', describe a machine that
will print a table of factors and primes of all the
integers from 1 to 100,000,000. Shannon notes on page
68: ``As to the practicality of such a device, it might
be said that J. P. Kulik spent 20 years in constructing
a table of primes up to 100,000,000 and when finished
it was found to contain so many errors that it was not
worth publishing. The machine described here could
probably be made to handle 5 numbers per second so that
the table would require only about 2 months to
construct.''",
}
}*}~Z #-'E57=m;C]WsEe'ESarticlefparith.bibBenford:1938:LANFrank BenfordThe Law of Anomalous NumbersNCW '#-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 twenty-one and pubEJs Numbers",
journal = j-PROC-AMER-PHIL-SOC,
volume = "78",
number = "4",
pages = "551--572",
month = mar,
year = "1938",
CODEN = "PAPCAA",
ISSN = "0003-049X",
bibdate = "Thu Feb 15 16:28:28 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-G",
abstract = "It has been observed that the first pages of a table
of common logarithms show more wear than do the last
pages, indicating that more used numbers begin with the
digit 1 than with the digit 9. A compilation of some
20,000 first digits taken from widely divergent sources
shows that there is a logarithmic distribution of first
digits when the numbers are composed of four or more
digits. An analysis of the numbers from differenKt
sources shows that the numbers taken from unrelated
subjects, such as a group of newspaper items, show a
much better agreement with a logarithmic distribution
than do numbers from mathematical tabulations or other
formal data. There is here the peculiar fact that
numbers that individually are without relationship are,
when considered in large groups, in good agreement with
a distribution law---hence the name ``Anomalous
Numbers.''\par
A further analysis of the data shows a strong tendency
for bodies of numerical data to fall into geometric
series. If the series is made up of numbers containing
three or more digits the first digits form a
logarithmic series. If the numbers contain only single
digits the geometric relation still holds but the
L simple logarithmic relation no longer applies.\par
An equation is given showing the frequencies of first
digits in the different orders of numbers 1 to 10, 10
to 100, etc.\par
The equation also gives the frequency of digits in the
second, third + place of a multi-digit number, and it
is shown that the same law applies to
reciprocals.\par
There are many instances showing that the geometric
series, or the logarithmic law, has long been
recognized as a common phenomenon in factual literature
and in the ordinary affairs of life. The wire gauge and
drill gauge of the mechanic, the magnitude scale of the
astronomer and the sensory response curves of the
psychologist are all particular examples of a
relationship that seems to extend to all human affairsM.
The Law of Anomalous Numbers is thus a general
probability law of widespread application.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From \cite{Logan:1978:FDP}: ``Benford's paper was
published in 1938 in a journal of rather limited
circulation and not usually read by mathematicians. It
so happened that it was immediately followed in the
same issue by a physics paper which became of some
importance for secret nuclear work during World War II
[H. A. Bethe, M. E. Rose, and L. P. Smith, `The
Multiple Scattering of Electrons', Proc. Amer. Phil.
Soc. 78(4), 573--585 (1938)]. That is why Benford's
paper caught the attention of physicists in the early
1940's and was much discussed. This led to the notes in
Nature by Goudsmit and Furry [3] and Furry and Hurwitz
[4] containing an effort to explain Benford's law. We
considered it at that time merely a welcome diversion
and did not expect that over thirty papers would be
devoted to this subject in subsequent years.'' The 2006
bibliography \cite{Hurlimann:2006:BLB} cites 325
publications about Benford's Law.",
}Oj-PROC-AMER-PHIL-SOC784551--572mar31938PAPCAA0003-049X 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=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-GIt has been observed that the first pages of a table of common logarithms show more wear than do the last pages, indicating that more used numbers begin with the digit 1 than with the digit 9. A compilation of some 20,000 first digits taken from widely divergent sources shows that there is a logarithmic distribution of first digits when the numbers are composed of four or more digits. An analysis of the numbers from different sources shows that the numbers taken from unrelated subjects, such as a group of newspaper items, show a much better agreement with a logarithmic distribution than do numbers from mathematical tabulations or other formal data. There is here the peculiar fact that numbers that individually are without relationship are, when considered inP large groups, in good agreement with a distribution law---hence the name ``Anomalous Numbers.''par A further analysis of the data shows a strong tendency for bodies of numerical data to fall into geometric series. If the series is made up of numbers containing three or more digits the first digits form a logarithmic series. If the numbers contain only single digits the geometric relation still holds but the simple logarithmic relation no longer applies.par An equation is given showing the frequencies of first digits in the different orders of numbers 1 to 10, 10 to 100, etc.par The equation also gives the frequency of digits in the second, third + place of a multi-digit number, and it is shown that the same law applies to reciprocals.par There are many instances showing that the geometric series, or the logarithmic law, has long been recognized as a common phenomenon in factual literature and in the ordinary affairs of life. The wire gauge and drill gauge of the mechanic, the magnitude scale of the astroQnomer and the sensory response curves of the psychologist are all particular examples of a relationship that seems to extend to all human affairs. The Law of Anomalous Numbers is thus a general probability law of widespread application.Proceedings of the American Philosophical Society held at Philadelphia for promoting useful knowledgeBenford's Law; Law of Anomalous Numbers; Zipf's LawFrom cite Logan:1978:FDP: ``Benford's paper was published in 1938 in a journal of rather limited circulation and not usually read by mathematicians. It so happened that it was immediately followed in the same issue by a physics paper which became of some importance for secret nuclear work during World War II [H. A. Bethe, M. E. Rose, and L. P. Smith, `The Multiple Scattering of Electrons', Proc. Amer. Phil. Soc. 78(4), 573--585 (1938)]. That is why Benford's paper caught the attention of physicists in the early 1940's and was much discussed. This led to the notes in Nature by Goudsmit and Furry [3] and Furry and Hurwitz [4] Rcontaining 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.ack-nhfbIt 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 Sare without relationship are, when considered in large groups, in good agreement with a distribution law---hence the name ``Anomalous Numbers.''\par A further analysis of the data shows a strong tendency for bodies of numerical data to fall into geometric series. If the series is made up of numbers containing three or more digits the first digits form a logarithmic series. If the numbers contain only single digits the geometric relation still holds but the simple logarithmic relation no longer applies.\par An equation is given showing the frequencies of first digits in the different orders of numbers 1 to 10, 10 to 100, etc.\par The equation also gives the frequency of digits in the second, third + place of a multi-digit number, and it is shown that the same law applies to reciprocals.\par There are many instances showing that the geometric series, or the logarithmic law, has long been recognized as a common phenomenon in factual literature and in the ordinary affairs of life. The wire gauge and drill gauTge of the mechanic, the magnitude scale of the astronomer and the sensory response curves of the psychologist are all particular examples of a relationship that seems to extend to all human affairs. The Law of Anomalous Numbers is thus a general probability law of widespread application.Frank BenfordThe Law of Anomalous Numbers
@Article{Benford:1938:LAN,
author = "Frank Benford",
title = "The Law of Anomalous Numbers",
journal = j-PROC-AMER-PHIL-SOC,
volume = "78",
number = "4",
pages = "551--572",
month = mar,
year = "1938",
CODEN = "PAPCAA",
ISSN = "0003-049X",
bibdate = "Thu Feb 15 16:28:28 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-G",
abstract = "It has been observed that the first pages of a table
of common logarithms show more wear than do the lUast
pages, indicating that more used numbers begin with the
digit 1 than with the digit 9. A compilation of some
20,000 first digits taken from widely divergent sources
shows that there is a logarithmic distribution of first
digits when the numbers are composed of four or more
digits. An analysis of the numbers from different
sources shows that the numbers taken from unrelated
subjects, such as a group of newspaper items, show a
much better agreement with a logarithmic distribution
than do numbers from mathematical tabulations or other
formal data. There is here the peculiar fact that
numbers that individually are without relationship are,
when considered in large groups, in good agreement with
a distribution law---hence the name ``Anomalous
Numbers.''\paVr
A further analysis of the data shows a strong tendency
for bodies of numerical data to fall into geometric
series. If the series is made up of numbers containing
three or more digits the first digits form a
logarithmic series. If the numbers contain only single
digits the geometric relation still holds but the
simple logarithmic relation no longer applies.\par
An equation is given showing the frequencies of first
digits in the different orders of numbers 1 to 10, 10
to 100, etc.\par
The equation also gives the frequency of digits in the
second, third + place of a multi-digit number, and it
is shown that the same law applies to
reciprocals.\par
There are many instances showing that the geometric
series, or the logarithmic law, has loWng been
recognized as a common phenomenon in factual literature
and in the ordinary affairs of life. The wire gauge and
drill gauge of the mechanic, the magnitude scale of the
astronomer and the sensory response curves of the
psychologist are all particular examples of a
relationship that seems to extend to all human affairs.
The Law of Anomalous Numbers is thus a general
probability law of widespread application.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From \cite{Logan:1978:FDP}: ``Benford's paper was
published in 1938 in a journal of rather limited
circulation and not usually read by mathematicians. It
so happened that it was immediately followed in the
same issue by a physics paper which became of some
importance for secret nuclear work during World War II
[H. A. Bethe, M. E. Rose, and L. P. Smith, `The
Multiple Scattering of Electrons', Proc. Amer. Phil.
Soc. 78(4), 573--585 (1938)]. That is why Benford's
paper caught the attention of physicists in the early
1940's and was much discussed. This led to the notes in
Nature by Goudsmit and Furry [3] and Furry and Hurwitz
[4] containing an effort to explain Benford's law. We
considered it at that time merely a welcome diversion
and did not expect that over thirty papers would be
devoted to this subject in subsequent years.'' The 2006
bibliography \cite{Hurlimann:2006:BLB} cites 325
publications about Benford's Law.",
}m{\'e}canique. Application aux machines
{\`a} calculer et aux calculs de la m{\'e}canique
c{\'e}leste. ({French}) [{On} mechanical analysis.
Application to calculating machines and to calculation
in celestial mechanics]",
publisher = "Gauthier-Villars",
school = "Facult{\'e} des Sciences de Paris",
address = "Paris, France",
year = "1938",
bibdate = "Wed Oct 13 11:17:22 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Extracts reprinted in \cite[\S 2.7]{Randell:1982:ODC}.
Translated by Mr. R. Basu.",
acknowledgement = ack-nhfb,
language = "French",
}x machines {\`a} calculer et aux calculs de la m{\'e}canique c{\'e}leste. ({French}) [{On} mechanical analysis. Application to calculating machines and to calculation in celestial mechanics]
@PhdThesis{Couffignal:1938:AMA,
author = "L. Couffignal",
title = "Sur l'analyse m{\'e}canique. Application aux machines
{\`a} calculer et aux calculs de la m{\'e}canique
c{\'e}leste. ({French}) [{On} mechanical analysis.
Application to calculating machines and to calculation
in celestial mechanics]",
publisher = "Gauthier-Villars",
school = "Facult{\'e} des Sciences de Paris",
address = "Paris, France",
year = "1938",
bibdate = "Wed Oct 13 11:17:22 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Extracts reprinted in \cite[\S 2.7]{Randell:1982:ODC}.
Translated by Mr. R. Basu.",
acknowledgement = ack-nhfb,
language = "French",
}
hY #3'7-G'=m;''/_ phdthesisfparith.bibCouffignal:1938:AMAL. CouffignalSur l'analyse mecanique. Application aux machines a calculer et aux calculs de la mecanique celeste. (French) [On mechanical analysis. Application to calculating machines and to calculation in celestial mechanics]Gauthier-VillarsFaculte des Sciences de ParisParis, France551--5721938Wed 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.Frenchack-nhfbL. CouffignalExtracts reprinted in \cite[\S 2.7]{Randell:1982:ODC}. Translated by Mr. R. Basu.Sur l'analyse m{\'e}canique. Application auY Maitland) Wright",
title = "An Introduction to the Theory of Numbers",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xvi + 403",
year = "1938",
LCCN = "QA241 .H28",
bibdate = "Fri Nov 30 06:49:15 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
DD9W#)]!)!=m;]Ibookfparith.bibHardy:1938:ITNG. H. (Godfrey Harold) Hardy and E. M. (Edward Maitland) WrightAn Introduction to the Theory of Numberspub-OXFORDpub-OXFORD:adrxvi + 4031938QA241 .H28Fri Nov 30 06:49:15 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.30 06:49:15 ???ack-nhfbG. H. (Godfrey Harold) Hardy and E. M. (Edward Maitland) WrightAn Introduction to the Theory of Numbers
@Book{Hardy:1938:ITN,
author = "G. H. (Godfrey Harold) Hardy and E. M. (Edward
Maitland) Wright",
title = "An Introduction to the Theory of Numbers",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xvi + 403",
year = "1938",
LCCN = "QA241 .H28",
bibdate = "Fri Nov 30 06:49:15 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}^ysis of Relay and Switching Circuits",
journal = j-TRANS-AMER-INST-ELEC-ENG,
volume = "57",
number = "??",
pages = "713--723",
month = dec,
year = "1938",
CODEN = "TAEEA5",
ISSN = "0096-3860",
bibdate = "Sat Nov 20 08:54:12 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www2.research.att.com/~njas/doc/shannonbio.html",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Institute of Electrical
Engineers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714",
remark = "This is Shannon's first published paper (his Master's
thesis). In 1940, it received the Alfred Noble Prize of
the combined engineering societies of the United
States, an award given each year to a person not over
thirty for a paper published in one of the journals of
the participating societies. H. H. Goldstine
\cite{Goldstine:1972:CPN} called this work ``one of the
most important master's theses ever written ... a
landmark in that it helped to change digital circuit
design from an art to a science.''",
}`ster'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.''ack-nhfbhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714Claude E. ShannonA Symbolic Analysis of Relay and Switching Circuits
@Article{Shannon:1938:SAR,
author = "Claude E. Shannon",
title = "A Symbolic Analysis of Relay and Switching Circuits",
journal = j-TRANS-AMER-INST-ELEC-ENG,
volume = "57",
number = "??",
pages = "713--723",
month = dec,
year = "1938",
CODEN = "TAEEA5",
ISSN = "0096-3860",
bibdate = "Sat Nov 20 08:54:12 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www2.research.att.com/~njas/doc/shannonbio.html",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Institute of Electrical
Engineers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714",
remark = "This is Shannon's first published paper (his Master's
thesis). In 1940, it received the Alfred Noble Prize of
the combined engineering societies of the United
States, an award given each year to a person not over
thirty for a paper published in one of the journals of
the participating societies. H. H. Goldstine
\cite{Goldstine:1972:CPN} called this work ``one of the
most important master's theses ever written ... a
landmark in that it helped to change digital circuit
design from an art to a science.''",
}
o7X #%5=m;#+5}miscfparith.bibBush:1940:AMV. BushArithmetical Machine713--7231940Wed Oct 13 11:37:32 2010http://wesW !#1+/91'=m;_+g/qtechreportfparith.bibAtanasoff:cY #-/sA7=]; }/sUarticlefparith.bibShannon:1938:SARClaude E. ShannonA Symbolic Analysis of Relay and Switching Circuitsj-TRANS-AMER-INST-ELEC-ENG57713--723dec121938TAEEA50096-3860 OR 00963860Sat Nov 20 08:54:12 2010http://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 Ma_chine for the solution of large systems of
linear algebraic equations",
type = "Unpublished memorandum",
institution = "Iowa State College",
address = "Ames, IA, USA",
month = aug,
year = "1940",
bibdate = "Wed Oct 13 11:36:11 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}1940:CMSJ. V. AtanasoffComputing machine for the solution of large systems of linear algebraic equationsUnpublished memorandumIowa State CollegeAmes, IA, USA713--723aug81940Wed 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.ack-nhfbJ. V. AtanasoffReprinted in \cite[\S 7.2]{Randell:1982:ODC}.Computing machine for the solution of large systems of linear algebraic equations
@TechReport{Atanasoff:1940:CMS,
author = "J. V. Atanasoff",
title = "Computing machine for the solution of large systems of
linear algebraic equations",
type = "Unpublished memorandum",
institution = "Iowa State College",
address = "Ames, IA, USA",
month = aug,
year = "1940",
bibdate = "Wed Oct 13 11:36:11 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}ished = "Vannevar Bush Papers, Container 18, Folder: Caldwell,
Samuel, 1939--1940",
year = "1940",
bibdate = "Wed Oct 13 11:37:32 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.3]{Randell:1982:ODC}.
Copyright interest in the unpublished writings of
Vannevar Bush has been dedicated to the public.",
acknowledgement = ack-nhfb,
}ww.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:37:32 ???Reprinted in cite [ 7.3]Randell:1982:ODC. Copyright interest in the unpublished writings of Vannevar Bush has been dedicated to the public.ack-nhfbVannevar Bush Papers, Container 18, Folder: Caldwell, Samuel, 1939--1940V. BushReprinted in \cite[\S 7.3]{Randell:1982:ODC}. Copyright interest in the unpublished writings of Vannevar Bush has been dedicated to the public.Arithmetical Machine
@Misc{Bush:1940:AM,
author = "V. Bush",
title = "Arithmetical Machine",
howpublished = "Vannevar Bush Papers, Container 18, Folder: Caldwell,
Samuel, 1939--1940",
year = "1940",
bibdate = "Wed Oct 13 11:37:32 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.3]{Randell:1982:ODC}.
Copyright interest in the unpublished writings of
Vannevar Bush has been dedicated to the public.",
acknowledgement = ack-nhfb,
}= "Unpublished memorandum",
institution = "Bell Telephone Laboratories",
address = "New York, NY, USA",
year = "1940",
bibdate = "Wed Oct 13 11:30:38 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.1]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
wU !#)'9C/=m;_'gtechreportfparith.bibStibitz:1940:CG. R. StibitzComputerUnpublished memorandumBell Telephone LaboratoriesNew York, NY, USA713--7231940Wed 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.ack-nhfbG. R. StibitzReprinted in \cite[\S 6.1]{Randell:1982:ODC}.Computer
@TechReport{Stibitz:1940:C,
author = "G. R. Stibitz",
title = "Computer",
type = "Unpublished memorandum",
institution = "Bell Telephone Laboratories",
address = "New York, NY, USA",
year = "1940",
bibdate = "Wed Oct 13 11:30:38 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.1]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}iof electrical data recording and reading
mechanism",
type = "{M.S.} thesis",
school = "Iowa State College",
address = "Ames, IA, USA",
pages = "32",
year = "1941",
bibdate = "Thu Nov 18 11:18:18 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
author-dates = "1918--1963",
historical-note = "From
http://www.lib.iastate.edu/arch/rgrp/5-2-1-1.html:
``John Vincent Atanasoff received his M.S. (1926) in
Mathematics from Iowa State College (University) and
received his Ph.D. (1930) in Theoretical Physics from
the University of Wisconsin-Madison. He returned to
Iowa State in 1930 as Assistant Professor in
mathematics and physics and was promoted to Associate
Professor (1936). Atanasoff began developing concepts
for an electronic computjing machine in 1937. It was
shortly thereafter that he, along with graduate student
Clifford Berry, started work on the world's first
electronic digital computer. The computer would later
be named the Atanasoff-Berry Computer (ABC).
Work on the machine stopped at the start of World War
II in 1941 and the ABC was never patented. Atanasoff
and Berry were both called to support the war effort
and left Iowa State. By the end of the decade, the ABC
was removed from the basement of Physics Hall and
dismantled.
Atanasoff and the ABC were part of a major court case
between Honeywell, Inc. and Sperry Rand Corporation
which occurred 1967-1973. The case involved the ENIAC
patent which covered basic ownership rights to the
design of electronic digital computers. Dukring the
trial, the judge concluded that the invention of the
ENIAC was derived from the work of John Vincent
Atanasoff at Iowa State University.
A replica of the Atanasoff-Berry Computer was completed
and unveiled to the public in 1996. The ABC replica was
constructed by a team of Iowa State scientists at the
Ames Laboratory and was exhibited at museums throughout
the country over the next several years.''",
remark = "This thesis may be one of the earliest surviving
records of the ABC computer built by John Atanasoff and
Clifford Berry in the late 1930s. The one-of-a-kind ABC
was destroyed in 1948, and most of its parts were lost.
Also cited in ``Charles W. Bradley Collection on the
ENIAC Trial, 1930--1966'', (found in
http://discover.lib.umn.edu/): CWB as an attorney for
the group retained by Honeywell in the Honeywell v.
Sperry Rand ENIAC trial. The ABC had a 50-bit word.",
}mard 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 one-of-a-kind ABC was destroyed in 1948, and most of its parts were lost. Also cited in ``Charles W. Bradley Collection on the ENIAC Trial, 1930--1966'', (found in http://discover.lib.umn.edu/): CWB as an attorney for the group retained by Honeywell in the Honeywell v. Sperry Rand ENIAC trial. The ABC had a 50-bit word.ack-nhfb1918--1963Clifford Edward BerryDesign of electrical data recording and reading mechanism
@MastersThesis{Berry:1941:DED,
author = "Clifford Edward Berry",
title = "Design of electrical data recording and reading
mechanism",
type = "{M.S.} thesis",
school = "Iowa State College",
addressn = "Ames, IA, USA",
pages = "32",
year = "1941",
bibdate = "Thu Nov 18 11:18:18 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
author-dates = "1918--1963",
historical-note = "From
http://www.lib.iastate.edu/arch/rgrp/5-2-1-1.html:
``John Vincent Atanasoff received his M.S. (1926) in
Mathematics from Iowa State College (University) and
received his Ph.D. (1930) in Theoretical Physics from
the University of Wisconsin-Madison. He returned to
Iowa State in 1930 as Assistant Professor in
mathematics and physics and was promoted to Associate
Professor (1936). Atanasoff began developing concepts
for an electronic computing machine in 1937. It was
shortly thereafter that he, along with graduate student
Clifford Berry, started work on thoe world's first
electronic digital computer. The computer would later
be named the Atanasoff-Berry Computer (ABC).
Work on the machine stopped at the start of World War
II in 1941 and the ABC was never patented. Atanasoff
and Berry were both called to support the war effort
and left Iowa State. By the end of the decade, the ABC
was removed from the basement of Physics Hall and
dismantled.
Atanasoff and the ABC were part of a major court case
between Honeywell, Inc. and Sperry Rand Corporation
which occurred 1967-1973. The case involved the ENIAC
patent which covered basic ownership rights to the
design of electronic digital computers. During the
trial, the judge concluded that the invention of the
ENIAC was derived from the work of John Vincent
Atanasoff at Iowa State University.
A replica of the Atanasoff-Berry Computer was completed
and unveiled to the public in 1996. The ABC replica was
constructed by a team of Iowa State scientists at the
Ames Laboratory and was exhibited at museums throughout
the country over the next several years.''",
remark = "This thesis may be one of the earliest surviving
records of the ABC computer built by John Atanasoff and
Clifford Berry in the late 1930s. The one-of-a-kind ABC
was destroyed in 1948, and most of its parts were lost.
Also cited in ``Charles W. Bradley Collection on the
ENIAC Trial, 1930--1966'', (found in
http://discover.lib.umn.edu/): CWB as an attorney for
the group retained by Honeywell in the Honeywell v.
Sperry Rand ENIAC trial. The ABC had a 50-bit word.",
}
qLk Y #//357E
;G/marticlefparith.bibCrawford:1943:DNSW. S. H. CrawfordDiscussions and Notes: Square Roots from a Table of Cosinesj-AMER-MATH-MONTHLY503190--191mar31943AMMYAE0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)0002-9890 OR 00029890Mon Jun 28 12:36:w]X!#/k +m_kg Qtechreportfparu,V !#-'K7=m;_'g]techreportfparith.bibMauchly:1942:UHSJ. W. MauchlyThe use of high speed vacuum tube devicesxV '#)7#1'=m;-!7kmastersthesisfparith.bibBerry:1941:DEDClifford Edwlspeed vacuum tube devices for
calculating",
type = "Privately circulated memorandum",
institution = "Moore School of Electrical Engineering, University of
Pennsylvania",
address = "Philadelphia, PA, USA",
month = aug,
year = "1942",
bibdate = "Wed Oct 13 11:52:54 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.6]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
+rL&+JP!
@Article{Alimohammad:2010:UAA,
author = "A. Alimohammad and S. F. Fard and B. F. Cockburn"L#G
@Article{Aldous:2010:WCO,
author = "David Aldous and Tung Phan",
title = "When CaLO
@Article{Al-Twaijry:1998:TSE,
author = "H. A. Al-Twaijry and M. J. Flynn",
title = 2
@Article{Alam:1993:RTO,
author = "M. S. Alam and M. A. Karim",
title = "Real-Time'>}
@Article{Alexander:1977:SRR,
author = "V. L. Alexander",
title = "Square Root Roux
@Article{Aley:1897:DES,
author = "Robert J. Aley",
title = "A Device for ExtractiK
@Article{Alia:1984:VAD,
author = "G. Alia and E. Martinelli",
title = "A {VLSI} aD2e
@Article{Alia:1991:VMM,
author = "G. Alia and E. Martinelli",
title = "A {VLSI} m!B
@Article{Allaart:1997:ISC,
author = "Pieter C. Allaart",
title = "An Invariant-Su0s for calculatingPrivately circulated memorandumMoore School of Electrical Engineering, University of PennsylvaniaPhiladelphia, PA, USA32aug81942Wed 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.ack-nhfbJ. 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 = ack-nhfb,
}
title = "Report on Electronic Predictors for Anti-Aircraft Fire
Control",
institution = "Research Laboratories, R. C. A. Manufacturing Company,
Inc.",
address = "Camden, NJ, USA",
month = apr,
year = "1942",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}ith.bibRajchman:1942:REPJ. A. Rajchman and G. A. Morton and A. W. VanceReport on Electronic Predictors for Anti-Aircraft Fire ControlResearch Laboratories, R. C. A. Manufacturing Company, Inc.Camden, NJ, USA32apr41942http://www.math.utah.edu/pub/tex/bib/fparith.bibReprinted in cite [ 7.4]Randell:1982:ODC.ack-nhfbJ. A. Rajchman and G. A. Morton and A. W. VanceReprinted in \cite[\S 7.4]{Randell:1982:ODC}.Report on Electronic Predictors for Anti-Aircraft Fire Control
@TechReport{Rajchman:1942:REP,
author = "J. A. Rajchman and G. A. Morton and A. W. Vance",
title = "Report on Electronic Predictors for Anti-Aircraft Fire
Control",
institution = "Research Laboratories, R. C. A. Manufacturing Company,
Inc.",
address = "Camden, NJ, USA",
month = apr,
year = "1942",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}d Notes: Square Roots from a Table of
Cosines",
journal = j-AMER-MATH-MONTHLY,
volume = "50",
number = "3",
pages = "190--191",
month = mar,
year = "1943",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:36:57 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
} 57 MDT 1999http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1999.06.28 12:36:57 MDTAmerican Mathematical Monthlyack-nhfbhttp://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 = j-AMER-MATH-MONTHLY,
volume = "50",
number = "3",
pages = "190--191",
month = mar,
year = "1943",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:36:57 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}yignificant Figures of Numbers in Statistical Tables",
journal = j-NATURE,
volume = "154",
number = "3921",
pages = "800--801",
day = "23",
month = dec,
year = "1944",
CODEN = "NATUAS",
DOI = "http://dx.doi.org/10.1038/154800a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Sun Sep 18 11:57:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf",
abstract = "A rough qualitative explanation of this fact can
easily be given. If we consider tables in which the
entries become rarer the larger they are, we can draw
the obvious conclusion that in any interval, say,
between 10 and 99, or 10,000 and 99,999, there are more
entries on the small side than on the large side.",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}!{we consider tables in which the entries become rarer the larger they are, we can draw the obvious conclusion that in any interval, say, between 10 and 99, or 10,000 and 99,999, there are more entries on the small side than on the large side.NatureBenford's Law; Law of Anomalous Numbers; Zipf's Lawack-nhfbhttp://www.nature.com/nature/archive/A rough qualitative explanation of this fact can easily be given. If we consider tables in which the entries become rarer the larger they are, we can draw the obvious conclusion that in any interval, say, between 10 and 99, or 10,000 and 99,999, there are more entries on the small side than on the large side.S. A. Goudsmit and W. H. FurrySignificant Figures of Numbers in Statistical Tables
@Article{Goudsmit:1944:SFN,
author = "S. A. Goudsmit and W. H. Furry",
title = "Significant Figures of Numbers in Statistical Tables",
journal = j-NATURE,
volume = "154",
number = "3921",
pages = "800--801",
day = "23",
month = dec,
year = "1944",
CODEN = "NATUAS",
DOI = "http://dx.doi.org/10.1038/154800a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Sun Sep 18 11:57:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf",
abstract = "A rough qualitative explanation of this fact can
easily be given. If we consider tables in which the
entries become rarer the larger they are, we can draw
the obvious conclusion that in any interval, say,
between 10 and 99, or 10,000 and 99,999, there are more
entries on the small side than on the large side.",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
_!Y#/IuQ57=m;
ysWyIu?articlefparith.bibGoudsmit:1944:SFNS. A. Goudsmit and W. H. FurrySignificant Figures of Numbers in Statistical Tablesj-NATURE1543921800--80123dec121944NATUAShttp://dx.doi.org/10.1038/154800a00028-0836 (print), 1476-4687 (electronic) OR 00280836 (print), 14764687 (electronic)0028-0836 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 zibution of Numbers and Distribution of
Significant Figures",
journal = j-NATURE,
volume = "155",
number = "??",
pages = "52--53",
day = "13",
month = jan,
year = "1945",
CODEN = "NATUAS",
DOI = "http://dx.doi.org/10.1038/155052a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Sun Sep 18 11:51:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}"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 = j-NATURE,
volume = "155",
number = "??",
pages = "52--53",
day = "13",
month = jan,
year = "1945",
CODEN = "NATUAS",
DOI = "http://dx.doi.org/10.1038/155052a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Sun Sep 18 11:51:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
q"Y#)GQ57=m;
sWG'articlefparith.bibFurry:1945:DNDW. H. Furry and Henry HurwitzDistribution of Numbers and Distribution of Significant Figuresj-NATURE15552--5313jan11945NATUAShttp://dx.doi.org/10.1038/155052a00028-0836 (print), 1476-4687 (electronic) OR 00280836 (print), 14764687 (electronic)0028-0836 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 Lawack-nhfbhttp://www.nature.~EDVAC}",
institution = "University of Pennsylvania",
day = "30",
month = jun,
year = "1945",
bibdate = "Mon Jun 06 19:17:03 2005",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
remark = "This is the report that got von Neumann's name
associated with the serial, stored-program, general
purpose, digital architecture upon which 99.99\% of all
computers today are based.",
xxnote = "Report prepared for U.S. Army Ordinance Department
under Contract W-670-ORD-4926. Reprinted in
\cite[pp.~177--246]{Stern:1981:EUA},
\cite[pp.~399--413]{Randell:1982:ODC},
\cite{vonNeumann:1993:FDR}, and
\cite{Laplante:1996:GPC}.",
}#{EDVAC}",
institution = "University of Pennsylvania",
day = "30",
month = jun,
year = "1945",
bibdate = "Mon Jun 06 19:17:03 2005",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
remark = "This is the report that got von Neumann's name
associated with the serial, stored-program, general
purpose, digital architecture upon which 99.99\% of all
computers today are based.",
xxnote = "Report prepared for U.S. Army Ordinance Department
under Contract W-670-ORD-4926. Reprinted in
\cite[pp.~177--246]{Stern:1981:EUA},
\cite[pp.~399--413]{Randell:1982:ODC},
\cite{vonNeumann:1993:FDR}, and
\cite{Laplante:1996:GPC}.",
}
G#W !#3-UA= ;_u-gYutechreportfparith.bibvonNeumann:1945:FDRJohn von NeumannFirst Draft of a Report on the EDVACUniversity of Pennsylvania52--5330jun61945Mon Jun 06 19:17:03 2005ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib; 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, stored-program, general purpose, digital architecture upon which 99.99% of all computers today are based.ack-nhfbJohn von NeumannReprinted in \cite[\S 8.2]{Randell:1982:ODC}.First Draft of a Report on the {EDVAC}
@TechReport{vonNeumann:1945:FDR,
author = "John von Neumann",
title = "First Draft of a Report on the utomatic Sequence Controlled Calculator}",
journal = j-ELECTR-ENG,
volume = "65",
number = "??",
pages = "384--391, 449--454, 522--528",
year = "1946",
CODEN = "ELENAC",
ISSN = "0095-9197",
bibdate = "Wed Oct 13 11:26:29 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Electrical Engineering (American Institute of
Electrical Engineers)",
}$NAC0095-9197 OR 00959197Wed Oct 13 11:26:29 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:26:29 ???Reprinted in cite [ 5.2]Randell:1982:ODC.Electrical Engineering (American Institute of Electrical Engineers)ack-nhfbH. H. Aiken and G. M. HopperReprinted in \cite[\S 5.2]{Randell:1982:ODC}.The {Automatic Sequence Controlled Calculator}
@Article{Aiken:1946:ASC,
author = "H. H. Aiken and G. M. Hopper",
title = "The {Automatic Sequence Controlled Calculator}",
journal = j-ELECTR-ENG,
volume = "65",
number = "??",
pages = "384--391, 449--454, 522--528",
year = "1946",
CODEN = "ELENAC",
ISSN = "0095-9197",
bibdate = "Wed Oct 13 11:26:29 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Electrical Engineering (American Institute of
Electrical Engineers)",
}
Qn&U #+!917=m;_=!g9[articlefparith.bi%]!#)13;=q;YUi1]techreportfparith.bibBurks:1946:PDLArthur W. Burks and Herman H. Goldstine and John von NeumannPreliminary discussion of the logical design of an electronic computing instrumentinst-INST-ADV-STUDYinst-INST-ADV-STUDY:adr4228jun61946Wed Oct 13 08:17:48 2004ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithm$V#)Ee%E7=m;_EgiAarticlefparith.bibAiken:1946:ASCH. H. Aiken and G. M. HopperThe Automatic Sequence Controlled Calculatorj-ELECTR-ENG65384--391, 449--454, 522--5281946ELE
Neumann",
title = "Preliminary discussion of the logical design of an
electronic computing instrument",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "42",
day = "28",
month = jun,
year = "1946",
bibdate = "Wed Oct 13 08:17:48 2004",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/arith.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Report to the U.S. Army Ordnance Department. Reprinted
in \cite[pp.~221--259]{Swartzlander:1976:CDD}, \cite[\S
8.3]{Randell:1982:ODC}, and
\cite[pp.~97--146]{Aspray:1987:PJN}",
acknowledgement = ack-nhfb,
remark = "Discusses floating-point versus fixed-point
computation, and concludes that floating-point is
probably not justifiable. They wrote:\par
``There appear to be two major purposes in a `floating'
decimal point system both of which arise from the fact
that the number of digits in a word is a constant fixed
by design considerations for each particular machine.
