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;;:Z #1!{57EU;G3]articlefparith.bibAnonymous:1875:AOMAnonymousThe Arithmetical Operations of Multiplication and Divisionj-SCI-AMER32341--4216jan11875SCAMAChttp://dx.doi.org/10.1038/scientificamerican01161875-410036-8733 (print), 1946-7087 (electronic) OR 00368733 (print), 19467087 (electronic)0036-8733 OR 00368733Fri May 17 10:29:24 MDT 2013http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/sciam1870.bib2013.05.17 10:29:24 MDThttp://www.nature.com/scientificamerican/journal/v32/n3/pdf/scientificamerican01161875-41.pdfScientific Americanack-nhfbhttp://www.nature.com/scientificamericanAnviating Multiplication",
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abstract = "That the ten digits do not occur with equal frequency
must be evident to any one making much use of
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first pages wear out than the last ones. The first
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acknowledgement = ack-nhfb,
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}11893-309b.pdfScientific Americanack-nhfbhttp://www.nature.com/scientificamericanDorr E. FeltMechanical Arithmetic
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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",
}Xbolic Analysis of Relay and Switching Circuits",
type = "{Master of Science}",
school = "Department of Electrical Engineering, MIT",
address = "Cambridge, MA, USA",
pages = "72",
day = "10",
month = aug,
year = "1937",
bibdate = "Thu Nov 18 10:35:20 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Not submitted until 1940",
URL = "http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425.pdf",
acknowledgement = 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.''",
}Zlished when he was twenty-two, is considered to be one of the most important, if not the most important, master's thesis of the twentieth century.''par Pages 59--61 of the thesis are a section called ``Electric Adder to the Base Two'', and pages 62--68, ``A Factor Table Machine'', describe a machine that will print a table of factors and primes of all the integers from 1 to 100,000,000. Shannon notes on page 68: ``As to the practicality of such a device, it might be said that J. P. Kulik spent 20 years in constructing a table of primes up to 100,000,000 and when finished it was found to contain so many errors that it was not worth publishing. The machine described here could probably be made to handle 5 numbers per second so that the table would require only about 2 months to construct.''ack-nhfbApril 30, 1916--February 24, 2001Claude Elwood ShannonNot submitted until 1940A Symbolic Analysis of Relay and Switching Circuits
@MastersThesis{Shannon:1937:SAR,
author = "Claude Elwood Shannon",
title [= "A Symbolic Analysis of Relay and Switching Circuits",
type = "{Master of Science}",
school = "Department of Electrical Engineering, MIT",
address = "Cambridge, MA, USA",
pages = "72",
day = "10",
month = aug,
year = "1937",
bibdate = "Thu Nov 18 10:35:20 2010",
bibsource = "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 NumbersbCW '#-7s/_1=m;=
=O7=s%mastersthesisfparith.bibShannon:1937:SARClaude Elwood ShannonA Symbolic Analysis of Relay and Switching CircuitsMaster of ScienceDepartment of Electrical Engineering, MITCambridge, MA, USA7210aug81937Thu Nov 18 10:35:20 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.11.18 10:35:20 ???Not submitted until 1940http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425.pdfSmiley cite [p. 91]Smiley:2010:MWI claims: ``He [Shannon] also had the insight, like Atanasoff, that the binary arithmetic that relay switches represented would simplify information systems. His master's thesis, written when he as twenty-one and pubY^s 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 differen_t
sources shows that the numbers taken from unrelated
subjects, such as a group of newspaper items, show a
much better agreement with a logarithmic distribution
than do numbers from mathematical tabulations or other
formal data. There is here the peculiar fact that
numbers that individually are without relationship are,
when considered in large groups, in good agreement with
a distribution law---hence the name ``Anomalous
Numbers.''\par
A further analysis of the data shows a strong tendency
for bodies of numerical data to fall into geometric
series. If the series is made up of numbers containing
three or more digits the first digits form a
logarithmic series. If the numbers contain only single
digits the geometric relation still holds but the
` simple logarithmic relation no longer applies.\par
An equation is given showing the frequencies of first
digits in the different orders of numbers 1 to 10, 10
to 100, etc.\par
The equation also gives the frequency of digits in the
second, third + place of a multi-digit number, and it
is shown that the same law applies to
reciprocals.\par
There are many instances showing that the geometric
series, or the logarithmic law, has long been
recognized as a common phenomenon in factual literature
and in the ordinary affairs of life. The wire gauge and
drill gauge of the mechanic, the magnitude scale of the
astronomer and the sensory response curves of the
psychologist are all particular examples of a
relationship that seems to extend to all human affairsa.
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.",
}cj-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 ind 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 astroenomer and the sensory response curves of the psychologist are all particular examples of a relationship that seems to extend to all human affairs. The Law of Anomalous Numbers is thus a general probability law of widespread application.Proceedings of the American Philosophical Society held at Philadelphia for promoting useful knowledgeBenford's Law; Law of Anomalous Numbers; Zipf's LawFrom cite Logan:1978:FDP: ``Benford's paper was published in 1938 in a journal of rather limited circulation and not usually read by mathematicians. It so happened that it was immediately followed in the same issue by a physics paper which became of some importance for secret nuclear work during World War II [H. A. Bethe, M. E. Rose, and L. P. Smith, `The Multiple Scattering of Electrons', Proc. Amer. Phil. Soc. 78(4), 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] fcontaining an effort to explain Benford's law. We considered it at that time merely a welcome diversion and did not expect that over thirty papers would be devoted to this subject in subsequent years.'' The 2006 bibliography cite Hurlimann:2006:BLB cites 325 publications about Benford's Law.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 gare 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 gauhge of the mechanic, the magnitude scale of the astronomer and the sensory response curves of the psychologist are all particular examples of a relationship that seems to extend to all human affairs. The Law of Anomalous Numbers is thus a general probability law of widespread application.Frank BenfordThe Law of Anomalous Numbers
@Article{Benford:1938:LAN,
author = "Frank Benford",
title = "The Law of Anomalous Numbers",
journal = 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 liast
pages, indicating that more used numbers begin with the
digit 1 than with the digit 9. A compilation of some
20,000 first digits taken from widely divergent sources
shows that there is a logarithmic distribution of first
digits when the numbers are composed of four or more
digits. An analysis of the numbers from different
sources shows that the numbers taken from unrelated
subjects, such as a group of newspaper items, show a
much better agreement with a logarithmic distribution
than do numbers from mathematical tabulations or other
formal data. There is here the peculiar fact that
numbers that individually are without relationship are,
when considered in large groups, in good agreement with
a distribution law---hence the name ``Anomalous
Numbers.''\pajr
A further analysis of the data shows a strong tendency
for bodies of numerical data to fall into geometric
series. If the series is made up of numbers containing
three or more digits the first digits form a
logarithmic series. If the numbers contain only single
digits the geometric relation still holds but the
simple logarithmic relation no longer applies.\par
An equation is given showing the frequencies of first
digits in the different orders of numbers 1 to 10, 10
to 100, etc.\par
The equation also gives the frequency of digits in the
second, third + place of a 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 lokng been
recognized as a common phenomenon in factual literature
and in the ordinary affairs of life. The wire gauge and
drill gauge of the mechanic, the magnitude scale of the
astronomer and the sensory response curves of the
psychologist are all particular examples of a
relationship that seems to extend to all human affairs.
The Law of Anomalous Numbers is thus a general
probability law of widespread application.",
acknowledgement = 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",
}
+&+Lr
@Article{Ahmadifar:2015:NRN,
author = "H. Ahmadifar and G. Jaberipur",
title = "AT29s
@Article{Akbarpour:2002:FCS,
author = "Behzad Akbarpour and Abdelkader Dekdouk and
<[9
@Article{Akamine:1983:SMQ,
author = "Masami Akamine and Tatsuo Higuchi",
title = #D
@Article{Ait-Ameur:1999:RRE,
author = "Y. Ait-Ameur",
title = "Refinement of rati4X1
@Article{Aird:1973:SUM,
author = "T. Aird and D. Dodson and E. Houstis and J. Rice",
titJ>}
@Article{Aiken:1964:PAC,
author = "H. H. Aiken",
title = "Proposed automatic calc:A
@Article{Aiken:1946:ASC,
author = "H. H. Aiken and G. M. Hopper",
title = "The {Azu
@Article{Ahmadi:2008:PFS,
author = "O. Ahmadi and D. Hankerson and F.
RodJ
@Article{Ahmad:1987:IDA,
author = "M. Ahmad",
title = "Implementable Decimal Aritx machines {\`a} calculer et aux calculs de la m{\'e}canique c{\'e}leste. ({French}) [{On} mechanical analysis. Application to calculating machines and to calculation in celestial mechanics]
@PhdThesis{Couffignal:1938:AMA,
author = "L. Couffignal",
title = "Sur l'analyse m{\'e}canique. Application aux machines
{\`a} calculer et aux calculs de la m{\'e}canique
c{\'e}leste. ({French}) [{On} mechanical analysis.
Application to calculating machines and to calculation
in celestial mechanics]",
publisher = "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 aun 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,
}sysis 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.''",
} uster's thesis). In 1940, it received the Alfred Noble Prize of the combined engineering societies of the United States, an award given each year to a person not over thirty for a paper published in one of the journals of the participating societies. H. H. Goldstine cite Goldstine:1972:CPN called this work ``one of the most important master's theses ever written ... a landmark in that it helped to change digital circuit design from an art to a science.''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.''",
}
Y #-/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 MatThe Artificial Arithmetick in Decimals of {Robert
Jager} ({London}, 1651)",
journal = j-ISIS,
volume = "31",
number = "1",
pages = "25--31",
month = nov,
year = "1939",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:26:49 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302217;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/isis1930.bib",
URL = "http://www.jstor.org/stable/226014",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/page/journal/isis/about.html",
}!ficial Arithmetick in Decimals of {Robert Jager} ({London}, 1651)
@Article{Jager:1939:AAD,
author = "Robert Jager and Boyd C. Patterson",
title = "The Artificial Arithmetick in Decimals of {Robert
Jager} ({London}, 1651)",
journal = j-ISIS,
volume = "31",
number = "1",
pages = "25--31",
month = nov,
year = "1939",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:26:49 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302217;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/isis1930.bib",
URL = "http://www.jstor.org/stable/226014",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/page/journal/isis/about.html",
}
g!Y#)Q57E;QoQarticlefparith.bibJager:1939:AADRobert Jager and Boyd C. PattersonThe Artificial Arithmetick in Decimals of Robert Jager (London, 1651)j-ISIS31125--31nov111939ISISA40021-1753 (print), 1545-6994 (electronic) OR 00211753 (print), 15456994 (electronic)0021-1753 OR 00211753Tue Jul 30 21:26:49 MDT 2013http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i302217; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/isis1930.bib2013.07.30 21:26:49 MDThttp://www.jstor.org/stable/226014Isisack-nhfbhttp://www.jstor.org/page/journal/isis/about.htmlRobert Jager and Boyd C. PattersonThe Artixdecimal Arithmetic}}, by
George S. Terry}",
journal = j-J-R-STAT-SOC,
volume = "102",
number = "2",
pages = "299--300",
month = "????",
year = "1939",
DOI = "http://dx.doi.org/10.2307/2980013",
bibdate = "Sat Jan 24 11:18:08 MST 2015",
bibsource = "http://www.jstor.org/stable/i349540;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jrss-a-1930.bib",
URL = "http://www.jstor.org/stable/2980013",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society",
}"tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/jrss-a-1930.bib2015.01.24 11:18:08 MSThttp://www.jstor.org/stable/2980013Journal of the Royal Statistical Societyack-nhfbM. G. K.Book Review: {{\booktitle{Duodecimal Arithmetic}}, by George S. Terry}
@Article{K:1939:BRBd,
author = "M. G. K.",
title = "Book Review: {{\booktitle{Duodecimal Arithmetic}}, by
George S. Terry}",
journal = j-J-R-STAT-SOC,
volume = "102",
number = "2",
pages = "299--300",
month = "????",
year = "1939",
DOI = "http://dx.doi.org/10.2307/2980013",
bibdate = "Sat Jan 24 11:18:08 MST 2015",
bibsource = "http://www.jstor.org/stable/i349540;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jrss-a-1930.bib",
URL = "http://www.jstor.org/stable/2980013",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society",
}
^ ^7$X #%5=m;#+5}miscfparith.bibBush:1940:AMV. BushArithmetical Machine299--3001940Wed Oct 13 11:37:32 2010http://ws#W !#1+/91'=m;_+g/qtechreportfparith.bibAtanasoff:~W"X ##
)OE#;S]articlefparith.bibK:1939:BRBdM. G. K.Book Review: booktitle Duodecimal Arithmetic, by George S. Terryj-J-R-STAT-SOC1022299--3001939http://dx.doi.org/10.2307/2980013Sat Jan 24 11:18:08 MST 2015http://www.jstor.org/stable/i349540; http://www.math.utah.edu/pub/{chine for the solution of large systems of
linear algebraic equations",
type = "Unpublished memorandum",
institution = "Iowa State College",
address = "Ames, IA, USA",
month = aug,
year = "1940",
bibdate = "Wed Oct 13 11:36:11 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}#1940:CMSJ. V. AtanasoffComputing machine for the solution of large systems of linear algebraic equationsUnpublished memorandumIowa State CollegeAmes, IA, USA299--300aug81940Wed Oct 13 11:36:11 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,
}%
w%U !#)'9C/=m;_'gtechreportfparith.bibStibitz:1940:CG. R. StibitzComputerUnpublished memorandumBell Telephone LaboratoriesNew York, NY, USA299--3001940Wed 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,
}of electrical data recording and reading
mechanism",
type = "{M.S.} thesis",
school = "Iowa State College",
address = "Ames, IA, USA",
pages = "32",
year = "1941",
bibdate = "Thu Nov 18 11:18:18 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
author-dates = "1918--1963",
historical-note = "From
http://www.lib.iastate.edu/arch/rgrp/5-2-1-1.html:
``John Vincent Atanasoff received his M.S. (1926) in
Mathematics from Iowa State College (University) and
received his Ph.D. (1930) in Theoretical Physics from
the University of Wisconsin-Madison. He returned to
Iowa State in 1930 as Assistant Professor in
mathematics and physics and was promoted to Associate
Professor (1936). Atanasoff began developing concepts
for an electronic computing machine in 1937. It was
shortly thereafter that he, along with graduate student
Clifford Berry, started work on the world's first
electronic digital computer. The computer would later
be named the Atanasoff-Berry Computer (ABC).