The first of these purposes is to retain in a sum or
product as many significant digits as possible and the
second of these is to free the human operator from the
burden of estimating and inserting into a problem
`scale factors' --- multiplicative constants which
serve to keep numbers within the limits of the
machine.\par
There is, of course, no denying the fact that human
time is consumed in arranging for the introduction of
suitable scale factors. We only argue that the time so
consumed is a very small percentage of the total time
we will spend in preparing an interesting problem for
our machine. The first advantage of the floating point
is, we feel, somewhat illusory. In order to have such a
floating point, one must waste memory capacity which
could otherwise be used for carrying more digits per
word. It would therefore seem to us not at all clear
whether the modest advantages of a floating binary
point offset the loss of memory capacity and the
increased complexity of the arithmetic and control
circuits.''",
}%metic.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.~221--259]Swartzlander:1976:CDD, cite [ 8.3]Randell:1982:ODC, and cite [pp.~97--146]Aspray:1987:PJNDiscusses floating-point versus fixed-point computation, and concludes that floating-point is probably not justifiable. They wrote:par ``There appear to be two major purposes in a `floating' decimal point system both of which arise from the fact that the number of digits in a word is a constant fixed by design considerations for each particular machine. The first of these purposes is to retain in a sum or product as many significant digits as possible and the second of these is to free the human operator from the burden of estimating and inserting into a problem `scale factors' --- multiplicative constants which serve to keep numbers within the limits of the machine.par There is, of course, no denying the fact that human time is consumed in arranging for the introduction of suitable scale factors. We only argue that the time so consumed is a very small percentage of the total time we will spend in preparing an interesting problem for our machine. The first advantage of the floating point is, we feel, somewhat illusory. In order to have such a floating point, one must waste memory capacity which could otherwise be used for carrying more digits per word. It would therefore seem to us not at all clear whether the modest advantages of a floating binary point offset the loss of memory capacity and the increased complexity of the arithmetic and control circuits.''ack-nhfbArthur W. Burks and Herman H. Goldstine and John von NeumannReport to the U.S. Army Ordnance Department. Reprinted in \cite[pp.~221--259]{Swartzlander:1976:CDD}, \cite[\S 8.3]{Randell:1982:ODC}, and \cite[pp.~97--146]{Aspray:1987:PJN}Preliminary discussion of the logical design of an electronic computing instrument
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title = "Preliminary discussion of the logical design of an
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note = "Report to the U.S. Army Ordnance Department. Reprinted
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\cite[pp.~97--146]{Aspray:1987:PJN}",
acknowledgement = ack-nhfb,
remark = "Discusses floating-point versus fixed-point
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``There appear to be two major purposes in a `floating'
decimal point system both of which arise from the fact
that the number of digits in a word is a constant fixed
by design considerations for each particular machine.
The first of these purposes is to retain in a sum or
product as many significant digits as possible and the
second of these is to free the human operator from the
burden of estimating and inserting into a problem
`scale factors' --- multiplicative constants which
serve to keep numbers within the limits of the
machine.\par
There is, of course, no denying the fact that human
time is consumed in arranging for the introduction of
suitable scale factors. We only argue that the time so
consumed is a very small percentage of the total time
we will spend in preparing an interesting problem for
our machine. The first advantage of the floating point
is, we feel, somewhat illusory. In order to have such a
floating point, one must waste memory capacity which
could otherwise be used for carrying more digits per
word. It would therefore seem to us not at all clear
whether the modest advantages of a floating binary
point offset the loss of memory capacity and the
increased complexity of the arithmetic and control
circuits.''",
},
journal = j-BELL-LABS-RECORD,
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@Article{Ercegovac:1992:FRC,
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@Article{Ercegovac:1994:VHR,
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ti*d|y
@Article{Ercegovac:2000:IGD,
author = "Milo{\v{s}} D. Ercegovac and Laurent Imbert and Dav7?
@Article{Ercegovac:2000:RSR,
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7lY
@Article{Ercegovac:2007:CSR,
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GƆM
@Article{Ercoli:1957:EDO,
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title = "ErrS)
@Article{Ercoli:1959:BAD,
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title = "Binsqc
@Article{Ercoli:1960:LEE,
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title = "Letter to the {EditorbCesareo:1946:RIO. CesareoThe Relay Interpolatorj-BELL-LABS-RECORD23457--4601946BLRCAB0005-8564 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 Recordack-nhfbO. CesareoReprinted in \cite[\S 6.2]{Randell:1982:ODC}.The Relay Interpolator
@Article{Cesareo:1946:RI,
author = "O. Cesareo",
title = "The Relay Interpolator",
journal = j-BELL-LABS-RECORD,
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bibdate = "Wed Oct 13 11:31:47 2010",
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acknowledgement = ack-nhfb,
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}r Rechenautomat Ipm. Entwicklung Mathematischer
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[{The} {Ipm} Calculator. {The} development of
mathematical instruments in {Germany} 1939--1945]",
type = "{Bericht}",
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institution = "Institut f{\"u}r Praktische Mathematik, Technische
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 3.3]{Randell:1982:ODC}.
Translated by Mr. and Mrs. P. Jones",
acknowledgement = ack-nhfb,
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title = "{Der Rechenautomat Ipm. Entwicklung Mathematischer
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[{The} {Ipm} Calculator. {The} development of
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acknowledgement = ack-nhfb,
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}
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(ENIAC)}",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
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number = "15",
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title = "The {Electronic Numerical Integrator and Computer
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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note = "Reprinted in \cite[\S 7.7]{Randell:1982:ODC}.",
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V)Y!#1]-3;=m;;]Ctechreportfpa(W#1S}K7E
;_o=Sgarticlefparith.bibGoldstine:1946:ENIH. H. Goldstine and Adele GoldstineThe Electronic Numerical Integrator and Computer (ENIAC)j-MATH-TABLES-OTHER-AIDS-COMPUT21597--110jul71946MTTCAS0891-6837 OR 08916837Tue Oct 13 08:44:19 MDT 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:44:19 MDTReprinted inle = "Planning and coding of problems for an electronic
computing instrument",
type = "Technical report",
number = "1",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "69",
day = "1",
month = apr,
year = "1947",
bibdate = "Wed Jun 01 17:41:33 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Report prepared for U.S. Army Ordnance Department
under contract W-36-034-OKD-7481. Reprinted in
\cite[80--151]{Taub:1963:JNCa}. Knuth
\cite[p.~278]{Knuth:1997:SA} cites pp.~142--151 of this
report as the first published treatment of
double-precision arithmetic on digital computers.",
acknowledgement = ack-nhfb,
})rith.bibGoldstine:1947:PCPHerman H. Goldstine and John von NeumannPlanning and coding of problems for an electronic computing instrumentTechnical report1inst-INST-ADV-STUDYinst-INST-ADV-STUDY: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 W-36-034-OKD-7481. Reprinted in cite [80--151]Taub:1963:JNCa. Knuth cite [p.~278]Knuth:1997:SA cites pp.~142--151 of this report as the first published treatment of double-precision arithmetic on digital computers.ack-nhfbHerman H. Goldstine and John von NeumannReport prepared for U.S. Army Ordnance Department under contract W-36-034-OKD-7481. Reprinted in \cite[80--151]{Taub:1963:JNCa}. Knuth \cite[p.~278]{Knuth:1997:SA} cites pp.~142--151 of this report as the first published treatment of double-precision arithmetic on digital computers.Planning and coding of problems for an electronic computing instrument
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author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
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\cite[80--151]{Taub:1963:JNCa}. Knuth
\cite[p.~278]{Knuth:1997:SA} cites pp.~142--151 of this
report as the first published treatment of
double-precision arithmetic on digital computers.",
acknowledgement = ack-nhfb,
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number = "??",
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!!\*U #'917=m;_=g9Karticlefparith.bibJuley:1947:BCJ. JuleyThe Ballistic Computerj-BELL-LABS-RECORD245--91947BLRCAB0005-8564 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 Recordack-nhfbJ. JuleyReprinted in \cite[\S 6.3]{Randell:1982:ODC}.The Ballistic Computer
@Article{Juley:1947:BC,
author = "J. Juley",
title = "The Ballistic Computer",
journal = j-BELL-LABS-RECORD,
volume = "24",
number = "??",
pages = "5--9",
year = "1947",
CODEN = "BLRCAB",
ISSN = "0005-8564",
bibdate = "Wed Oct 13 11:32:38 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.3]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
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}of a Symposium on Large Scale Digital
Calculating Machinery, 7--10 January 1947}",
title = "Preparation of problems for {EDVAC}-type machines",
publisher = "Harvard University Press",
address = "Cambridge, MA, USA",
year = "1947",
bibdate = "Wed Oct 13 11:55:58 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in {\em Annals of the Computation Laboratory
of Harvard University}, {\bf 16}, 203--207 (1948).
Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}+roceedings of a Symposium on Large Scale Digital Calculating Machinery, 7--10 January 1947}Reprinted in {\em Annals of the Computation Laboratory of Harvard University}, {\bf 16}, 203--207 (1948). Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.Preparation of problems for {EDVAC}-type machines
@InProceedings{Mauchly:1947:PPE,
author = "J. W. Mauchly",
booktitle = "{Proceedings of a Symposium on Large Scale Digital
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title = "Preparation of problems for {EDVAC}-type machines",
publisher = "Harvard University Press",
address = "Cambridge, MA, USA",
year = "1947",
bibdate = "Wed Oct 13 11:55:58 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in {\em Annals of the Computation Laboratory
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Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
J+Y '#-'Ck=1=m;''G;o?inproceedingsfparith.bibMauchly:1947:PPEJ. W. MauchlyProceedings of a Symposium on Large Scale Digital Calculating Machinery, 7--10 January 1947Preparation of problems for EDVAC-type machinesHarvard University PressCambridge, MA, USA5--91947Wed Oct 13 11:55:58 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:55:58 ???Reprinted in em Annals of the Computation Laboratory of Harvard University, bf 16, 203--207 (1948). Reprinted in cite [ 8.2]Randell:1982:ODC.ack-nhfbJ. W. Mauchly{P = "Numerical Inverting of Matrices of High Order",
journal = j-BULL-AMS,
volume = "53",
number = "11",
pages = "1021--1099",
month = nov,
year = "1947",
CODEN = "BAMOAD",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
MRclass = "65.0X",
MRnumber = "MR0024235 (9,471b)",
MRreviewer = "E. Bodewig",
bibdate = "Thu Nov 8 14:49:36 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Goldstine:1951:NIM} for Part II. Reprinted
in \cite[v.~5, pp.~479--557]{Taub:1961:JNC}.",
ZMnumber = "0031.31402",
acknowledgement = ack-nhfb # " and " # ack-jg,
fjournal = "Bulletin of the American Mathematical Society",
kwds = "nla, linear system, rounding error",
referred = "[Markov1999a].",
remark = "This may be the first journal publication about the
use of double-precision arithmetic on computers, used
for the accumulation of inner products and matrix
products. On pp.~1035--1038, the authors show that when
the sum of $m$ products of two $s$-digit numbers is
accumulated in precision $ 2 s $, with rounding to $s$
digits only after the final sum is complete, then the
rounding error is essentially one unit in the last
place, instead of $m$ times that value. Cited in
\cite{Sterbenz:1974:FPC}.",
},e final sum is complete, then the rounding error is essentially one unit in the last place, instead of $m$ times that value. Cited in cite Sterbenz:1974:FPC.0031.31402ack-nhfbJohn von Neumann and Herman H. GoldstineSee \cite{Goldstine:1951:NIM} for Part II. Reprinted in \cite[v.~5, pp.~479--557]{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 = j-BULL-AMS,
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number = "11",
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bibdate = "Thu Nov 8 14:49:36 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Goldstine:1951:NIM} for Part II. Reprinted
in \cite[v.~5, pp.~479--557]{Taub:1961:JNC}.",
ZMnumber = "0031.31402",
acknowledgement = ack-nhfb # " and " # ack-jg,
fjournal = "Bulletin of the American Mathematical Society",
kwds = "nla, linear system, rounding error",
referred = "[Markov1999a].",
remark = "This may be the first journal publication about the
use of double-precision arithmetic on computers, used
for the accumulation of inner products and matrix
products. On pp.~1035--1038, the authors show that when
the sum of $m$ products of two $s$-digit numbers is
accumulated in precision $ 2 s $, with rounding to $s$
digits only after the final sum is complete, then the
rounding error is essentially one unit in the last
place, instead of $m$ times that value. Cited in
\cite{Sterbenz:1974:FPC}.",
}
889,Y#3]g!!571!;m;Ggm!]Og3Oarticlefparith.bibvonNeumann:1947:NIMJohn von Neumann and Herman H. GoldstineNumerical Inverting of Matrices of High Orderj-BULL-AMS53111021--1099nov111947BAMOAD0002-9904 (print), 1936-881X (electronic) OR 00029904 (print), 1936881X (electronic)0002-9904 OR 0002990465.0XMR0024235 (9,471b)E. BodewigThu Nov 8 14:49:36 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.~479--557]Taub:1961:JNC.Bulletin of the American Mathematical SocietyThis may be the first journal publication about the use of double-precision arithmetic on computers, used for the accumulation of inner products and matrix products. On pp.~1035--1038, the authors show that when the sum of $m$ products of two $s$-digit numbers is accumulated in precision $ 2 s $, with rounding to $s$ digits only after thatories}' Computing
Machine---{I}",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "3",
number = "21",
pages = "1--13",
month = jan,
year = "1948",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
note = "Reprinted in \cite[\S 6.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
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@TechReport{Tukey:1948:NSR,
author = "John W. Tukey",
title = "A note on the square-root iteration",
type = "SRG Memorandum report",
number = "10",
institution = inst-PRINCETON,
address = inst-PRINCETON:adr,
pages = "18",
year = "1948",
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MRnumber = "MR0028100 (10,405c)",
MRreviewer = "E. Bodewig",
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fjournal = "Quarterly Journal of Mechanics and Applied
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mynote = "The notes are not very good. They mainly correct
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author = "A. M. Turing",
title = "Rounding-Off Errors in Matrix Processes",
journal = j-QUART-J-MECH-APPLIED-MATH,
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month = sep,
year = "1948",
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MRnumber = "MR0028100 (10,405c)",
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URL = "http://turing.ecs.soton.ac.uk/browse.php/B/18",
ZMnumber = "0033.28501",
acknowledgement = ack-nhfb,
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wrong.",
}ectronic digital computers",
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}1 00280836 (print), 14764687 (electronic)0028-0836 OR 00280836Wed Oct 13 12:00:02 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 12:00:02 ???Reprinted in cite [ 8.4]Randell:1982:ODC.Natureack-nhfbhttp://www.nature.com/nature/archive/F. C. Williams and T. KilburnReprinted in \cite[\S 8.4]{Randell:1982:ODC}.Electronic digital computers
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ISSN = "0028-0836 (print), 1476-4687 (electronic)",
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iarticlefparith.}2W #-S{=m;SIarticlefparith.by1V#/GE57=m;_WGgEIarticlefparith.bibWilliams:1948:EDCF. C. Williams and T. KilburnElectronic digital computersj-NATURE162487??--??1948NATUAS0028-0836 (print), 1476-4687 (electronic) OR "Note On Systematic Roundoff Errors in Numerical
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title = "Note On Systematic Roundoff Errors in Numerical
Integration",
journal = "Journal of Research of the National Bureau of
Standards",
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pages = "62--??",
month = "????",
year = "1949",
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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} Certain Procedure of Numerical
Integration",
journal = j-J-RES-NATL-BUR-STAND,
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volume = "42",
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square-root",
type = "SRG Memorandum report",
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remark = "Supervised by Charles Brown Tompkins and C. H.
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of this volume were first assembled in the form of a
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publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xiii + 451",
year = "1950",
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remark = "Supervised by Charles Brown Tompkins and C. H.
Wakelin, Engineering Research Associates. The contents
of this volume were first assembled in the form of a
report to the Office of Naval Research, prepared under
a provision of contract N6-ONR-240, Task 1. Cited in
\cite{Sterbenz:1974:FPC}.",
subject = "computers",
}
N6W'#'C7Q'=m;_C;g#Oinproceedingsfparith.bibWilkes:1950:EM. V. Wilkes and W. RenwickReport of a Conference on High Speed Automatic Calculatin65W #-1E+3!E%;I5Ebookfparith.bibStifler:1950:HSCW. W. Stifler, Jr.High-speed computing devicespub-MCGRAW-HILLpub-MCGRAW-HILL: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 provisioneport of a Conference on High Speed Automatic
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}nference on High Speed Automatic
Calculating Machines, {22--25 June 1949}",
title = "The {EDSAC} demonstration",
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}7 June 1949The EDSAC demonstrationUniversity Mathematical LaboratoryCambridge, UK12--16jan11950Wed 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.ack-nhfbB. H. WorsleyReport of a Conference on High Speed Automatic Calculating Machines, {22--25 June 1949}Reprinted in \cite[\S 8.6]{Randell:1982:ODC}.The {EDSAC} demonstration
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author = "B. H. Worsley",
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title = "The {EDSAC} demonstration",
publisher = "University Mathematical Laboratory",
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pages = "12--16",
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year = "1950",
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note = "Reprinted in \cite[\S 8.6]{Randell:1982:ODC}.",
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"G8U #)#]C77;m;y#]{articlefparith.biS7W '#+'7;Q'=m;_';g?Uinproceedingsfparith.bibWorsley:1950:EDB. H. WorsleyReport of a Conference on High Speed Automatic Calculating Machines, 22--25ication technique",
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}8bBooth:1951:SBMA. D. BoothA signed binary multiplication techniquej-QUART-J-MECH-APPLIED-MATH42236--2401951QJMMAV0033-5614 OR 003356140033-5614 OR 00335614Thu Apr 2 08:38:35 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib1998.04.02 08:38:35 ???Quarterly Journal of Mechanics and Applied Mathematicsack-sfoA. D. BoothA signed binary multiplication technique
@Article{Booth:1951:SBM,
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title = "A signed binary multiplication technique",
journal = j-QUART-J-MECH-APPLIED-MATH,
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month = "????",
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CODEN = "QJMMAV",
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bibdate = "Thu Apr 2 08:38:35 1998",
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acknowledgement = ack-sfo # " and " # ack-nhfb,
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}s random digits",
crossref = "Householder:1951:MCM",
pages = "31--32",
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gg\:Z #'i?7=m;9'Ci1
articlefpariǆ(9U %#)#K5=m;g#OWincollectionfparith.bibBrown:1951:HRRG. W. BrownHistory of RAND's random digitsHouseholder:1951:MCM31--321951Sun Sep 18 12:02:43 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib2011.09.18 12:02:43 ???http://www.rand.org/pubs/papers/2008/P113.pdfack-nhfbG. W. BrownHistory of {RAND}'s random digits
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author = "G. W. Brown",
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}tions in an automatic digital
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volume = "47",
pages = "96--108",
year = "1951",
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ISSN = "0008-1981",
bibdate = "Tue Aug 28 05:54:12 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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remark = "Higham \cite{Higham:1993:AFP} comments ``In 1951 Gill
[8] noticed that the rounding error in the sum of two
numbers could be estimated by subtracting one of the
numbers from the sum, and he made use of this estimate
in a Runge--Kutta code in a program library for the
EDSAC computer.''",
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^8K-
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author = "W. Kahan and J. Palmer",
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@Article{Gill:1951:PSS,
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title = "A process for the step-by-step integration of
differential equations in an automatic digital
computing machine",
journal = j-PROC-CAMBRIDGE-PHIL-SOC,
volume = "47",
pages = "96--108",
year = "1951",
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ISSN = "0008-1981",
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}= "Numerical Inverting of Matrices of High Order. {II}",
journal = j-PROC-AM-MATH-SOC,
volume = "2",
pages = "188--202",
year = "1951",
CODEN = "PAMYAR",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "65.0X",
MRnumber = "MR0041539 (12,861b)",
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bibdate = "Thu Nov 8 14:49:46 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{vonNeumann:1947:NIM} for Part I. Reprinted
in \cite[Paper~15, pp.~558--572]{Taub:1963:JNCa}.",
URL = "http://www.jstor.org/view/00029939/di970628/97p0185x/0",
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acknowledgement = ack-nhfb,
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@Article{Goldstine:1951:NIM,
author = "Herman H. Goldstine and John von Neumann",
title = "Numerical Inverting of Matrices of High Order. {II}",
journal = j-PROC-AM-MATH-SOC,
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year = "1951",
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bibdate = "Thu Nov 8 14:49:46 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{vonNeumann:1947:NIM} for Part I. Reprinted
in \cite[Paper~15, pp.~558--572]{Taub:1963:JNCa}.",
URL = "http://www.jstor.org/view/00029939/di970628/97p0185x/0",
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acknowledgement = ack-nhfb,
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NNg>W#-EQQ=a;EQearticlefparith.bibMorrill:1952:SEMC. D. Morrill and R. V. BaumA Stabilized Electronic Multiplierj-TRANS-Iӈf=U#)]Y/77=m;e]Yearticlefparith.bibDabilized Electronic Multiplier",
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title = "The {IBM} card-programmed electronic calculator",
publisher = "American Institute of Electrical Engineers",
address = "New York, NY, USA",
pages = "30--36",
year = "1952",
bibdate = "Wed Oct 13 11:28:45 2010",
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}?28:45 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:28:45 ???Reprinted in cite [ 5.4]Randell:1982:ODC.ack-nhfbJ. W. Sheldon and L. TatumReview of Electronic Digital Computers. Joint {AIEE--IRE} Computer Confer ence. {10--12 December 1951}Reprinted in \cite[\S 5.4]{Randell:1982:ODC}.The {IBM} card-programmed electronic calculator
@InProceedings{Sheldon:1952:ICP,
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bibdate = "Wed Oct 13 11:28:45 2010",
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}n: Type 701 and Associated
Equipment",
publisher = pub-IBM,
address = pub-IBM:adr,
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bibdate = "Wed Sep 14 23:17:49 1994",
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**%AY #+%I57=m;'1e%MMarticlefparith.bibBackus:1954:ISSJ. W. BackusThe IBM 701 Speedcoding Systemj-J-ACM114--چ@W #%+#=m;/7bookfparith.bibIBM:1953:POTIBM CorporationPrinciples of Operation: Type 701 and Associated Equipmentpub-IBMpub-IBM:adr1031953Wed Sep 14 23:17:49 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.14 23:17:49 ???ack-nhfb{IBM Corporation}Principles of Operation: Type 701 and Associated Equipment
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bibdate = "Fri Nov 04 00:18:27 1994",
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URL = "http://community.computerhistory.org/scc/projects/FORTRAN/paper/p4-backus.pdf",
abstract = "The IBM 701 Speedcoding System is a set of
instructions which causes the 701 to behave like a
three-address floating point calculator. Let us call
this the Speedcoding calculator. In addition to
operating in floating point, this Speedcoding
calculator has extremely convenient means for getting
information into the machine and for printing results;
it has an extensive set of operations to make the job
of programming as easy as possible. Speedcoding also
provides automatic address modification, flexible
tracing, convenient use of auxiliary storage, and
built-in checking.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
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}A6jan11954JACOAH0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)0004-5411 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/p4-backus.pdfThe IBM 701 Speedcoding System is a set of instructions which causes the 701 to behave like a three-address floating point calculator. Let us call this the Speedcoding calculator. In addition to operating in floating point, this Speedcoding calculator has extremely convenient means for getting information into the machine and for printing results; it has an extensive set of operations to make the job of programming as easy as possible. Speedcoding also provides automatic address modification, flexible tracing, convenient use of auxiliary storage, and built-in checking.Journal of the ACMack-nhfbhttp://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 three-address floating point calculator. Let us call this the Speedcoding calculator. In addition to operating in floating point, this Speedcoding calculator has extremely convenient means for getting information into the machine and for printing results; it has an extensive set of operations to make the job of programming as easy as possible. Speedcoding also provides automatic address modification, flexible tracing, convenient use of auxiliary storage, and built-in checking.J. W. BackusThe {IBM 701 Speedcoding} System
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abstract = "The IBM 701 Speedcoding System is a set of
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three-address floating point calculator. Let us call
this the Speedcoding calculator. In addition to
operating in floating point, this Speedcoding
calculator has extremely convenient means for getting
information into the machine and for printing results;
it has an extensive set of operations to make the job
of programming as easy as possible. Speedcoding also
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address = "Pasadena, CA, USA",
year = "1954",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "12 volumes in 1.",
acknowledgement = ack-nhfb,
keywords = "Datatron (Computer)",
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--- Floating point control unit handbook --- External
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Cardatron system handbook --- Model 560 DATAFILE
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KBV #/Q1%/Em;-3WU-1
manualfparith.bibBurroughs:1954:DHBurroughs Corporation. ElectroDataDatatron handbooksThe DivisionPasadena, CA, USA4--61954Sat 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.ack-nhfb{Burroughs Corporation. ElectroData}12 volumes in 1.Datatron handbooks
@Maaring Analog Multiplier ({TSAM})",
journal = j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT,
volume = "EC-3",
number = "1",
pages = "11--17",
month = mar,
year = "1954",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Jul 15 15:20:53 2011",
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acknowledgement = ack-nhfb,
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.",
}C
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@Article{McCann:2005:SDA,
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@Article{Gower:1958:NIM,
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&&ulU #3+[;7;m;]+[articlefparith.biPpkX#3QW;a7=o;]MQW}articlefparith.bibMetropolis:1958:SDCN. Metropolis and R. L. AshenhurstSignificant Digit Computer Arithmeticj-IRE-TRANS-ELEC-COMPUTEC-74265--2671958IRELAOhttp://dx.doi.org/10.1109/TEC.1958.52226570367-9950 OR 03679950Wed Feb 14 19:23:38 2007http://www.math.utah.edu/pub/bibnet/authors/mMbjZ #9157;K;[1%Uarticlefparith.bibKogbetliantz:1958:CANbE. G. KogbetliantzComputation of Arcsin $N$ for $ 0 < N < 1 $ Using an Electronic Computerj-IBM-JRD23218--222jul71958IBMJAE0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)0018-8646 OR 00188646Thu Sep 1 10:16:10 1994ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.0Jolume = "EC-7",
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abstract = "The usual floating point arithmetic makes error
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acknowledgement = ack-nhfb,
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@Article{Metropolis:1958:SDC,
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}lbRobertson:1958:NCDaJ. E. RobertsonA new class of digital division methodsj-IRE-TRANS-ELEC-COMPUTEC-7388--92sep91958IRELAO0367-9950 OR 03679950Thu Apr 2 08:38:35 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib1998.04.02 08:38:35 ???IRE Transactions on Electronic Computersack-sfoJ. E. RobertsonA new class of digital division methods
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[E
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IЅbE
@Book{Hart:1968:CA,
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@Book{Hastings:1955:ADC,
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@Book{Heinrich:1993:MRM,
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title = "{MIPS R4000} Microproc'011.07.14 15:56:43 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222579IRE Transactions on Electronic Computersack-nhfbJames E. RobertsonA New Class of Digital Division Methods
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..GmW #31[;a7E;]1[ articlefparith.bibRobertson:1958:NCDbJames E. RobertsonA New Class of Digital Division Methodsj-IRE-TRANS-ELEC-COMPUTEC-73218--222sep91958IRELAOhttp://dx.doi.org/10.1109/TEC.1958.52225790367-9950 OR 03679950Thu Jul 14 15:56:43 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.bib2Sur-Quadrant Time-Division
Multiplier with an Accuracy of 0.1 Per Cent",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-7",
number = "1",
pages = "41--47",
month = mar,
year = "1958",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1958.5222094",
ISSN = "0367-9950",
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}n on Electronic Computersack-nhfbHermann SchmidA Transistorized Four-Quadrant Time-Division Multiplier with an Accuracy of 0.1 Per Cent
@Article{Schmid:1958:TFQ,
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UnY #+)=;a7E;])=yarticlefparith.bibSchmid:1958:TFQHermann SchmidA Transistorized Four-Quadrant Time-Division Multiplier with an Accuracy of 0.1 Per Centj-IRE-TRANS-ELEC-COMPUTEC-7141--47mar31958IRELAOhttp://dx.doi.org/10.1109/TEC.1958.52220940367-9950 OR 03679950Thu Jul 14 15:56:43 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 15:56:43 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222094IRE TransactionsVYl Redundancy Check",
journal = j-CACM,
volume = "1",
number = "5",
pages = "10--12",
month = may,