Work on the machine stopped at the start of World War
II in 1941 and the ABC was never patented. Atanasoff
and Berry were both called to support the war effort
and left Iowa State. By the end of the decade, the ABC
was removed from the basement of Physics Hall and
dismantled.
Atanasoff and the ABC were part of a major court case
between Honeywell, Inc. and Sperry Rand Corporation
which occurred 1967-1973. The case involved the ENIAC
patent which covered basic ownership rights to the
design of electronic digital computers. During the
trial, the judge concluded that the invention of the
ENIAC was derived from the work of John Vincent
Atanasoff at Iowa State University.
A replica of the Atanasoff-Berry Computer was completed
and unveiled to the public in 1996. The ABC replica was
constructed by a team of Iowa State scientists at the
Ames Laboratory and was exhibited at museums throughout
the country over the next several years.''",
remark = "This thesis may be one of the earliest surviving
records of the ABC computer built by John Atanasoff and
Clifford Berry in the late 1930s. The one-of-a-kind ABC
was destroyed in 1948, and most of its parts were lost.
Also cited in ``Charles W. Bradley Collection on the
ENIAC Trial, 1930--1966'', (found in
http://discover.lib.umn.edu/): CWB as an attorney for
the group retained by Honeywell in the Honeywell v.
Sperry Rand ENIAC trial. The ABC had a 50-bit word.",
}&ard BerryDesign of electrical data recording and reading mechanismM.S. thesisIowa State CollegeAmes, IA, USA321941Thu Nov 18 11:18:18 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.11.18 11:18:18 ???This thesis may be one of the earliest surviving records of the ABC computer built by John Atanasoff and Clifford Berry in the late 1930s. The one-of-a-kind ABC was destroyed in 1948, and most of its parts were lost. Also cited in ``Charles W. Bradley Collection on the ENIAC Trial, 1930--1966'', (found in http://discover.lib.umn.edu/): CWB as an attorney for the group retained by Honeywell in the Honeywell v. Sperry Rand ENIAC trial. The ABC had a 50-bit word.ack-nhfb1918--1963Clifford Edward BerryDesign of electrical data recording and reading mechanism
@MastersThesis{Berry:1941:DED,
author = "Clifford Edward Berry",
title = "Design of electrical data recording and reading
mechanism",
type = "{M.S.} thesis",
school = "Iowa State College",
address = "Ames, IA, USA",
pages = "32",
year = "1941",
bibdate = "Thu Nov 18 11:18:18 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
author-dates = "1918--1963",
historical-note = "From
http://www.lib.iastate.edu/arch/rgrp/5-2-1-1.html:
``John Vincent Atanasoff received his M.S. (1926) in
Mathematics from Iowa State College (University) and
received his Ph.D. (1930) in Theoretical Physics from
the University of Wisconsin-Madison. He returned to
Iowa State in 1930 as Assistant Professor in
mathematics and physics and was promoted to Associate
Professor (1936). Atanasoff began developing concepts
for an electronic computing machine in 1937. It was
shortly thereafter that he, along with graduate student
Clifford Berry, started work on the world's first
electronic digital computer. The computer would later
be named the Atanasoff-Berry Computer (ABC).
Work on the machine stopped at the start of World War
II in 1941 and the ABC was never patented. Atanasoff
and Berry were both called to support the war effort
and left Iowa State. By the end of the decade, the ABC
was removed from the basement of Physics Hall and
dismantled.
Atanasoff and the ABC were part of a major court case
between Honeywell, Inc. and Sperry Rand Corporation
which occurred 1967-1973. The case involved the ENIAC
patent which covered basic ownership rights to the
design of electronic digital computers. During the
trial, the judge concluded that the invention of the
ENIAC was derived from the work of John Vincent
Atanasoff at Iowa State University.
A replica of the Atanasoff-Berry Computer was completed
and unveiled to the public in 1996. The ABC replica was
constructed by a team of Iowa State scientists at the
Ames Laboratory and was exhibited at museums throughout
the country over the next several years.''",
remark = "This thesis may be one of the earliest surviving
records of the ABC computer built by John Atanasoff and
Clifford Berry in the late 1930s. The one-of-a-kind ABC
was destroyed in 1948, and most of its parts were lost.
Also cited in ``Charles W. Bradley Collection on the
ENIAC Trial, 1930--1966'', (found in
http://discover.lib.umn.edu/): CWB as an attorney for
the group retained by Honeywell in the Honeywell v.
Sperry Rand ENIAC trial. The ABC had a 50-bit word.",
}
q&'W #1/i/57E;SkW/i]articlefparith.bibLancaster:1942:MMEOtis E. LancasterMachine Method for the Extraction of Cube Rootj-J-AM-STAT-ASSOC37217112--115mar31942JSTNAL0162-1459 (print), 1537-274X (electronic) OR 01621459 (print), 1537274X (electronic)0162-1459 OR 01621459Wed Jan 25 08:05:24 MST 2012http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314096; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib2012.01.25 08:05:24 MSThttp://www.jstor.org/stable/2279437Journal of the American Statistical Associationack-nhfbhttp://www.tandfx&V '#)7#1'=m;-!7kmastersthesisfparith.bibBerry:1941:DEDClifford Edwd for the Extraction of Cube Root",
journal = j-J-AM-STAT-ASSOC,
volume = "37",
number = "217",
pages = "112--115",
month = mar,
year = "1942",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:24 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314096;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
URL = "http://www.jstor.org/stable/2279437",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}'
+Lr+&
@Article{Alam:1993:RTO,
author = "M. S. Alam and M. A. Karim",
title = "Real-Time'O
@Article{Al-Twaijry:1998:TSE,
author = "H. A. Al-Twaijry and M. J. Flynn",
title = 3f5
@Article{Al-Twaijry:1998:SPB,
author = "H. A. Al-Twaijry and S. F. Oberman and S. T. Fu an3c
@Article{Al-Mouhamed:1995:ELF,
author = "Mayez Al-Mouhamed and Lubomir Bic",
title = -
@Article{Akleylek:2012:MRR,
author = "Sedat Akleylek and Ferruh Ozbudak",
title = Q9
@Article{Akishita:2001:FSS,
author = "Toru Akishita",
title = "Fast Simultaneous 9qc
@Article{Al-Mohy:2012:MAB,
author = "Awad H. Al-Mohy",
title = "A more accurate {Q<>}
@Article{Alexander:1977:SRR,
author = "V. L. Alexander",
title = "Square Root Rou#G
@Article{Aldous:2010:WCO,
author = "David Aldous and Tung Phan",
title = "When CaMonline.com/loi/uasa20Otis E. LancasterMachine Method for the Extraction of Cube Root
@Article{Lancaster:1942:MME,
author = "Otis E. Lancaster",
title = "Machine Method for the Extraction of Cube Root",
journal = j-J-AM-STAT-ASSOC,
volume = "37",
number = "217",
pages = "112--115",
month = mar,
year = "1942",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:24 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314096;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
URL = "http://www.jstor.org/stable/2279437",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}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,
}(calculatingPrivately circulated memorandumMoore School of Electrical Engineering, University of PennsylvaniaPhiladelphia, PA, USA112--115aug81942Wed 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,
}
]B]k*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:d)X!#/k +m_kg Qtechreportfpar3(V !#-'K7=m;_'g]techreportfparith.bibMauchly:1942:UHSJ. W. MauchlyThe use of high speed vacuum tube devices for
title = "Report on Electronic Predictors for 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, USA112--115apr41942http://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",
}ignificant 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",
}
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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 ibution of Numbers and Distribution of
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volume = "155",
number = "??",
pages = "52--53",
day = "13",
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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}",
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bibdate = "Mon Jun 06 19:17:03 2005",
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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,
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CODEN = "ELENAC",
ISSN = "0095-9197",
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@Article{Anonymous:1998:ANO,
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@Article{Anonymous:1996:IBT,
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title = "Inquiry Board Traces /J
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title = "{IBM}'s new {Model 3C-m-
@Article{Anonymous:2002:AIVf,
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iarticlefparith.ׇ}=W #-S{=m;SIarticlefparith.bՉybibHuskey:1949:PCPH. D. HuskeyOn the Precision of a Certain Procedure of Numerical Integrationj-J-RES-NATL-BUR-STAND4257--621949JRNBAG0091-0635 OR 00910635Fri Aug 20 09:32:34 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.08.20 09:32:34 ???Cited in cite Sterbenz:1974:FPC.ack-nhfbH. D. HuskeyOn the Precision of a Certain Procedure of Numerical Integration
@Article{Huskey:1949:PCP,
author = "H. D. Huskey",
title = "On the Precision of a Certain Procedure of Numerical
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journal = j-J-RES-NATL-BUR-STAND,
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type = "SRG Memorandum report",
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@TechReport{Tukey:1949:TRA,
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}uting devices",
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bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
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remark = "Supervised by Charles Brown Tompkins and C. H.
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a provision of contract N6-ONR-240, Task 1. Cited in
\cite{Sterbenz:1974:FPC}.",
subject = "computers",
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bibdate = "Fri Aug 20 10:18:44 MDT 2010",
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z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
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NAW'#'C7Q'=m;_C;g#Oinproceedingsfparith.bibWilkes:1950:EM. V. Wilkes and W. RenwickReport of a Conference on High Speed Automatic Calculatinތ6@W #-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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author = "M. V. Wilkes and W. Renwick",
booktitle = "{Report of a Conference on High Speed Automatic
Calculating Machines, 22--25 June 1949}",
title = "The {EDSAC}",
publisher = "University Mathematical Laboratory",
address = "Cambridge, UK",
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year = "1950",
bibdate = "Wed Oct 13 12:00:41 2010",
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@InProceedings{Worsley:1950:ED,
author = "B. H. Worsley",
booktitle = "Report of a Conference on High Speed Automatic
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bibdate = "Wed Oct 13 11:39:09 2010",
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}CbBooth: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
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number = "2",
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month = "????",
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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,
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[8] noticed that the rounding error in the sum of two
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fjournal = "Proceedings of the Cambridge Philosophical Society.