year = "1958",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:22:12 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Sisson58;
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abstract = "As more emphasis is placed on improving the accuracy
of data fed into automatic computing systems, more
emphasis will be placed on redundancy checking of
predictable fields within the input. Two systems (at
least) of checking a field of decimal digits have been
proposed. In both of these it is assumed that the field
to be checked is all numeric and that the redundancy
must be of only one digit.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
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}o[dancy must be of only one digit.Communications of the ACMdecimal floating-point arithmeticack-nhfbhttp://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
@Article{Sisson:1958:IDR,
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:oY #++U57Ek;'?Oc'+Ucarticlefparith.bibSisson:1958:IDRRoger L. SissonAn Improved Decimal Redundancy Checkj-CACM1510--12may51958CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Mon Jan 22 07:22:12 MST 2001http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Sisson58; 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 redunZication and Division for
Automatic Binary Computers",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "11",
number = "3",
pages = "364--384",
month = "????",
year = "1958",
CODEN = "QJMMAV",
ISSN = "0033-5614",
ISSN-L = "0033-5614",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "Quarterly Journal of Mechanics and Applied
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}pomputersj-QUART-J-MECH-APPLIED-MATH113364--3841958QJMMAV0033-5614 OR 003356140033-5614 OR 00335614Thu Apr 2 08:38:35 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib1998.04.02 08:38:35 ???Quarterly Journal of Mechanics and Applied Mathematicsack-sfoK. D. TocherTechniques of Multiplication and Division for Automatic Binary Computers
@Article{Tocher:1958:TMD,
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[4[NqW #)#I57E;?c#I}articlefparith.bibWadey:1958:TSRW. G. WadeyTwo Square-Root Approximationsj-CACM11113--14nov111958CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Wed Jul 14 15:48:22 MDT 2004http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Wadey58; http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2004.07.aApW #+%C77;m;y%carticlefparith.bibTocher:1958:TMDK. D. TocherTechniques of Multiplication and Division for Automatic Binary C^mations",
journal = j-CACM,
volume = "1",
number = "11",
pages = "13--14",
month = nov,
year = "1958",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Wadey58;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
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}q14 15:48:22 MDTCommunications of the ACMack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79W. G. WadeyTwo Square-Root Approximations
@Article{Wadey:1958:TSR,
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title = "Two Square-Root Approximations",
journal = j-CACM,
volume = "1",
number = "11",
pages = "13--14",
month = nov,
year = "1958",
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}citle = "Unnormalized Floating Point Arithmetic",
journal = j-J-ACM,
volume = "6",
number = "3",
pages = "415--428",
month = jul,
year = "1959",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "68.00",
MRnumber = "MR0105833 (21 \#4568)",
MRreviewer = "H. H. Goldstine",
bibdate = "Fri Dec 08 13:06:24 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0121.12102",
abstract = "Algorithms for floating point computer arithmetic are
described, in which fractional parts are not subject to
the usual normalization convention. These algorithms
give results in a form which furnishes some indication
of their degree of precision. An analysis of one-stage
error propagation is developed for each operation; a
suggested statistical model for long-run error
propagation is also set forth.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}reon for Computing Machinery0121.12102ack-nhfbhttp://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 one-stage error propagation is developed for each operation; a suggested statistical model for long-run error propagation is also set forth.Robert L. Ashenhurst and Nicholas MetropolisUnnormalized Floating Point Arithmetic
@Article{Ashenhurst:1959:UFP,
author = "Robert L. Ashenhurst and Nicholas Metropolis",
title = "Unnormalized Floating Point Arithmetic",
journal = j-J-ACM,
volume = "6",
number = "3",
pages = "415--428",
month = jul,
year = "1959",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "68.00",
MRnumber = "MR0105833 (21 \#4568)",
MRreviewer = "H. H. Goldstine",
bibdate = "Fri Dec 08 13:06:24 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0121.12102",
abstract = "Algorithms for floating point computer arithmetic are
described, in which fractional parts are not subject to
the usual normalization convention. These algorithms
give results in a form which furnishes some indication
of their degree of precision. An analysis of one-stage
error propagation is developed for each operation; a
suggested statistical model for long-run error
propagation is also set forth.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
%%LrY#3eY577+={;3q!e3eYarticlefparith.bibAshenhurst:1959:UFPRobert L. Ashenhurst and Nicholas MetropolisUnnormalized Floating Point Arithmeticj-J-ACM63415--428jul71959JACOAH0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)0004-5411 OR 0004541168.00MR0105833 (21 \#4568)H. H. GoldstineFri Dec 08 13:06:24 1995http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.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 one-stage error propagation is developed for each operation; a suggested statistical model for long-run error propagation is also set forth.Journal of the Associatidts? (The Choice of Decimal or Binary
Representation)",
journal = j-CACM,
volume = "2",
number = "12",
pages = "3--11",
month = "????",
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:28:45 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Buchholz59;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "decimal floating-point arithmetic",
oldlabel = "Buchholz59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Buchholz59",
xxnote = "Check author first name: article has W. Buchholz; I
think it should be Werner, not Wilfried.",
}s
rL&I:u
@Article{Bajard:1998:NED,
author = "Jean-Claude Bajard and Laurent-St{\'e}phane Didier and2:u
@Article{Bajard:1998:NED,
author = "Jean-Claude Bajard and Laurent-St{\'e}phane Didier and2sg
@Article{Bajard:1998:RMM,
author = "J.-C. Bajard and L.-S. Didier and P. Kornerup",
titl2>}
@Article{Bajard:2004:FRI,
author = "J.-C. Bajard and L. Imbert",
title = "A full ?%K
@Article{Bajard:2006:AOF,
author = "J.-C. Bajard and L. Imbert and C. Negre",
title = EfN
@Article{Baker:1975:MER,
author = "P. W. Baker",
title = "More Efficient Radix-2 h
@Article{Baker:1976:SFB,
author = "P. W. Baker",
title = "Suggestion for a fast b
х;
@Article{Baker:1992:LCE,
author = "H. G. Baker",
title = "Less Complex Elementary$Յ
@Article{Baker:1997:LEP,
author = "Louis Baker",
title = "Letter to the {Editor}:1"Fingers or Fists? (The Choice of Decimal or Binary
Representation)",
journal = j-CACM,
volume = "2",
number = "12",
pages = "3--11",
month = "????",
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:28:45 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Buchholz59;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "decimal floating-point arithmetic",
oldlabel = "Buchholz59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Buchholz59",
xxnote = "Check author first name: article has W. Buchholz; I
think it should be Werner, not Wilfried.",
}
sY #//57Eo;?Oc/- articlefparith.bibBuchholz:1959:FFCWilfried BuchholzFingers or Fists? (The Choice of Decimal or Binary Representation)j-CACM2123--111959CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Mon Jan 22 06:28:45 MST 2001http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Buchholz59; http://www.math.utah.edu/pub/tex/bib/fparith.bib2001.01.22 06:28:45 MSTCommunications of the ACMdecimal floating-point arithmeticack-nhfbhttp://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 = i Floating Point Arithmetic",
journal = j-CACM,
volume = "2",
number = "5",
pages = "10--15",
month = may,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:23 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Carr59a;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Carr59a",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Carr59a",
}tCMack-nhfbhttp://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 = j-CACM,
volume = "2",
number = "5",
pages = "10--15",
month = may,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:23 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Carr59a;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Carr59a",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Carr59a",
}
tW #'-c57E;?c1c!articlefparith.bibCarr:1959:EAFJohn W. Carr IIIError Analysis in Floating Point Arithmeticj-CACM2510--15may51959CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Wed Jul 14 15:48:23 MDT 2004http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Carr59a; http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2004.07.14 15:48:23 MDTCommunications of the Albbe and Simon Ramo and Dean E.
Wooldridge",
booktitle = "Handbook of Automation, Computation, and Control",
title = "Programming and Coding",
publisher = pub-WILEY,
address = pub-WILEY:adr,
year = "1959",
LCCN = "TJ213 .G72",
bibdate = "Fri Aug 20 08:41:16 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "Chapter 2.",
acknowledgement = ack-nhfb,
bookpages = "????",
remark = "1958--1961: Volume 1. Control fundamentals. Volume 2.
Computers and data processing. Volume 3. Systems and
components. Cited in \cite{Sterbenz:1974:FPC}.",
subject = "automation; mathematics; computers; operations
research",
}uugene 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 = pub-WILEY,
address = pub-WILEY: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 = ack-nhfb,
bookpages = "????",
remark = "1958--1961: Volume 1. Control fundamentals. Volume 2.
Computers and data processing. Volume 3. Systems and
components. Cited in \cite{Sterbenz:1974:FPC}.",
subject = "automation; mathematics; computers; operations
research",
}
)*vU #-'U;7=m;]O'Y?articlefparith.birLuW %#%-ym9'!=%;!;{1my!9[incollectionfparith.bibCarr:1959:PCJohn W. Carr IIIEugene M. Grabbe and Simon Ramo and Dean E. WooldridgeHandbook of Automation, Computation, and ControlProgramming and Codingpub-WILEYpub-WILEY:adr10--151959TJ213 .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 2.1958--1961: 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 researchack-nhfbJohn W. {Carr III}Handbook of Automation, Computation, and ControlEoersions in {CORDIC}",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "5",
pages = "335--339",
month = sep,
year = "1959",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Thu Sep 08 08:14:00 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IRE Transactions on Electronic Computers",
keywords = "decimal floating-point arithmetic",
}vbDaggett:1959:DBCD. H. DaggettDecimal-Binary Conversions in CORDICj-IRE-TRANS-ELEC-COMPUTEC-85335--339sep91959IRELAO0367-9950 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 floating-point arithmeticack-njD. H. DaggettDecimal-Binary Conversions in {CORDIC}
@Article{Daggett:1959:DBC,
author = "D. H. Daggett",
title = "Decimal-Binary Conversions in {CORDIC}",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "5",
pages = "335--339",
month = sep,
year = "1959",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Thu Sep 08 08:14:00 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IRE Transactions on Electronic Computers",
keywords = "decimal floating-point arithmetic",
}ary Arithmetic for Discretely Variable Word Length
in a Serial Computer",
journal = j-CACM,
volume = "2",
number = "4",
pages = "13--15",
month = apr,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#ErcoliV59;
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http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
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XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/ErcoliV59",
}wtely Variable Word Length in a Serial Computer
@Article{Ercoli:1959:BAD,
author = "Paolo Ercoli and Roberto Vacca",
title = "Binary Arithmetic for Discretely Variable Word Length
in a Serial Computer",
journal = j-CACM,
volume = "2",
number = "4",
pages = "13--15",
month = apr,
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bibdate = "Wed Jul 14 15:48:22 MDT 2004",
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acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
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XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/ErcoliV59",
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OO&wY#+I!57E;?cI!)articlefparith.bibErcoli:1959:BADPaolo Ercoli and Roberto VaccaBinary Arithmetic for Discretely Variable Word Length in a Serial Computerj-CACM2413--15apr41959CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Wed Jul 14 15:48:22 MDT 2004http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#ErcoliV59; http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2004.07.14 15:48:22 MDTCommunications of the ACMack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Paolo Ercoli and Roberto VaccaBinary Arithmetic for DiscretNote on Rounding-Off Errors",
journal = j-SIAM-REVIEW,
volume = "1",
number = "1",
pages = "66--67",
month = "????",
year = "1959",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65.00",
MRnumber = "MR0099119 (20 \#5563)",
bibdate = "Tue Nov 22 09:08:17 MST 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
ZMnumber = "0168.14002",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
keywords = "numerical analysis",
}x "Reprint of a Note on Rounding-Off Errors",
journal = j-SIAM-REVIEW,
volume = "1",
number = "1",
pages = "66--67",
month = "????",
year = "1959",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65.00",
MRnumber = "MR0099119 (20 \#5563)",
bibdate = "Tue Nov 22 09:08:17 MST 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
ZMnumber = "0168.14002",
acknowledgement = ack-nhfb,
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journal-URL = "http://epubs.siam.org/sirev",
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}
ccxW #/1]'577E};#1!C1]%articlefparith.bibForsythe:1959:RNRGeorge E. ForsytheReprint of a Note on Rounding-Off Errorsj-SIAM-REVIEW1166--671959SIREAD0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)0036-1445 OR 0036144565.00MR0099119 (20 \#5563)Tue Nov 22 09:08:17 MST 2005http://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib; http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/siamreview.bib2005.11.22 09:08:17 MSTSIAM Reviewnumerical analysis0168.14002ack-nhfbhttp://epubs.siam.org/sirevGeorge E. ForsytheReprint of a Note on Rounding-Off Errors
@Article{Forsythe:1959:RNR,
author = "George E. Forsythe",
title = wthe Study of Multiplication for
Complement Codes",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "1",
pages = "25--30",
month = mar,
year = "1959",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1959.5222757",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:44 MDT 2011",
bibsource = "http://www.computer.org/tc/;
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http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222757",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}yp.jsp?tp=&arnumber=5222757IRE Transactions on Electronic Computersack-nhfbHarvey L. GarnerA Ring Model for the Study of Multiplication for Complement Codes
@Article{Garner:1959:RMS,
author = "Harvey L. Garner",
title = "A Ring Model for the Study of Multiplication for
Complement Codes",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "1",
pages = "25--30",
month = mar,
year = "1959",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1959.5222757",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:44 MDT 2011",
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222757",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
EEzW #+-?;a7E;]-?aarticlefparith.bibGarner:1959:RNSHarvey L. GarnerThe Residue Number Systemj-IRE-TRANS-ELEC-COMPUTEC-82140--147jun61959IRELAOhttp://dx.doi.org/10.1109/TEC.1959.52195150367-9950 OR 03679950Thu Jul 14 15:56:44 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.}yY #+-;a7E;]-Oarticlefparith.bibGarner:1959:RMSHarvey L. GarnerA Ring Model for the Study of Multiplication for Complement Codesj-IRE-TRANS-ELEC-COMPUTEC-8125--30mar31959IRELAOhttp://dx.doi.org/10.1109/TEC.1959.52227570367-9950 OR 03679950Thu Jul 14 15:56:44 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 15:56:44 MDThttp://ieeexplore.ieee.org/stamp/stamzr System",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "2",
pages = "140--147",
month = jun,
year = "1959",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1959.5219515",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:44 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=5219515",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}zedu/pub/tex/bib/ieeetranscomput.bib2011.07.14 15:56:44 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219515IRE Transactions on Electronic Computersack-nhfbHarvey L. GarnerThe Residue Number System
@Article{Garner:1959:RNS,
author = "Harvey L. Garner",
title = "The Residue Number System",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "2",
pages = "140--147",
month = jun,
year = "1959",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1959.5219515",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:44 MDT 2011",
bibsource = "http://www.computer.org/tc/;
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219515",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}ceedings of the Eastern Joint Computer Conference,
Boston, MA, December 1--3, 1959",
title = "Normalized floating-point arithmetic with an index of
significance",
volume = "16",
publisher = pub-AFIPS,
address = pub-AFIPS:adr,
pages = "244--248",
year = "1959",
LCCN = "TK7885.A1 J6",
bibdate = "Tue Oct 09 09:43:31 2007",
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note = "Errata, {\sl Commun\-i\-ca\-tions of the ACM\/ \bf 4}
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square root.",
abstract = "For centuries the decimal number system reigned
supreme, except, perhaps, among the Mayan Indians,
until the advent of digital computers brought the
binary and octal systems into the limelight. This paper
introduces another number system which may prove useful
for manipulating complex numbers on machines.",
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RRU %#3//#=m;//;Nincollectionfparith.bibReitwiesner:1960:BAG. W. ReitwiesnerBinary arithmeticAlt:1960:AC231--3081960Sat May 18 14:36:56 2002http://www.math.utah.edu/pub/tex/bib/fparith.bib2002.05.18 14:36:56 ???ack-nhfbG. W. ReitwiesnerBinary arithmetic
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}utation of square roots through
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JJ*Y #/)57E5;?Mc)articlefparith.bibSarafyan:1960:DCSDiran SarafyanDivisionless computation of square roots through continued squaringj-CACM35319--321may51960CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 0001078265.0022\#8639Fri Nov 25 18:19:26 MST 2005http://www.acm.org/pubs/contents/journals/cacm/; 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 ACM$sqrt (x)$; elementary functionsack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Diran SarafyanDivisionlesr}: Rounding in Floating-Point
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?Y #+'57E5;?ac'karticlefparith.bibSilver:1960:LERRoland SilverLetter to the Editor: Rounding in Floating-Point Arithmeticj-CACM312A9--A9dec121960CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Fri Nov 25 18:19:29 MST 2005http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:29 MSTCommunications of the ACMfloating-point arithmetic;tion Logic",
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http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
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TY #)#S57E1;C?c#GWkarticlefparith.bibTraub:1960:CNMJ. F. TraubComments on a recent paper [``A New Method of Computation of Square Roots Without Using Division'']j-CACM3286--86feb21960CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Fri Nov 25 18:19:25 MST 2005http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Traub60; http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:25 MSTSee cite Sarafyan:1959:NMC.Communications of the ACMack-nhfbhttp://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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bibdate = "Fri Dec 08 14:44:46 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Three types of floating-point arithmetics with error
control are discussed and compared with conventional
floating-point arithmetic. General multiplication and
division shift criteria are derived (for any base) for
Metropolis-style arithmetics. The limitations and most
suitable range of application for each arithmetic are
discussed.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
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}e discussed and compared with conventional floating-point arithmetic. General multiplication and division shift criteria are derived (for any base) for Metropolis-style arithmetics. The limitations and most suitable range of application for each arithmetic are discussed.Journal of the ACMCited in cite Sterbenz:1974:FPC.ack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401C. B. HaselgroveThree types of floating-point arithmetics with error control are discussed and compared with conventional floating-point arithmetic. General multiplication and division shift criteria are derived (for any base) for Metropolis-style arithmetics. The limitations and most suitable range of application for each arithmetic are discussed.W. G. WadeyFloating-Point Arithmetics
@Article{Wadey:1960:FA,
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V V>W #1+e!577-=;7S+ekarticlefparith.bibWilkinson:1960:EAFJ. H. WilkinsonError Analysis of Floating-Point Computationj-NUM-MATH2319--340dec121960NUMMA70029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)0029-599X OR 0029599X65.00MR0116477 (22 \#7264)C. B. HaselgroveFri May 14 17:18:08 2010http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-ܓPX #'#A57'=m;)1Me-)#A
articlefparith.bibWadey:1960:FAW. G. WadeyFloating-Point Arithmeticsj-J-ACM72129--139apr41960JACOAH0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)0004-5411 OR 0004541165.00 (68.00)22\#6090Fri Dec 08 14:44:46 1995http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 14:44:46 ???Three types of floating-point arithmetics with error control arof Floating-Point Computation",
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volume = "2",
pages = "319--340",
month = dec,
year = "1960",
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}hardy.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.05.14 17:18:08 ???Numerische Mathematikack-nhfbhttp://link.springer.com/journal/16J. H. WilkinsonError Analysis of Floating-Point Computation
@Article{Wilkinson:1960:EAF,
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title = "Error Analysis of Floating-Point Computation",
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}Accuracy of Floating Point Computers {[BIT {\bf
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number = "3",
pages = "220--222",
month = sep,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01933434",
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@Article{Bailey:1995:FBM,
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title = "A {Fortran-90} Based Multiprecision System",
journal = j-TOMS,
volume = "21",
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@Article{Bajard:1994:SOL,
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)hjU
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$ngerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF019334340006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)0006-3835 OR 00063835Wed Jan 4 18:52:07 MST 2006http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=3; 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=0006-3835&volume=1&issue=3&spage=220floating-point accuracy; floating-point arithmeticack-nhfbhttp://link.springer.com/journal/10543O. Amble and Jan V. GarwickSee \cite{Garwick:1961:AFP,Garwick:1961:RAF}.On the Accuracy of Floating Point Computers {[BIT {\bf 1}(2), 1961, pp. 87--88]}
@Article{Amble:1961:AFP,
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title = "On the Accuracy of Floating Point Computers {[BIT {\bf
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([#)C#I)+57C;cKqYCg-Qarticlefparith.bibAmble:1961:AFPO. Amble and Jan V. GarwickOn the Accuracy of Floating Point Computers [BIT bf 1(2), 1961, pp. 87--88]j-NORDISK-TIDSKR-INFORM-BEHAND13220--222sep91961BITTEL, NBITABhttp://www.spriethods",
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institution = "National Physical Laboratory",
address = "Her Majesty's Stationery Office, London",
year = "1961",
bibdate = "Fri Aug 20 10:05:25 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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OO-U !#1==E[=m;M= techreportfparith.bibAnonymous:1961:MCMAnonymousModern Computing MethodsNotes on Applied Science16National Physical LaboratoryHer Majesty's Stationery Office, London220--2221961Fri Aug 20 10:05:25 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.08.20 10:05:25 ???Cited in cite Sterbenz:1974:FPC.ack-nhfbAnonymousModern Computing Methods
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bibdate = "Fri Aug 20 10:05:25 2010",
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}-Digit Number Representations for Fast Parallel
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number = "3",
pages = "389--400",
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year = "1961",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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}219227IRE Transactions on Electronic Computersack-nhfbAlgirdas Avi{\v{z}}ienisSigned-Digit Number Representations for Fast Parallel Arithmetic
@Article{Avizienis:1961:SDN,
author = "Algirdas Avi{\v{z}}ienis",
title = "Signed-Digit Number Representations for Fast Parallel
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1Y #11
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iarticlefparith.bibAvizienis:1961:SDNAlgirdas AvizienisSigned-Digit Number Representations for Fast Parallel Arithmeticj-IRE-TRANS-ELEC-COMPUTEC-103389--400sep91961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.52192270367-9950 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=5relator Based on the Residue Number
System",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "1",
pages = "63--70",
month = mar,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219154",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:02 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=5219154",
abstract = "A system design for a digital correlator based on the
application of the residue number system for
computation is presented. Areas of investigation
include sampling, analog-to-residue conversion, logical
design of the arithmetic units, residue-to-analog
conversion, and modes of operation of the proposed
digital correlator. The advantages of speed of
computation and simplicity of logic due to the use of a
residue number system are shown to result in a
significantly faster and simpler system than if a
conventional number system were used. The resulting
digital correlator is designed for megacycle sampling
and computation with a 0.1 per cent system precision.",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}igation include sampling, analog-to-residue conversion, logical design of the arithmetic units, residue-to-analog conversion, and modes of operation of the proposed digital correlator. The advantages of speed of computation and simplicity of logic due to the use of a residue number system are shown to result in a significantly faster and simpler system than if a conventional number system were used. The resulting digital correlator is designed for megacycle sampling and computation with a 0.1 per cent system precision.IRE Transactions on Electronic Computersack-nhfbA system design for a digital correlator based on the application of the residue number system for computation is presented. Areas of investigation include sampling, analog-to-residue conversion, logical design of the arithmetic units, residue-to-analog conversion, and modes of operation of the proposed digital correlator. The advantages of speed of computation and simplicity of logic due to the use of a residue number system are shown to result in a significantly faster and simpler system than if a conventional number system were used. The resulting digital correlator is designed for megacycle sampling and computation with a 0.1 per cent system precision.Philip Warren CheneyA Digital Correlator Based on the Residue Number System
@Article{Cheney:1961:DCB,
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title = "A Digital Correlator Based on the Residue Number
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219154",
abstract = "A system design for a digital correlator based on the
application of the residue number system for
computation is presented. Areas of investigation
include sampling, analog-to-residue conversion, logical
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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
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acknowledgement = ack-nhfb,
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=!V #/)c57=m;?c)carticlefparith.bibClarkson:1961:DMIW. K. ClarksonA Divisionless Method of Inte/Y #+5{;a7E;=]=5{7articlefparith.bibCheney:1961:DCBPhilip Warren CheneyA Digital Correlator Based on the Residue Number Systemj-IRE-TRANS-ELEC-COMPUTEC-10163--70mar31961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.52191540367-9950 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 investthod of Integer Conversion",
journal = j-CACM,
volume = "4",
number = "7",
pages = "315--316",
month = jul,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 08:14:59 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}ger Conversionj-CACM47315--316jul71961CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Thu Sep 08 08:14:59 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.08 08:14:59 ???Communications of the ACMack-njhttp://portal.acm.org/browse_dl.cfm?idx=J79W. K. ClarksonA Divisionless Method of Integer Conversion
@Article{Clarkson:1961:DMI,
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@Article{Cox:1961:NMP,
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ISSN-L = "0001-0782",
bibdate = "Thu Sep 15 18:36:06 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
RR!Y #'%];a7E;]%]articlefparith.bibCroy:1961:RTMJohn E. CroyRapid Technique of Manual or Machine Binary-to-Decimal Integer Conversion Using Decimal Radix Arithmeticj-IRE-TRANS-ELEC-COMPUTEC-104777--777dec121961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.52192860367-9950 OR 03679950Thu Jul 14 14:45:05 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 14:45:05 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219286IRE Transactions on Electronic Computersack-n W#%A[57=K;?cA[articlefparith.bibCox:1961:NMPA. G. Cox and H. A. LutherA Note on Multiple Precision Arithmeticj-CACM48353aug81961CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (al or Machine Binary-to-Decimal
Integer Conversion Using Decimal Radix Arithmetic",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "4",
pages = "777--777",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219286",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:05 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=5219286",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}hfbJohn E. CroyRapid Technique of Manual or Machine Binary-to-Decimal Integer Conversion Using Decimal Radix Arithmetic
@Article{Croy:1961:RTM,
author = "John E. Croy",
title = "Rapid Technique of Manual or Machine Binary-to-Decimal
Integer Conversion Using Decimal Radix Arithmetic",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "4",
pages = "777--777",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219286",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:05 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=5219286",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}s of certain binary division
algorithms",
journal = j-IRE-PROC,
volume = "49",
number = "1",
pages = "91--103",
month = jan,
year = "1961",
bibdate = "Mon Sep 16 16:12:21 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IRE Proceedings",
xxnote = "Check author name: I have found this paper cited both
as Freiman and as Frieman?? Hennessy and Patterson
\cite{Hennessy:2002:CAQ} have Freiman.",
}bibFreiman:1961:SACC. V. FreimanStatistical analysis of certain binary division algorithmsj-IRE-PROC49191--103jan11961Mon Sep 16 16:12:21 2002http://www.math.utah.edu/pub/tex/bib/fparith.bib2002.09.16 16:12:21 ???IRE Proceedingsack-sfoC. V. FreimanStatistical analysis of certain binary division algorithms
@Article{Freiman:1961:SAC,
author = "C. V. Freiman",
title = "Statistical analysis of certain binary division
algorithms",
journal = j-IRE-PROC,
volume = "49",
number = "1",
pages = "91--103",
month = jan,
year = "1961",
bibdate = "Mon Sep 16 16:12:21 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IRE Proceedings",
xxnote = "Check author name: I have found this paper cited both
as Freiman and as Frieman?? Hennessy and Patterson
\cite{Hennessy:2002:CAQ} have Freiman.",
}
O
O+$[ #-)]I)+57C;
IqY)]Qarticlefparith.bibGarwick:1961:AFPJan V. GarwickThe Accuracy of Floating Point Computerg#\!#+[U51=m;#yy[Uw
techreportfparith.bibGarner:1961:["W #-'!=m;+'
articlefparith.C.
G. Brockus and R. J. Gonzalez and D. P. Rozenberg",
title = "Residue number systems for computers",
type = "{ASD} Technical Report",
number = "61-483",
institution = "Electronic Technology Laboratory, The University of
Michigan",
address = "Ann Arbor, MI, USA",
month = oct,
year = "1961",
bibdate = "Thu Nov 18 09:27:06 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txt",
abstract = "The purpose of the research performed under this
contract was to investigate the feasibility of residue
number systems in their applications to digital
computers. The problems of such an application are the
ones of magnitude determination, sign determination,
overflow, scaling, and division. These problems are not
independent, but are found to be quite interrelated. A
theoretical treatment of residue number systems is
given which lays the foundation for a unified study of
the complete problem. Treatments of an organizational
nature are given which deal with multiplication,
division, and scaling. The matter of correlating the
theoretical and organizational studies to physical
realizations involving networks is treated also. The
question of whether the residue number system can be
successfully applied to general purpose computers is
still an open one. Their application to special purpose
machines is considered both feasible and practical.",
acknowledgement = ack-nhfb,
remark = "This report represents the results of research
performed by the group at The University of Michigan
under the direction of Professor H. L. Garner.
Concurrently, research on the same subject was being
conducted at Harvard University under the direction of
Professor Howard Aiken, and at the Lockheed Missile
System Division under the direction of Dr. Richard
Tanaka. There was a considerable exchange of
information among the above groups during the course of
the research effort. The efforts attained exhibit
little overlap, rather they are complementary. A
portion of this report was extracted from the doctoral
dissertation of D. P. Rozenberg. His work was supported
by this contract, and led to the Ph.D..",
}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 Report61-483Electronic Technology Laboratory, The University of MichiganAnn Arbor, MI, USA91--103oct101961Thu Nov 18 09:27:06 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.11.18 09:27:06 ???http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txtThe purpose of the research performed under this contract was to investigate the feasibility of residue number systems in their applications to digital computers. The problems of such an application are the ones of magnitude determination, sign determination, overflow, scaling, and division. These problems are not independent, but are found to be quite interrelated. A theoretical treatment of residue number systems is given which lays the foundation for a unified study of the complete problem. Treatments of an organizational nature are given which deal with multiplication, division, and scaling. The matter of correlating the theoretical and organizational studies to physical realizations involving networks is treated also. The question of whether the residue number system can be successfully applied to general purpose computers is still an open one. Their application to special purpose machines is considered both feasible and practical.This report represents the results of research performed by the group at The University of Michigan under the direction of Professor H. L. Garner. Concurrently, research on the same subject was being conducted at Harvard University under the direction of Professor Howard Aiken, and at the Lockheed Missile System Division under the direction of Dr. Richard Tanaka. There was a considerable exchange of information among the above groups during the course of the research effort. The efforts attained exhibit little overlap, rather they are complementary. A portion of this report was extracted from the doctoral dissertation of D. P. Rozenberg. His work was supported by this contract, and led to the Ph.D..ack-nhfbThe purpose of the research performed under this contract was to investigate the feasibility of residue number systems in their applications to digital computers. The problems of such an application are the ones of magnitude determination, sign determination, overflow, scaling, and division. These problems are not independent, but are found to be quite interrelated. A theoretical treatment of residue number systems is given which lays the foundation for a unified study of the complete problem. Treatments of an organizational nature are given which deal with multiplication, division, and scaling. The matter of correlating the theoretical and organizational studies to physical realizations involving networks is treated also. The question of whether the residue number system can be successfully applied to general purpose computers is still an open one. Their application to special purpose machines is considered both feasible and practical.H. L. Garner 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 = "61-483",
institution = "Electronic Technology Laboratory, The University of
Michigan",
address = "Ann Arbor, MI, USA",
month = oct,
year = "1961",
bibdate = "Thu Nov 18 09:27:06 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txt",
abstract = "The purpose of the research performed under this
contract was to investigate the feasibility of residue
number systems in their applications to digital
computers. The problems of such an application are the
ones of magnitude determination, sign determination,
overflow, scaling, and division. These problems are not
independent, but are found to be quite interrelated. A
theoretical treatment of residue number systems is
given which lays the foundation for a unified study of
the complete problem. Treatments of an organizational
nature are given which deal with multiplication,
division, and scaling. The matter of correlating the
theoretical and organizational studies to physical
realizations involving networks is treated also. The
question of whether the residue number system can be
successfully applied to general purpose computers is
still an open one. Their application to special purpose
machines is considered both feasible and practical.",
acknowledgement = ack-nhfb,
remark = "This report represents the results of research
performed by the group at The University of Michigan
under the direction of Professor H. L. Garner.
Concurrently, research on the same subject was being
conducted at Harvard University under the direction of
Professor Howard Aiken, and at the Lockheed Missile
System Division under the direction of Dr. Richard
Tanaka. There was a considerable exchange of
information among the above groups during the course of
the research effort. The efforts attained exhibit
little overlap, rather they are complementary. A
portion of this report was extracted from the doctoral
dissertation of D. P. Rozenberg. His work was supported
by this contract, and led to the Ph.D..",
}AND,
volume = "1",
number = "2",
pages = "87--88",
month = jun,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01939221",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=2;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also comment and reply
\cite{Amble:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=2&spage=87",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
}sj-NORDISK-TIDSKR-INFORM-BEHAND1287--88jun61961BITTEL, NBITABhttp://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF019392210006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)0006-3835 OR 00063835Wed Jan 4 18:52:07 MST 2006http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=2; 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=0006-3835&volume=1&issue=2&spage=87floating-point accuracy; floating-point arithmeticack-nhfbhttp://link.springer.com/journal/10543Jan V. GarwickSee also comment and reply \cite{Amble:1961:AFP,Garwick:1961:RAF}.The Accuracy of Floating Point Computers
@Article{Garwick:1961:AFP,
author = "Jan V. Garwick",
title = "The Accuracy of Floating Point Computers",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "2",
pages = "87--88",
month = jun,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01939221",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=2;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also comment and reply
\cite{Amble:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=2&spage=87",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
}Accuracy of Floating Point
Computers'' [BIT {\bf 1}(3), 1961, pp. 220--221]}",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "3",
pages = "222--222",
year = "1961",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon Nov 16 14:36:22 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Garwick:1961:AFP,Amble:1961:AFP}.",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
}
wQ&
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K
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titF V. GarwickSee \cite{Garwick:1961:AFP,Amble:1961:AFP}.Reply to {``On the Accuracy of Floating Point Computers'' [BIT {\bf 1}(3), 1961, pp. 220--221]}
@Article{Garwick:1961:RAF,
author = "J. V. Garwick",
title = "Reply to {``On the Accuracy of Floating Point
Computers'' [BIT {\bf 1}(3), 1961, pp. 220--221]}",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "3",
pages = "222--222",
year = "1961",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon Nov 16 14:36:22 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Garwick:1961:AFP,Amble:1961:AFP}.",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
}
[G&W '#1+oQ#-]=m;?1?+sQinproceedingsfparith.bibHenderson:1961:RCED. S. HendersonProceedings of the 1961 16th ACM national meetingResidue class
%Y #-'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. 220--221]j-NORDISK-TIDSKR-INFORM-BEHAND13222--2221961BITTEL, NBITAB0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)0006-3835 OR 00063835Mon Nov 16 14:36:22 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.floating-point accuracy; floating-point arithmeticack-nhfbhttp://link.springer.com/journal/10543J.ngs of the 1961 16th ACM national meeting}",
title = "Residue class error checking codes",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "132.101--132.104",
year = "1961",
DOI = "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 parity-based codes of monitoring
arithmetic as well as transmission operations. Codes
may be devised to detect burst-type errors, to correct
single errors in a binary arithmetic operation, to
correct burst errors and finally to correct any
single-digit error in a decimal operation.",
acknowledgement = ack-nhfb,
keywords = "decimal arithmetic",
} error checking codespub-ACMpub-ACM:adr132.101--132.1041961http://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 parity-based codes of monitoring arithmetic as well as transmission operations. Codes may be devised to detect burst-type errors, to correct single errors in a binary arithmetic operation, to correct burst errors and finally to correct any single-digit error in a decimal operation.decimal arithmeticack-nhfbError checking codes based on residues have the advantage over parity-based codes of monitoring arithmetic as well as transmission operations. Codes may be devised to detect burst-type errors, to correct single errors in a binary arithmetic operation, to correct burst errors and finally to correct any single-digit error in a decimal operation.D. S. Henderson{Proceedings of the 1961 16th ACM national meeting}Residue class error checking codes
@InProceedings{Henderson:1961:RCE,
author = "D. S. Henderson",
booktitle = "{Proceedings of the 1961 16th ACM national meeting}",
title = "Residue class error checking codes",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "132.101--132.104",
year = "1961",
DOI = "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 parity-based codes of monitoring
arithmetic as well as transmission operations. Codes
may be devised to detect burst-type errors, to correct
single errors in a binary arithmetic operation, to
correct burst errors and finally to correct any
single-digit error in a decimal operation.",
acknowledgement = ack-nhfb,
keywords = "decimal arithmetic",
}rate Analog Multiplier and Divider",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "2",
pages = "269--272",
month = jun,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219198",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:03 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219198",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}3 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219198IRE Transactions on Electronic Computersack-nhfbE. 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 = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "2",
pages = "269--272",
month = jun,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219198",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:03 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219198",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
o(W #)+Y57=S;=?c+A]warticlefparith.bibKnuth:1961:EINDonald E. KnuthErrata: ``An imaginary number system''j-CACM48355--355aug81961CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Tue Jan 09 07:10:22 1996http://www.math.utah.edu/pub/tex/bib/cac`'W#+A_;a7E;]A_articlefparith.bibKettel:1961:AAME. Kettel and W. SchneiderAn Accurate Analog Multiplier and Dividerj-IRE-TRANS-ELEC-COMPUTEC-102269--272jun61961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.52191980367-9950 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 14:45:0
nary number system''}",
journal = j-CACM,
volume = "4",
number = "8",
pages = "355--355",
month = aug,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Jan 09 07:10:22 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1960:INS}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}m1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.01.09 07:10:22 ???See cite Knuth:1960:INS.Communications of the ACMack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Donald E. KnuthSee \cite{Knuth:1960:INS}.Errata: {``An imaginary number system''}
@Article{Knuth:1961:EIN,
author = "Donald E. Knuth",
title = "Errata: {``An imaginary number system''}",
journal = j-CACM,
volume = "4",
number = "8",
pages = "355--355",
month = aug,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Jan 09 07:10:22 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1960:INS}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
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}{Hall-Effect} Analog Multiplier",
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ISSN = "0367-9950",
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T)W#-EO;a7E;]ESarticlefparith.bibKovatch:1961:HEAG. Kovatch and W. E. MeserveThe Hall-Effect Analog Multiplierj-IRE-TRANS-ELEC-COMPUTEC-103512--515sep91961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.52192400367-9950 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 ques for High-Speed Carry-Propagation in
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}actions on Electronic Computersack-nhfbM. Lehman and N. BurlaSkip Techniques for High-Speed Carry-Propagation in Binary Arithmetic Units
@Article{Lehman:1961:STH,
author = "M. Lehman and N. Burla",
title = "Skip Techniques for High-Speed Carry-Propagation in
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N*Y#+9#;a7E;]9#uarticlefparith.bibLehman:1961:STHM. Lehman and N. BurlaSkip Techniques for High-Speed Carry-Propagation in Binary Arithmetic Unitsj-IRE-TRANS-ELEC-COMPUTEC-104691--698dec121961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.52192740367-9950 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 Transhmetic in binary computers",
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''U+U #1+_!=m;]++a_articlefparith.bibMacSorley:1961:HSAO. L. MacSorleyHigh-speed arithmetic in binary computersj-IRE-PROC4967--91jan11961Sat May 18 14:34:55 2002http://www.math.utah.edu/pub/tex/bib/fparith.bib2002.05.18 14:34:55 ???Reprinted in cite Swartzlander:1976:CDD.IRE Proceedingsack-nhfbO. L. MacSorleyReprinted in \cite{Swartzlander:1976:CDD}.High-speed arithmetic in binary computers
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volume = "49",
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fjournal = "IRE Proceedings",
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MRclass = "65.99",
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|,Y #+' 57E5;=?Mc'A qarticlefparith.bibNadler:1961:DSRMorton NadlerDivision and square root in the quater-imaginary number systemj-CACM44192--193apr41961CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 0001078265.9923\#B555Fri Nov 25 18:19:32 MST 2005http://www.acm.org/pubs/contents/journals/cacm/; 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 functionsack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Morton NadlerSee \cite{Knuth:1960:INS}.Division and square root in the quater-imaginary num "1223--1230",
month = dec,
year = "1961",
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URL = "http://links.jstor.org/sici?sici=0003-4851%28196112%2932%3A4%3C1223%3AOTDOFS%3E2.0.CO%3B2-T",
abstract = "It has been noticed by astute observers that well used
tables of logarithms are invariably dirtier at the
front than at the back. Upon reflection one is led to
inquire whether there are more physical constants with
low order first significant digits than high. Actual
counts by Benford [2] show that not only is this the
case but that it seems to be an empirical truth that
whenever one has a large body of physical data,
Farmer's Almanac, Census Reports, Chemical Rubber
Handbook, etc., the proportion of these data with first
significant digit $n$ or less is approximately $
\log_{10}(n + 1) $. Any reader formerly unaware of this
``peculiarity'' will find an actual sampling experiment
wondrously tantalizing. Thus, for example,
approximately $ 0.7 $ of the physical constants in the
Chemical Rubber Handbook begin with $4$ or less ($
\log_{10}(4 + 1) = 0.699 $ ). This is to be contrasted
with the widespread intuitive evaluation $ 4 / 9 $
ths.",
acknowledgement = ack-nhfb,
fjournal = "Annals of Mathematical Statistics",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From p. 1223: ``\ldots{} the proportion of these data
with first significant digit $n$ or less is
approximately $ \log_{10}(n + 1) $.''\par
\ldots{} ``The only distribution for first significant
digits which is invariant under scale change of the
underlying distribution is $ \log_{10}(n + 1) $.
Contrary to suspicion this is a non-trivial
mathematical result, for the variable $n$ is
discrete.''.\par
From p. 1230: ``The foregoing results bear on questions
of round-off in computing machines. Since $ d(u v) = u
d v + v d u $, the error resulting from multiplying two
rounded numbers will be governed primarily by the first
significant digits of the two numbers being multiplied.
Now the distribution of first significant digits,
favoring as it does low order digits, tends to produce
less error than would be the case if first significant
digits were uniform as has sometimes been
assumed.''\par
Cited in \cite{Sterbenz:1974:FPC}.",
}
rL&vm
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author = "K. M. Sammut and S. R. JonesfMfM
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author = "S. M. Rump",
title = "{Sichere Ergebnisse auf R!. 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 non-trivial mathematical result, for the variable $n$ is discrete.''.par From p. 1230: ``The foregoing results bear on questions of round-off in computing machines. Since $ d(u v) = u d v + v d u $, the error resulting from multiplying two rounded numbers will be governed primarily by the first significant digits of the two numbers being multiplied. Now the distribution of first significant digits, favoring as it does low order digits, tends to produce less error than would be the case if first significant digits were uniform as has sometimes been assumed.''par Cited in cite Sterbenz:1974:FPC.ack-nhfbIt 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.Roger S. PinkhamOn the Distribution of First Significant Digits
@Article{Pinkham:1961:DFS,
author = "Roger S. Pinkham",
title = "On the Distribution of First Significant Digits",
journal = j-ANN-MATH-STAT,
volume = "32",
number = "4",
pages = $ "1223--1230",
month = dec,
year = "1961",
CODEN = "AASTAD",
ISSN = "0003-4851",
bibdate = "Thu Feb 15 15:07:57 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0003-4851%28196112%2932%3A4%3C1223%3AOTDOFS%3E2.0.CO%3B2-T",
abstract = "It has been noticed by astute observers that well used
tables of logarithms are invariably dirtier at the
front than at the back. Upon reflection one is led to
inquire whether there are more physical constants with
low order first significant digits than high. Actual
counts by Benford [2] show that not only is this the
case but that it seems to be an empirical truth that
whenever one has a large body of physical data,
Farmer's Almanac, Census Reports, Chemical Rubber
Handbook, etc., the proporti%on of these data with first
significant digit $n$ or less is approximately $
\log_{10}(n + 1) $. Any reader formerly unaware of this
``peculiarity'' will find an actual sampling experiment
wondrously tantalizing. Thus, for example,
approximately $ 0.7 $ of the physical constants in the
Chemical Rubber Handbook begin with $4$ or less ($
\log_{10}(4 + 1) = 0.699 $ ). This is to be contrasted
with the widespread intuitive evaluation $ 4 / 9 $
ths.",
acknowledgement = ack-nhfb,
fjournal = "Annals of Mathematical Statistics",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From p. 1223: ``\ldots{} the proportion of these data
with first significant digit $n$ or less is
approximately $ \log_{10}(n + 1) $.''\par
\ldots{} ``The only distribution for first significant
digits which is invariant under scale change of the
underlying distribution is $ \log_{10}(n + 1) $.
Contrary to suspicion this is a non-trivial
mathematical result, for the variable $n$ is
discrete.''.\par
From p. 1230: ``The foregoing results bear on questions
of round-off in computing machines. Since $ d(u v) = u
d v + v d u $, the error resulting from multiplying two
rounded numbers will be governed primarily by the first
significant digits of the two numbers being multiplied.
Now the distribution of first significant digits,
favoring as it does low order digits, tends to produce
less error than would be the case if first significant
digits were uniform as has sometimes been
assumed.''\par
Cited in \cite{Sterbenz:1974:FPC}.",
}
JJm.V #3'C57=m;?c'Cuarticlefparith.bibRabinowit(-Y #--k+!7=m;CmOs7u-k5articlefparith.bibPinkham:1961:DFSRoger S. PinkhamOn the Distribution of First Significant Digitsj-ANN-MATH-STAT3241223--1230dec121961AASTAD0003-4851 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=0003-4851%28196112%2932%3A4%3C1223%3AOTDOFS%3E2.0.CO%3B2-TIt has been noticed by astute observers that well used tables of logarithms are invariably dirtier at the front than at the back on Division",
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year = "1961",
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ISSN = "0001-0782 (print), 1557-7317 (electronic)",
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} Time for Synchronous Binary
Division",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "2",
pages = "169--174",
month = jun,
year = "1961",
CODEN = "IRELAO",
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@Article{Saltman:1961:RCT,
author = "Roy G. Saltman",
title = "Reducing Computing Time for Synchronous Binary
Division",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "2",
pages = "169--174",
month = jun,
year = "1961",
CODEN = "IRELAO",
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ISSN = "0367-9950",
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219186",
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fjournal = "IRE Transactions on Electronic Computers",
}
EE+0Y #1)'57Ek;A=)M articlefparith.bibSpielberg:1961:ECFKurt SpielbergEfficient Continued Fraction Approximations To Elementary Functionsj-MATH-COMPUT1576409--417oct101961MCMPAF0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)0025-5718 OR 00255718Tue Oct 13 08:06:19 MDT 1998ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http-x/W #-){;a7E;]){?articlefparith.bibSaltman:1961:RCTRoy G. SaltmanReducing Computing Time for Synchronous Binary Divisionj-IRE-TRANS-ELEC-COMPUTEC-102169--174jun61961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.52191860367-9950 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*ued Fraction Approximations To
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@Article{Spielberg:1961:ECF,
author = "Kurt Spielberg",
title = "Efficient Continued Fraction Approximations To
Elementary Functions",
journal = j-MATH-COMPUT,
volume = "15",
number = "76",
pages = "409--417",
month = oct,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
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fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}Power Series in Terms of
Polynomials, Rational Approximations and Continued
Fractions",
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bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}x/bib/fparith.bib1995.12.09 14:01:44 ???Journal of the ACMack-njhttp://portal.acm.org/browse_dl.cfm?idx=J401K. SpielbergRepresentation of Power Series in Terms of Polynomials, Rational Approximations and Continued Fractions
@Article{Spielberg:1961:RPS,
author = "K. Spielberg",
title = "Representation of Power Series in Terms of
Polynomials, Rational Approximations and Continued
Fractions",
journal = j-J-ACM,
volume = "8",
number = "4",
pages = "613--627",
month = oct,
year = "1961",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Sat Dec 09 14:01:44 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
2X #'!O%-1%=m;M!MSEbookfparith.bibTaub:1961:JNCA. H. TaubJohn von Neumann: Collected Workspub-PERGAMONpub-PERGAMON:adr??? (vol. 1), 568 (vol. 2), 574 (vol. 3), 516 (vol. 4), ??? (vol. 5), ??? (vol. 6)19612\1Y #1%[57=K;1e%[Garticlefparith.bibSpielberg:1961:RPSK. SpielbergRepresentation of Power Series in Terms of Polynomials, Rational Approximations and Continued Fractionsj-J-ACM84613--627oct101961JACOAH0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)0004-5411 OR 00045411Sat Dec 09 14:01:44 1995ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.math.utah.edu/pub/te/d Works",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "??? (vol. 1), 568 (vol. 2), 574 (vol. 3), 516 (vol.
4), ??? (vol. 5), ??? (vol. 6)",
year = "1961--1963",
LCCN = "????",
bibdate = "Wed Jun 01 16:58:29 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Six volumes. Volume I: Logic, Theory of Sets and
Quantum Mechanics (1961); Volume II: Operators, Ergodic
Theory and Almost Periodic Functions in a Group (1961);
Volume III: Rings of Operators (1961); Volume IV:
Continuous Geometry and Other Topics (1962); Volume V:
Design of Computers, Theory of Automata and Numerical
Analysis (1963); Volume VI: Theory of Games,
Astrophysics, Hydrodynamics and Meteorology (1963).",
acknowledgement = ack-nhfb,
}3 -- 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).ack-nhfbA. 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 = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "??? (vol. 1), 568 (vol. 2), 574 (vol. 3), 516 (vol.
4), ??? (vol. 5), ??? (vol. 6)",
year = "1961--1963",
LCCN = "????",
bibdate = "Wed Jun 01 16:58:29 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Six volumes. Volume I: Logic, Theory of Sets and
Quantum Mechanics (1961); Volume II: Operators, Ergodic
Theory and Almost Periodic Functions in a Group (1961);
Volume III: Rings of Operators (1961); Volume IV:
Continuous Geometry and Other Topics (1962); Volume V:
Design of Computers, Theory of Automata and Numerical
Analysis (1963); Volume VI: Theory of Games,
Astrophysics, Hydrodynamics and Meteorology (1963).",
acknowledgement = ack-nhfb,
}Square Root Expansions for the Inverse Cosine
and Inverse Hyperbolic Cosine",
journal = j-MATH-COMPUT,
volume = "15",
number = "76",
pages = "399--403",
month = oct,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}ue Oct 13 08:06:19 MDT 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:06:19 MDTMathematics of Computationack-nhfbhttp://www.ams.org/mcom/Henry C. {Thacher, Jr.}Iterated Square Root Expansions for the Inverse Cosine and Inverse Hyperbolic Cosine
@Article{Thacher:1961:ISR,
author = "Henry C. {Thacher, Jr.}",
title = "Iterated Square Root Expansions for the Inverse Cosine
and Inverse Hyperbolic Cosine",
journal = j-MATH-COMPUT,
volume = "15",
number = "76",
pages = "399--403",
month = oct,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
s3Y #-75'57E
;A=;5Warticlefparith.bibThacher:1961:ISRHenry C. Thacher, Jr.Iterated Square Root Expansions for the Inverse Cosine and Inverse Hyperbolic Cosinej-MATH-COMPUT1576399--403oct101961MCMPAF0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)0025-5718 OR 00255718T58Domestic Electronic Digital
Computing Systems",
type = "Report",
number = "1115",
institution = "Ballistic Research Laboratories",
address = "Aberdeen Proving Ground, MD, USA",
pages = "1131",
month = mar,
year = "1961",
bibdate = "Fri Nov 28 19:37:51 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Based on the results of a third survey, the
engineering and programming characteristics of two
hundred twenty-two different electronic digital
computing systems are given. The data are presented
from the point of view of application, numerical and
arithmetic characteristics, input, output and storage
systems, construction and checking features, power,
space, weight, and site preparation and personnel
requirements, production records, cost and rental
rates, sale and lease policy, reliability, operating
experience, and time availability, engineering
modifications and improvements and other related
topics. An analysis of the survey data, fifteen
comparative tables, a discussion of trends, a revised
bibliography, and a complete glossary of computer
engineering and programming terminology are included.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}: output and storage systems, construction and checking features, power, space, weight, and site preparation and personnel requirements, production records, cost and rental rates, sale and lease policy, reliability, operating experience, and time availability, engineering modifications and improvements and other related topics. An analysis of the survey data, fifteen comparative tables, a discussion of trends, a revised bibliography, and a complete glossary of computer engineering and programming terminology are included.ack-mfcBased on the results of a third survey, the engineering and programming characteristics of two hundred twenty-two different electronic digital computing systems are given. The data are presented from the point of view of application, numerical and arithmetic characteristics, input, output and storage systems, construction and checking features, power, space, weight, and site preparation and personnel requirements, production records, cost and rental rates, sale and lease policy, rel;iability, operating experience, and time availability, engineering modifications and improvements and other related topics. An analysis of the survey data, fifteen comparative tables, a discussion of trends, a revised bibliography, and a complete glossary of computer engineering and programming terminology are included.Martin H. WeikA Third Survey of Domestic Electronic Digital Computing Systems
@TechReport{Weik:1961:TSD,
author = "Martin H. Weik",
title = "A Third Survey of Domestic Electronic Digital
Computing Systems",
type = "Report",
number = "1115",
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address = "Aberdeen Proving Ground, MD, USA",
pages = "1131",
month = mar,
year = "1961",
bibdate = "Fri Nov 28 19:37:51 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Based on the results of a third survey, the
engineering and programming characteristics of two
hundred twenty-two different electronic digital
computing systems are given. The data are presented
from the point of view of application, numerical and
arithmetic characteristics, input, output and storage
systems, construction and checking features, power,
space, weight, and site preparation and personnel
requirements, production records, cost and rental
rates, sale and lease policy, reliability, operating
experience, and time availability, engineering
modifications and improvements and other related
topics. An analysis of the survey data, fifteen
comparative tables, a discussion of trends, a revised
bibliography, and a complete glossary of computer
engineering and programming terminology are included.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
bb
4Y !#')KM=m;]])atechreportfparith.bibWeik:1961:TSDMartin H. WeikA Third Survey of Domestic Electronic Digital Computing SystemsReport1115Ballistic Research LaboratoriesAberdeen Proving Ground, MD, USA1131mar31961Fri Nov 28 19:37:51 2003http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 19:37:51 ???Based on the results of a third survey, the engineering and programming characteristics of two hundred twenty-two different electronic digital computing systems are given. The data are presented from the point of view of application, numerical and arithmetic characteristics, input,9lgorithm for Rapid Binary Division",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "4",
pages = "662--670",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219271",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219271",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}4 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219271IRE Transactions on Electronic Computersack-nhfbJ. B. Wilson and R. S. LedleyAn Algorithm for Rapid Binary Division
@Article{Wilson:1961:ARB,
author = "J. B. Wilson and R. S. Ledley",
title = "An Algorithm for Rapid Binary Division",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "4",
pages = "662--670",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219271",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219271",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
}
a5W#+GY;a7E;]GY articlefparith.bibWilson:1961:ARBJ. B. Wilson and R. S. LedleyAn Algorithm for Rapid Binary Divisionj-IRE-TRANS-ELEC-COMPUTEC-104662--670dec121961IRELAOhttp://dx.doi.org/10.1109/TEC.1961.52192710367-9950 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 14:45:0>niac III} Arithmetic System",
crossref = "AFIPS:1962:APS",
pages = "192--202",
year = "1962",
bibdate = "Wed Feb 14 17:14:21 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
--O6U '#3-M)=m;-Qcinproceedingsfparith.bibAshenhurst:1962:MIAR. L. AshenhurstThe Maniac III Arithmetic SystemAFIPS:1962:APS192--2021962Wed Feb 14 17:14:21 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.02.14 17:14:21 ???ack-nhfbR. L. AshenhurstThe {Maniac III} Arithmetic System
@InProceedings{Ashenhurst:1962:MIA,
author = "R. L. Ashenhurst",
title = "The {Maniac III} Arithmetic System",
crossref = "AFIPS:1962:APS",
pages = "192--202",
year = "1962",
bibdate = "Wed Feb 14 17:14:21 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}Cr system: {Project Stretch}",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xvii + 322",
year = "1962",
LCCN = "1876",
bibdate = "Fri Nov 19 10:02:31 MST 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
http://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
library.ox.ac.uk:210/ADVANCE",
note = "This important book is the primary description of the
influential IBM 7030 Stretch computer, written by its
architects.",
URL = "http://ed-thelen.org/comp-hist/IBM-7030-Planning-McJones.pdf",
acknowledgement = ack-nhfb,
remark = "The text of the book is in the public domain, with the
permission of the author in 2003.
See \cite{MacKenzie:1991:DIAL} for a remark about the
noisy mode for floating-point arithmetic in the IBM
7030 Stretch. That mode is first mentioned on page 25
of this book, and described in detail on page 102,
which states:
``By definition of ordinary normalized FLP operations,
numbers are frequently extended on the right by
attaching zeros. During addition the n-digit operand
that is not preshifted is extended with n zeros, so as
to provide the extra positions to which the preshifted
operand can be added. Any operand or result that is
shifted left to be normalized requires a corresponding
number of zeros to be shifted in at the right. Both
sets of zeros tend to produce numbers smaller in
absolute value than they would have been if more digits
had been carried. In the noisy modeE these numbers are
simply extended with 1 s instead of zeros (1 s in a
binary machine, 9s in a decimal machine). Sow all
numbers tend to be too large in absolute value. The
true value, if there had been no significance loss,
should lie between these two extremes. Hence, two runs,
one made without and one made with the noisy mode,
should show differences in result that indicate which
digits may have been affected by significance loss.