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numbers could be estimated by subtracting one of the
numbers from the sum, and he made use of this estimate
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}= "Numerical Inverting of Matrices of High Order. {II}",
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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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fjournal = "Proceedings of the American Mathematical Society",
}F{Taub:1963:JNCa}.Numerical Inverting of Matrices of High Order. {II}
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author = "Herman H. Goldstine and John von Neumann",
title = "Numerical Inverting of Matrices of High Order. {II}",
journal = j-PROC-AM-MATH-SOC,
volume = "2",
pages = "188--202",
year = "1951",
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ISSN = "0002-9939 (print), 1088-6826 (electronic)",
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MRnumber = "MR0041539 (12,861b)",
MRreviewer = "F. J. Murray",
bibdate = "Thu Nov 8 14:49:46 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{vonNeumann:1947:NIM} for Part I. Reprinted
in \cite[Paper~15, pp.~558--572]{Taub:1963:JNCa}.",
URL = "http://www.jstor.org/view/00029939/di970628/97p0185x/0",
ZMnumber = "043.12301",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
}
NNgGZ '#-'+
#_=m;'+inproceeding9FX#1]o1573%;m;Qym]Ys}articlefparith.bibGoldstine:1951:NIMHerman H. Goldstine and John von NeumannNumerical Inverting of Matrices of High Order. IIj-PROC-AM-MATH-SOC2188--2021951PAMYAR0002-9939 (print), 1088-6826 (electronic) OR 00029939 (print), 10886826 (electronic)0002-9939 OR 0002993965.0XMR0041539 (12,861b)F. J. MurrayThu Nov 8 14:49:46 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.08 14:49:46 ???See cite vonNeumann:1947:NIM for Part I. Reprinted in cite [Paper~15, pp.~558--572]Taub:1963:JNCa.http://www.jstor.org/view/00029939/di970628/97p0185x/0Proceedings of the American Mathematical Society043.12301ack-nhfbHerman H. Goldstine and John von NeumannSee \cite{vonNeumann:1947:NIM} for Part I. Reprinted in \cite[Paper~15, pp.~558--572]on",
booktitle = "Proceedings of the AIEE-IRE '51: Papers and
discussions presented at the December 10--12, 1951,
joint AIEE-IRE computer conference, Philadelphia, PA:
Review of electronic digital computers",
title = "A review of the {Bell Laboratories}' digital computer
developments",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "101--105",
year = "1952",
DOI = "http://dx.doi.org/10.1145/1434770.1434787",
LCCN = "????",
bibdate = "Fri Dec 03 09:17:58 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bookpages = "vi + 114",
keywords = "Bell Laboratories Model 1--5 relay computers; complex
fixed-point decimal arithmetic; complex floating-point
decimal arithmetic",
}Gsfparith.bibAndrews:1952:RBLE. G. AndrewsJ. C. McPhersonProceedings of the AIEE-IRE '51: Papers and discussions presented at the December 10--12, 1951, joint AIEE-IRE computer conference, Philadelphia, PA: Review of electronic digital computersA review of the Bell Laboratories' digital computer developmentspub-ACMpub-ACM:adr101--1051952http://dx.doi.org/10.1145/1434770.1434787Fri Dec 03 09:17:58 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.12.03 09:17:58 ???Bell Laboratories Model 1--5 relay computers; complex fixed-point decimal arithmetic; complex floating-point decimal arithmeticack-nhfbvi + 114E. G. AndrewsProceedings of the AIEE-IRE '51: Papers and discussions presented at the December 10--12, 1951, joint AIEE-IRE computer conference, Philadelphia, PA: Review of electronic digital computersJ. C. McPhersonA review of the {Bell Laboratories}' digital computer developments
@InProceedings{Andrews:1952:RBL,
author = "E. G. Andrews",
editor = "J. C. McPherson",
booktitle = "Proceedings of the AIEE-IRE '51: Papers and
discussions presented at the December 10--12, 1951,
joint AIEE-IRE computer conference, Philadelphia, PA:
Review of electronic digital computers",
title = "A review of the {Bell Laboratories}' digital computer
developments",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "101--105",
year = "1952",
DOI = "http://dx.doi.org/10.1145/1434770.1434787",
LCCN = "????",
bibdate = "Fri Dec 03 09:17:58 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bookpages = "vi + 114",
keywords = "Bell Laboratories Model 1--5 relay computers; complex
fixed-point decimal arithmetic; complex floating-point
decimal arithmetic",
} "Automatic Recognition of Spoken Digits",
journal = j-J-ACOUST-SOC-AM,
volume = "24",
number = "6",
pages = "637--642",
month = nov,
year = "1952",
CODEN = "JASMAN",
ISSN = "0001-4966",
ISSN-L = "0001-4966",
bibdate = "Fri Nov 28 16:38:51 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "Journal of the Acoustical Society of America",
}Havis:1952:ARSK. Davis and R. Biddulph and S. BalashekAutomatic Recognition of Spoken Digitsj-J-ACOUST-SOC-AM246637--642nov111952JASMAN0001-4966 OR 000149660001-4966 OR 00014966Fri Nov 28 16:38:51 2003http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 16:38:51 ???Journal of the Acoustical Society of Americaack-mfcK. Davis and R. Biddulph and S. BalashekAutomatic Recognition of Spoken Digits
@Article{Davis:1952:ARS,
author = "K. Davis and R. Biddulph and S. Balashek",
title = "Automatic Recognition of Spoken Digits",
journal = j-J-ACOUST-SOC-AM,
volume = "24",
number = "6",
pages = "637--642",
month = nov,
year = "1952",
CODEN = "JASMAN",
ISSN = "0001-4966",
ISSN-L = "0001-4966",
bibdate = "Fri Nov 28 16:38:51 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "Journal of the Acoustical Society of America",
}
%%>JW#-EQQ=a;EQearticlefparith.bibMorrill:1952:SEMC. D. Morrill and R. V. BaumA Stabilized Electronic Multiplierj-TRANS-IIV #1-/!O77E#;SGc-/articlefparith.bibMichaelson:1952:BAR. L. MichaelsonBinary Arithmeticj-INC-STAT3135--40feb21952http://dx.doi.org/10.2307/29865911466-9404 OR 146694041466-9404 OR 14669404Thu Jan 22 18:10:18 MST 2015http://www.jstor.org/stable/i349863; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/jfHU#)]Y/77=m;e]Yearticlefparith.bibDtic",
journal = j-INC-STAT,
volume = "3",
number = "1",
pages = "35--40",
month = feb,
year = "1952",
CODEN = "????",
DOI = "http://dx.doi.org/10.2307/2986591",
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bibdate = "Thu Jan 22 18:10:18 MST 2015",
bibsource = "http://www.jstor.org/stable/i349863;
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URL = "http://www.jstor.org/stable/2986591",
acknowledgement = ack-nhfb,
fjournal = "The Incorporated Statistician",
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}Irss-d-1950.bib2015.01.22 18:10:18 MSThttp://www.jstor.org/stable/2986591The Incorporated Statisticianack-nhfbhttp://www.jstor.org/journals/14669404.htmlR. L. MichaelsonBinary Arithmetic
@Article{Michaelson:1952:BA,
author = "R. L. Michaelson",
title = "Binary Arithmetic",
journal = j-INC-STAT,
volume = "3",
number = "1",
pages = "35--40",
month = feb,
year = "1952",
CODEN = "????",
DOI = "http://dx.doi.org/10.2307/2986591",
ISSN = "1466-9404",
ISSN-L = "1466-9404",
bibdate = "Thu Jan 22 18:10:18 MST 2015",
bibsource = "http://www.jstor.org/stable/i349863;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jrss-d-1950.bib",
URL = "http://www.jstor.org/stable/2986591",
acknowledgement = ack-nhfb,
fjournal = "The Incorporated Statistician",
journal-URL = "http://www.jstor.org/journals/14669404.html",
}abilized Electronic Multiplier",
journal = j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT,
volume = "EC-1",
number = "??",
pages = "52--59",
month = dec,
year = "1952",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Jul 15 15:20:53 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the I.R.E. Professional Group on
Electronic Computers",
}JRE-PROF-GROUP-ELEC-COMPUTEC-152--59dec121952Fri Jul 15 15:20:53 2011http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.15 15:20:53 ???Transactions of the I.R.E. Professional Group on Electronic Computersack-nhfbC. D. Morrill and R. V. BaumA Stabilized Electronic Multiplier
@Article{Morrill:1952:SEM,
author = "C. D. Morrill and R. V. Baum",
title = "A Stabilized Electronic Multiplier",
journal = j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT,
volume = "EC-1",
number = "??",
pages = "52--59",
month = dec,
year = "1952",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Jul 15 15:20:53 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the I.R.E. Professional Group on
Electronic Computers",
}Review of Electronic Digital Computers. Joint
{AIEE--IRE} Computer Confer ence. {10--12 December
1951}",
title = "The {IBM} card-programmed electronic calculator",
publisher = "American Institute of Electrical Engineers",
address = "New York, NY, USA",
pages = "30--36",
year = "1952",
bibdate = "Wed Oct 13 11:28:45 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}K28:45 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib2010.10.13 11:28:45 ???Reprinted in cite [ 5.4]Randell:1982:ODC.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,
author = "J. W. Sheldon and L. Tatum",
booktitle = "Review of Electronic Digital Computers. Joint
{AIEE--IRE} Computer Confer ence. {10--12 December
1951}",
title = "The {IBM} card-programmed electronic calculator",
publisher = "American Institute of Electrical Engineers",
address = "New York, NY, USA",
pages = "30--36",
year = "1952",
bibdate = "Wed Oct 13 11:28:45 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
||yKW'#-AQga/=m;_AYgkIinproceedingsfparith.bibSheldon:1952:ICPJ. W. Sheldon and L. TatumReview of Electronic Digital Computers. Joint AIEE--IRE Computer Confer ence. 10--12 December 1951The IBM card-programmed electronic calculatorAmerican Institute of Electrical EngineersNew York, NY, USA30--361952Wed Oct 13 11:n: Type 701 and Associated
Equipment",
publisher = pub-IBM,
address = pub-IBM:adr,
pages = "103",
year = "1953",
bibdate = "Wed Sep 14 23:17:49 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}L
**%MY #+%I57=m;'1e%MMarticlefparith.bibBackus:1954:ISSJ. W. BackusThe IBM 701 Speedcoding Systemj-J-ACM114--LW #%+#=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
@Book{IBM:1953:POT,
author = "{IBM Corporation}",
title = "Principles of Operation: Type 701 and Associated
Equipment",
publisher = pub-IBM,
address = pub-IBM:adr,
pages = "103",
year = "1953",
bibdate = "Wed Sep 14 23:17:49 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}ing} System",
journal = j-J-ACM,
volume = "1",
number = "1",
pages = "4--6",
month = jan,
year = "1954",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Fri Nov 04 00:18:27 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://community.computerhistory.org/scc/projects/FORTRAN/paper/p4-backus.pdf",
abstract = "The IBM 701 Speedcoding System is a set of
instructions which causes the 701 to behave like a
three-address floating point calculator. Let us call
this the Speedcoding calculator. In addition to
operating in floating point, this Speedcoding
calculator has extremely convenient means for getting
information into the machine and for printing results;
it has an extensive set of operations to make the job
of programming as easy as possible. Speedcoding also
provides automatic address modification, flexible
tracing, convenient use of auxiliary storage, and
built-in checking.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}M
++&Lr
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author = "O. Amble and Jan V. Garwick",
title = "On the Accuracy of Floating Point Computers {[BIT {\bf
1}(2), 1961, pp. 87--88]} OF4i
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author = "H. Alt",
title = "Square Rooting Is as Difficult as Multiplication",
journal = j-COMPUTING,
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@Article{Anonymous:2002:AIVf,
author = "Anonymous",
title = "Author index volume W #1-[;a7E;]-[articlefparith.bibRothstein:1959:RBNJerome RothsteinResidues of Binary Numbers Modulo Threej-IRE-TRANS-ELEC-COMPUTEC-82229--229jun61959IRELAOhttp://dx.doi.org/10.1109/TEC.1959.52195290367-9950 OR 03679950Thu Jul 14 15:56:45 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomputomputation of Square Roots Without
Using Division",
journal = j-CACM,
volume = "2",
number = "11",
pages = "23--24",
month = nov,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:24 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sarafyan59;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See comments \cite{Traub:1960:CNM}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Sarafyan59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sarafyan59",
}Division
@Article{Sarafyan:1959:NMC,
author = "Diran Sarafyan",
title = "A New Method of Computation of Square Roots Without
Using Division",
journal = j-CACM,
volume = "2",
number = "11",
pages = "23--24",
month = nov,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:24 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sarafyan59;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See comments \cite{Traub:1960:CNM}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Sarafyan59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sarafyan59",
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dY #/)57E;O?c)Suarticlefparith.bibSarafyan:1959:NMCDiran SarafyanA New Method of Computation of Square Roots Without Using Divisionj-CACM21123--24nov111959CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Wed Jul 14 15:48:24 MDT 2004http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sarafyan59; http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2004.07.14 15:48:24 MDTSee comments cite Traub:1960:CNM.Communications of the ACMack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Diran SarafyanSee comments \cite{Traub:1960:CNM}.A New Method of Computation of Square Roots Without Using Translator Compiler of the {IBM FORTRAN
Automatic Coding System}",
journal = j-CACM,
volume = "2",
number = "2",
pages = "9--21",
month = feb,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sheridan59;
http://ei.cs.vt.edu/~cs4304/bibliography.html;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Sheridan59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sheridan59",
}idan:1959:ATC,
author = "Peter B. Sheridan",
title = "The Arithmetic Translator Compiler of the {IBM FORTRAN
Automatic Coding System}",
journal = j-CACM,
volume = "2",
number = "2",
pages = "9--21",
month = feb,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sheridan59;
http://ei.cs.vt.edu/~cs4304/bibliography.html;
http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
oldlabel = "Sheridan59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sheridan59",
}
Y #//'57E};?c/+!