The principal weakness of the noisy-mode procedure is
that it requires two runs for the same problem. A much
less important weakness is that the loss of
significance cannot be guaranteed to show up-it merely
has a very high probability of showing up-whereas
built-in significance checks can be made slightly
pessimistic, so thFat actual significance loss will not
be greater than indicated. On the other hand, little
extra hardware and no extra storage are required for
the noisy-mode approach. Furthermore, significance loss
is relatively rare, so that running a problem twice
when Significance loss is suspected does not pose a
serious problem. What is serious is the possibility of
unsuspected significance loss.
In discussions of significance two points are often
overlooked. The first of these is trivial: the best way
of ensuring significant results is to use an adequate
number of fraction digits. The second is almost equally
mundane: for a given procedure, normalized FLP
arithmetic will ordinarily produce the greatest
precision possible for the number of fraction digits
used. NorGmalized FLP arithmetic has been criticized
with respect to significance loss, because such loss is
not indicated by the creation of leading zeros, as it
is with fixed-point arithmetic. In other words, the
contention is not that normalized FLP arithmetic is
more prone to significance loss than equivalent
fixed-point arithmetic, which would be untrue, but that
an equivalent indication of such loss is not provided.
Loss of significance, however, is also a serious
problem in fixed-point arithmetic; multiplication and
division do not handle it at all correctly by means of
leading zeros. (In particular, fixed-point
multiplication may lead to serious or even total
significance loss, which would not have occurred with
normalized FLP arithmetic: and although leading zeros
H in addition and subtraction of fixed-point operands do
give correct significance indications, the use of other
operations and of built-in waling loops frequently
destroys entirely the leading-zeros method of counting
significance.)''",
subject = "Computer architecture",
tableofcontents = "Foreword v \\
Preface vii \\
1. Project Stretch 1 \\
[by W. Buchholz] \\
2. Architectural Philosophy 5 \\
[by F. P. Brooks, Jr.] \\
2.1. The Two Objectives of Project Stretch 5 \\
2.2. Resources 6 \\
2.3. Guiding Principles 7 \\
2.4. Contemporary Trends in Computer Architecture 10
\\
2.5. Hindsight 15 \\
3. System Summary of IBM 7030 17 \\
[by W. Buchholz] \\
3.1. System Organization 17 \\
I 3.2. Memory Units 17 \\
3.3. Index Memory 19 \\
3.4. Special Registers 19 \\
3.5. Input and Output Facilities 19 \\
3.6. High-speed Disk Units 20 \\
3.7. Central Processing Unit 20 \\
3.8. Instruction Controls 21 \\
3.9. Index-arithmetic Unit 21 \\
3.10. Instruction Look-ahead 21 \\
3.11. Arithmetic Unit 22 \\
3.12. Instruction Set 24 \\
3.13. Data Arithmetic 24 \\
3.14. Radix-conversion Operations 27 \\
3.15. Connective Operations 27 \\
3.16. Index-arithmetic Operations 27 \\
3.17. Branching Operations 28 \\
3.18. Transmission Operations 28 \\
3.19. Input-Output Operations 29 \\
3.20. New Features 29 \\
3.21. Performance 32 \\
4. Natural Data Units 33 \\
J [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. BuchhoKlz] \\
6.1. Introduction 60 \\
6.2. Size of Set 62 \\
6.3. Subsets 62 \\
6.4. Expansion of Set 63 \\
6.5. Code 63 \\
6.6. Parity Bit 66 \\
6.7. Sequence 66 \\
6.8. Blank 67 \\
6.9. Decimal Digits 68 \\
6.10. Typewriter Keyboard 68 \\
6.11. Adjacency 69 \\
6.12. Uniqueness 69 \\
6.13. Signs 70 \\
6.14. Tape-recording Convention 71 \\
6.15. Card-punching Convention 71 \\
6.16. List of 7030 Character Set 72 \\
7. Variable-field-length Operation 75 \\
[by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
\\
7.1. Introduction 75 \\
7.2. Addressing of Variable-field-length Data 76 \\
7.3. Field Length 77 \\
7.4. Byte Size 78 \\L
7.5. Universal Accumulator 79 \\
7.6. Accumulator Operand 79 \\
7.7. Binary and Decimal Arithmetic 80 \\
7.8. Integer Arithmetic 81 \\
7.9. Numerical Signs 82 \\
7.10. Indicators 84 \\
7.11. Arithmetical Operations 85 \\
7.12. Radix-conversion Operation 87 \\
7.13. Logical Connectives of Two Variables 87 \\
7.14. Connective Operations 89 \\
8. Floating-point Operation 92 \\
[by S. G. Campbell] \\
General Discussion \\
8.1. Problems of Fixed-point Arithmetic 92 \\
8.2. Floating-point Arithmetic 94 \\
8.3. Normalization 97 \\
8.4. Floating-point Singularities 98 \\
8.5. Range and Precision 99 \\
8.6. Round-off Error 100 \\
8.7. Significance Checks 101 \\
8M.8. Forms of Floating-point Arithmetic 103 \\
8.9. Structure of Floating-point Data 104 \\
Floating-point Features of the 7030 \\
8.10. Floating-point Instruction Format 106 \\
8.11. Floating-point Data Formats 106 \\
8.12. Singular Floating-point Numbers 108 \\
8.13. Indicators 112 \\
8.14. Universal Accumulator 113 \\
8.15. Fraction Arithmetic 114 \\
8.16. Floating-point-arithmetic Operations 114 \\
8.17. Fixed-point Arithmetic Using Unnormalized \\
Floating-point Operations 118 \\
8.18. Special Functions and Forms of Arithmetic 119 \\
8.19. Multiple-precision Arithmetic 119 \\
8.20. General Remarks 121 \\
9. Instruction Formats 122 \\
[by W. Buchholz] \\
9.1. Introduction 122 \\
9.2. Earlier InstructioNn Languages 122 \\
9.3. Evolution of the Single-address Instruction 124
\\
9.4. Implied Addresses 125 \\
9.5. Basic 7030 Instruction Formats 126 \\
9.6. Instruction Efficiency 127 \\
9.7. The Simplicity of Complexity 131 \\
9.8. Relationship to Automatic Programming Languages
132 \\
10. Instruction Sequencing 133 \\
[by F. P. Brooks, Jr.] \\
10.1. Modes of Instruction Sequencing 133 \\
10.2. Instruction Counter 134 \\
10.3. Unconditional Branching 135 \\
10.4. Conditional Branching 136 \\
10.5. Program-interrupt System 136 \\
10.6. Components of the Program-interrupt System 137
\\
10.7. Examples of Program-interrupt Techniques 140 \\
10.8. Execute Instructions 146 \\
10.9O. Execute Operations in the 7030 148 \\
11. Indexing 150 \\
[by G. P. Blaauw] \\
11.1. Introduction 150 \\
11.2. Indexing Functions 151 \\
11.3. Instruction Format for Indexing 155 \\
11.4. Incrementing 157 \\
11.5. Counting 159 \\
11.6. Advancing by One 161 \\
11.7. Progressive Indexing 161 \\
11.8. Data Transmission 162 \\
11.9. Data Ordering 163 \\
11.10. Refilling 165 \\
11.11. Indirect Addressing and Indirect Indexing 167
\\
11.12. Indexing Applications 169 \\
11.13. Record-handling Applications 172 \\
11.14. File Maintenance 175 \\
11.15. Subroutine Control 177 \\
11.16. Conclusion 178 \\
12. Input-Output Control 179 \\
[by W. Buchholz] \\
P 12.1. A Generalized Approach to Connecting \\
Input-Output and External Storage 179 \\
12.2. Input-Output Instructions 180 \\
12.3. Defining the Memory Area 181 \\
12.4. Writing and Reading 182 \\
12.5. Controlling and Locating 183 \\
12.6. An Alternative Approach 184 \\
12.7. Program Interruptions 184 \\
12.8. Buffering 180 \\
12.9. Interface 188 \\
12.10. Operator Control of Input-Output Units 190 \\
13. Multiprogramming 192 \\
[by E. F. Codd, E. S. Lowry, E. McDonough, and C. A.
Scalzi] \\
13.1. Introduction 192 \\
13.2. Multiprogramming Requirements 193 \\
13.3. 7030 Features that Assist Multiprogramming 195
\\
13.4. Programmed Logic 197 \\
13.5. Concluding Remarks 200 \\
Q 13.6. References 201 \\
14. The Central Processing Unit 202 \\
[by E. Bloch] \\
14.1. Concurrent System Operation 202 \\
14.2. Concurrency within the Central Processing Unit
204 \\
14.3. Data Flow 204 \\
14.4. Arithmetic Unit 208 \\
14.5. Checking 216 \\
14.6. Component Count 216 \\
14.7. Performance 217 \\
14.8. Circuits 218 \\
14.9. Packaging 223 \\
15. The Look-ahead Unit 228 \\
[by R. S. Balance, J. Cocke, and H. G. Kolsky] \\
15.1. General Description 228 \\
15.2. Timing-simulation Program 230 \\
15.3. Description of the Look-ahead Unit 238 \\
15.4. Forwarding 240 \\
15.5. Counter Sequences 241 \\
15.6. Recovery after Interrupt 246 \\
15R.7. A Look-back at the Look-ahead 247 \\
16. The Exchange 248 \\
[by W. Buchholz] \\
16.1. General Description 248 \\
16.2. Starting a WRITE or READ Operation 250 \\
16.3. Data Transfer during Writing 250 \\
16.4. Data Transfer during Reading 251 \\
16.5. Terminating a WRITE or READ Operation 252 \\
16.6. Multiple Operations 252 \\
16.7. CONTROL and LOCATE Operations 252 \\
16.8. Interrogating the Control Word 253 \\
16.9. Forced Termination 253 \\
17. A Nonarithmetical System Extension 254 \\
[by S. G. Campbell, P.S. Herwitz, and J. H. Pomerene]
\\
17.1. Nonarithmetical Processing 254 \\
17.2. The Set-up Mode 258 \\
17.3. Byte-sequence Formation 259 \\
17.4. Pattern Selection 260 \\
17.5S. Transformation Facilities 261 \\
17.6. Statistical Aids 263 \\
17.7. The BYTE-BY-BYTE Instruction 263 \\
17.8. Monitoring for Special Conditions 264 \\
17.9. Instruction Set 265 \\
17.10. Collating Operations 266 \\
17.11. Table Look-up Operations 267 \\
17.12. Example 267 \\
Appendix A. Summary Data 273 \\
A.1. List of the Larger IBM Stored-program Computers
273 \\
A.2. Instruction Formats 275 \\
A.3. List of Registers and Special Addresses 276 \\
A.4. Summary of Operations and Modifiers 277 \\
A.5. Summary of Indicators 287 \\
Appendix B. Programming Examples 292 \\
Notation 292 \\
B.1. Polynomial Evaluation 295 \\
B.2. Cube-root Extraction 296 \\
B.3. Matrix Multiplication 298 \\
B.4. Conversion of Decimal Numbers to a \\
Floating-point Normalized Vector 299 \\
B.5. Editing a Typed Message 301 \\
B.6. Transposition of a Large Bit Matrix 303 \\
Index 305",
}U text of the book is in the public domain, with the permission of the author in 2003. See cite MacKenzie:1991:IAL for a remark about the noisy mode for floating-point arithmetic in the IBM 7030 Stretch. That mode is first mentioned on page 25 of this book, and described in detail on page 102, which states: ``By definition of ordinary normalized FLP operations, numbers are frequently extended on the right by attaching zeros. During addition the n-digit operand that is not preshifted is extended with n zeros, so as to provide the extra positions to which the preshifted operand can be added. Any operand or result that is shifted left to be normalized requires a corresponding number of zeros to be shifted in at the right. Both sets of zeros tend to produce numbers smaller in absolute value than they would have been if more digits had been carried. In the noisy mode these numbers are simply extended with 1 s instead of zeros (1 s in a binary machine, 9s in a decimal machine). Sow all numbers tend to be too larVge in absolute value. The true value, if there had been no significance loss, should lie between these two extremes. Hence, two runs, one made without and one made with the noisy mode, should show differences in result that indicate which digits may have been affected by significance loss. The principal weakness of the noisy-mode procedure is that it requires two runs for the same problem. A much less important weakness is that the loss of significance cannot be guaranteed to show up-it merely has a very high probability of showing up-whereas built-in significance checks can be made slightly pessimistic, so that actual significance loss will not be greater than indicated. On the other hand, little extra hardware and no extra storage are required for the noisy-mode approach. Furthermore, significance loss is relatively rare, so that running a problem twice when Significance loss is suspected does not pose a serious problem. What is serious is the possibility of unsuspected significance loss. In discussionsW of significance two points are often overlooked. The first of these is trivial: the best way of ensuring significant results is to use an adequate number of fraction digits. The second is almost equally mundane: for a given procedure, normalized FLP arithmetic will ordinarily produce the greatest precision possible for the number of fraction digits used. Normalized FLP arithmetic has been criticized with respect to significance loss, because such loss is not indicated by the creation of leading zeros, as it is with fixed-point arithmetic. In other words, the contention is not that normalized FLP arithmetic is more prone to significance loss than equivalent fixed-point arithmetic, which would be untrue, but that an equivalent indication of such loss is not provided. Loss of significance, however, is also a serious problem in fixed-point arithmetic; multiplication and division do not handle it at all correctly by means of leading zeros. (In particular, fixed-point multiplication may lead to serious or evenX total significance loss, which would not have occurred with normalized FLP arithmetic: and although leading zeros in addition and subtraction of fixed-point operands do give correct significance indications, the use of other operations and of built-in waling loops frequently destroys entirely the leading-zeros method of counting significance.)''Computer architectureForeword v Preface vii 1. Project Stretch 1 [by W. Buchholz] 2. Architectural Philosophy 5 [by F. P. Brooks, Jr.] 2.1. The Two Objectives of Project Stretch 5 2.2. Resources 6 2.3. Guiding Principles 7 2.4. Contemporary Trends in Computer Architecture 10 2.5. Hindsight 15 3. System Summary of IBM 7030 17 [by W. Buchholz] 3.1. System Organization 17 3.2. Memory Units 17 3.3. Index Memory 19 3.4. Special Registers 19 3.5. Input and Output Facilities 19 3.6. High-speed Disk Units 20 3.7. Central Processing Unit 20 3.8. Instruction Controls 21 3.9. Index-arithmetic Unit 21 3.10. Instruction Look-ahead 21 3.11. Arithmetic Unit 22 3.12. Instruction YSet 24 3.13. Data Arithmetic 24 3.14. Radix-conversion Operations 27 3.15. Connective Operations 27 3.16. Index-arithmetic Operations 27 3.17. Branching Operations 28 3.18. Transmission Operations 28 3.19. Input-Output Operations 29 3.20. New Features 29 3.21. Performance 32 4. Natural Data Units 33 [by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz] 4.1. Lengths and Structures of Natural Data Units 33 4.2. Procedures for Specifying Natural Data Units 36 4.3. Data Hierarchies 39 4.4. Classes of Operations 40 5. Choosing a Number Base 42 [by W. Buchholz] 5.1. Introduction 42 5.2. Information Content 45 5.3. Arithmetic Speed 49 5.4. Numerical Data 50 5.5. Nonnumerical Data 51 5.6. Addresses 52 5.7. Transformation 53 5.8. Partitioning of Memory 54 5.9. Program Interpretation 56 5.10. Other Number Bases 58 5.11. Conclusion 58 6. Character Set 60 [by R. W. Bemer and W. Buchholz] 6.1. Introduction 60 6.2. Size of Set 62 6.3. Subsets 62 6.4. Expansion of Set 63 6.5. Code 63 6.6. Parity Bit 66 6.7. Sequence 66 Z6.8. Blank 67 6.9. Decimal Digits 68 6.10. Typewriter Keyboard 68 6.11. Adjacency 69 6.12. Uniqueness 69 6.13. Signs 70 6.14. Tape-recording Convention 71 6.15. Card-punching Convention 71 6.16. List of 7030 Character Set 72 7. Variable-field-length Operation 75 [by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz] 7.1. Introduction 75 7.2. Addressing of Variable-field-length Data 76 7.3. Field Length 77 7.4. Byte Size 78 7.5. Universal Accumulator 79 7.6. Accumulator Operand 79 7.7. Binary and Decimal Arithmetic 80 7.8. Integer Arithmetic 81 7.9. Numerical Signs 82 7.10. Indicators 84 7.11. Arithmetical Operations 85 7.12. Radix-conversion Operation 87 7.13. Logical Connectives of Two Variables 87 7.14. Connective Operations 89 8. Floating-point Operation 92 [by S. G. Campbell] General Discussion 8.1. Problems of Fixed-point Arithmetic 92 8.2. Floating-point Arithmetic 94 8.3. Normalization 97 8.4. Floating-point Singularities 98 8.5. Range and Precision 99 8.6. Round-off Error 100 8.7. Significance Chec[ks 101 8.8. Forms of Floating-point Arithmetic 103 8.9. Structure of Floating-point Data 104 Floating-point Features of the 7030 8.10. Floating-point Instruction Format 106 8.11. Floating-point Data Formats 106 8.12. Singular Floating-point Numbers 108 8.13. Indicators 112 8.14. Universal Accumulator 113 8.15. Fraction Arithmetic 114 8.16. Floating-point-arithmetic Operations 114 8.17. Fixed-point Arithmetic Using Unnormalized Floating-point Operations 118 8.18. Special Functions and Forms of Arithmetic 119 8.19. Multiple-precision Arithmetic 119 8.20. General Remarks 121 9. Instruction Formats 122 [by W. Buchholz] 9.1. Introduction 122 9.2. Earlier Instruction Languages 122 9.3. Evolution of the Single-address Instruction 124 9.4. Implied Addresses 125 9.5. Basic 7030 Instruction Formats 126 9.6. Instruction Efficiency 127 9.7. The Simplicity of Complexity 131 9.8. Relationship to Automatic Programming Languages 132 10. Instruction Sequencing 133 [by F. P. Brooks, Jr.] 10.1. Modes of Instruction Sequenci\ng 133 10.2. Instruction Counter 134 10.3. Unconditional Branching 135 10.4. Conditional Branching 136 10.5. Program-interrupt System 136 10.6. Components of the Program-interrupt System 137 10.7. Examples of Program-interrupt Techniques 140 10.8. Execute Instructions 146 10.9. Execute Operations in the 7030 148 11. Indexing 150 [by G. P. Blaauw] 11.1. Introduction 150 11.2. Indexing Functions 151 11.3. Instruction Format for Indexing 155 11.4. Incrementing 157 11.5. Counting 159 11.6. Advancing by One 161 11.7. Progressive Indexing 161 11.8. Data Transmission 162 11.9. Data Ordering 163 11.10. Refilling 165 11.11. Indirect Addressing and Indirect Indexing 167 11.12. Indexing Applications 169 11.13. Record-handling Applications 172 11.14. File Maintenance 175 11.15. Subroutine Control 177 11.16. Conclusion 178 12. Input-Output Control 179 [by W. Buchholz] 12.1. A Generalized Approach to Connecting Input-Output and External Storage 179 12.2. Input-Output Instructions 180 12.3. Defining the Memory Area 181 ]12.4. Writing and Reading 182 12.5. Controlling and Locating 183 12.6. An Alternative Approach 184 12.7. Program Interruptions 184 12.8. Buffering 180 12.9. Interface 188 12.10. Operator Control of Input-Output Units 190 13. Multiprogramming 192 [by E. F. Codd, E. S. Lowry, E. McDonough, and C. A. Scalzi] 13.1. Introduction 192 13.2. Multiprogramming Requirements 193 13.3. 7030 Features that Assist Multiprogramming 195 13.4. Programmed Logic 197 13.5. Concluding Remarks 200 13.6. References 201 14. The Central Processing Unit 202 [by E. Bloch] 14.1. Concurrent System Operation 202 14.2. Concurrency within the Central Processing Unit 204 14.3. Data Flow 204 14.4. Arithmetic Unit 208 14.5. Checking 216 14.6. Component Count 216 14.7. Performance 217 14.8. Circuits 218 14.9. Packaging 223 15. The Look-ahead Unit 228 [by R. S. Balance, J. Cocke, and H. G. Kolsky] 15.1. General Description 228 15.2. Timing-simulation Program 230 15.3. Description of the Look-ahead Unit 238 15.4. Forwarding 240 15.5. Counter Se^quences 241 15.6. Recovery after Interrupt 246 15.7. A Look-back at the Look-ahead 247 16. The Exchange 248 [by W. Buchholz] 16.1. General Description 248 16.2. Starting a WRITE or READ Operation 250 16.3. Data Transfer during Writing 250 16.4. Data Transfer during Reading 251 16.5. Terminating a WRITE or READ Operation 252 16.6. Multiple Operations 252 16.7. CONTROL and LOCATE Operations 252 16.8. Interrogating the Control Word 253 16.9. Forced Termination 253 17. A Nonarithmetical System Extension 254 [by S. G. Campbell, P.S. Herwitz, and J. H. Pomerene] 17.1. Nonarithmetical Processing 254 17.2. The Set-up Mode 258 17.3. Byte-sequence Formation 259 17.4. Pattern Selection 260 17.5. Transformation Facilities 261 17.6. Statistical Aids 263 17.7. The BYTE-BY-BYTE Instruction 263 17.8. Monitoring for Special Conditions 264 17.9. Instruction Set 265 17.10. Collating Operations 266 17.11. Table Look-up Operations 267 17.12. Example 267 Appendix A. Summary Data 273 A.1. List of the Larger IBM Stored-program C_omputers 273 A.2. Instruction Formats 275 A.3. List of Registers and Special Addresses 276 A.4. Summary of Operations and Modifiers 277 A.5. Summary of Indicators 287 Appendix B. Programming Examples 292 Notation 292 B.1. Polynomial Evaluation 295 B.2. Cube-root Extraction 296 B.3. Matrix Multiplication 298 B.4. Conversion of Decimal Numbers to a Floating-point Normalized Vector 299 B.5. Editing a Typed Message 301 B.6. Transposition of a Large Bit Matrix 303 Index 305ack-nhfbWerner BuchholzThis important book is the primary description of the influential IBM 7030 Stretch computer, written by its architects.Planning a computer system: {Project Stretch}
@Book{Buchholz:1962:PCS,
editor = "Werner Buchholz",
title = "Planning a computer system: {Project Stretch}",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xvii + 322",
year = "1962",
LCCN = "1876",
bibdate = "Fri Nov 19 10:02:31 MST 2010",
bibsource = "http://www.m`ath.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
http://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
library.ox.ac.uk:210/ADVANCE",
note = "This important book is the primary description of the
influential IBM 7030 Stretch computer, written by its
architects.",
URL = "http://ed-thelen.org/comp-hist/IBM-7030-Planning-McJones.pdf",
acknowledgement = ack-nhfb,
remark = "The text of the book is in the public domain, with the
permission of the author in 2003.
See \cite{MacKenzie:1991:IAL} for a remark about the
noisy mode for floating-point arithmetic in the IBM
7030 Stretch. That mode is first mentioned on page 25
of this book, and described in detail on page 102,
which staates:
``By definition of ordinary normalized FLP operations,
numbers are frequently extended on the right by
attaching zeros. During addition the n-digit operand
that is not preshifted is extended with n zeros, so as
to provide the extra positions to which the preshifted
operand can be added. Any operand or result that is
shifted left to be normalized requires a corresponding
number of zeros to be shifted in at the right. Both
sets of zeros tend to produce numbers smaller in
absolute value than they would have been if more digits
had been carried. In the noisy mode these numbers are
simply extended with 1 s instead of zeros (1 s in a
binary machine, 9s in a decimal machine). Sow all
numbers tend to be too large in absolute value. The
true value, if there bhad been no significance loss,
should lie between these two extremes. Hence, two runs,
one made without and one made with the noisy mode,
should show differences in result that indicate which
digits may have been affected by significance loss.
The principal weakness of the noisy-mode procedure is
that it requires two runs for the same problem. A much
less important weakness is that the loss of
significance cannot be guaranteed to show up-it merely
has a very high probability of showing up-whereas
built-in significance checks can be made slightly
pessimistic, so that actual significance loss will not
be greater than indicated. On the other hand, little
extra hardware and no extra storage are required for
the noisy-mode approach. Furthermore, significance loss
c is relatively rare, so that running a problem twice
when Significance loss is suspected does not pose a
serious problem. What is serious is the possibility of
unsuspected significance loss.
In discussions of significance two points are often
overlooked. The first of these is trivial: the best way
of ensuring significant results is to use an adequate
number of fraction digits. The second is almost equally
mundane: for a given procedure, normalized FLP
arithmetic will ordinarily produce the greatest
precision possible for the number of fraction digits
used. Normalized FLP arithmetic has been criticized
with respect to significance loss, because such loss is
not indicated by the creation of leading zeros, as it
is with fixed-point arithmetic. In other words, the
d contention is not that normalized FLP arithmetic is
more prone to significance loss than equivalent
fixed-point arithmetic, which would be untrue, but that
an equivalent indication of such loss is not provided.
Loss of significance, however, is also a serious
problem in fixed-point arithmetic; multiplication and
division do not handle it at all correctly by means of
leading zeros. (In particular, fixed-point
multiplication may lead to serious or even total
significance loss, which would not have occurred with
normalized FLP arithmetic: and although leading zeros
in addition and subtraction of fixed-point operands do
give correct significance indications, the use of other
operations and of built-in waling loops frequently
destroys entirely the leading-zeros metheod of counting
significance.)''",
subject = "Computer architecture",
tableofcontents = "Foreword v \\
Preface vii \\
1. Project Stretch 1 \\
[by W. Buchholz] \\
2. Architectural Philosophy 5 \\
[by F. P. Brooks, Jr.] \\
2.1. The Two Objectives of Project Stretch 5 \\
2.2. Resources 6 \\
2.3. Guiding Principles 7 \\
2.4. Contemporary Trends in Computer Architecture 10
\\
2.5. Hindsight 15 \\
3. System Summary of IBM 7030 17 \\
[by W. Buchholz] \\
3.1. System Organization 17 \\
3.2. Memory Units 17 \\
3.3. Index Memory 19 \\
3.4. Special Registers 19 \\
3.5. Input and Output Facilities 19 \\
3.6. High-speed Disk Units 20 \\
3.7. Central Processing fUnit 20 \\
3.8. Instruction Controls 21 \\
3.9. Index-arithmetic Unit 21 \\
3.10. Instruction Look-ahead 21 \\
3.11. Arithmetic Unit 22 \\
3.12. Instruction Set 24 \\
3.13. Data Arithmetic 24 \\
3.14. Radix-conversion Operations 27 \\
3.15. Connective Operations 27 \\
3.16. Index-arithmetic Operations 27 \\
3.17. Branching Operations 28 \\
3.18. Transmission Operations 28 \\
3.19. Input-Output Operations 29 \\
3.20. New Features 29 \\
3.21. Performance 32 \\
4. Natural Data Units 33 \\
[by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
\\
4.1. Lengths and Structures of Natural Data Units 33
\\
4.2. Procedures for Specifying Natural Data Units 36
\\
g 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.h Sequence 66 \\
6.8. Blank 67 \\
6.9. Decimal Digits 68 \\
6.10. Typewriter Keyboard 68 \\
6.11. Adjacency 69 \\
6.12. Uniqueness 69 \\
6.13. Signs 70 \\
6.14. Tape-recording Convention 71 \\
6.15. Card-punching Convention 71 \\
6.16. List of 7030 Character Set 72 \\
7. Variable-field-length Operation 75 \\
[by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
\\
7.1. Introduction 75 \\
7.2. Addressing of Variable-field-length Data 76 \\
7.3. Field Length 77 \\
7.4. Byte Size 78 \\
7.5. Universal Accumulator 79 \\
7.6. Accumulator Operand 79 \\
7.7. Binary and Decimal Arithmetic 80 \\
7.8. Integer Arithmetic 81 \\
7.9. Numerical Signs 82 \\
i 7.10. Indicators 84 \\
7.11. Arithmetical Operations 85 \\
7.12. Radix-conversion Operation 87 \\
7.13. Logical Connectives of Two Variables 87 \\
7.14. Connective Operations 89 \\
8. Floating-point Operation 92 \\
[by S. G. Campbell] \\
General Discussion \\
8.1. Problems of Fixed-point Arithmetic 92 \\
8.2. Floating-point Arithmetic 94 \\
8.3. Normalization 97 \\
8.4. Floating-point Singularities 98 \\
8.5. Range and Precision 99 \\
8.6. Round-off Error 100 \\
8.7. Significance Checks 101 \\
8.8. Forms of Floating-point Arithmetic 103 \\
8.9. Structure of Floating-point Data 104 \\
Floating-point Features of the 7030 \\
8.10. Floating-point Instruction Format 106 \\
8.11. Floating-pojint Data Formats 106 \\
8.12. Singular Floating-point Numbers 108 \\
8.13. Indicators 112 \\
8.14. Universal Accumulator 113 \\
8.15. Fraction Arithmetic 114 \\
8.16. Floating-point-arithmetic Operations 114 \\
8.17. Fixed-point Arithmetic Using Unnormalized \\
Floating-point Operations 118 \\
8.18. Special Functions and Forms of Arithmetic 119 \\
8.19. Multiple-precision Arithmetic 119 \\
8.20. General Remarks 121 \\
9. Instruction Formats 122 \\
[by W. Buchholz] \\
9.1. Introduction 122 \\
9.2. Earlier Instruction Languages 122 \\
9.3. Evolution of the Single-address Instruction 124
\\
9.4. Implied Addresses 125 \\
9.5. Basic 7030 Instruction Formats 126 \\
9.6. Instruction Efficiency 1k27 \\
9.7. The Simplicity of Complexity 131 \\
9.8. Relationship to Automatic Programming Languages
132 \\
10. Instruction Sequencing 133 \\
[by F. P. Brooks, Jr.] \\
10.1. Modes of Instruction Sequencing 133 \\
10.2. Instruction Counter 134 \\
10.3. Unconditional Branching 135 \\
10.4. Conditional Branching 136 \\
10.5. Program-interrupt System 136 \\
10.6. Components of the Program-interrupt System 137
\\
10.7. Examples of Program-interrupt Techniques 140 \\
10.8. Execute Instructions 146 \\
10.9. Execute Operations in the 7030 148 \\
11. Indexing 150 \\
[by G. P. Blaauw] \\
11.1. Introduction 150 \\
11.2. Indexing Functions 151 \\
11.3. Instruction Format for Indexing l155 \\
11.4. Incrementing 157 \\
11.5. Counting 159 \\
11.6. Advancing by One 161 \\
11.7. Progressive Indexing 161 \\
11.8. Data Transmission 162 \\
11.9. Data Ordering 163 \\
11.10. Refilling 165 \\
11.11. Indirect Addressing and Indirect Indexing 167
\\
11.12. Indexing Applications 169 \\
11.13. Record-handling Applications 172 \\
11.14. File Maintenance 175 \\
11.15. Subroutine Control 177 \\
11.16. Conclusion 178 \\
12. Input-Output Control 179 \\
[by W. Buchholz] \\
12.1. A Generalized Approach to Connecting \\
Input-Output and External Storage 179 \\
12.2. Input-Output Instructions 180 \\
12.3. Defining the Memory Area 181 \\
12.4. Writing and Readming 182 \\
12.5. Controlling and Locating 183 \\
12.6. An Alternative Approach 184 \\
12.7. Program Interruptions 184 \\
12.8. Buffering 180 \\
12.9. Interface 188 \\
12.10. Operator Control of Input-Output Units 190 \\
13. Multiprogramming 192 \\
[by E. F. Codd, E. S. Lowry, E. McDonough, and C. A.
Scalzi] \\
13.1. Introduction 192 \\
13.2. Multiprogramming Requirements 193 \\
13.3. 7030 Features that Assist Multiprogramming 195
\\
13.4. Programmed Logic 197 \\
13.5. Concluding Remarks 200 \\
13.6. References 201 \\
14. The Central Processing Unit 202 \\
[by E. Bloch] \\
14.1. Concurrent System Operation 202 \\
14.2. Concurrency within the Central Processing Unit
n 204 \\
14.3. Data Flow 204 \\
14.4. Arithmetic Unit 208 \\
14.5. Checking 216 \\
14.6. Component Count 216 \\
14.7. Performance 217 \\
14.8. Circuits 218 \\
14.9. Packaging 223 \\
15. The Look-ahead Unit 228 \\
[by R. S. Balance, J. Cocke, and H. G. Kolsky] \\
15.1. General Description 228 \\
15.2. Timing-simulation Program 230 \\
15.3. Description of the Look-ahead Unit 238 \\
15.4. Forwarding 240 \\
15.5. Counter Sequences 241 \\
15.6. Recovery after Interrupt 246 \\
15.7. A Look-back at the Look-ahead 247 \\
16. The Exchange 248 \\
[by W. Buchholz] \\
16.1. General Description 248 \\
16.2. Starting a WRITE or READ Operation 250 \\
16.3. Data oTransfer during Writing 250 \\
16.4. Data Transfer during Reading 251 \\
16.5. Terminating a WRITE or READ Operation 252 \\
16.6. Multiple Operations 252 \\
16.7. CONTROL and LOCATE Operations 252 \\
16.8. Interrogating the Control Word 253 \\
16.9. Forced Termination 253 \\
17. A Nonarithmetical System Extension 254 \\
[by S. G. Campbell, P.S. Herwitz, and J. H. Pomerene]
\\
17.1. Nonarithmetical Processing 254 \\
17.2. The Set-up Mode 258 \\
17.3. Byte-sequence Formation 259 \\
17.4. Pattern Selection 260 \\
17.5. Transformation Facilities 261 \\
17.6. Statistical Aids 263 \\
17.7. The BYTE-BY-BYTE Instruction 263 \\
17.8. Monitoring for Special Conditions 264 \\
17.9. Instruction Set 265 \\
17.10. Collating Operations 266 \\
17.11. Table Look-up Operations 267 \\
17.12. Example 267 \\
Appendix A. Summary Data 273 \\
A.1. List of the Larger IBM Stored-program Computers
273 \\
A.2. Instruction Formats 275 \\
A.3. List of Registers and Special Addresses 276 \\
A.4. Summary of Operations and Modifiers 277 \\
A.5. Summary of Indicators 287 \\
Appendix B. Programming Examples 292 \\
Notation 292 \\
B.1. Polynomial Evaluation 295 \\
B.2. Cube-root Extraction 296 \\
B.3. Matrix Multiplication 298 \\
B.4. Conversion of Decimal Numbers to a \\
Floating-point Normalized Vector 299 \\
B.5. Editing a Typed Message 301 \\
B.6. Transposition of a Large Bit Matrix 303 \\
Index 305",
}
~+~!8V %#/)+c=+3%=%;M)g+=incollectionfparith.bibCampbell:1962:FPOS. G. CampbellWerner BuchholzPlanning r\7\ #/+c+3!E{;{37%+{gUSbookfparith.bibBuchholz:1962:PCSWerner BuchholzPlanning a computer system: Project Stretchpub-MCGRAW-HILLpub-MCGRAW-HILL:adrxvii + 32219621876Fri Nov 19 10:02:31 MST 2010http://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib; http://www.math.utah.edu/pub/tex/bib/annhistcomput.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib; library.ox.ac.uk:210/ADVANCE2010.11.19 10:02:31 MSTThis important book is the primary description of the influential IBM 7030 Stretch computer, written by its architects.http://ed-thelen.org/comp-hist/IBM-7030-Planning-McJones.pdfTheTolz",
booktitle = "Planning a Computer System: {Project Stretch}",
title = "Floating-Point Operation",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "92--121",
year = "1962",
LCCN = "QA76.8.I2 I5",
bibdate = "Wed Feb 14 17:24:27 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
bookpages = "322",
subject = "IBM 7030 (Computer); IBM Stretch",
}a Computer System: Project StretchFloating-Point Operationpub-MCGRAW-HILLpub-MCGRAW-HILL:adr92--1211962QA76.8.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 Stretchack-nhfb322S. G. CampbellPlanning a Computer System: {Project Stretch}Werner BuchholzFloating-Point Operation
@InCollection{Campbell:1962:FPO,
author = "S. G. Campbell",
editor = "Werner Buchholz",
booktitle = "Planning a Computer System: {Project Stretch}",
title = "Floating-Point Operation",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "92--121",
year = "1962",
LCCN = "QA76.8.I2 I5",
bibdate = "Wed Feb 14 17:24:27 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
bookpages = "322",
subject = "IBM 7030 (Computer); IBM Stretch",
} "Logarithmic and Exponential Function Evaluation in a
Variable Structure Digital Computer",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "2",
pages = "155--164",
month = apr,
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institution = "University of Illinois Graduate College, Digital
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address = "Urbana, IL, USA",
pages = "7",
year = "1962",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
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acknowledgement = ack-nhfb,
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}iterative processes with floating-point computers
@TechReport{Descloux:1962:REF,
author = "J. Descloux",
title = "Remarks on errors in first order iterative processes
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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
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(Urbana-Champaign campus). Digital Computer
Laboratory); no. 113.",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers.; Numerical
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remark = "Supported by: National Science Foundation under grant
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}
u:Z !#/#1+Em;Yy/#1#techreportfparith.bibDescloux:1962:REFJ. DesclouxRemarks on errors in first order iterative processes with floating-point 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 (Urbana-Champaign campus). Digital Computer Laboratory); no. 113.Electronic digital computers.; Numerical calculations.Supported by: National Science Foundation under grant G16489. ``March 22, 1962.''ack-nhfbJ. DesclouxRemarks on errors in first order weshold Realization of Arithmetic Circuits",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
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month = apr,
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}ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219366IRE Transactions on Electronic Computersack-nhfbM. A. Fischler and E. A. PoeThreshold Realization of Arithmetic Circuits
@Article{Fischler:1962:TRA,
author = "M. A. Fischler and E. A. Poe",
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s;W#/Ee;a7E;]Ee%articlefparith.bibFischler:1962:TRAM. A. Fischler and E. A. PoeThreshold Realization of Arithmetic Circuitsj-IRE-TRANS-ELEC-COMPUTEC-112287--288apr41962IRELAOhttp://dx.doi.org/10.1109/TEC.1962.52193660367-9950 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://z}r representation for use with
algorithmic languages",
journal = j-CACM,
volume = "5",
number = "3",
pages = "160--161",
month = mar,
year = "1962",
CODEN = "CACMA2",
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bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Algorithmic languages, such as ALGOL, make provision
for two types of numbers, real and integer, which are
usually implemented on the computer by means of
floating-point and fixed-point numbers respectively.
The concepts real and integer, however, are taken from
mathematics, where the set of integers forms a proper
subset of the set of real numbers. In implementation a
real problem is posed by the fact that the set of
fixed-point numbers is not a proper subset of the set
of floating-point numbers; this problem becomes very
apparent in attempts to implement ALGOL 60.
Furthermore, the {\em one\/} mathematical operation of
addition is implemented in the machine by one of {\em
two\/} machine operations, fixed-point addition or
floating-point addition.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
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} of fixed-point numbers is not a proper subset of the set of floating-point numbers; this problem becomes very apparent in attempts to implement ALGOL 60. Furthermore, the em one mathematical operation of addition is implemented in the machine by one of em two machine operations, fixed-point addition or floating-point addition.Communications of the ACMack-nhfbhttp://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 floating-point and fixed-point numbers respectively. The concepts real and integer, however, are taken from mathematics, where the set of integers forms a proper subset of the set of real numbers. In implementation a real problem is posed by the fact that the set of fixed-point numbers is not a proper subset of the set of floating-point numbers; this problem becomes very apparent in attempts to implement ALGOL 60. Furthermore, the {\em one\/} mathematical operation of addition is implemented in the machine by one of {\em two\/} machine operations, fixed-point addition or floating-point addition.A. A. GrauOn a floating-point number representation for use with algorithmic languages
@Article{Grau:1962:FNR,
author = "A. A. Grau",
title = "On a floating-point number representation for use with
algorithmic languages",
journal = j-CACM,
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MRnumber = "26\#4506",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Algorithmic languages, such as ALGOL, make provision
for two types of numbers, real and integer, which are
usually implemented on the computer by means of
floating-point and fixed-point numbers respectively.
The concepts real and integer, however, are taken from
mathematics, where the set of integers forms a proper
subset of the set of real numbers. In implementation a
real problem is posed by the fact that the set of
fixed-point numbers is not a proper subset of the set
of floating-point numbers; this problem becomes very
apparent in attempts to implement ALGOL 60.
Furthermore, the {\em one\/} mathematical operation of
addition is implemented in the machine by one of {\em
two\/} machine operations, fixed-point addition or
floating-point addition.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
reviewer = "R. L. Ashenhurst",
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XV #-Ii+3!E%;uMmIiibookfparith.bibHamming:1962:NMSR. W. (Richard Wesley) HammingNumerical methods for scientists and engineerspub-MCGRAW-HILLpub-MCGRAW-HILL:adr4111962QA297 .H28Fri Aug 2U=Y #+-5;a7E;]-5{
articlefparith.bibGuffin:1962:CSLRonald M. GuffinA Computer for Solving Linear Simultaneous Equations Using the Residue Number Systemj-IRE-TRANS-ELEC-COMPUTEC-112164--173apr41962IRELAOhttp://dx.doi.org/10.1109/TEC.1962.52193490367-9950 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 Transactionical methods for scientists and engineers",
publisher = pub-MCGRAW-HILL,
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pages = "411",
year = "1962",
LCCN = "QA297 .H28",
bibdate = "Fri Aug 20 09:12:08 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "International series in pure and applied mathematics",
acknowledgement = ack-nhfb,
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subject = "Numerical analysis; Electronic digital computers",
}0 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 computersack-nhfbR. W. (Richard Wesley) HammingNumerical methods for scientists and engineers
@Book{Hamming:1962:NMS,
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pages = "411",
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acknowledgement = ack-nhfb,
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subject = "Numerical analysis; Electronic digital computers",
}ng Point Feature on the {IBM Type 1620}",
journal = j-IBM-TDB,
volume = "05-62",
pages = "43--46",
month = may,
year = "1962",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Fri Nov 28 11:26:02 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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}cal Disclosure Bulletindecimal floating-point arithmeticThe IBM 1620 normalized variable-precision arithmetic provides up to 100 decimal digits with an exponent range of $ pm 99 $.ack-nhfbF. B. Jones and A. W. WymoreFloating Point Feature on the {IBM Type 1620}
@Article{Jones:1962:FPF,
author = "F. B. Jones and A. W. Wymore",
title = "Floating Point Feature on the {IBM Type 1620}",
journal = j-IBM-TDB,
volume = "05-62",
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**s@U#1?m-7=m;A?mcarticlefparith.b[?V#)Ec7=m;OOEg{articlefparith.bibJones:1962:FPFF. B. Jones and A. W. WymoreFloating Point Feature on the IBM Type 1620j-IBM-TDB05-6243--46may51962IBMTAA0018-8689 OR 00188689Fri Nov 28 11:26:02 2003http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 11:26:02 ???IBM Techniplication of multidigit numbers on automata",
journal = j-DOKL-AKAD-NAUK,
volume = "145",
number = "??",
pages = "293--294",
month = "????",
year = "1962",
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@Article{Karatsuba:1962:MMN,
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}= "Division and overflow detection in residue number
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pages = "501--507",
month = aug,
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@Article{Keir:1962:DOD,
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qBW #)#W57;K;?c#Warticlefparith.bibKnuth:1962:EPCD. E. KnuthEvaluation of Polynomials By Computerj-CACM512595--599dec121962CACMA20001-0782 (print), 1557-7317 (electronic) OR _AW#'g;a75%E;]gCarticlefparith.bibKeir:1962:DODY. A. Keir and P. W. Cheney and M. TannenbaumDivision and overflow detection in residue number systemsj-IRE-TRANS-ELEC-COMPUTEC-114501--507aug81962IRELAOhttp://dx.doi.org/10.1109/TEC.1962.52193890367-9950 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 Computersack-nhfbY. A. Keir and P. W. Cheney and M. TannenbaumDivision and overflow dels By Computer",
journal = j-CACM,
volume = "5",
number = "12",
pages = "595--599",
month = dec,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Thu Sep 1 10:15:40 1994ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:40 ???Communications of the ACMack-njhttp://portal.acm.org/browse_dl.cfm?idx=J79D. E. KnuthEvaluation of Polynomials By Computer
@Article{Knuth:1962:EPC,
author = "D. E. Knuth",
title = "Evaluation of Polynomials By Computer",
journal = j-CACM,
volume = "5",
number = "12",
pages = "595--599",
month = dec,
year = "1962",
CODEN = "CACMA2",
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acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
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}dware Conversion of Decimal
and Binary Numbers",
journal = j-CACM,
volume = "5",
number = "9",
pages = "468--469",
month = sep,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 28 18:16:30 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
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}03http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 18:16:30 ???Communications of the ACMdecimal floating-point arithmeticack-mfchttp://portal.acm.org/browse_dl.cfm?idx=J79G. T. LakeLetter to the Editor: Hardware Conversion of Decimal and Binary Numbers
@Article{Lake:1962:LEH,
author = "G. T. Lake",
title = "Letter to the Editor: Hardware Conversion of Decimal
and Binary Numbers",
journal = j-CACM,
volume = "5",
number = "9",
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month = sep,
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CODEN = "CACMA2",
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acknowledgement = ack-mfc # " and " # ack-nhfb,
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HuH!EX #1+A;7=a;]+I articlefparith.bibMacSorley:1962:RBAO. L. MacSorleyReview: booktitle An Algorithm for Rapid Binary Division, by J. B. Wilson and R. S. Ledleyj-IRE-TRANS-ELEC-COMPUTEC-113420--420jun61962IRELAO0367-9950 OR DV #)#o57=m;?Oc#o/articlefparith.bibLynch:1962:WBDW. C. LynchOn a Wired-In Binary-to-Decimal Conversion Schemej-CACM53159--159mar31962CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 155773bCX #'!57=m;?Oc!yarticlefparith.bibLake:1962:LEHG. T. LakeLetter to the Editor: Hardware Conversion of Decimal and Binary Numbersj-CACM59468--469sep91962CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Fri Nov 28 18:16:30 20-Decimal Conversion Scheme",
journal = j-CACM,
volume = "5",
number = "3",
pages = "159--159",
month = mar,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
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bibdate = "Fri Nov 28 18:21:41 2003",
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acknowledgement = ack-mfc # " and " # ack-nhfb,
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keywords = "decimal floating-point arithmetic",
}
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ccGY #)%;a7E;]%Qarticlefparith.bibMetze:1962:CBDGernot MetzeA Class of Binary Divisions Yielding Minimally Represented Quotientsj-IRE-TRANS-ELEC-COMPUTEC-116761--764dec121962IRELAOhttp://dx.doi.org/10.1109/TEC.1962.52194600367-9950 OR 03679950Thu Jul 14 09:11:53 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 09:11:53 MDThttp://ieeexplore.ieee.org/stamp/stammFX #-'s57;K;['skarticlefparith.bibMeggitt:1962:PDPJ. E. MeggittPseudo Division and Pseudo Multiplication Processesj-IBM-JRD62210--226apr41962IBMJAE0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)0018-8646 OR 00188646Thu Sep 1 10:15:31 1994ftp://garbo.uwasa.fi/sions Yielding Minimally
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@Article{Lehmer:1963:RDO,
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title = "{R63--17} Division and Overflow Detection in Residue
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}) OR 00361445 (print), 10957200 (electronic)0036-1445 OR 00361445Wed Apr 29 18:26:14 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib1998.04.29 18:26:14 ???SIAM Reviewack-nhfbhttp://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",
journal = j-SIAM-REVIEW,
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number = "4",
pages = "342--350",
month = "????",
year = "1963",
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} "Basic Operations in an Unnormalized Arithmetic
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journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-12",
number = "6",
pages = "896--904",
month = dec,
year = "1963",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1963.263593;
http://dx.doi.org/10.1109/PGEC.1963.263592",
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abstract = "A particular set of unnormalized arithmetic operations
termed ``basic'' are described, in the context of the
University of Chicago Maniac III Computer. Each basic
operation involves three operand words and generates
two result words, all in unnormalized floating point
format. The use of these operations in the
implementation of multi-precision arithmetic is
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nontentative manner with their aid.",
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fjournal = "IEEE Transactions on Electronic Computers",
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}h.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 08:10:44 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038037A particular set of unnormalized arithmetic operations termed ``basic'' are described, in the context of the University of Chicago Maniac III Computer. Each basic operation involves three operand words and generates two result words, all in unnormalized floating point format. The use of these operations in the implementation of multi-precision 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.0124.07910ack-nhfbA particular set of unnormalized arithmetic operations termed ``basic'' are described, in the context of the University of Chicago Maniac III Computer. Each basic operation involves three operand words and generates two result words, all in unnormalized floating point format. The use of these operations in the implementation of multi-precision arithmetic is explained; in particular, it is demonstrated that multiprecision division can be effected in a nontentative manner with their aid.N. Metropolis and R. L. AshenhurstBasic Operations in an Unnormalized Arithmetic System
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title = "Basic Operations in an Unnormalized Arithmetic
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journal = j-IEEE-TRANS-ELEC-COMPUT,
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format. The use of these operations in the
implementation of multi-precision arithmetic is
explained; in particular, it is demonstrated that
multiprecision division can be effected in a
nontentative manner with their aid.",
acknowledgement = ack-nhfb,
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remark = "Cited in \cite{Sterbenz:1974:FPC}.",
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]V#'o]+3)E%;mM;o]bookfparith.bibMood:1963:ITSAlexander McFarlane Mood and Franklin A. GraybillIntroduction to the theory of statisticspub-MCGRAW-HILLpub-MCGRAW-HILL:adrSecond4431963HA29 .M75 1963Fri A1\Z#3Qw=97E);a_M!aQws articlefparith.bibMetropolis:1963:BOUN. Metropolis and R. L. AshenhurstBasic Operations in an Unnormalized Arithmetic Systemj-IEEE-TRANS-ELEC-COMPUTEC-126896--904dec121963IEECA8http://dx.doi.org/10.1109/PGEC.1963.263593; http://dx.doi.org/10.1109/PGEC.1963.2635920367-7508 OR 03677508Thu Jul 14 08:10:44 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.uta = "Introduction to the theory of statistics",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
edition = "Second",
pages = "443",
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address = pub-MCGRAW-HILL:adr,
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remark = "Cited in \cite{Sterbenz:1974:FPC}.",
subject = "Mathematical statistics",
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diodes alone. The required relationship between
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} title = "A circuit for the square root of the sum of the
squares",
journal = j-PROC-IEEE,
volume = "51",
number = "4",
pages = "593--596",
month = apr,
year = "1963",
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summary = "A piecewise-linear network can produce an output
proportional to the square root of the sum of the
squares of a set of input voltages, using resistors and
diodes alone. The required relationship between
voltages can be represented by a multi- \ldots{}",
}
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http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/62.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/63.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/64.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/65.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/66.tif",
acknowledgement = ack-nhfb # " and " # ack-nj,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
N_Z#+C157EK;5OC5;articlefparith.bibStroud:1963:MPFA. H. Stroud and D. SecrestA multiple-precision floating-point interpretive program for the Control Data 1604j-COMP-J6162--66apr41963CMPJA60010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)0010-4620 OR 00104620Fri Sep 29 08:55:45 MDT 2000ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/2000.09.29 08:55:45 MDThttp://www3.oup.co.on",
journal = j-INF-PROCESS-MACH,
volume = "9",
number = "??",
pages = "25--33",
month = "????",
year = "1963",
CODEN = "IPRMDD",
ISSN = "0373-885X",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "Information processing machines",
}
kk`U #+!?17;m;K!?= articlefparith.bibSvoboda:1963:ADA. SvobodaAn algorithm for divisionj-INF-PROCESS-MACH925--331963IPRMDD0373-885X OR 0373885XThu Apr 2 08:38:35 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib1998.04.02 08:38:35 ???Information processing machinesack-sfoA. SvobodaAn algorithm for division
@Article{Svoboda:1963:AD,
author = "A. Svoboda",
title = "An algorithm for division",
journal = j-INF-PROCESS-MACH,
volume = "9",
number = "??",
pages = "25--33",
month = "????",
year = "1963",
CODEN = "IPRMDD",
ISSN = "0373-885X",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "Information processing machines",
}ations in floating-point arithmetic",
crossref = "Metropolis:1963:PFS",
pages = "185--198",
year = "1963",
MRclass = "65.35",
MRnumber = "28\#1744",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "A. S. Householder",
}
maU '#1+e3;m;/+e5inproceedingsfparith.bibWilkinson:1963:PSAJ. H. WilkinsonPlane rotations in floating-point arithmeticMetropolis:1963:PFS185--198196365.3528\#1744Fri Dec 8 08:24:14 1995http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 08:24:14 ???ack-nhfbA. S. HouseholderJ. H. WilkinsonPlane rotations in floating-point arithmetic
@InProceedings{Wilkinson:1963:PSA,
author = "J. H. Wilkinson",
title = "Plane rotations in floating-point arithmetic",
crossref = "Metropolis:1963:PFS",
pages = "185--198",
year = "1963",
MRclass = "65.35",
MRnumber = "28\#1744",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "A. S. Householder",
} in Algebraic Processes",
publisher = pub-PH,
address = pub-PH: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 = ack-nj,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
mbU #11Y!-=m;M1Y5bookfparith.bibWilkinson:1963:REAJames H. WilkinsonRounding Errors in Algebraic Processespub-PHpub-PH: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.ack-njJames H. WilkinsonRounding Errors in Algebraic Processes
@Book{Wilkinson:1963:REA,
author = "James H. Wilkinson",
title = "Rounding Errors in Algebraic Processes",
publisher = pub-PH,
address = pub-PH: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 = ack-nj,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}ulating machine",
journal = j-IEEE-SPECTRUM,
volume = "1",
number = "??",
pages = "62--69",
month = aug,
year = "1964",
CODEN = "IEESAM",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
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 = ack-nhfb,
fjournal = "IEEE Spectrum",
remark = "This article does not appear in the IEEE Xplore
database, and that source lists only volume 1, number
1, for 1964. I found multiple references to this paper
as the August 1964 issue, so perhaps IEEE Xplore is
missing early journal issues??",
}title = "Proposed automatic calculating machine",
journal = j-IEEE-SPECTRUM,
volume = "1",
number = "??",
pages = "62--69",
month = aug,
year = "1964",
CODEN = "IEESAM",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
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 = ack-nhfb,
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??",
}
""RcZ #)#Y+57=O;%'k#-Y}articlefparith.bibAiken:1964:PACH. H. AikenProposed automatic calculating machinej-IEEE-SPECTRUM162--69aug81964IEESAM0018-9235 (print), 1939-9340 (electronic) OR 00189235 (print), 19399340 (electronic)0018-9235 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??ack-nhfbH. H. AikenPreviously unpublished memorandum. Reprinted in \cite[\S 5.1]{Randell:1982:ODC}.Proposed automatic calculating machine
@Article{Aiken:1964:PAC,
author = "H. H. Aiken",
ing point interpretive system:
for the {RPC 4000 General Precision} electronic
computer",
organization = "General Precision, Inc.",
address = "West Lafayette, IN, USA",
pages = "45",
year = "1964",
bibdate = "Mon May 06 10:24:31 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.; Purdue
University School of Electrical Engineering; RPC 4000
(Computer)",
remark = "Program no. H1-02.0",
}x/bib/fparith.bib2002.05.06 10:24:31 ???Electronic digital computers --- Programming.; Purdue University School of Electrical Engineering; RPC 4000 (Computer)Program no. H1-02.0ack-nhfbAnonymous{PINT}: {Purdue} floating point interpretive system: for the {RPC 4000 General Precision} electronic computer
@Manual{Anonymous:1964:PPF,
author = "Anonymous",
title = "{PINT}: {Purdue} floating point interpretive system:
for the {RPC 4000 General Precision} electronic
computer",
organization = "General Precision, Inc.",
address = "West Lafayette, IN, USA",
pages = "45",
year = "1964",
bibdate = "Mon May 06 10:24:31 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.; Purdue
University School of Electrical Engineering; RPC 4000
(Computer)",
remark = "Program no. H1-02.0",
}
::_gV '#/=U9K-Em;E=U9mastersthesisfpar-f[#'U_57E;;?c;U_'articlefparith.bibBaer:1964:MPARobert M. Baer and Martin G. RedlichMultiple-precision arithmetic and the exact calculation of the $ 3 - j $, $ 6 - j $ and $ 9 - j $ symbolsj-CACM711657--659nov111964CACMA20001-0782 (p0eV #3-i57=m;1e-i!articlefparith.bibAshenhurst:1964:FEUR. L. AshenhurstFunction Evaluation in Unnormalized AritRdX #1[;;=m;y3g'manualfparith.bibAnonymous:1964:PPFAnonymousPINT: Purdue floating point interpretive system: for the RPC 4000 General Precision electronic computerGeneral Precision, Inc.West Lafayette, IN, USA451964Mon May 06 10:24:31 2002http://www.math.utah.edu/pub/texuuz$).38=BGLQV[`ejoty~
"(.4:@FLRX^djpv|# (
*-
27:?HZ\agp # (
*-
27:?HZ\agp |!"#&')*+,0468:<?ABEHLMOSTVXZ$\)_2c@BEGHJLofflrx~ &,28>DJPV\bhntz
"(.4:@FLRX^djpv|NPSTÁUǁWρXӁ[ށ]^_`abcNPSTÁUǁWρXӁ[ށ]^_`abcgjmnqt&w-z6{8|<CNUX[ a
ce
kny~ !$%'*Ƃ,͂-Ђ.ӂ/ւ1܂45678:;<=>?