articlefparith.bibSheridan:1959:ATCPeter B. SheridanThe Arithmetic Translator Compiler of the IBM FORTRAN Automatic Coding Systemj-CACM229--21feb21959CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Wed Jul 14 15:48:22 MDT 2004http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sheridan59; http://ei.cs.vt.edu/~cs4304/bibliography.html; http://portal.acm.org/; 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=J79Peter B. SheridanThe Arithmetic Translator Compiler of the {IBM FORTRAN Automatic Coding System}
@Article{Sher root of a complex number",
journal = j-COMP-J,
volume = "2",
number = "2",
pages = "89--89",
month = jul,
year = "1959",
CODEN = "CMPJA6",
DOI = "http://dx.doi.org/10.1093/comjnl/2.2.89",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:55:11 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/020089.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/tiff/89.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}acheyOn taking the square root of a complex number
@Article{Strachey:1959:TSR,
author = "C. Strachey",
title = "On taking the square root of a complex number",
journal = j-COMP-J,
volume = "2",
number = "2",
pages = "89--89",
month = jul,
year = "1959",
CODEN = "CMPJA6",
DOI = "http://dx.doi.org/10.1093/comjnl/2.2.89",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:55:11 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/020089.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/tiff/89.tif",
acknowledgement = ack-nhfb,
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7W #'%e;a7E;]%e{articlefparith.bibCroy:1960:IADJohn E. CroyImproved Arrangement of a Decimal Multiplierj-IRE-TRANS-ELEC-COMPUTEC-92263--263jun61960IRELAOhttp://dx.doi.org/10.1109/TEC.1960.52198300367-9950 OR 03679950Thu Jul 14 15:34:11 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomY #));a7E;])Uarticlefparith.bibBrown:1960:EDCDavid T. BrownError Detecting and Correcting Binary Codes for Arithmetic Operationsj-IRE-TRANS-ELEC-COMPUTEC-93333--337sep91960IRELAOhttp://dx.doi.org/10.1109/TEC.1960.52198550367-9950 OR 03679950Thu Jul 14 15:34:12 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 15:34:12 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp a Decimal Multiplier",
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@Article{Croy:1960:IAD,
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month = dec,
year = "1960",
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WW #)!57E1;?c!articlefparith.bibGurzi:1960:HSMFred GurziA High-Speed Multiplication Process for Digital Computersj-CACM34241--245apr41960CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 00010782Fri Nov 25 18:19:26 MST 2005http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Gurzi60; http://www.acm.org/pubs/contents/journals/cacm/; 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 ACMack-nhfbhttp://portal.acm.org/browse_dl.cfm?idx=J79Fred GurziA High-Speed Multiplication Process for Digital Computers
@Arts for floating point trigonometric,
inverse trigonometric hyperbolic and exponential
functions",
type = "Group report",
number = "30G-0009",
institution = "Massachusetts Institute of Technology, Lincoln
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address = "Lexington, MA, USA",
pages = "7",
year = "1960",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
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}``Millstone Hill Radar Station.'' ``1 November 1960.'' Air Force Contractack-nhfbB. A. JensenCoding instructions for floating point trigonometric, inverse trigonometric hyperbolic and exponential functions
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title = "Coding instructions for floating point trigonometric,
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ll| [ #)+A57-E[;7q?cq+WAarticlefparith.bibKnuth:1960:INSDonald E. KnuthAn Imaginary Number Systemj-CACM34245--247apr41960CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 0001078265.9923\#B554C. B. HaselgroveFri Nov 25 18:19:26 MST 2005http://dblp.uni-trier.de/db/journalxX !#+%m%1Em;m9%mktechreportfparith.bibJensen:1960:CIFB. A. JensenCoding instructions for floating point trigonometric, inverse trigonometric hyperbolic and exponential functionsGroup report30G-0009Massachusetts Institute of Technology, Lincoln LaboratoryLexington, MA, USA71960Sat Feb 24 15:01:45 MST 1996http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MSTTrigonometrical functions --- Computer programs.Cover title. System",
journal = j-CACM,
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pages = "245--247",
month = apr,
year = "1960",
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MRreviewer = "C. B. Haselgrove",
bibdate = "Fri Nov 25 18:19:26 MST 2005",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Knuth60;
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http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
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MathSciNet database",
note = "Errata, {\sl Commun\-i\-ca\-tions of the ACM\/ \bf 4}
(August 1961), 355 \cite{Knuth:1961:EIN}. See
\cite{Nadler:1961:DSR} for extension to division and
square root.",
abstract = "For centuries the decimal number system reigned
supreme, except, perhaps, among the Mayan Indians,
until the advent of digital computers brought the
binary and octal systems into the limelight. This paper
introduces another number system which may prove useful
for manipulating complex numbers on machines.",
acknowledgement = ack-nhfb,
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note = "Errata, {\sl Commun\-i\-ca\-tions of the ACM\/ \bf 4}
(August 1961), 355 \cite{Knuth:1961:EIN}. See
\cite{Nadler:1961:DSR} for extension to division and
square root.",
abstract = "For centuries the decimal number system reigned
supreme, except, perhaps, among the Mayan Indians,
until the advent of digital computers brought the
binary and octal systems into the limelight. This paper
introduces another number system which may prove useful
for manipulating complex numbers on machines.",
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} of Round-Off Errors in the
Numerical Integration of the Heat Equation",
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pages = "139--146",
month = apr,
year = "1960",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
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bibdate = "Tue Oct 13 08:06:19 MDT 1998",
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acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
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@Article{Bailey:1988:EHS,
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@Article{Barnes:1982:RNI,
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title = "Roundoff, 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. GarnerA and R. F. Arnold and B. C. Benson and C. G. Brockus and R. J. Gonzalez and D. P. RozenbergResidue number systems for computers
@TechReport{Garner:1961:RNS,
author = "H. L. Garner and R. F. Arnold and B. C. Benson and C.
G. Brockus and R. J. Gonzalez and D. P. Rozenberg",
title = "Residue number systems for computers",
type = "{ASD} Technical Report",
number = "61-483",
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address = "Ann Arbor, MI, USA",
month = oct,
year = "1961",
bibdate = "Thu Nov 18 09:27:06 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txt",
abstract = "The purpose of the research performed under this
contract was to investigate the feasibility of residue
number systems in their applications to digitBal
computers. The problems of such an application are the
ones of magnitude determination, sign determination,
overflow, scaling, and division. These problems are not
independent, but are found to be quite interrelated. A
theoretical treatment of residue number systems is
given which lays the foundation for a unified study of
the complete problem. Treatments of an organizational
nature are given which deal with multiplication,
division, and scaling. The matter of correlating the
theoretical and organizational studies to physical
realizations involving networks is treated also. The
question of whether the residue number system can be
successfully applied to general purpose computers is
still an open one. Their application to special purpose
machines is considered both feasible and practical.",
acknowledgement = ack-nhfb,
remark = "This report represents the results of research
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System Division under the direction of Dr. Richard
Tanaka. There was a considerable exchange of
information among the above groups during the course of
the research effort. The efforts attained exhibit
little overlap, rather they are complementary. A
portion of this report was extracted from the doctoral
dissertation of D. P. Rozenberg. His work was supported
by this contract, and led to the Ph.D..",
} journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "2",
pages = "87--88",
month = jun,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "http://dx.doi.org/10.1007/BF01939221",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=2;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
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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",
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}Eth.bibGarwick:1961:AFPJan V. GarwickThe Accuracy of Floating Point Computersj-NORDISK-TIDSKR-INFORM-BEHAND1287--88jun61961BITTEL, NBITABhttp://dx.doi.org/10.1007/BF019392210006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)0006-3835 OR 00063835Wed Jan 4 18:52:07 MST 2006http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=2; 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,
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title = "The Accuracy of Floating Point Computers",
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acknowledgement = ack-nhfb,
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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,
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} 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,
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title = "Reply to {``On the Accuracy of 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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[G9W '#1+oQ#-]=m;?1?+sQinproceedingsfparith.bibHenderson:1961:RCED. S. HendersonProceedings of the 1961 16th ACM national meetingResidue classK8Y #-'AI)57=I;_qY'cK[articlefparith.bibGarwick:1961:RAFJ. V. GarwickReply to ``On the Accuracy of Floating Point Computers'' [BIT bf 1(3), 1961, pp. 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.Gngs of the 1961 16th ACM national meeting}",
title = "Residue class error checking codes",
publisher = pub-ACM,
address = pub-ACM:adr,
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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",
}
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@Book{Seife:2000:ZBD,
author = "Charles Seife",
title = "Zero: The Biography of a9g^=
@Book{Sites:1992:AAR,
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title = 'fE
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$jU
@Book{Shauman:1979:OMA,
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@Book{Shannon:1993:CES,
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*7%K
@Book{Scott:1985:CNS,
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title = "Computer Number System%
@Book{Scott:1968:OET,
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@Book{Schmid:1983:DC,
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5
@Book{Schmid:1978:EDS,
author = "Hermann Schmid",
title = "{Elektronische Dezimal)L 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,
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booktitle = "{Proceedings of the 1961 16th ACM national meeting}",
title = "Residue class error checking codes",
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abstract = "Error checking codes based on residues have the
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acknowledgement = ack-nhfb,
keywords = "decimal arithmetic",
}rate Analog Multiplier and Divider",
journal = j-IRE-TRANS-ELEC-COMPUT,
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@Article{Kettel:1961:AAM,
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bibdate = "Thu Jul 14 14:45:03 MDT 2011",
bibsource = "http://www.computer.org/tc/;
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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/cacQ`: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 14:45:0Nnary number system''}",
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volume = "4",
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month = aug,
year = "1961",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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}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",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}{Hall-Effect} Analog Multiplier",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "3",
pages = "512--515",
month = sep,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219240",
ISSN = "0367-9950",
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219240",
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fjournal = "IRE Transactions on Electronic Computers",
}14:45:04 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219240IRE Transactions on Electronic Computersack-nhfbG. Kovatch and W. E. MeserveThe {Hall-Effect} Analog Multiplier
@Article{Kovatch:1961:HEA,
author = "G. Kovatch and W. E. Meserve",
title = "The {Hall-Effect} Analog Multiplier",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "3",
pages = "512--515",
month = sep,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219240",
ISSN = "0367-9950",
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219240",
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fjournal = "IRE Transactions on Electronic Computers",
}
TU #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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author = "O. L. MacSorley",
title = "High-speed arithmetic in binary computers",
journal = j-IRE-PROC,
volume = "49",
number = "??",
pages = "67--91",
month = jan,
year = "1961",
bibdate = "Sat May 18 14:34:55 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite{Swartzlander:1976:CDD}.",
acknowledgement = ack-nhfb,
fjournal = "IRE Proceedings",
}root in the quater-imaginary
number system",
journal = j-CACM,
volume = "4",
number = "4",
pages = "192--193",
month = apr,
year = "1961",
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ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.99",
MRnumber = "23\#B555",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1960:INS}.",
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fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$\sqrt(x)$; elementary functions",
ZMreviewer = "C. B. Haselgrove",
}ber system
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author = "Morton Nadler",
title = "Division and square root in the quater-imaginary
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volume = "4",
number = "4",
pages = "192--193",
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MRclass = "65.99",
MRnumber = "23\#B555",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
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note = "See \cite{Knuth:1960:INS}.",
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journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$\sqrt(x)$; elementary functions",
ZMreviewer = "C. B. Haselgrove",
}
|?Y #+' 57E5;=?Mc'A qarticlefparith.bibNadler:1961:DSRMorton NadlerDivision and square root in the quater-imaginary number systemj-CACM44192--193apr41961CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 0001078265.9923\#B555Fri Nov 25 18:19:32 MST 2005http://www.acm.org/pubs/contents/journals/cacm/; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.11.25 18:19:32 MSTSee cite Knuth:1960:INS.Communications of the ACM$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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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 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}.",
}
+Lr&+)U
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author = "Daniel Shanks and John W. {Wrench, Jr.}",
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@Article{Shary:1999:OEG,
author = "S. P. Shary",
title = "Outer Estimation of Gen7 b. Upon reflection one is led to inquire whether there are more physical constants with low order first significant digits than high. Actual counts by Benford [2] show that not only is this the case but that it seems to be an empirical truth that whenever one has a large body of physical data, Farmer's Almanac, Census Reports, Chemical Rubber Handbook, etc., the proportion of these data with first significant digit $n$ or less is approximately $ log _10(n + 1) $. Any reader formerly unaware of this ``peculiarity'' will find an actual sampling experiment wondrously tantalizing. Thus, for example, approximately $ 0.7 $ of the physical constants in the Chemical Rubber Handbook begin with $4$ or less ($ log _10(4 + 1) = 0.699 $ ). This is to be contrasted with the widespread intuitive evaluation $ 4 / 9 $ ths.Annals of Mathematical StatisticsBenford's Law; Law of Anomalous Numbers; Zipf's LawFrom p. 1223: ``ldots the proportion of these data with first significant digit $n$ or less is approximately $ log _10(nc + 1) $.''par ldots ``The only distribution for first significant digits which is invariant under scale change of the underlying distribution is $ log _10(n + 1) $. Contrary to suspicion this is a 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 dlow order first significant digits than high. Actual counts by Benford [2] show that not only is this the case but that it seems to be an empirical truth that whenever one has a large body of physical data, Farmer's Almanac, Census Reports, Chemical Rubber Handbook, etc., the proportion of these data with first significant digit $n$ or less is approximately $ \log_{10}(n + 1) $. Any reader formerly unaware of this ``peculiarity'' will find an actual sampling experiment wondrously tantalizing. Thus, for example, approximately $ 0.7 $ of the physical constants in the Chemical Rubber Handbook begin with $4$ or less ($ \log_{10}(4 + 1) = 0.699 $ ). This is to be contrasted with the widespread intuitive evaluation $ 4 / 9 $ ths.Roger S. PinkhamOn the Distribution of First Significant Digits
@Article{Pinkham:1961:DFS,
author = "Roger S. Pinkham",
title = "On the Distribution of First Significant Digits",
journal = j-ANN-MATH-STAT,
volume = "32",
number = "4",
pages = e "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 proportifon of these data with first
significant digit $n$ or less is approximately $
\log_{10}(n + 1) $. Any reader formerly unaware of this
``peculiarity'' will find an actual sampling experiment
wondrously tantalizing. Thus, for example,
approximately $ 0.7 $ of the physical constants in the
Chemical Rubber Handbook begin with $4$ or less ($
\log_{10}(4 + 1) = 0.699 $ ). This is to be contrasted
with the widespread intuitive evaluation $ 4 / 9 $
ths.",
acknowledgement = 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}.",
}
JJmAV #3'C57=m;?c'Cuarticlefparith.bibRabinowiti@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 backaon Division",
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@Article{Rabinowitz:1961:MPD,
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month = feb,
year = "1961",
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ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 00:29:25 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
} 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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}.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219186IRE Transactions on Electronic Computersack-nhfbRoy G. SaltmanReducing Computing Time for Synchronous Binary Division
@Article{Saltman:1961:RCT,
author = "Roy G. Saltman",
title = "Reducing Computing Time for Synchronous Binary
Division",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "2",
pages = "169--174",
month = jun,
year = "1961",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1961.5219186",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:03 MDT 2011",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219186",
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fjournal = "IRE Transactions on Electronic Computers",
}
EE+CY #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; httpnxBW #-){;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://ieeexplorekued Fraction Approximations To
Elementary Functions",
journal = j-MATH-COMPUT,
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http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
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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",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}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",
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@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",
}
EX #'!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)1961s\DY #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/tepd 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,
}t -- 1963Wed Jun 01 16:58:29 2005http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.06.01 16:58:29 ???Six volumes. Volume I: Logic, Theory of Sets and Quantum Mechanics (1961); Volume II: Operators, Ergodic Theory and Almost Periodic Functions in a Group (1961); Volume III: Rings of Operators (1961); Volume IV: Continuous Geometry and Other Topics (1962); Volume V: Design of Computers, Theory of Automata and Numerical Analysis (1963); Volume VI: Theory of Games, Astrophysics, Hydrodynamics and Meteorology (1963).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/",
}
sFY #-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 00255718TvyDomestic Electronic Digital
Computing Systems",
type = "Report",
number = "1115",
institution = "Ballistic Research Laboratories",
address = "Aberdeen Proving Ground, MD, USA",
pages = "1131",
month = mar,
year = "1961",
bibdate = "Fri Nov 28 19:37:51 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Based on the results of a third survey, the
engineering and programming characteristics of two
hundred 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",
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,
}
bb
GY !#')KM=m;]])atechreportfparith.bibWeik:1961:TSDMartin H. WeikA Third Survey of Domestic Electronic Digital Computing SystemsReport1115Ballistic Research LaboratoriesAberdeen Proving Ground, MD, USA1131mar31961Fri Nov 28 19:37:51 2003http://www.math.utah.edu/pub/tex/bib/fparith.bib2003.11.28 19:37:51 ???Based on the results of a third survey, the engineering and programming characteristics of two hundred 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,zlgorithm 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",
}
aHW#+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 14:45:0niac 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,
}
--OIU '#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,
}r system: {Project Stretch}",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xvii + 322",
year = "1962",
LCCN = "1876",
bibdate = "Fri Nov 19 10:02:31 MST 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
http://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
library.ox.ac.uk:210/ADVANCE",
note = "This important book is the primary description of the
influential IBM 7030 Stretch computer, written by its
architects.",
URL = "http://ed-thelen.org/comp-hist/IBM-7030-Planning-McJones.pdf",
acknowledgement = ack-nhfb,
remark = "The text of the book is in the public domain, with the
permission of the author in 2003.