@
BCEF G"I(K.L3M6O:P@RETIULWTXXZ]\g]i^m_s`uazb}cefghjklnoqrtÂŵxςyтzԂ{uation in Unnormalized Arithmetic",
journal = j-J-ACM,
volume = "11",
number = "2",
pages = "168--187",
month = apr,
year = "1964",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Thu Nov 03 22:33:52 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}hmeticj-J-ACM112168--187apr41964JACOAH0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)0004-5411 OR 00045411Thu Nov 03 22:33:52 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.11.03 22:33:52 ???Journal of the ACMack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401R. L. AshenhurstFunction Evaluation in Unnormalized Arithmetic
@Article{Ashenhurst:1964:FEU,
author = "R. L. Ashenhurst",
title = "Function Evaluation in Unnormalized Arithmetic",
journal = j-J-ACM,
volume = "11",
number = "2",
pages = "168--187",
month = apr,
year = "1964",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Thu Nov 03 22:33:52 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
} calculation of the $ 3 - j $, $ 6 - j $ and $ 9 - j $
symbols",
journal = j-CACM,
volume = "7",
number = "11",
pages = "657--659",
month = nov,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.25",
MRnumber = "31\#865",
bibdate = "Mon Oct 24 09:33:02 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Described in this paper is a system of general-purpose
multiple-precision fixed-point routines and their use
in subroutines which calculate exactly the
quantum-mechanical 3-j, 6-j and 9-j symbols of large
arguments.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
++rL&\9fM
@Article{Beckmann:1993:FFTb,
author = "P. E. Beckmann and B. R. Musicus",
title = 'T"E
@Article{Beebe:2007:ETM,
author = "Nelson H. F. Beebe",
title = "Extending {\TeX}G.qc
@Article{Beebe:2009:NML,
author = "Nelson H. F. Beebe",
title = "A new math libraJ݊Z5
@Article{Behringer:1970:BFI,
author = "F. A. Behringer",
title = "{Eine bedingte
@Article{Belanovic:2002:LPF,
author = "Pavle Belanovic and Miriam Leeser",
title = ;E
@Article{Bemer:1958:MMS,
author = "Robert W. Bemer",
title = "A Machine Method fo7B
@Article{Bemer:1958:SMC,
author = "R. W. Bemer",
title = "A Subroutine Method for9ti
@Article{Bemer:1963:NRT,
author = "R. W. Bemer",
title = "A Note on Range Transfo(S
@Article{Benford:1938:LAN,
author = "Frank Benford",
title = "The Law of AnomalouIrint), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 0001078265.2531\#865Mon Oct 24 09:33:02 MDT 2005http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.10.24 09:33:02 MDTDescribed in this paper is a system of general-purpose multiple-precision fixed-point routines and their use in subroutines which calculate exactly the quantum-mechanical 3-j, 6-j and 9-j symbols of large arguments.Communications of the ACMack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Described in this paper is a system of general-purpose multiple-precision fixed-point routines and their use in subroutines which calculate exactly the quantum-mechanical 3-j, 6-j and 9-j symbols of large arguments.Robert M. Baer and Martin G. RedlichMultiple-precision arithmetic and the exact calculation of the $ 3 - j $, $ 6 - j $ and $ 9 - j $ symbols
@Article{Baer:1964:MPA,
author = "Robert M. Baer and Martin G. Redlich",
title = "Multiple-precision arithmetic and the exact
calculation of the $ 3 - j $, $ 6 - j $ and $ 9 - j $
symbols",
journal = j-CACM,
volume = "7",
number = "11",
pages = "657--659",
month = nov,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.25",
MRnumber = "31\#865",
bibdate = "Mon Oct 24 09:33:02 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Described in this paper is a system of general-purpose
multiple-precision fixed-point routines and their use
in subroutines which calculate exactly the
quantum-mechanical 3-j, 6-j and 9-j symbols of large
arguments.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
} study of floating point arithmetic",
type = "Thesis ({M.S. in Math.})",
school = "Georgia Institute of Technology",
address = "Atlanta, GA, USA",
pages = "51",
year = "1964",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers.; Number theory.;
Numerical calculations --- Computer programs.",
}ith.bibBookhart:1964:SFPThomas Woodward BookhartA study of floating point arithmeticThesis (M.S. in Math.)Georgia Institute of TechnologyAtlanta, GA, USA511964Sat Feb 24 15:01:45 MST 1996http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MSTElectronic digital computers.; Number theory.; Numerical calculations --- Computer programs.ack-nhfbThomas Woodward BookhartA study of floating point arithmetic
@MastersThesis{Bookhart:1964:SFP,
author = "Thomas Woodward Bookhart",
title = "A study of floating point arithmetic",
type = "Thesis ({M.S. in Math.})",
school = "Georgia Institute of Technology",
address = "Atlanta, GA, USA",
pages = "51",
year = "1964",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers.; Number theory.;
Numerical calculations --- Computer programs.",
} some general modes of
arithmetic",
journal = j-CACM,
volume = "7",
number = "2",
pages = "119--127",
month = feb,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Oct 24 09:33:00 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An interpretive programming package is described for
computation with operands which may be real, complex,
single or double precision, or real multiple precision.
It also performs operations on matrices formed from
these elements. A simple language structure is used to
describe the computation.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}10782 (print), 15577317 (electronic)0001-0782 OR 00010782Mon Oct 24 09:33:00 MDT 2005http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.10.24 09:33:00 MDTAn interpretive programming package is described for computation with operands which may be real, complex, single or double precision, or real multiple precision. It also performs operations on matrices formed from these elements. A simple language structure is used to describe the computation.Communications of the ACMack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79An interpretive programming package is described for computation with operands which may be real, complex, single or double precision, or real multiple precision. It also performs operations on matrices formed from these elements. A simple language structure is used to describe the computation.R. A. BrookerA programming package for some general modes of arithmetic
@Article{Brooker:1964:PPS,
author = "R. A. Brooker",
title = "A programming package for some general modes of
arithmetic",
journal = j-CACM,
volume = "7",
number = "2",
pages = "119--127",
month = feb,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Oct 24 09:33:00 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An interpretive programming package is described for
computation with operands which may be real, complex,
single or double precision, or real multiple precision.
It also performs operations on matrices formed from
these elements. A simple language structure is used to
describe the computation.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
ZZjY #'+g]57;O;A?_cA/kkarticlefparith.bibCody:1964:DPSW. J. Cody, Jr.Double-Precision Square Root for the CDC-3600j-CACM712715--718dec121964CACMA2http://doi.acm.org/10.1145/355588.3651220001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Thu Sep 1 10:15:43 1994ftp://garbo.uwasa.fi/pc/do `iX #177-=m;Ou;# manualfparith.bibBurroughs:1964:BBIBurroughs CorporationBurroughs B5500 Information Processing Systems Reference ManualBurroughs Corporatioh[ #-'57E;[?c['S articlefparith.bibBrooker:1964:PPSR. A. BrookerA programming package for some general modes of arithmeticj-CACM72119--127feb21964CACMA20001-0782 (print), 1557-7317 (electronic) OR 000hs B5500} Information Processing Systems
Reference Manual",
organization = "Burroughs Corporation",
address = "Detroit, MI, USA",
year = "1964",
bibdate = "Wed Nov 22 21:15:11 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "The B5500 uses a decimal integer or fixed-point
coefficient of 21 or 22 digits, with an exponent range
of $ \pm 63 $.",
}nDetroit, MI, USA119--1271964Wed Nov 22 21:15:11 2006http://www.math.utah.edu/pub/tex/bib/fparith.bib2006.11.22 21:15:11 ???decimal floating-point arithmeticThe B5500 uses a decimal integer or fixed-point coefficient of 21 or 22 digits, with an exponent range of $ pm 63 $.ack-nhfb{Burroughs Corporation}{Burroughs B5500} Information Processing Systems Reference Manual
@Manual{Burroughs:1964:BBI,
author = "{Burroughs Corporation}",
title = "{Burroughs B5500} Information Processing Systems
Reference Manual",
organization = "Burroughs Corporation",
address = "Detroit, MI, USA",
year = "1964",
bibdate = "Wed Nov 22 21:15:11 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "The B5500 uses a decimal integer or fixed-point
coefficient of 21 or 22 digits, with an exponent range
of $ \pm 63 $.",
}quare Root for the {CDC-3600}",
journal = j-CACM,
volume = "7",
number = "12",
pages = "715--718",
month = dec,
year = "1964",
CODEN = "CACMA2",
DOI = "http://doi.acm.org/10.1145/355588.365122",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In January of 1960, the late Hans J. Maehly completed
a summary of approximations to the elementary functions
for the CDC-1604 computer. The approximations and
techniques suggested by Maehly are equally applicable
to the second large computer in the CDC line, the 3600.
Unlike the 1604, however, the 3600 has built-in
double-precision floating-point arithmetic. The present
work, largely inspired by the successes of Maehly and
his associates, concerns the extension of one of
Maehly's ideas to a double-precision subroutine for the
3600.",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$sqrt(x)$; CDC 3600; elementary functions",
}
c-soft/fpbibl18.zip; http://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:43 ???In January of 1960, the late Hans J. Maehly completed a summary of approximations to the elementary functions for the CDC-1604 computer. The approximations and techniques suggested by Maehly are equally applicable to the second large computer in the CDC line, the 3600. Unlike the 1604, however, the 3600 has built-in double-precision floating-point arithmetic. The present work, largely inspired by the successes of Maehly and his associates, concerns the extension of one of Maehly's ideas to a double-precision subroutine for the 3600.Communications of the ACM$sqrt(x)$; CDC 3600; elementary functionsack-njhttp://portal.acm.org/browse_dl.cfm?idx=J79In January of 1960, the late Hans J. Maehly completed a summary of approximations to the elementary functions for the CDC-1604 computer. The approximations and techniques suggested by Maehly are equally applicable to the second large computer in the CDC line, the 3600. Unlike the 1604, however, the 3600 has built-in double-precision floating-point arithmetic. The present work, largely inspired by the successes of Maehly and his associates, concerns the extension of one of Maehly's ideas to a double-precision subroutine for the 3600.W. J. {Cody, Jr.}Double-Precision Square Root for the {CDC-3600}
@Article{Cody:1964:DPS,
author = "W. J. {Cody, Jr.}",
title = "Double-Precision Square Root for the {CDC-3600}",
journal = j-CACM,
volume = "7",
number = "12",
pages = "715--718",
month = dec,
year = "1964",
CODEN = "CACMA2",
DOI = "http://doi.acm.org/10.1145/355588.365122",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
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http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In January of 1960, the late Hans J. Maehly completed
a summary of approximations to the elementary functions
for the CDC-1604 computer. The approximations and
techniques suggested by Maehly are equally applicable
to the second large computer in the CDC line, the 3600.
Unlike the 1604, however, the 3600 has built-in
double-precision floating-point arithmetic. The present
work, largely inspired by the successes of Maehly and
his associates, concerns the extension of one of
Maehly's ideas to a double-precision subroutine for the
3600.",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
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}Built-In Square Root Method",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "2",
pages = "156--157",
month = apr,
year = "1964",
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DOI = "http://dx.doi.org/10.1109/PGEC.1964.263791",
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bibdate = "Thu Jul 14 06:56:59 MDT 2011",
bibsource = "http://www.computer.org/tc/;
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}7.14 06:56:59 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038119IEEE Transactions on Electronic Computersack-nhfbD. CowgillLogic Equations for a Built-In Square Root Method
@Article{Cowgill:1964:LEB,
author = "D. Cowgill",
title = "Logic Equations for a Built-In Square Root Method",
journal = j-IEEE-TRANS-ELEC-COMPUT,
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articlefparith.bibCowgill:1964:LEBD. CowgillLogic Equations for a Built-In Square Root Methodj-IEEE-TRANS-ELEC-COMPUTEC-132156--157apr41964IEECA8http://dx.doi.org/10.1109/PGEC.1964.2637910367-7508 OR 03677508Thu Jul 14 06:56:59 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.0
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@Article{Eve:1964:EP,
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}cations of division by convergence",
type = "Thesis ({M.S.})",
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title = "Applications of division by convergence",
type = "Thesis ({M.S.})",
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} of Zero in Floating-Point
Arithmetic",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
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author = "Christian Gram",
title = "On the Representation of Zero in Floating-Point
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journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
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number = "3",
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acknowledgement = ack-nhfb,
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journal = j-CACM,
volume = "7",
pages = "10--13",
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
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@Article{Gregory:1964:FAN,
author = "Robert T. Gregory and James L. Raney",
title = "Floating-point arithmetic with $ 84 $-bit numbers",
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journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
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*qW #1%Q=a7E;_%Qwarticlefparith.bibJacobsohn:1964:SFMD. JacobsohnA Suggestion for a Fast Multiplierj-IEEE-TRANS-ELEC-COMPUTEC-136754--754dec121964IEECA8http://dx.doi.org/10.1109/PGEC.1964.2639420367-7508 OR 03677508Thu Jul 14 06:57:06 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ipW #-'I'E%;c1'IOWbookfparith.bibHenrici:1964:ENAPeter HenriciElements of numerical analysispub-WILEYpub-WILEY:adrxv + 3281964QA297 .H4Fri Aug 20 09:17:19 MDT 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.oV#-Uo57;m;?cUoaarticlefparith.bibGregory:1964:FANRobert T. Gregory and James L. RaneyFloating-point arithmetic with $ 84 $-bit numbersj-CACM710--131964CACMA20001-0782 (print), 1557-7317 (electanalysis",
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address = pub-WILEY:adr,
pages = "xv + 328",
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bibdate = "Fri Aug 20 09:17:19 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Based on the author's lecture notes for a course
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\cite{Sterbenz:1974:FPC}.",
subject = "Numerical analysis",
}loc.gov:7090/Voyager2010.08.20 09:17:19 MDTBased on the author's lecture notes for a course entitled em Numerical Mathematical Analysis at the University of California, Los Angeles. Cited in cite Sterbenz:1974:FPC.Numerical analysisack-nhfbPeter HenriciElements of numerical analysis
@Book{Henrici:1964:ENA,
author = "Peter Henrici",
title = "Elements of numerical analysis",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xv + 328",
year = "1964",
LCCN = "QA297 .H4",
bibdate = "Fri Aug 20 09:17:19 MDT 2010",
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z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Based on the author's lecture notes for a course
entitled {\em Numerical Mathematical Analysis\/} at the
University of California, Los Angeles. Cited in
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subject = "Numerical analysis",
} Fast Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "6",
pages = "754--754",
month = dec,
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}eeetranscomput.bib2011.07.14 06:57:06 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038318IEEE Transactions on Electronic Computersack-nhfbD. JacobsohnA Suggestion for a Fast Multiplier
@Article{Jacobsohn:1964:SFM,
author = "D. Jacobsohn",
title = "A Suggestion for a Fast Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "6",
pages = "754--754",
month = dec,
year = "1964",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1964.263942",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:57:06 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",
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}nued fractions",
publisher = "P. Noordhoff",
address = "Groningen, The Netherlands",
pages = "101",
year = "1964",
LCCN = "QA295 .K513 1964a",
bibdate = "Fri Nov 30 06:55:53 MST 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "Translated by Peter Wynn",
URL = "http://www.loc.gov/catdir/description/dover032/97008056.html;
http://www.loc.gov/catdir/toc/dover031/97008056.html",
acknowledgement = ack-nhfb,
author-dates = "1894--1959",
}th.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2007.11.30 06:55:53 MSTTranslated by Peter Wynnhttp://www.loc.gov/catdir/description/dover032/97008056.html; http://www.loc.gov/catdir/toc/dover031/97008056.htmlack-nhfb1894--1959Aleksandr Iakovlevich KhinchinTranslated by Peter WynnContinued fractions
@Book{Khinchin:1964:CF,
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title = "Continued fractions",
publisher = "P. Noordhoff",
address = "Groningen, The Netherlands",
pages = "101",
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LCCN = "QA295 .K513 1964a",
bibdate = "Fri Nov 30 06:55:53 MST 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "Translated by Peter Wynn",
URL = "http://www.loc.gov/catdir/description/dover032/97008056.html;
http://www.loc.gov/catdir/toc/dover031/97008056.html",
acknowledgement = ack-nhfb,
author-dates = "1894--1959",
}
P{PtY#);=a7E;_;Warticlefparith.bibKundu:1964:TMDP. Kundu and S. BanerjiTransistorized Multiplier and Divider and Its Applicationsj-IEEE-TRANS-ELEC-COMPUTEC-133288--295jun61964IEECA8http://dx.doi.org/10.1109/PGEC.1964.2639190367-7508 OR 03677508Thu Jul 14 06:57:00 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 06:57:00 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp#1sW #/)GC;m;5Kyarticlefparith.!
rW #-I3%A/E%;=q!I=3bookfparith.bibKhinchin:1964:CFAleksandr Iakovlevich KhinchinContinued fractionsP. NoordhoffGroningen, The Netherlands1011964QA295 .K513 1964aFri Nov 30 06:55:53 MST 2007http://www.mat of the normalized floating point number
notation on digital computers. ({Russian})",
journal = "{\v{Z}}. Vy{\v{c}}isl. Mat. i Mat. Fiz.",
volume = "4",
pages = "192--194",
year = "1964",
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}bibKlokacev:1964:RNFI. V. KlokacevA refinement of the normalized floating point number notation on digital computers. (Russian)Z. Vycisl. Mat. i Mat. Fiz.4192--194196468.0028\#4694Fri Dec 8 08:24:14 1995http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 08:24:14 ???Russianack-nhfbI. V. Kloka{\v{c}}evA refinement of the normalized floating point number notation on digital computers. ({Russian})
@Article{Klokacev:1964:RNF,
author = "I. V. Kloka{\v{c}}ev",
title = "A refinement of the normalized floating point number
notation on digital computers. ({Russian})",
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acknowledgement = ack-nhfb,
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}zed Multiplier and Divider and Its
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journal = j-IEEE-TRANS-ELEC-COMPUT,
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number = "3",
pages = "288--295",
month = jun,
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@Article{Kundu:1964:TMD,
author = "P. Kundu and S. Banerji",
title = "Transistorized Multiplier and Divider and Its
Applications",
journal = j-IEEE-TRANS-ELEC-COMPUT,
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number = "3",
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bibdate = "Thu Jul 14 06:57:00 MDT 2011",
bibsource = "http://www.computer.org/tc/;
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http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
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}hm for a Digital Differential
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journal = j-IEEE-TRANS-ELEC-COMPUT,
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month = feb,
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bibdate = "Thu Jul 14 06:56:57 MDT 2011",
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fjournal = "IEEE Transactions on Electronic Computers",
}e.org/stamp/stamp.jsp?tp=&arnumber=4038079IEEE Transactions on Electronic Computersack-nhfbRoger C. LamsonA Division Algorithm for a Digital Differential Analyzer
@Article{Lamson:1964:DAD,
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title = "A Division Algorithm for a Digital Differential
Analyzer",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "1",
pages = "54--55",
month = feb,
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;A=)articlefparith.bibLynn:1964:REMM. Stuart LynnOn the Round-Off Error in the Method of Successive Over-Relaxationj-MATH-COMPUT188536--49jan11964MCMPAF0025-5718 (print), 1088-6842 (electronic) OR 00(|uW #++}=a7E;_+}Aarticlefparith.bibLamson:1964:DADRoger C. LamsonA Division Algorithm for a Digital Differential Analyzerj-IEEE-TRANS-ELEC-COMPUTEC-13154--55feb21964IEECA8http://dx.doi.org/10.1109/PGEC.1964.2638380367-7508 OR 03677508Thu Jul 14 06:56:57 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 06:56:57 MDThttp://ieeexplore.iee%r in the Method of Successive
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acknowledgement = ack-nhfb,
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acknowledgement = ack-nhfb,
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publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xii + 457",
year = "1964",
bibdate = "Sat Jan 27 13:40:57 MST 1996",
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7/zY #+%i57E;E?McE%iGarticlefparith30yZ #-)=97EU;__) articlefparith.bibMerrill:1964:IDCRoy D. MerrillImproving Digital Computer Performance Using Residue Number Theoryj-IEEE-TRANS-ELEC-COMPUTEC-13293--101apr41964IEECA8http://dx.doi.org/10.1109/PGEC.1964.263777; http://dx.doi.org/10.1109/PGEC.1964.2637760367-7508 OR 03677508Thu Jul 14 06:56:58 MDT 2011http://ieeexplore.ieee.org/; http://www.computer.0}xX#1[;'Em;%M[?bookfparith.bibMcCracken:1964:NMFDaniel D. McCracken and William S. DornNumerical methods and FORTRAN programming, with applications in engineering and sciencepub-WIL,/Computer Performance Using Residue
Number Theory",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "2",
pages = "93--101",
month = apr,
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bibdate = "Thu Jul 14 06:56:58 MDT 2011",
bibsource = "http://ieeexplore.ieee.org/;
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038105;
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acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
keywords = "residue arithmetic; residue number system",
summary = "Residue arithmetic has the interesting characteristic
that in multiplication, addition and subtraction any
digit in the result is dependent only on its two
corresponding operand digits. Consequently, for these
operations, residue arithmetic is \ldots{}",
}1org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 06:56:58 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038105; http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4038099IEEE Transactions on Electronic Computersresidue arithmetic; residue number systemack-nhfbRoy D. MerrillImproving Digital Computer Performance Using Residue Number Theory
@Article{Merrill:1964:IDC,
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}ficant-digit'' arithmetic",
journal = j-CACM,
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number = "1",
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year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
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bibdate = "Mon Oct 24 09:33:00 MDT 2005",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Different methods of handling the summing process for
the geometric series are shown to give results
indicating widely differing significances when carried
out in a machine incorporating ``significant-digit''
arithmetic.",
acknowledgement = ack-nhfb,
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}4.bibMiller:1964:ESDR. H. MillerAn example in ``significant-digit'' arithmeticj-CACM7121--21jan11964CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Mon Oct 24 09:33:00 MDT 2005http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.10.24 09:33:00 MDTDifferent methods of handling the summing process for the geometric series are shown to give results indicating widely differing significances when carried out in a machine incorporating ``significant-digit'' arithmetic.Communications of the ACMCited in cite Sterbenz:1974:FPC.ack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Different methods of handling the summing process for the geometric series are shown to give results indicating widely differing significances when carried out in a machine incorporating ``significant-digit'' arithmetic.R. H. MillerAn example in ``significant-digit'' arithmetic
@Article{Miller:1964:ESD,
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CC9{W '#';'97Em;?gmastersthesisfparith.bibMoss:1964:RDCGeorge Joseph Moss, Jr.Recording digital counter with floating point output formatThesis (M.S.)University of MarylandCollege Park, MD, USA1551964Sat Feb 24 15:01:45 MST 1996http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MSTack-nhfbGeorge Joseph {Moss, Jr.}Recording digital counter with floating point output format
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acknowledgement = ack-nj,
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c|V #'%I!+=K;%IIbookfparith.bibRice:1964:AFVJohn R. RiceThe Approximation of Functions1pub-AWpub-AW:adrvarious1964QA221 .R5 V.1-2Fri Dec 08 13:02:52 1995ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 13:02:52 ???ack-njJohn R. RiceThe Approximation of Functions
@Book{Rice:1964:AFV,
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journal = j-IEEE-TRANS-ELEC-COMPUT,
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month = oct,
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@O
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@Article{Tropp:1999:NRI,
author = "Henry S. Tropp and Jean Sammett",
title = "{Nat R6eeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038256IEEE Transactions on Electronic Computersack-nhfbJ. Santos and H. ArangoBase $3$ vs Base $2$ Synchronous Arithmetic Units
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author = "J. Santos and H. Arango",
title = "Base $3$ vs Base $2$ Synchronous Arithmetic Units",
journal = j-IEEE-TRANS-ELEC-COMPUT,
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number = "5",
pages = "608--609",
month = oct,
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BBfX '#'/'15Em;/7mastersthesisfpari@@~Y #)#57;K;?c#Iarticlefparith.bibStein:1964:DCMM. L. SteinDivide-and-Correct Methods for Multiple Precision Divisionj-CACM78472--474aug81964CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 000107>t}W#+;o=a7E;_;o%articlefparith.bibSantos:1964:BVBJ. Santos and H. ArangoBase $3$ vs Base $2$ Synchronous Arithmetic Unitsj-IEEE-TRANS-ELEC-COMPUTEC-135608--609oct101964IEECA8http://dx.doi.org/10.1109/PGEC.1964.2637340367-7508 OR 03677508Thu Jul 14 06:57:04 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 06:57:04 MDThttp://i;ods for Multiple Precision
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journal = j-CACM,
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year = "1964",
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}82Thu Sep 1 10:15:08 1994ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:08 ???Communications of the ACMack-njhttp://portal.acm.org/browse_dl.cfm?idx=J79M. L. SteinDivide-and-Correct Methods for Multiple Precision Division
@Article{Stein:1964:DCM,
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title = "Divide-and-Correct Methods for Multiple Precision
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journal = j-CACM,
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}loating point arithmetic with the residue
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type = "Thesis ({M.S.})",
school = "UCLA - Engineering",
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pages = "89",
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bibdate = "Sat Feb 24 15:01:45 MST 1996",
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acknowledgement = ack-nhfb,
keywords = "Congruences and residues.; Electronic digital
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}th.bibSweo:1964:SFPDavid Ernest SweoA study of floating point arithmetic with the residue number systemThesis (M.S.)UCLA - EngineeringLos Angeles, CA, USA891964Sat Feb 24 15:01:45 MST 1996http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MSTCongruences and residues.; Electronic digital computers --- Programming.ack-nhfbDavid Ernest SweoA study of floating point arithmetic with the residue number system
@MastersThesis{Sweo:1964:SFP,
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title = "A study of floating point arithmetic with the residue
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type = "Thesis ({M.S.})",
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bibdate = "Sat Feb 24 15:01:45 MST 1996",
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journal = j-IEEE-TRANS-ELEC-COMPUT,
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number = "1",
pages = "14--17",
month = feb,
year = "1964",
CODEN = "IEECA8",
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}/ieeetranscomput.bib2011.07.14 06:56:56 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038071IEEE Transactions on Electronic Computersack-nhfbC. S. WallaceA Suggestion for a Fast Multiplier
@Article{Wallace:1964:SFM,
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title = "A Suggestion for a Fast Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
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3O3sU '#3-!Ew';m;-E!w-#inproceedingsfparKY#3Q]3!5751={;KOc!QK]warticlefparith.bibAshenhurst:1965:EECR. L. Ashenhurst and N. MetropolisError Estimation in Computer Calculationj-AMER-MATH-MONTHLY722 (Part 2)47--581965AMMYAE0002-9890 (print), 1GV #)#_57=m;?c#_articlefparith.bibWolfe:1964:RTEJ. M. WolfeReducing TruncE%W #-'Q=a7E;_'Qqarticlefparith.bibWallace:1964:SFMC. S. WallaceA Suggestion for a Fast Multiplierj-IEEE-TRANS-ELEC-COMPUTEC-13114--17feb21964IEECA8http://dx.doi.org/10.1109/PGEC.1964.2638300367-7508 OR 03677508Thu Jul 14 06:56:56 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bibBors by Programming",
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@Article{Wolfe:1964:RTE,
author = "J. M. Wolfe",
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bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
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note = "Reprinted in Department of Economics, Graduate School
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Mathematical Studies in Business and Economics, number
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ZMnumber = "0216.49602",
acknowledgement = ack-jr,
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}H930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)0002-9890 OR 0002989065.80MR0192671 (33 \#896)James H. WilkinsonFri Jan 12 11:37:56 1996http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.01.12 11:37:56 ???Reprinted in Department of Economics, Graduate School of Business, University of Chicago, Center for Mathematical Studies in Business and Economics, number 45.The American Mathematical Monthlyerror estimation; floating-point arithmetic0216.49602ack-jrhttp://www.jstor.org/page/journal/amermathmont/about.htmlR. L. Ashenhurst and N. MetropolisReprinted in Department of Economics, Graduate School of Business, University of Chicago, Center for Mathematical Studies in Business and Economics, number 45.Error Estimation in Computer Calculation
@Article{Ashenhurst:1965:EEC,
author = "R. L. Ashenhurst and N. Metropolis",
title = "Error Estimation in Computer Calculation",
journal = j-AMER-MATH-MONTHLY,
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bibdate = "Fri Jan 12 11:37:56 1996",
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note = "Reprinted in Department of Economics, Graduate School
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acknowledgement = ack-jr,
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journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
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}all",
booktitle = "Error in digital computation",
title = "Experimental investigation of unnormalized
arithmetic",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "3--37",
year = "1965",
bibdate = "Thu Nov 8 14:49:59 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARI FLP",
}
+rL&+E
@Manual{Cowlishaw:2007:DCL,
author = "Mike Cowlishaw",
title = "The {decNumber C}GS'
@Manual{Anonymous:1964:PPF,
author = "Anonymous",
title = "{PINT}: {Purdue} float A
@Manual{Apple:1978:AIR,
key = "Apple",
title = "{Applesoft II} reference manuaV
@Manual{AppleComputer:1977:ARM,
author = "{Apple Computer, Inc}",
title = "{APPLE~kW
@Manual{BellHowellCo:1978:BHF,
author = "{Bell and Howell Co} and {Apple Computer, Inc}",
n
@Manual{Burroughs:1954:DH,
author = "{Burroughs Corporation. ElectroData}",
title = ݅#
@Manual{Burroughs:1964:BBI,
author = "{Burroughs Corporation}",
title = "{Burroug3
@Manual{Cheng:1981:AAF,
author = "Steven Cheng",
title = "{Am9511A\slash Am9512} E
@Manual{Cowlishaw:2006:DCL,
author = "Mike Cowlishaw",
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@InProceedings{Ashenhurst:1965:EIU,
author = "R. L. Ashenhurst",
editor = "L. B. Rall",
booktitle = "Error in digital computation",
title = "Experimental investigation of unnormalized
arithmetic",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "3--37",
year = "1965",
bibdate = "Thu Nov 8 14:49:59 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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booktitle = "Error in digital computation",
title = "Techniques for automatic error monitoring and
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publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "43--59",
year = "1965",
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}ith.bibAshenhurst:1965:TAER. L. AshenhurstL. B. RallError in digital computationTechniques for automatic error monitoring and controlpub-WILEYpub-WILEY:adr43--591965Tue Oct 9 09:42:56 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.10.09 09:42:56 ???ARI FLPack-nhfbR. L. AshenhurstError in digital computationL. B. RallTechniques for automatic error monitoring and control
@InProceedings{Ashenhurst:1965:TAE,
author = "R. L. Ashenhurst",
editor = "L. B. Rall",
booktitle = "Error in digital computation",
title = "Techniques for automatic error monitoring and
control",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "43--59",
year = "1965",
bibdate = "Tue Oct 9 09:42:56 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
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TW #'!I57;K;?c!Ikarticlefparith.bibBlum:1965:EAPB. I. BlumAn Extended Arithmetic Packagej-CACM85318--320may51965CACMA20001-0782 (print), 1557-731RSW #-'m=a7E;_'marticlefparith.bibAtrubin:1965:ODRA. J. AtrubinA One-Dimensional Real-Time Iterative Multiplierj-IEEE-TRANS-ELEC-COMPUTEC-143394--399jun61965IEECA8http://dx.doi.org/10.1109/PGEC.1965.2641450367-7508 OR 03677508Thu Jul 14 06:26:33 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.bib2011.07.14PuU '#3-!Ew';m;-E!w/inproceedingsfparMeal-Time Iterative Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "3",
pages = "394--399",
month = jun,
year = "1965",
CODEN = "IEECA8",
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} 06:26:33 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038457IEEE Transactions on Electronic Computersack-nhfbA. J. AtrubinA One-Dimensional Real-Time Iterative Multiplier
@Article{Atrubin:1965:ODR,
author = "A. J. Atrubin",
title = "A One-Dimensional Real-Time Iterative Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
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bibdate = "Thu Sep 8 08:20:53 1994",
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}7 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Thu Sep 8 08:20:53 1994ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.08 08:20:53 ???Communications of the ACMack-njhttp://portal.acm.org/browse_dl.cfm?idx=J79B. I. BlumAn Extended Arithmetic Package
@Article{Blum:1965:EAP,
author = "B. I. Blum",
title = "An Extended Arithmetic Package",
journal = j-CACM,
volume = "8",
number = "5",
pages = "318--320",
month = may,
year = "1965",
CODEN = "CACMA2",
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bibdate = "Thu Sep 8 08:20:53 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}tle = "Computation of the Base Two Logarithm of Binary
Numbers",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "6",
pages = "863--867",
month = dec,
year = "1965",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1965.264080",
ISSN = "0367-7508",
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fjournal = "IEEE Transactions on Electronic Computers",
}lectronic Computersack-nhfbM. Combet and H. {Van Zonneveld} and L. VerbeekComputation of the Base Two Logarithm of Binary Numbers
@Article{Combet:1965:CBT,
author = "M. Combet and H. {Van Zonneveld} and L. Verbeek",
title = "Computation of the Base Two Logarithm of Binary
Numbers",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "6",
pages = "863--867",
month = dec,
year = "1965",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1965.264080",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:41 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=4038605",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
]W#+g{=a7E;_k{articlefparith.bibCombet:1965:CBTM. Combet and H. Van Zonneveld and L. VerbeekComputation of the Base Two Logarithm of Binary Numbersj-IEEE-TRANS-ELEC-COMPUTEC-146863--867dec121965IEECA8http://dx.doi.org/10.1109/PGEC.1965.2640800367-7508 OR 03677508Thu Jul 14 06:26:41 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 06:26:41 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038605IEEE Transactions on ETel Multipliers",
journal = j-ALTA-FREQ,
volume = "34",
number = "??",
pages = "349--356",
month = mar,
year = "1965",
CODEN = "ALFRAJ",
ISSN = "0002-6557",
ISSN-L = "0002-6557",
bibdate = "Fri Nov 09 10:47:42 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[pages
118--225]{Swartzlander:1990:CAa}.",
URL = "http://en.wikipedia.org/wiki/Dadda_multiplier;
http://en.wikipedia.org/wiki/luigi_dadda",
acknowledgement = ack-nhfb,
author-dates = "29 April 1923--26 October 2012",
fjournal = "Alta frequenza",
remark = "According to an ARITH'21 conference attendee, this is
a recommended article for understanding the Wallace and
Dadda multipliers.",
}hemes for Parallel Multipliers
@Article{Dadda:1965:SSP,
author = "Luigi Dadda",
title = "Some Schemes for Parallel Multipliers",
journal = j-ALTA-FREQ,
volume = "34",
number = "??",
pages = "349--356",
month = mar,
year = "1965",
CODEN = "ALFRAJ",
ISSN = "0002-6557",
ISSN-L = "0002-6557",
bibdate = "Fri Nov 09 10:47:42 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[pages
118--225]{Swartzlander:1990:CAa}.",
URL = "http://en.wikipedia.org/wiki/Dadda_multiplier;
http://en.wikipedia.org/wiki/luigi_dadda",
acknowledgement = ack-nhfb,
author-dates = "29 April 1923--26 October 2012",
fjournal = "Alta frequenza",
remark = "According to an ARITH'21 conference attendee, this is
a recommended article for understanding the Wallace and
Dadda multipliers.",
}
`X #)#W#77=m;};)
I#WIarticlefparith.bibDadda:1965:SSPLuigi DaddaSome Schemes for Parallel Multipliersj-ALTA-FREQ34349--356mar31965ALFRAJ0002-6557 OR 000265570002-6557 OR 00026557Fri Nov 09 10:47:42 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.09 10:47:42 ???Reprinted in cite [pages 118--225]Swartzlander:1990:CAa.http://en.wikipedia.org/wiki/Dadda_multiplier; http://en.wikipedia.org/wiki/luigi_daddaAlta frequenzaAccording to an ARITH'21 conference attendee, this is a recommended article for understanding the Wallace and Dadda multipliers.ack-nhfb29 April 1923--26 October 2012Luigi DaddaReprinted in \cite[pages 118--225]{Swartzlander:1990:CAa}.Some ScWof a Diode Squarer by Applying the
Criterion of Square Root of the Integral of Per Cent
Error Squared",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "3",
pages = "456--463",
month = jun,
year = "1965",
CODEN = "IEECA8",
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acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
} Applying the Criterion of Square Root of the Integral of Per Cent Error Squared
@Article{Deiters:1965:ODD,
author = "Robert M. Deiters",
title = "Optimum Design of a Diode Squarer by Applying the
Criterion of Square Root of the Integral of Per Cent
Error Squared",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "3",
pages = "456--463",
month = jun,
year = "1965",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1965.264153",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:34 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=4038465",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
%%O Y #-/u=a7E;_/uearticlefparith.bibDeiters:1965:ODDRobert M. DeitersOptimum Design of a Diode Squarer by Applying the Criterion of Square Root of the Integral of Per Cent Error Squaredj-IEEE-TRANS-ELEC-COMPUTEC-143456--463jun61965IEECA8http://dx.doi.org/10.1109/PGEC.1965.2641530367-7508 OR 03677508Thu Jul 14 06:26:34 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 06:26:34 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038465IEEE Transactions on Electronic Computersack-nhfbRobert M. DeitersOptimum Design of a Diode Squarer byZ] of {Boolean} Functions",
journal = j-CACM,
volume = "8",
number = "8",
pages = "517--517",
month = aug,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:01 MST 2005",
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http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Recently M. Morris Mano presented a method for
performing Boolean OR, AND and NOT operations by means
of arithmetic and conditional transfer operations in a
decimal computer lacking builtin logical
instructions.",
acknowledgement = ack-nhfb,
checked = "19940407",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "Boolean operations; decimal arithmetic",
sjb = "Commenting on \cite{Mano:1965:PSB}.",
}
..u&o(Q
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ԆH
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author = "Richard P. Brent",
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journal = j-CACM,
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number = "8",
pages = "517--517",
month = aug,
year = "1965",
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ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:01 MST 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
http://www.acm.org/pubs/contents/journals/cacm/;
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http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Recently M. Morris Mano presented a method for
performing Boolean OR, AND and NOT operations by means
of arithmetic and conditional transfer operations in a
decimal computer lacking builtin logical
instructions.",
acknowledgement = ack-nhfb,
checked = "19940407",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
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sjb = "Commenting on \cite{Mano:1965:PSB}.",
}
QQ
Y #')a57E);3?Yc3)e7articlefparith.bibDodd:1965:RSBGeorge G. DoddRemarks on Simulation of Boolean Functionsj-CACM88517--517aug81965CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Fri Nov 25 18:20:01 MST 2005ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib; http://www.acm.org/pubs/co_r",
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pages = "909--910",
month = mar,
year = "1965",
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}nd arithmetic",
crossref = "Alt:1965:AC",
volume = "6",
pages = "131--194",
year = "1965",
bibdate = "Sat May 18 14:18:19 2002",
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?