See \cite{MacKenzie:1991:IAL} for a remark about the
noisy mode for floating-point arithmetic in the IBM
7030 Stretch. That mode is first mentioned on page 25
of this book, and described in detail on page 102,
which states:
``By definition of ordinary normalized FLP operations,
numbers are frequently extended on the right by
attaching zeros. During addition the n-digit operand
that is not preshifted is extended with n zeros, so as
to provide the extra positions to which the preshifted
operand can be added. Any operand or result that is
shifted left to be normalized requires a corresponding
number of zeros to be shifted in at the right. Both
sets of zeros tend to produce numbers smaller in
absolute value than they would have been if more digits
had been carried. In the noisy mode these numbers are
simply extended with 1 s instead of zeros (1 s in a
binary machine, 9s in a decimal machine). So all
numbers tend to be too large in absolute value. The
true value, if there had been no significance loss,
should lie between these two extremes. Hence, two runs,
one made without and one made with the noisy mode,
should show differences in result that indicate which
digits may have been affected by significance loss.
The principal weakness of the noisy-mode procedure is
that it requires two runs for the same problem. A much
less important weakness is that the loss of
significance cannot be guaranteed to show up --- it
merely has a very high probability of showing up ---
whereas built-in significance checks can be made
slightly pessimistic, so that actual significance loss
will not be greater than indicated. On the other hand,
little extra hardware and no extra storage are required
for the noisy-mode approach. Furthermore, significance
loss is relatively rare, so that running a problem
twice when Significance loss is suspected does not pose
a serious problem. What is serious is the possibility
of unsuspected significance loss.
In discussions of significance two points are often
overlooked. The first of these is trivial: the best way
of ensuring significant results is to use an adequate
number of fraction digits. The second is almost equally
mundane: for a given procedure, normalized FLP
arithmetic will ordinarily produce the greatest
precision possible for the number of fraction digits
used. Normalized FLP arithmetic has been criticized
with respect to significance loss, because such loss is
not indicated by the creation of leading zeros, as it
is with fixed-point arithmetic. In other words, the
contention is not that normalized FLP arithmetic is
more prone to significance loss than equivalent
fixed-point arithmetic, which would be untrue, but that
an equivalent indication of such loss is not provided.
Loss of significance, however, is also a serious
problem in fixed-point arithmetic; multiplication and
division do not handle it at all correctly by means of
leading zeros. (In particular, fixed-point
multiplication may lead to serious or even total
significance loss, which would not have occurred with
normalized FLP arithmetic: and although leading zeros
in addition and subtraction of fixed-point operands do
give correct significance indications, the use of other
operations and of built-in scaling loops frequently
destroys entirely the leading-zeros method of counting
significance.)''",
subject = "Computer architecture",
tableofcontents = "Foreword v \\
Preface vii \\
1. Project Stretch 1 \\
[by W. Buchholz] \\
2. Architectural Philosophy 5 \\
[by F. P. Brooks, Jr.] \\
2.1. The Two Objectives of Project Stretch 5 \\
2.2. Resources 6 \\
2.3. Guiding Principles 7 \\
2.4. Contemporary Trends in Computer Architecture 10
\\
2.5. Hindsight 15 \\
3. System Summary of IBM 7030 17 \\
[by W. Buchholz] \\
3.1. System Organization 17 \\
3.2. Memory Units 17 \\
3.3. Index Memory 19 \\
3.4. Special Registers 19 \\
3.5. Input and Output Facilities 19 \\
3.6. High-speed Disk Units 20 \\
3.7. Central Processing Unit 20 \\
3.8. Instruction Controls 21 \\
3.9. Index-arithmetic Unit 21 \\
3.10. Instruction Look-ahead 21 \\
3.11. Arithmetic Unit 22 \\
3.12. Instruction Set 24 \\
3.13. Data Arithmetic 24 \\
3.14. Radix-conversion Operations 27 \\
3.15. Connective Operations 27 \\
3.16. Index-arithmetic Operations 27 \\
3.17. Branching Operations 28 \\
3.18. Transmission Operations 28 \\
3.19. Input-Output Operations 29 \\
3.20. New Features 29 \\
3.21. Performance 32 \\
4. Natural Data Units 33 \\
[by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
\\
4.1. Lengths and Structures of Natural Data Units 33
\\
4.2. Procedures for Specifying Natural Data Units 36
\\
4.3. Data Hierarchies 39 \\
4.4. Classes of Operations 40 \\
5. Choosing a Number Base 42 \\
[by W. Buchholz] \\
5.1. Introduction 42 \\
5.2. Information Content 45 \\
5.3. Arithmetic Speed 49 \\
5.4. Numerical Data 50 \\
5.5. Nonnumerical Data 51 \\
5.6. Addresses 52 \\
5.7. Transformation 53 \\
5.8. Partitioning of Memory 54 \\
5.9. Program Interpretation 56 \\
5.10. Other Number Bases 58 \\
5.11. Conclusion 58 \\
6. Character Set 60 \\
[by R. W. Bemer and W. Buchholz] \\
6.1. Introduction 60 \\
6.2. Size of Set 62 \\
6.3. Subsets 62 \\
6.4. Expansion of Set 63 \\
6.5. Code 63 \\
6.6. Parity Bit 66 \\
6.7. Sequence 66 \\
6.8. Blank 67 \\
6.9. Decimal Digits 68 \\
6.10. Typewriter Keyboard 68 \\
6.11. Adjacency 69 \\
6.12. Uniqueness 69 \\
6.13. Signs 70 \\
6.14. Tape-recording Convention 71 \\
6.15. Card-punching Convention 71 \\
6.16. List of 7030 Character Set 72 \\
7. Variable-field-length Operation 75 \\
[by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
\\
7.1. Introduction 75 \\
7.2. Addressing of Variable-field-length Data 76 \\
7.3. Field Length 77 \\
7.4. Byte Size 78 \\
7.5. Universal Accumulator 79 \\
7.6. Accumulator Operand 79 \\
7.7. Binary and Decimal Arithmetic 80 \\
7.8. Integer Arithmetic 81 \\
7.9. Numerical Signs 82 \\
7.10. Indicators 84 \\
7.11. Arithmetical Operations 85 \\
7.12. Radix-conversion Operation 87 \\
7.13. Logical Connectives of Two Variables 87 \\
7.14. Connective Operations 89 \\
8. Floating-point Operation 92 \\
[by S. G. Campbell] \\
General Discussion \\
8.1. Problems of Fixed-point Arithmetic 92 \\
8.2. Floating-point Arithmetic 94 \\
8.3. Normalization 97 \\
8.4. Floating-point Singularities 98 \\
8.5. Range and Precision 99 \\
8.6. Round-off Error 100 \\
8.7. Significance Checks 101 \\
8.8. Forms of Floating-point Arithmetic 103 \\
8.9. Structure of Floating-point Data 104 \\
Floating-point Features of the 7030 \\
8.10. Floating-point Instruction Format 106 \\
8.11. Floating-point Data Formats 106 \\
8.12. Singular Floating-point Numbers 108 \\
8.13. Indicators 112 \\
8.14. Universal Accumulator 113 \\
8.15. Fraction Arithmetic 114 \\
8.16. Floating-point-arithmetic Operations 114 \\
8.17. Fixed-point Arithmetic Using Unnormalized \\
Floating-point Operations 118 \\
8.18. Special Functions and Forms of Arithmetic 119 \\
8.19. Multiple-precision Arithmetic 119 \\
8.20. General Remarks 121 \\
9. Instruction Formats 122 \\
[by W. Buchholz] \\
9.1. Introduction 122 \\
9.2. Earlier Instruction Languages 122 \\
9.3. Evolution of the Single-address Instruction 124
\\
9.4. Implied Addresses 125 \\
9.5. Basic 7030 Instruction Formats 126 \\
9.6. Instruction Efficiency 127 \\
9.7. The Simplicity of Complexity 131 \\
9.8. Relationship to Automatic Programming Languages
132 \\
10. Instruction Sequencing 133 \\
[by F. P. Brooks, Jr.] \\
10.1. Modes of Instruction Sequencing 133 \\
10.2. Instruction Counter 134 \\
10.3. Unconditional Branching 135 \\
10.4. Conditional Branching 136 \\
10.5. Program-interrupt System 136 \\
10.6. Components of the Program-interrupt System 137
\\
10.7. Examples of Program-interrupt Techniques 140 \\
10.8. Execute Instructions 146 \\
10.9. Execute Operations in the 7030 148 \\
11. Indexing 150 \\
[by G. P. Blaauw] \\
11.1. Introduction 150 \\
11.2. Indexing Functions 151 \\
11.3. Instruction Format for Indexing 155 \\
11.4. Incrementing 157 \\
11.5. Counting 159 \\
11.6. Advancing by One 161 \\
11.7. Progressive Indexing 161 \\
11.8. Data Transmission 162 \\
11.9. Data Ordering 163 \\
11.10. Refilling 165 \\
11.11. Indirect Addressing and Indirect Indexing 167
\\
11.12. Indexing Applications 169 \\
11.13. Record-handling Applications 172 \\
11.14. File Maintenance 175 \\
11.15. Subroutine Control 177 \\
11.16. Conclusion 178 \\
12. Input-Output Control 179 \\
[by W. Buchholz] \\
12.1. A Generalized Approach to Connecting \\
Input-Output and External Storage 179 \\
12.2. Input-Output Instructions 180 \\
12.3. Defining the Memory Area 181 \\
12.4. Writing and Reading 182 \\
12.5. Controlling and Locating 183 \\
12.6. An Alternative Approach 184 \\
12.7. Program Interruptions 184 \\
12.8. Buffering 180 \\
12.9. Interface 188 \\
12.10. Operator Control of Input-Output Units 190 \\
13. Multiprogramming 192 \\
[by E. F. Codd, E. S. Lowry, E. McDonough, and C. A.