Y #+%=a7EU;__%#articlefparithg=U %#+%G#=m;%Gm@incollectionfparith.bibGarner:1965:NSAH. L. GarnerNumber systems and arithmeticAlt:1965:AC6131--1941965Sat May 18 14:18:19 2002http://www.math.utah.edu/pub/tex/bib/fparith.bib2002.05.18 14:18:19 ???ack-nhfbH. L. GarnerNumber systems and arithmetic
@InCollection{Garner:1965:NSA,
author = "H. L. Garner",
title = "Number systems and arithmetic",
crossref = "Alt:1965:AC",
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pages = "131--194",
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bibdate = "Sat May 18 14:18:19 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}ing
Residue Number Theory",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
pages = "277--277",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1965.263975",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:23 MDT 2011",
bibsource = "http://ieeexplore.ieee.org/;
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acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
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}
h.bibGarner:1965:RIDH. L. GarnerR65-22 Improving Digital Computer Performance Using Residue Number Theoryj-IEEE-TRANS-ELEC-COMPUTEC-142277--277apr41965IEECA8http://dx.doi.org/10.1109/PGEC.1965.2639750367-7508 OR 03677508Thu Jul 14 06:26:23 MDT 2011http://ieeexplore.ieee.org/; http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 06:26:23 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038430; http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4038385IEEE Transactions on Electronic Computersresidue arithmetic; residue number systemack-nhfbH. L. Garner{R65-22} Improving Digital Computer Performance Using Residue Number Theory
@Article{Garner:1965:RID,
author = "H. L. Garner",
title = "{R65-22} Improving Digital Computer Performance Using
Residue Number Theory",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
pages = "277--277",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1965.263975",
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bibdate = "Thu Jul 14 06:26:23 MDT 2011",
bibsource = "http://ieeexplore.ieee.org/;
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acknowledgement = ack-nhfb,
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}mputer Arithmetic",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "4",
pages = "670--670",
month = aug,
year = "1965",
CODEN = "IEECA8",
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bibdate = "Thu Jul 14 06:26:40 MDT 2011",
bibsource = "http://www.computer.org/tc/;
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}anscomput.bib2011.07.14 06:26:40 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038535IEEE Transactions on Electronic Computersack-nhfbD. Hammel{R65-54} The Logic of Computer Arithmetic
@Article{Hammel:1965:RLC,
author = "D. Hammel",
title = "{R65-54} The Logic of Computer Arithmetic",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "4",
pages = "670--670",
month = aug,
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GG-W #+[=a7E;__yarticlefparith.bibHammel:1965:RLCD. HammelR65-54 The Logic of Computer Arithmeticj-IEEE-TRANS-ELEC-COMPUTEC-144670--670aug81965IEECA8http://dx.doi.org/10.1109/PGEC.1965.2640310367-7508 OR 03677508Thu Jul 14 06:26:40 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetrjem Experimental Arithmetic, High Speed
Computing and Mathematics} by N. C. Metropolis, A. H.
Taub, John Todd, and C. B. Tompkins}",
journal = j-TECHNOMETRICS,
volume = "7",
number = "1",
pages = "82--82",
month = feb,
year = "1965",
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bibdate = "Tue Mar 20 13:44:52 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
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acknowledgement = ack-nhfb,
fjournal = "Technometrics",
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@Article{Hammer:1965:BRE,
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title = "Book Review: {{\em Experimental Arithmetic, High Speed
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Taub, John Todd, and C. B. Tompkins}",
journal = j-TECHNOMETRICS,
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URL = "http://links.jstor.org/sici?sici=0040-1706%28196502%297%3A1%3C82%3AEAHSCA%3E2.0.CO%3B2-9",
acknowledgement = ack-nhfb,
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- -HZ#-I=a7E ;_'Icarticlefparith.bibHamming:1965:NLBR. W. Hamming and W. L. MammelA Note on the Location of the Binary Point in a ComputinqkZ #+/%+57={;='//-articlefparith.bibHammer:1965:BREPreston C. HammerBook Review: em Experimental Arithmetic, High Speed Computing and Mathematics by N. C. Metropolis, A. H. Taub, John Todd, and C. B. Tompkinsj-TECHNOMETRICS7182--82feb21965TCMTA20040-1706 (print), 1537-2723 (electronic) OR 00401706 (print), 15372723 (electronic)0040-1706 OR 00401706Tue Mar 20 13:44:52 2007http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.03.20 13:44:52 ???http://links.jstor.org/sici?sici=0040-1706%28196502%297%3A1%3C82%3AEAHSCA%3E2.0.CO%3B2-9Technometricsack-nhfbPreston C. HammerBook Review: {{\em Experimental ArithmpNote on the Location of the Binary Point in a
Computing Machine",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
pages = "260--261",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1965.264258",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:22 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038414",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
remark = "The authors consider the low-level multiplication
circuit efficiency of placing the binary point before
or after the first bit. If the leading bit is equally
likely to be a 0 or a 1, then their analysis shows that
it is better to place the point before the leading bit.
However, they report that a more likely distribution is
logarithmic (as predicted by Benford's Law, although
the Newcomb / Benford work is neither mentioned nor
cited), in which case there is no advantage for either
choice of placement of the binary point. The conclude
that it would be humane to place it after the leading
digit, by analogy with how people learn decimal
arithmetic.",
}rg Machinej-IEEE-TRANS-ELEC-COMPUTEC-142260--261apr41965IEECA8http://dx.doi.org/10.1109/PGEC.1965.2642580367-7508 OR 03677508Thu Jul 14 06:26:22 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 06:26:22 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038414IEEE Transactions on Electronic ComputersThe authors consider the low-level multiplication circuit efficiency of placing the binary point before or after the first bit. If the leading bit is equally likely to be a 0 or a 1, then their analysis shows that it is better to place the point before the leading bit. However, they report that a more likely distribution is logarithmic (as predicted by Benford's Law, although the Newcomb / Benford work is neither mentioned nor cited), in which case there is no advantage for either choice of placement of the binary point. The conclude that it wousld be humane to place it after the leading digit, by analogy with how people learn decimal arithmetic.ack-nhfbR. W. Hamming and W. L. MammelA Note on the Location of the Binary Point in a Computing Machine
@Article{Hamming:1965:NLB,
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title = "A Note on the Location of the Binary Point in a
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it is better to place the point before the leading bit.
However, they report that a more likely distribution is
logarithmic (as predicted by Benford's Law, although
the Newcomb / Benford work is neither mentioned nor
cited), in which case there is no advantage for either
choice of placement of the binary point. The conclude
that it would be humane to place it after the leading
digit, by analogy with how people learn decimal
arithmetic.",
}usion Floating-Point Arithmetic
with 132-Bit Numbers",
journal = j-CACM,
volume = "8",
number = "3",
pages = "175--177",
month = mar,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00",
MRnumber = "30\#2707",
bibdate = "Fri Dec 08 14:32:51 1995",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In a recent paper, Gregory and Raney described a
technique for double-precision floating-point
arithmetic. A similar technique can be developed for
triple-precision floating-point arithmetic and its is
the purpose of this note to describe this technique.
Only the multiplication and the division algorithms are
described, since the addition-subtraction algorithm can
be obtained by a trivial modification of the algorithm
in Gregory's and Raney's paper.",
acknowledgement = ack-nhfb,
checked = "19940404",
fjournal = "Communications of the ACM",
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}with.bibIkebe:1965:NTPYasuhiko IkebeNote on Triple-Precision Floating-Point Arithmetic with 132-Bit Numbersj-CACM83175--177mar31965CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 0001078268.0030\#2707Fri Dec 08 14:32:51 1995ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 14:32:51 ???In a recent paper, Gregory and Raney described a technique for double-precision floating-point arithmetic. A similar technique can be developed for triple-precision floating-point arithmetic and its is the purpose of this note to describe this technique. Only the multiplication and the division algorithms are described, since the addition-subtraction algorithm can be obtained by a trivial modification of the algorithm in Gregory's and Raney's paper.Communications of the ACMack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79In a recent paper, Gregory and Raney described a technique for double-precision floaxting-point arithmetic. A similar technique can be developed for triple-precision floating-point arithmetic and its is the purpose of this note to describe this technique. Only the multiplication and the division algorithms are described, since the addition-subtraction algorithm can be obtained by a trivial modification of the algorithm in Gregory's and Raney's paper.Yasuhiko IkebeNote on Triple-Precision Floating-Point Arithmetic with 132-Bit Numbers
@Article{Ikebe:1965:NTP,
author = "Yasuhiko Ikebe",
title = "Note on Triple-Precision Floating-Point Arithmetic
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abstract = "In a recent paper, Gregory and Raney described a
technique for double-precision floating-point
arithmetic. A similar technique can be developed for
triple-precision floating-point arithmetic and its is
the purpose of this note to describe this technique.
Only the multiplication and the division algorithms are
described, since the addition-subtraction algorithm can
be obtained by a trivial modification of the algorithm
in Gregory's and Raney's paper.",
acknowledgement = ack-nhfb,
checked = "19940404",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
Y#)A'57E?;A=Ayarticlefparith.bibJames:1965:GSRWendy James and P. JarrattThe Generation of Square Roots on a Computer with Rapid Multiplication Compared with Division (in Technical Notes and Short Papers)j-MATH-COMPUT1991497--500jul71965MCMPAF0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)0025-5718 OR 00255718Tue Oct 13 08:06:19 MDT 1998ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database1998.10.13 08:06:19 MDTMathematics of Computationack-njhttp://www.ams.org/mcom/Wendy James and P. JarrattThe Generation of Square Roots on a Computer with Rapid Multipl{[[ #))57=a;?c)qarticlefparvration of Square Roots on a Computer with
Rapid Multiplication Compared with Division (in
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journal = j-MATH-COMPUT,
volume = "19",
number = "91",
pages = "497--500",
month = jul,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
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bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nj # " and " # ack-nhfb,
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journal-URL = "http://www.ams.org/mcom/",
}ication Compared with Division (in {Technical Notes and Short Papers})
@Article{James:1965:GSR,
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title = "The Generation of Square Roots on a Computer with
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volume = "19",
number = "91",
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}e Manual",
title = "The Floating-Point Over\slash Underflow Trap Routine
{{\tt FPTRP}}",
publisher = "Institute of Computer Science, University of Toronto",
address = "Toronto, Ontario, Canada",
year = "1965",
LCCN = "????",
bibdate = "Wed Feb 14 19:11:11 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Section 4.1.",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
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@InCollection{Kahan:1965:FPO,
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title = "The Floating-Point Over\slash Underflow Trap Routine
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journal = j-CACM,
volume = "8",
number = "1",
pages = "40--40",
month = jan,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 00:18:17 1994",
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acknowledgement = ack-nj,
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remark = "Gives summation error estimate formula `s = fl(a + b);
error = (a - s) + b', also discovered independently by
\cite{Moller:1965:QDP}. Extends Gill's earlier
fixed-point result \cite{Gill:1951:PSS}. Cited in
\cite{Sterbenz:1974:FPC}.",
}
++rL&A
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@Article{Caprani:1971:ILR,
author = "Ole Caprani",
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@Article{Kahan:1965:FRR,
author = "W. Kahan",
title = "Further Remarks on Reducing Truncation Errors",
journal = j-CACM,
volume = "8",
number = "1",
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bibdate = "Thu Sep 08 00:18:17 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
remark = "Gives summation error estimate formula `s = fl(a + b);
error = (a - s) + b', also discovered independently by
\cite{Moller:1965:QDP}. Extends Gill's earlier
fixed-point result \cite{Gill:1951:PSS}. Cited in
\cite{Sterbenz:1974:FPC}.",
}
F"V #+)y57=m;1Me)y5articlefparith.bibKanner:1965:NBCHerbert KannerNumber Base Conversion in Significant Digit Arithmeticj-J-ACM122242--246apr41965JACOAH0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (e.W #)g57=m;?Qcgarticlefparith.bibKahan:1965:FRRW. KahanFurther Remarks on Reducing Truncation Errorsj-CACM8140--40jan11965CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Thu Sep 08 00:18:17 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.08 00:18:17 ???Communications of the ACMGives summation error estimate formula `s = fl(a + b); error = (a - s) + b', also discovered independently by cite Moller:1965:QDP. Extends Gill's earlier fixed-point result cite Gill:1951:PSS. Cited in cite Sterbenz:1974:FPC.ack-njhttp://portal.acm.org/browse_dl.cion in Significant Digit
Arithmetic",
journal = j-J-ACM,
volume = "12",
number = "2",
pages = "242--246",
month = apr,
year = "1965",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Thu Nov 03 08:47:50 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}lectronic)0004-5411 OR 00045411Thu Nov 03 08:47:50 1994http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.11.03 08:47:50 ???Journal of the ACMCited in cite Sterbenz:1974:FPC.ack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J401Herbert KannerNumber Base Conversion in Significant Digit Arithmetic
@Article{Kanner:1965:NBC,
author = "Herbert Kanner",
title = "Number Base Conversion in Significant Digit
Arithmetic",
journal = j-J-ACM,
volume = "12",
number = "2",
pages = "242--246",
month = apr,
year = "1965",
CODEN = "JACOAH",
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}he Double-Precision Square
Root Routine",
journal = j-CACM,
volume = "8",
number = "4",
pages = "202",
month = apr,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
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http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$\sqrt(x)$; elementary functions; floating-point
arithmetic",
}ck-njhttp://portal.acm.org/browse_dl.cfm?idx=J79R. KingLetter to the {Editor}: On the Double-Precision Square Root Routine
@Article{King:1965:LED,
author = "R. King",
title = "Letter to the {Editor}: On the Double-Precision Square
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journal = j-CACM,
volume = "8",
number = "4",
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TZ #'57;1;?carticlefparith.bibKing:1965:LEDR. KingLetter to the Editor: On the Double-Precision Square Root Routinej-CACM84202apr41965CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Thu Sep 1 10:15:43 1994ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:43 ???Communications of the ACM$sqrt (x)$; elementary functions; floating-point arithmeticavide-and-Correct Method for Variable Precision
Division",
journal = j-CACM,
volume = "8",
number = "3",
pages = "179--181",
month = mar,
year = "1965",
CODEN = "CACMA2",
DOI = "http://doi.acm.org/10.1145/363791.363829",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00",
MRnumber = "30\#2709",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
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http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Described in this paper is a divide-and-correct method
for variable precision division in digital computers.
Unlike the earlier methods of Stein and Pope, the
present method uses a suitably rounded form of the
normalized divisor for getting an estimate of the
quotient characters. This result is a correction of at
most plus or minus one to the estimate, to obtain the
exact quotient character. It is believed that this
method will be widely applicable for division
operations in variable word-length character-oriented
machines.",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "floating-point arithmetic",
} is a divide-and-correct method for variable precision division in digital computers. Unlike the earlier methods of Stein and Pope, the present method uses a suitably rounded form of the normalized divisor for getting an estimate of the quotient characters. This result is a correction of at most plus or minus one to the estimate, to obtain the exact quotient character. It is believed that this method will be widely applicable for division operations in variable word-length character-oriented machines.Communications of the ACMfloating-point arithmeticack-njhttp://portal.acm.org/browse_dl.cfm?idx=J79Described in this paper is a divide-and-correct method for variable precision division in digital computers. Unlike the earlier methods of Stein and Pope, the present method uses a suitably rounded form of the normalized divisor for getting an estimate of the quotient characters. This result is a correction of at most plus or minus one to the estimate, to obtain the exact quotient character. It is believed that this method will be widely applicable for division operations in variable word-length character-oriented machines.E. V. KrishnamurthyOn a Divide-and-Correct Method for Variable Precision Division
@Article{Krishnamurthy:1965:DCM,
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abstract = "Described in this paper is a divide-and-correct method
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acknowledgement = ack-nj,
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%%G[ #93 ]57;;/??c/3 warticlefparith.bibKrishnamurthy:1965:DCME. V. KrishnamurthyOn a Divide-and-Correct Method for Variable Precision Divisionj-CACM83179--181mar31965CACMA2http://doi.acm.org/10.1145/363791.3638290001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 0001078268.0030\#2709Thu Sep 1 10:15:08 1994ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib; ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:15:08 ???Described in this papersus, {FLPPEG}",
type = "{ISD-Bericht}",
number = "12",
institution = "ISD, Inst. f{\"u}r Statik u. Dynamik d. Luft- u.
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bibdate = "Thu May 09 09:05:51 2002",
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--OV !#-!I#C1=m;!MEtechreportfparith.bibLederer:1965:FPPE. LedererFloating-point-Pegasus, FLPPEGISD-Bericht12ISD, Inst. fur Statik u. Dynamik d. Luft- u. Raumfahrtkonstruktionen, Universitat StuttgartStuttgart, Germany51965Thu May 09 09:05:51 2002http://www.math.utah.edu/pub/tex/bib/fparith.bib2002.05.09 09:05:51 ???ack-nhfbE. LedererFloating-point-Pegasus, {FLPPEG}
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}Techniques",
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pages = "715--725",
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bibdate = "Tue Jan 08 23:08:35 2008",
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ZZ"U '#+E)=m;EAinproceedingsfparith.bibLehman:1965:SATM. LehmanSerial Arithmetic TechniquesAFIPS:1965:FJC715--7251965Tue Jan 08 23:08:35 2008http://www.math.utah.edu/pub/tex/bib/fparith.bib2008.01.08 23:08:35 ???ack-nhfbM. LehmanSerial Arithmetic Techniques
@InProceedings{Lehman:1965:SAT,
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bibdate = "Tue Jan 08 23:08:35 2008",
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type = "Thesis ({M.S.})",
school = "University of Minnesota",
address = "????",
pages = "various",
year = "1965",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
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<<@U '#/?a';Em;W?amastersthesisfparith.bibLiddiard:1965:DPFLawrence Anthony LiddiardDouble precision floating point arithmeticThesis (M.S.)University of Minnesotavarious1965Sat Feb 24 15:01:45 MST 1996http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MSTCalculators.; Numerical calculations.ack-nhfbLawrence Anthony LiddiardDouble precision floating point arithmetic
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year = "1965",
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note = "Translated from the Russian by G. J. Tee. Translation
edited by K. L. Stewart.",
acknowledgement = ack-nj,
}c-soft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:13:16 ???Translated from the Russian by G. J. Tee. Translation edited by K. L. Stewart.ack-njL. A. Lyusternik and O. A. Chervonenkis and A. R. YanpolskiTranslated from the Russian by G. J. Tee. Translation edited by K. L. Stewart.Handbook for Computing Elementary Functions
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acknowledgement = ack-nj,
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=?=vW#+O]=a7E;_O]'articlefparith.bibMartin:1965:SHSA. R. Martin and A. B. RosensteinA Shiftrix for High-Speed Multiplicationj-IEEE-TRANS-ELEC-COMPUTEC-144639--643aug81965IEECA8http://dx.doi.org/10.1109/PGEC.1965.2640100367-7508 OR 03677508Thu Jul 14 06:26:39 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 06:26:39 MDThttp://ieeY #')57E);K?c)OOarticlefparitFZ#3c%-!!;K;))c=bookfparith.bibLyusternik:1965:HCEL. A. Lyusternik and O. A. Chervonenkis and A. R. YanpolskiHandbook for Computing Elementary Functionspub-PERGAMONpub-PERGAMON:adrxiii + 2511965QA221.L513Thu Sep 1 10:13:16 1994ftp://garbo.uwasa.fi/pc/doon} of {Boolean} functions in a
decimal computer",
journal = j-CACM,
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number = "1",
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bibdate = "Fri Nov 25 18:19:58 MST 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
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http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
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note = "See remarks \cite{Dodd:1965:RSB}.",
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checked = "19940304",
fjournal = "Communications of the ACM",
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sjb = "Describes how to perform Boolean operations by means
of arithmetic and conditional transfer operations on a
decimal computer lacking any built in logical
instructions. See also \cite{Dodd:cacm:65}.",
}h.bibMano:1965:PSBM. Morris ManoPracniques: Simulation of Boolean functions in a decimal computerj-CACM8139--40jan11965CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Fri Nov 25 18:19:58 MST 2005ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib; http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:58 MSTSee remarks cite Dodd:1965:RSB.Communications of the ACMack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79M. Morris ManoSee remarks \cite{Dodd:1965:RSB}.Pracniques: {Simulation} of {Boolean} functions in a decimal computer
@Article{Mano:1965:PSB,
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}A Shiftrix for High-Speed Multiplication",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "4",
pages = "639--643",
month = aug,
year = "1965",
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}explore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038521IEEE Transactions on Electronic Computersack-nhfbA. R. Martin and A. B. RosensteinA Shiftrix for High-Speed Multiplication
@Article{Martin:1965:SHS,
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}f Inherent Errors in Matrix Decomposition
Using Unnormalized Arithmetic",
crossref = "Kalenich:1965:IPP",
volume = "2",
pages = "441--442",
year = "1965",
bibdate = "Wed Feb 14 19:21:38 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
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ZMnumber = "0161.35502",
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author = "Joseph D. Darcy",
title = "{Borneo 1.0}:2݃G
@MastersThesis{Daumas:1992:BIR,
author = "Marc Daumas",
title = "Basis for the im$I
@MastersThesis{Davies:1991:FPS,
author = "Davies, T. C. (Tudor Craddock)",
title = "Z_?
@MastersThesis{Delgado:1993:DSP,
author = "Maria Luisa Delgado",
title = "Design '|y
@MastersThesis{Dickinson:1976:PAA,
author = "Fred Kenneth Dickinson",
title = "Ps
@MastersThesis{Du:1992:CAB,
author = "Sihai Du",
title = "Cellular automata based%#!
@MastersThesis{Duerksen:1988:CAP,
author = "Joel L. Duerksen",
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title = "Maximal Clock ors in Matrix Decomposition Using Unnormalized ArithmeticKalenich:1965:IPP2441--4421965Wed Feb 14 19:21:38 2007http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.02.14 19:21:38 ???Cited in cite Sterbenz:1974:FPC.0161.35502ack-nhfbN. MetropolisAnalysis of Inherent Errors in Matrix Decomposition Using Unnormalized Arithmetic
@InProceedings{Metropolis:1965:AIE,
author = "N. Metropolis",
title = "Analysis of Inherent Errors in Matrix Decomposition
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crossref = "Kalenich:1965:IPP",
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bibdate = "Wed Feb 14 19:21:38 2007",
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Y #3'%!57-={;7S'1)articlefparith.bibMetropolis:1965:BAUN. MetropolisBerichtigung: Algorithms in unnormalized arithmetic. I. Recurrence relationsj-NUM-MATH74354aug81965NUMMA70029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)0029-599X OR 0029599XContributed ItemMR1553943Wed Nov 14 19:04:40 2007http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11. "Radix Conversion in an Unnormalized Arithmetic
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journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
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bibdate = "Thu Jul 14 06:26:22 MDT 2011",
bibsource = "http://www.computer.org/tc/;
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@Article{Metze:1965:MSR,
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title = "Minimal Square Rooting",
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+rL&+-
@ArticldI
@Article{Meter:2008:ADM,
author = "Rodney Van Meter and W. J. Munro and Kae Nemoto and
J0a
@Article{Meissner:1995:EAD,
author = "Loren P. Meissner",
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author = "Guillaume Melquiond and Sylvain Pion",
title = H<y
@Article{Menzel:1967:AUA,
author = "M. Menzel and N. Metropolis",
title = "Algorio_
@Article{Meo:1975:ANT,
author = "A. R. Meo",
title = "Arithmetic Networks and The
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@Article{Merrill:1964:IDC,
author = "Roy D. Merrill",
title = "Improving Digital .dI
@Article{Messine:2002:EAA,
author = "F. Messine",
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@Article{Henrici:1966:TPM,
author = "Peter Henrici",
title = "Test of probabilistic models for the propagation of
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journal = j-CACM,
volume = "9",
number = "6",
pages = "409--410",
month = jun,
year = "1966",
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