Scalzi] \\
13.1. Introduction 192 \\
13.2. Multiprogramming Requirements 193 \\
13.3. 7030 Features that Assist Multiprogramming 195
\\
13.4. Programmed Logic 197 \\
13.5. Concluding Remarks 200 \\
13.6. References 201 \\
14. The Central Processing Unit 202 \\
[by E. Bloch] \\
14.1. Concurrent System Operation 202 \\
14.2. Concurrency within the Central Processing Unit
204 \\
14.3. Data Flow 204 \\
14.4. Arithmetic Unit 208 \\
14.5. Checking 216 \\
14.6. Component Count 216 \\
14.7. Performance 217 \\
14.8. Circuits 218 \\
14.9. Packaging 223 \\
15. The Look-ahead Unit 228 \\
[by R. S. Balance, J. Cocke, and H. G. Kolsky] \\
15.1. General Description 228 \\
15.2. Timing-simulation Program 230 \\
15.3. Description of the Look-ahead Unit 238 \\
15.4. Forwarding 240 \\
15.5. Counter Sequences 241 \\
15.6. Recovery after Interrupt 246 \\
15.7. A Look-back at the Look-ahead 247 \\
16. The Exchange 248 \\
[by W. Buchholz] \\
16.1. General Description 248 \\
16.2. Starting a WRITE or READ Operation 250 \\
16.3. Data Transfer during Writing 250 \\
16.4. Data Transfer during Reading 251 \\
16.5. Terminating a WRITE or READ Operation 252 \\
16.6. Multiple Operations 252 \\
16.7. CONTROL and LOCATE Operations 252 \\
16.8. Interrogating the Control Word 253 \\
16.9. Forced Termination 253 \\
17. A Nonarithmetical System Extension 254 \\
[by S. G. Campbell, P.S. Herwitz, and J. H. Pomerene]
\\
17.1. Nonarithmetical Processing 254 \\
17.2. The Set-up Mode 258 \\
17.3. Byte-sequence Formation 259 \\
17.4. Pattern Selection 260 \\
17.5. Transformation Facilities 261 \\
17.6. Statistical Aids 263 \\
17.7. The BYTE-BY-BYTE Instruction 263 \\
17.8. Monitoring for Special Conditions 264 \\
17.9. Instruction Set 265 \\
17.10. Collating Operations 266 \\
17.11. Table Look-up Operations 267 \\
17.12. Example 267 \\
Appendix A. Summary Data 273 \\
A.1. List of the Larger IBM Stored-program Computers
273 \\
A.2. Instruction Formats 275 \\
A.3. List of Registers and Special Addresses 276 \\
A.4. Summary of Operations and Modifiers 277 \\
A.5. Summary of Indicators 287 \\
Appendix B. Programming Examples 292 \\
Notation 292 \\
B.1. Polynomial Evaluation 295 \\
B.2. Cube-root Extraction 296 \\
B.3. Matrix Multiplication 298 \\
B.4. Conversion of Decimal Numbers to a \\
Floating-point Normalized Vector 299 \\
B.5. Editing a Typed Message 301 \\
B.6. Transposition of a Large Bit Matrix 303 \\
Index 305",
}k is in the public domain, with the permission of the author in 2003. See cite MacKenzie:1991:IAL for a remark about the noisy mode for 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). So all numbers tend to be too large in absolute value. The true value, if there had been no significance loss, should lie between these two extremes. Hence, two runs, one made without and one made with the noisy mode, should show differences in result that indicate which digits may have been affected by significance loss. The principal weakness of the noisy-mode procedure is that it requires two runs for the same problem. A much less important weakness is that the loss of significance cannot be guaranteed to show up --- it merely has a very high probability of showing up --- whereas built-in significance checks can be made slightly pessimistic, so that actual significance loss will not be greater than indicated. On the other hand, little extra hardware and no extra storage are required for the noisy-mode approach. Furthermore, significance loss is relatively rare, so that running a problem twice when Significance loss is suspected does not pose a serious problem. What is serious is the possibility of unsuspected significance loss. In discussions of significance two points are often overlooked. The first of these is trivial: the best way of ensuring significant results is to use an adequate number of fraction digits. The second is almost equally mundane: for a given procedure, normalized FLP arithmetic will ordinarily produce the greatest precision possible for the number of fraction digits used. Normalized FLP arithmetic has been criticized with respect to significance loss, because such loss is not indicated by the creation of leading zeros, as it is with fixed-point arithmetic. In other words, the contention is not that normalized FLP arithmetic is more prone to significance loss than equivalent fixed-point arithmetic, which would be untrue, but that an equivalent indication of such loss is not provided. Loss of significance, however, is also a serious problem in fixed-point arithmetic; multiplication and division do not handle it at all correctly by means of leading zeros. (In particular, fixed-point multiplication may lead to serious or even total significance loss, which would not have occurred with normalized FLP arithmetic: and although leading zeros in addition and subtraction of fixed-point operands do give correct significance indications, the use of other operations and of built-in scaling loops frequently destroys entirely the leading-zeros method of counting significance.)''Computer architectureForeword v Preface vii 1. Project Stretch 1 [by W. Buchholz] 2. Architectural Philosophy 5 [by F. P. Brooks, Jr.] 2.1. The Two Objectives of Project Stretch 5 2.2. Resources 6 2.3. Guiding Principles 7 2.4. Contemporary Trends in Computer Architecture 10 2.5. Hindsight 15 3. System Summary of IBM 7030 17 [by W. Buchholz] 3.1. System Organization 17 3.2. Memory Units 17 3.3. Index Memory 19 3.4. Special Registers 19 3.5. Input and Output Facilities 19 3.6. High-speed Disk Units 20 3.7. Central Processing Unit 20 3.8. Instruction Controls 21 3.9. Index-arithmetic Unit 21 3.10. Instruction Look-ahead 21 3.11. Arithmetic Unit 22 3.12. Instruction Set 24 3.13. Data Arithmetic 24 3.14. Radix-conversion Operations 27 3.15. Connective Operations 27 3.16. Index-arithmetic Operations 27 3.17. Branching Operations 28 3.18. Transmission Operations 28 3.19. Input-Output Operations 29 3.20. New Features 29 3.21. Performance 32 4. Natural Data Units 33 [by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz] 4.1. Lengths and Structures of Natural Data Units 33 4.2. Procedures for Specifying Natural Data Units 36 4.3. Data Hierarchies 39 4.4. Classes of Operations 40 5. Choosing a Number Base 42 [by W. Buchholz] 5.1. Introduction 42 5.2. Information Content 45 5.3. Arithmetic Speed 49 5.4. Numerical Data 50 5.5. Nonnumerical Data 51 5.6. Addresses 52 5.7. Transformation 53 5.8. Partitioning of Memory 54 5.9. Program Interpretation 56 5.10. Other Number Bases 58 5.11. Conclusion 58 6. Character Set 60 [by R. W. Bemer and W. Buchholz] 6.1. Introduction 60 6.2. Size of Set 62 6.3. Subsets 62 6.4. Expansion of Set 63 6.5. Code 63 6.6. Parity Bit 66 6.7. Sequence 66 6.8. Blank 67 6.9. Decimal Digits 68 6.10. Typewriter Keyboard 68 6.11. Adjacency 69 6.12. Uniqueness 69 6.13. Signs 70 6.14. Tape-recording Convention 71 6.15. Card-punching Convention 71 6.16. List of 7030 Character Set 72 7. Variable-field-length Operation 75 [by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz] 7.1. Introduction 75 7.2. Addressing of Variable-field-length Data 76 7.3. Field Length 77 7.4. Byte Size 78 7.5. Universal Accumulator 79 7.6. Accumulator Operand 79 7.7. Binary and Decimal Arithmetic 80 7.8. Integer Arithmetic 81 7.9. Numerical Signs 82 7.10. Indicators 84 7.11. Arithmetical Operations 85 7.12. Radix-conversion Operation 87 7.13. Logical Connectives of Two Variables 87 7.14. Connective Operations 89 8. Floating-point Operation 92 [by S. G. Campbell] General Discussion 8.1. Problems of Fixed-point Arithmetic 92 8.2. Floating-point Arithmetic 94 8.3. Normalization 97 8.4. Floating-point Singularities 98 8.5. Range and Precision 99 8.6. Round-off Error 100 8.7. Significance Checks 101 8.8. Forms of Floating-point Arithmetic 103 8.9. Structure of Floating-point Data 104 Floating-point Features of the 7030 8.10. Floating-point Instruction Format 106 8.11. Floating-point Data Formats 106 8.12. Singular Floating-point Numbers 108 8.13. Indicators 112 8.14. Universal Accumulator 113 8.15. Fraction Arithmetic 114 8.16. Floating-point-arithmetic Operations 114 8.17. Fixed-point Arithmetic Using Unnormalized Floating-point Operations 118 8.18. Special Functions and Forms of Arithmetic 119 8.19. Multiple-precision Arithmetic 119 8.20. General Remarks 121 9. Instruction Formats 122 [by W. Buchholz] 9.1. Introduction 122 9.2. Earlier Instruction Languages 122 9.3. Evolution of the Single-address Instruction 124 9.4. Implied Addresses 125 9.5. Basic 7030 Instruction Formats 126 9.6. Instruction Efficiency 127 9.7. The Simplicity of Complexity 131 9.8. Relationship to Automatic Programming Languages 132 10. Instruction Sequencing 133 [by F. P. Brooks, Jr.] 10.1. Modes of Instruction Sequencing 133 10.2. Instruction Counter 134 10.3. Unconditional Branching 135 10.4. Conditional Branching 136 10.5. Program-interrupt System 136 10.6. Components of the Program-interrupt System 137 10.7. Examples of Program-interrupt Techniques 140 10.8. Execute Instructions 146 10.9. Execute Operations in the 7030 148 11. Indexing 150 [by G. P. Blaauw] 11.1. Introduction 150 11.2. Indexing Functions 151 11.3. Instruction Format for Indexing 155 11.4. Incrementing 157 11.5. Counting 159 11.6. Advancing by One 161 11.7. Progressive Indexing 161 11.8. Data Transmission 162 11.9. Data Ordering 163 11.10. Refilling 165 11.11. Indirect Addressing and Indirect Indexing 167 11.12. Indexing Applications 169 11.13. Record-handling Applications 172 11.14. File Maintenance 175 11.15. Subroutine Control 177 11.16. Conclusion 178 12. Input-Output Control 179 [by W. Buchholz] 12.1. A Generalized Approach to Connecting Input-Output and External Storage 179 12.2. Input-Output Instructions 180 12.3. Defining the Memory Area 181 12.4. Writing and Reading 182 12.5. Controlling and Locating 183 12.6. An Alternative Approach 184 12.7. Program Interruptions 184 12.8. Buffering 180 12.9. Interface 188 12.10. Operator Control of Input-Output Units 190 13. Multiprogramming 192 [by E. F. Codd, E. S. Lowry, E. McDonough, and C. A. Scalzi] 13.1. Introduction 192 13.2. Multiprogramming Requirements 193 13.3. 7030 Features that Assist Multiprogramming 195 13.4. Programmed Logic 197 13.5. Concluding Remarks 200 13.6. References 201 14. The Central Processing Unit 202 [by E. Bloch] 14.1. Concurrent System Operation 202 14.2. Concurrency within the Central Processing Unit 204 14.3. Data Flow 204 14.4. Arithmetic Unit 208 14.5. Checking 216 14.6. Component Count 216 14.7. Performance 217 14.8. Circuits 218 14.9. Packaging 223 15. The Look-ahead Unit 228 [by R. S. Balance, J. Cocke, and H. G. Kolsky] 15.1. General Description 228 15.2. Timing-simulation Program 230 15.3. Description of the Look-ahead Unit 238 15.4. Forwarding 240 15.5. Counter Sequences 241 15.6. Recovery after Interrupt 246 15.7. A Look-back at the Look-ahead 247 16. The Exchange 248 [by W. Buchholz] 16.1. General Description 248 16.2. Starting a WRITE or READ Operation 250 16.3. Data Transfer during Writing 250 16.4. Data Transfer during Reading 251 16.5. Terminating a WRITE or READ Operation 252 16.6. Multiple Operations 252 16.7. CONTROL and LOCATE Operations 252 16.8. Interrogating the Control Word 253 16.9. Forced Termination 253 17. A Nonarithmetical System Extension 254 [by S. G. Campbell, P.S. Herwitz, and J. H. Pomerene] 17.1. Nonarithmetical Processing 254 17.2. The Set-up Mode 258 17.3. Byte-sequence Formation 259 17.4. Pattern Selection 260 17.5. Transformation Facilities 261 17.6. Statistical Aids 263 17.7. The BYTE-BY-BYTE Instruction 263 17.8. Monitoring for Special Conditions 264 17.9. Instruction Set 265 17.10. Collating Operations 266 17.11. Table Look-up Operations 267 17.12. Example 267 Appendix A. Summary Data 273 A.1. List of the Larger IBM Stored-program Computers 273 A.2. Instruction Formats 275 A.3. List of Registers and Special Addresses 276 A.4. Summary of Operations and Modifiers 277 A.5. Summary of Indicators 287 Appendix B. Programming Examples 292 Notation 292 B.1. Polynomial Evaluation 295 B.2. Cube-root Extraction 296 B.3. Matrix Multiplication 298 B.4. Conversion of Decimal Numbers to a Floating-point Normalized Vector 299 B.5. Editing a Typed Message 301 B.6. Transposition of a Large Bit Matrix 303 Index 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.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
http://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
library.ox.ac.uk:210/ADVANCE",
note = "This important book is the primary description of the
influential IBM 7030 Stretch computer, written by its
architects.",
URL = "http://ed-thelen.org/comp-hist/IBM-7030-Planning-McJones.pdf",
acknowledgement = ack-nhfb,
remark = "The text of the book is in the public domain, with the
permission of the author in 2003.
See \cite{MacKenzie:1991:IAL} for a remark about the
noisy mode for floating-point arithmetic in the IBM
7030 Stretch. That mode is first mentioned on page 25
of this book, and described in detail on page 102,
which states:
``By definition of ordinary normalized FLP operations,
numbers are frequently extended on the right by
attaching zeros. During addition the n-digit operand
that is not preshifted is extended with n zeros, so as
to provide the extra positions to which the preshifted
operand can be added. Any operand or result that is
shifted left to be normalized requires a corresponding
number of zeros to be shifted in at the right. Both
sets of zeros tend to produce numbers smaller in
absolute value than they would have been if more digits
had been carried. In the noisy mode these numbers are
simply extended with 1 s instead of zeros (1 s in a
binary machine, 9s in a decimal machine). So all
numbers tend to be too large in absolute value. The
true value, if there had been no significance loss,
should lie between these two extremes. Hence, two runs,
one made without and one made with the noisy mode,
should show differences in result that indicate which
digits may have been affected by significance loss.
The principal weakness of the noisy-mode procedure is
that it requires two runs for the same problem. A much
less important weakness is that the loss of
significance cannot be guaranteed to show up --- it
merely has a very high probability of showing up ---
whereas built-in significance checks can be made
slightly pessimistic, so that actual significance loss
will not be greater than indicated. On the other hand,
little extra hardware and no extra storage are required
for the noisy-mode approach. Furthermore, significance
loss is relatively rare, so that running a problem
twice when Significance loss is suspected does not pose
a serious problem. What is serious is the possibility
of unsuspected significance loss.
In discussions of significance two points are often
overlooked. The first of these is trivial: the best way
of ensuring significant results is to use an adequate
number of fraction digits. The second is almost equally
mundane: for a given procedure, normalized FLP
arithmetic will ordinarily produce the greatest
precision possible for the number of fraction digits
used. Normalized FLP arithmetic has been criticized
with respect to significance loss, because such loss is
not indicated by the creation of leading zeros, as it
is with fixed-point arithmetic. In other words, the
contention is not that normalized FLP arithmetic is
more prone to significance loss than equivalent
fixed-point arithmetic, which would be untrue, but that
an equivalent indication of such loss is not provided.
Loss of significance, however, is also a serious
problem in fixed-point arithmetic; multiplication and
division do not handle it at all correctly by means of
leading zeros. (In particular, fixed-point
multiplication may lead to serious or even total
significance loss, which would not have occurred with
normalized FLP arithmetic: and although leading zeros
in addition and subtraction of fixed-point operands do
give correct significance indications, the use of other
operations and of built-in scaling loops frequently
destroys entirely the leading-zeros method of counting
significance.)''",
subject = "Computer architecture",
tableofcontents = "Foreword v \\
Preface vii \\
1. Project Stretch 1 \\
[by W. Buchholz] \\
2. Architectural Philosophy 5 \\
[by F. P. Brooks, Jr.] \\
2.1. The Two Objectives of Project Stretch 5 \\
2.2. Resources 6 \\
2.3. Guiding Principles 7 \\
2.4. Contemporary Trends in Computer Architecture 10
\\
2.5. Hindsight 15 \\
3. System Summary of IBM 7030 17 \\
[by W. Buchholz] \\
3.1. System Organization 17 \\
3.2. Memory Units 17 \\
3.3. Index Memory 19 \\
3.4. Special Registers 19 \\
3.5. Input and Output Facilities 19 \\
3.6. High-speed Disk Units 20 \\
3.7. Central Processing Unit 20 \\
3.8. Instruction Controls 21 \\
3.9. Index-arithmetic Unit 21 \\
3.10. Instruction Look-ahead 21 \\
3.11. Arithmetic Unit 22 \\
3.12. Instruction Set 24 \\
3.13. Data Arithmetic 24 \\
3.14. Radix-conversion Operations 27 \\
3.15. Connective Operations 27 \\
3.16. Index-arithmetic Operations 27 \\
3.17. Branching Operations 28 \\
3.18. Transmission Operations 28 \\
3.19. Input-Output Operations 29 \\
3.20. New Features 29 \\
3.21. Performance 32 \\
4. Natural Data Units 33 \\
[by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
\\
4.1. Lengths and Structures of Natural Data Units 33
\\
4.2. Procedures for Specifying Natural Data Units 36
\\
4.3. Data Hierarchies 39 \\
4.4. Classes of Operations 40 \\
5. Choosing a Number Base 42 \\
[by W. Buchholz] \\
5.1. Introduction 42 \\
5.2. Information Content 45 \\
5.3. Arithmetic Speed 49 \\
5.4. Numerical Data 50 \\
5.5. Nonnumerical Data 51 \\
5.6. Addresses 52 \\
5.7. Transformation 53 \\
5.8. Partitioning of Memory 54 \\
5.9. Program Interpretation 56 \\
5.10. Other Number Bases 58 \\
5.11. Conclusion 58 \\
6. Character Set 60 \\
[by R. W. Bemer and W. Buchholz] \\
6.1. Introduction 60 \\
6.2. Size of Set 62 \\
6.3. Subsets 62 \\
6.4. Expansion of Set 63 \\
6.5. Code 63 \\
6.6. Parity Bit 66 \\
6.7. Sequence 66 \\
6.8. Blank 67 \\
6.9. Decimal Digits 68 \\
6.10. Typewriter Keyboard 68 \\
6.11. Adjacency 69 \\
6.12. Uniqueness 69 \\
6.13. Signs 70 \\
6.14. Tape-recording Convention 71 \\
6.15. Card-punching Convention 71 \\
6.16. List of 7030 Character Set 72 \\
7. Variable-field-length Operation 75 \\
[by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
\\
7.1. Introduction 75 \\
7.2. Addressing of Variable-field-length Data 76 \\
7.3. Field Length 77 \\
7.4. Byte Size 78 \\
7.5. Universal Accumulator 79 \\
7.6. Accumulator Operand 79 \\
7.7. Binary and Decimal Arithmetic 80 \\
7.8. Integer Arithmetic 81 \\
7.9. Numerical Signs 82 \\
7.10. Indicators 84 \\
7.11. Arithmetical Operations 85 \\
7.12. Radix-conversion Operation 87 \\
7.13. Logical Connectives of Two Variables 87 \\
7.14. Connective Operations 89 \\
8. Floating-point Operation 92 \\
[by S. G. Campbell] \\
General Discussion \\
8.1. Problems of Fixed-point Arithmetic 92 \\
8.2. Floating-point Arithmetic 94 \\
8.3. Normalization 97 \\
8.4. Floating-point Singularities 98 \\
8.5. Range and Precision 99 \\
8.6. Round-off Error 100 \\
8.7. Significance Checks 101 \\
8.8. Forms of Floating-point Arithmetic 103 \\
8.9. Structure of Floating-point Data 104 \\
Floating-point Features of the 7030 \\
8.10. Floating-point Instruction Format 106 \\
8.11. Floating-point Data Formats 106 \\
8.12. Singular Floating-point Numbers 108 \\
8.13. Indicators 112 \\
8.14. Universal Accumulator 113 \\
8.15. Fraction Arithmetic 114 \\
8.16. Floating-point-arithmetic Operations 114 \\
8.17. Fixed-point Arithmetic Using Unnormalized \\
Floating-point Operations 118 \\
8.18. Special Functions and Forms of Arithmetic 119 \\
8.19. Multiple-precision Arithmetic 119 \\
8.20. General Remarks 121 \\
9. Instruction Formats 122 \\
[by W. Buchholz] \\
9.1. Introduction 122 \\
9.2. Earlier Instruction Languages 122 \\
9.3. Evolution of the Single-address Instruction 124
\\
9.4. Implied Addresses 125 \\
9.5. Basic 7030 Instruction Formats 126 \\
9.6. Instruction Efficiency 127 \\
9.7. The Simplicity of Complexity 131 \\
9.8. Relationship to Automatic Programming Languages
132 \\
10. Instruction Sequencing 133 \\
[by F. P. Brooks, Jr.] \\
10.1. Modes of Instruction Sequencing 133 \\
10.2. Instruction Counter 134 \\
10.3. Unconditional Branching 135 \\
10.4. Conditional Branching 136 \\
10.5. Program-interrupt System 136 \\
10.6. Components of the Program-interrupt System 137
\\
10.7. Examples of Program-interrupt Techniques 140 \\
10.8. Execute Instructions 146 \\
10.9. Execute Operations in the 7030 148 \\
11. Indexing 150 \\
[by G. P. Blaauw] \\
11.1. Introduction 150 \\
11.2. Indexing Functions 151 \\
11.3. Instruction Format for Indexing 155 \\
11.4. Incrementing 157 \\
11.5. Counting 159 \\
11.6. Advancing by One 161 \\
11.7. Progressive Indexing 161 \\
11.8. Data Transmission 162 \\
11.9. Data Ordering 163 \\
11.10. Refilling 165 \\
11.11. Indirect Addressing and Indirect Indexing 167
\\
11.12. Indexing Applications 169 \\
11.13. Record-handling Applications 172 \\
11.14. File Maintenance 175 \\
11.15. Subroutine Control 177 \\
11.16. Conclusion 178 \\
12. Input-Output Control 179 \\
[by W. Buchholz] \\
12.1. A Generalized Approach to Connecting \\
Input-Output and External Storage 179 \\
12.2. Input-Output Instructions 180 \\
12.3. Defining the Memory Area 181 \\
12.4. Writing and Reading 182 \\
12.5. Controlling and Locating 183 \\
12.6. An Alternative Approach 184 \\
12.7. Program Interruptions 184 \\
12.8. Buffering 180 \\
12.9. Interface 188 \\
12.10. Operator Control of Input-Output Units 190 \\
13. Multiprogramming 192 \\
[by E. F. Codd, E. S. Lowry, E. McDonough, and C. A.
Scalzi] \\
13.1. Introduction 192 \\
13.2. Multiprogramming Requirements 193 \\
13.3. 7030 Features that Assist Multiprogramming 195
\\
13.4. Programmed Logic 197 \\
13.5. Concluding Remarks 200 \\
13.6. References 201 \\
14. The Central Processing Unit 202 \\
[by E. Bloch] \\
14.1. Concurrent System Operation 202 \\
14.2. Concurrency within the Central Processing Unit
204 \\
14.3. Data Flow 204 \\
14.4. Arithmetic Unit 208 \\
14.5. Checking 216 \\
14.6. Component Count 216 \\
14.7. Performance 217 \\
14.8. Circuits 218 \\
14.9. Packaging 223 \\
15. The Look-ahead Unit 228 \\
[by R. S. Balance, J. Cocke, and H. G. Kolsky] \\
15.1. General Description 228 \\
15.2. Timing-simulation Program 230 \\
15.3. Description of the Look-ahead Unit 238 \\
15.4. Forwarding 240 \\
15.5. Counter Sequences 241 \\
15.6. Recovery after Interrupt 246 \\
15.7. A Look-back at the Look-ahead 247 \\
16. The Exchange 248 \\
[by W. Buchholz] \\
16.1. General Description 248 \\
16.2. Starting a WRITE or READ Operation 250 \\
16.3. Data Transfer during Writing 250 \\
16.4. Data Transfer during Reading 251 \\
16.5. Terminating a WRITE or READ Operation 252 \\
16.6. Multiple Operations 252 \\
16.7. CONTROL and LOCATE Operations 252 \\
16.8. Interrogating the Control Word 253 \\
16.9. Forced Termination 253 \\
17. A Nonarithmetical System Extension 254 \\
[by S. G. Campbell, P.S. Herwitz, and J. H. Pomerene]
\\
17.1. Nonarithmetical Processing 254 \\
17.2. The Set-up Mode 258 \\
17.3. Byte-sequence Formation 259 \\
17.4. Pattern Selection 260 \\
17.5. Transformation Facilities 261 \\
17.6. Statistical Aids 263 \\
17.7. The BYTE-BY-BYTE Instruction 263 \\
17.8. Monitoring for Special Conditions 264 \\
17.9. Instruction Set 265 \\
17.10. Collating Operations 266 \\
17.11. Table Look-up Operations 267 \\
17.12. Example 267 \\
Appendix A. Summary Data 273 \\
A.1. List of the Larger IBM Stored-program Computers
273 \\
A.2. Instruction Formats 275 \\
A.3. List of Registers and Special Addresses 276 \\
A.4. Summary of Operations and Modifiers 277 \\
A.5. Summary of Indicators 287 \\
Appendix B. Programming Examples 292 \\
Notation 292 \\
B.1. Polynomial Evaluation 295 \\
B.2. Cube-root Extraction 296 \\
B.3. Matrix Multiplication 298 \\
B.4. Conversion of Decimal Numbers to a \\
Floating-point Normalized Vector 299 \\
B.5. Editing a Typed Message 301 \\
B.6. Transposition of a Large Bit Matrix 303 \\
Index 305",
}
nn!KV %#/)+c=+3%=%;M)g+=incollectionfparith.bibCampbell:1962:FPOS. G. CampbellWerner BuchholzPlanning lJ\ #/+c+3!E{;{C7%+{geSbookfparith.bibBuchholz:1962:PCSWerner BuchholzPlanning a computer system: Project 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.pdfThe text of the booolz",
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",
}
50V|5
@InProceedings{Krithivasan:2004:SPM,
author = "S. Krithivasan and M. J. Schulte and J. GloB=
@InProceedings{Krueger:2004:DLI,
author = "S. D. Krueger and P.-M. Seidel",
booktitle = B
F
@InProceedings{Kubosawa:1992:BFP,
author = "H. Kubosawa and A. Katsuno and H. Takahashi an&[7
@InProceedings{Krithivasan:2003:MAM,
author = "S. Krithivasan and M. J. Schulte",
title ?N
@InProceedings{Krishnan:2001:PEM,
author = "Shankar Krishnan and Mark Foskey and Tim Culve:ىhQ
@InProceedings{Krishnan:1989:ESA,
author = "R. Krishnan",
booktitle = "International m[
@InProceedings{Krishnan:1989:CBN,
author = "R. Krishnan",
booktitle = "Twenty-Third AF
@InProceedings{Krishnan:1988:SCR,
author = "R. Krishnan",
booktitle = "International Conference on Acoustics, Speech, and
Signal Processing, ICASSP-88, 11--14 April 19sa 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,
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number = "2",
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DOI = "http://dx.doi.org/10.1109/TEC.1962.5219348",
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title = "Logarithmic and Exponential Function Evaluation in a
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with floating-point computers",
institution = "University of Illinois Graduate College, Digital
Computer Laboratory",
address = "Urbana, IL, USA",
pages = "7",
year = "1962",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Report / University of Illinois, Digital Computer
Laboratory; no. 113 Report (University of Illinois
(Urbana-Champaign campus). Digital Computer
Laboratory); no. 113.",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers.; Numerical
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remark = "Supported by: National Science Foundation under grant
G16489. ``March 22, 1962.''",
}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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institution = "University of Illinois Graduate College, Digital
Computer Laboratory",
address = "Urbana, IL, USA",
pages = "7",
year = "1962",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Report / University of Illinois, Digital Computer
Laboratory; no. 113 Report (University of Illinois
(Urbana-Champaign campus). Digital Computer
Laboratory); no. 113.",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers.; Numerical
calculations.",
remark = "Supported by: National Science Foundation under grant
G16489. ``March 22, 1962.''",
}
uMZ !#/#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 eshold Realization of Arithmetic Circuits",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "2",
pages = "287--288",
month = apr,
year = "1962",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1962.5219366",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:50 MDT 2011",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219366",
acknowledgement = ack-nhfb,
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@Article{Ercegovac:1988:LSC,
author = "Milo{\v{s}} D. Ercegovac and Tomas Lang",
title =R%
@Article{Ercegovac:1990:FMC,
author = "M. D. Ercegovac and T. Lang",
title = "Fas ˏ
@Article{Ercegovac:1992:FRC,
author = "M. D. Ercegovac and T. Lang",
title = "On-&;
@Article{Ercegovac:1991:MPM,
author = "Milo{\v{s}} D. Ercegovac and Tomas Lang",
title =#YH
@Article{Ercegovac:1990:RSR,
author = "M. D. Ercegovac and T. Lang",
title = "Rad Ά:u
@Article{Ercegovac:1987:FCR,
author = "M. D. Ercegovac and T. Lang",
title = "On-6m
@Article{Ercegovac:1973:REC,
author = "Milo{\v{s}} D. Ercegovac",
title = "Radix-v0a
@Article{Ercegovac:1984:LAO,
author = "Milo{\v{s}} D. Ercegovac",
title = "On-linm`A
@Article{Ercegovac:1990:SRD,
author = "M. D. Ercegovac and T. Lang",
title = "Sim 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",
title = "Threshold Realization of Arithmetic Circuits",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "2",
pages = "287--288",
month = apr,
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bibdate = "Thu Jul 14 09:11:50 MDT 2011",
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sNW#/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://r representation for use with
algorithmic languages",
journal = j-CACM,
volume = "5",
number = "3",
pages = "160--161",
month = mar,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00",
MRnumber = "26\#4506",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Algorithmic languages, such as ALGOL, make provision
for two types of numbers, real and integer, which are
usually implemented on the computer by means of
floating-point and fixed-point numbers respectively.
The concepts real and integer, however, are taken from
mathematics, where the set of integers forms a proper
subset of the set of real numbers. In implementation a
real problem is posed by the fact that the set of
fixed-point numbers is not a proper subset of the set
of floating-point numbers; this problem becomes very
apparent in attempts to implement ALGOL 60.
Furthermore, the {\em one\/} mathematical operation of
addition is implemented in the machine by one of {\em
two\/} machine operations, fixed-point addition or
floating-point addition.",
acknowledgement = ack-nhfb,
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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,
volume = "5",
number = "3",
pages = "160--161",
month = mar,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
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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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XOZ #'!%57;m;c?c-w!%articlefparith.bibGrau:1962:FNRA. A. GrauOn a floating-point number representation for use with algorithmic languagesj-CACM53160--161mar31962CACMA20001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)0001-0782 OR 0001078268.0026\#4506Fri Dec 8 08:24:14 1995http://www.math.utah.edu/pub/tex/bib/fparith.bib1995.12.08 08:24:14 ???Algorithmic languages, such as ALGOL, make provision for two types of numbers, real and integer, which are usually implemented on the computer by means of 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 setlving Linear Simultaneous Equations
Using the Residue Number System",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "2",
pages = "164--173",
month = apr,
year = "1962",
CODEN = "IRELAO",
DOI = "http://dx.doi.org/10.1109/TEC.1962.5219349",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:49 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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acknowledgement = ack-nhfb,
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}s on Electronic Computersack-nhfbRonald M. GuffinA Computer for Solving Linear Simultaneous Equations Using the Residue Number System
@Article{Guffin:1962:CSL,
author = "Ronald M. Guffin",
title = "A Computer for Solving Linear Simultaneous Equations
Using the Residue Number System",
journal = j-IRE-TRANS-ELEC-COMPUT,
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acknowledgement = ack-nhfb,
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yQV #-Ii+3!E%;uMmIiibookfparith.bibHamming:1962:NMSR. W. (Richard Wesley) HammingNumerical methods for scientists and engineerspub-MCGRAW-HILLpub-MCGRAW-HILL:adr4111962QA297 .H28Fri Aug 2ɌUPY #+-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,
address = pub-MCGRAW-HILL:adr,
pages = "411",
year = "1962",
LCCN = "QA297 .H28",
bibdate = "Fri Aug 20 09:12:08 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "International series in pure and applied mathematics",
acknowledgement = ack-nhfb,
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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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title = "Numerical methods for scientists and engineers",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "411",
year = "1962",
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bibdate = "Fri Aug 20 09:12:08 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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series = "International series in pure and applied mathematics",
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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keywords = "decimal floating-point arithmetic",
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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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month = may,
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**sSU#1?m-7=m;A?mcarticlefparith.bΊ[RV#)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,
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number = "??",
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month = "????",
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}ibKaratsuba:1962:MMNA. Karatsuba and Y. OfmanMultiplication of multidigit numbers on automataj-DOKL-AKAD-NAUK145293--2941962DANKAS0002-3264 OR 00023264Tue Jul 05 10:35:11 2005http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.07.05 10:35:11 ???Doklady Akademii nauk SSSRack-nhfbA. Karatsuba and Y. OfmanMultiplication of multidigit numbers on automata
@Article{Karatsuba:1962:MMN,
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title = "Multiplication of multidigit numbers on automata",
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}= "Division and overflow detection in residue number
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journal = j-IRE-TRANS-ELEC-COMPUT,
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month = aug,
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}tection in residue number systems
@Article{Keir:1962:DOD,
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title = "Division and overflow detection in residue number
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qUW #)#W57;K;?c#Warticlefparith.bibKnuth:1962:EPCD. E. KnuthEvaluation of Polynomials By Computerj-CACM512595--599dec121962CACMA20001-0782 (print), 1557-7317 (electronic) OR ԍ_TW#'g;a75%E;]gCarticlefparith.bibKeir:1962:DODY. A. Keir and P. W. Cheney and M. TannenbaumDivision and overflow detection in residue number 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",
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acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
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@Article{Perlin:1960:HPC,
author = "I. E. Perlin and J. R. Garrett",
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@Article{Perry:2006:BSF,
author = "Tekla S. Perry",
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author = "C. Pettus",
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IjV #+M!#;K;Mbookfparith.bibFlores:1963:LCAI. FloresThe Logic of Computer Arithmeticpub-PHpub-PH:adrxii + 4931963QA76.5 .F46Thu Sep 1 10:12:51 1994ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.math.utah.edu/pub/tex/bib/fparith.bib1994.09.01 10:12:51 ???ack-njI. FloresThe Logic of Computer Arithmetic
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LWLwlY #1'g[57E5;1?c1'gMarticlefparith.bibGoldstein:1963:SADMax GoldsteinSignificance arithmetic on a digital computerj-CACM63111--117mar31963CACMA2http://dx.doi.org/10.1145/366274.3663390001-0kW#)7[=m;!7articlefparith.bibGeier:1963:ACDA. Geier and I. SturzThe approximate calculation of a definite integral with automatic choice of integration steps (intervals). The program for the computer $ rm MECIPTI $ in a floating point regime. (Romanian)An. Univ. Timisoara Ser. Sti. Mat.-Fiz.1133--139196368.0030\#3588Fri Dec 08 13:52:47 1hmetic on a digital computer",
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abstract = "The 7090 at NYU has been modified to include a
``Significance Mode'' of operation which is intended to
facilitate the identification of significant bits in
the results of floating-point arithmetic operations.
The manner in which floating-point arithmetic is
handled in this mode is discussed. Several numerical
experiments using this mode are described and
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abstract = "The 7090 at NYU has been modified to include a
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acknowledgement = ack-nhfb,
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journal = j-IEEE-TRANS-ELEC-COMPUT,
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}arnumber=4037921IEEE Transactions on Electronic Computersack-nhfbM. LehmanThe Minimization of Assimilations in Binary Carry-Storage Arithmetic Units
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D!h.bibLehmer:1963:RDOD. H. LehmerR63--17 Division and Overflow Detection in Residue Number Systemsj-IEEE-TRANS-ELEC-COMPUTEC-12136--37feb21963IEECA8http://dx.doi.org/10.1109/PGEC.1963.2634930367-7508 OR 03677508Thu Jul 14 08:10:36 MDT 2011http://ieeexplore.ieee.org/; http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 08:10:36 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037786; http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4037754IEEE Transactions on Electronic Computersresidue arithmetic; residue number systemack-nhfbD. H. Lehmer{R63--17} Division and Overflow Detection in Residue Number Systems
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}% "Basic Operations in an Unnormalized Arithmetic
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bibdate = "Thu Jul 14 08:10:44 MDT 2011",
bibsource = "http://www.computer.org/tc/;
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038037",
ZMnumber = "0124.07910",
abstract = "A particular set of unnormalized arithmetic operations
termed ``basic'' are described, in the context of the
University of Chicago Maniac III Computer. Each basic
operation involves three operand words and generates
two result words, all in unnormalized floating point
format. The use of these operations in the
implementation of 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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}'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 impl(ementation 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
@Article{Metropolis:1963:BOU,
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remark = "Cited in \cite{Sterbenz:1974:FPC}.",
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rV#'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 A+1qZ#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",
year = "1963",
LCCN = "HA29 .M75 1963",
bibdate = "Fri Aug 20 10:02:03 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "McGraw-Hill series in probability and statistics",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
subject = "Mathematical statistics",
}ug 20 10:02:03 MDT 2010http://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager2010.08.20 10:02:03 MDTMcGraw-Hill series in probability and statisticsCited in cite Sterbenz:1974:FPC.Mathematical statisticsack-nhfbAlexander McFarlane Mood and Franklin A. GraybillIntroduction to the theory of statistics
@Book{Mood:1963:ITS,
author = "Alexander McFarlane Mood and Franklin A. Graybill",
title = "Introduction to the theory of statistics",
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address = pub-MCGRAW-HILL:adr,
edition = "Second",
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bibdate = "Fri Aug 20 10:02:03 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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remark = "Cited in \cite{Sterbenz:1974:FPC}.",
subject = "Mathematical statistics",
}uit for the square root of the sum of the
squares",
journal = j-PROC-IEEE,
volume = "51",
number = "4",
pages = "593--596",
month = apr,
year = "1963",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "A piecewise-linear network can produce an output
proportional to the square root of the sum of the
squares of a set of input voltages, using resistors and
diodes alone. The required relationship between
voltages can be represented by a multi- \ldots{}",
} 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,
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bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "http://ieeexplore.ieee.org/;
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acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "A piecewise-linear network can produce an output
proportional to the square root of the sum of the
squares of a set of input voltages, using resistors and
diodes alone. The required relationship between
voltages can be represented by a multi- \ldots{}",
}
))KsW#)E{#57E';;E{articlefparith.bibStern:1963:CSRT. E. Stern and R. M. LernerA circuit for the square root of the sum of the squaresj-PROC-IEEE514593--596apr41963IEEPAD0018-9219 (print), 1558-2256 (electronic) OR 00189219 (print), 15582256 (electronic)0018-9219 OR 00189219Sat Jul 16 15:28:13 MDT 2005http://ieeexplore.ieee.org/; http://www.math.utah.edu/pub/tex/bib/fparith.bib2005.07.16 15:28:13 MDTProceedings of the IEEEack-nhfbhttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5T. E. Stern and R. M. LernerA circuit for the square root of the sum of the squares
@Article{Stern:1963:CSR,
author = "T. E. Stern and R. M. Lerner",
-0iple-precision floating-point interpretive
program for the {Control Data} 1604",
journal = j-COMP-J,
volume = "6",
number = "1",
pages = "62--66",
month = apr,
year = "1963",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:55:45 MDT 2000",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/060062.sgm.abs.html;
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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/",
}2uk/computer_journal/hdb/Volume_06/Issue_01/060062.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/62.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/63.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/64.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/65.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/66.tifThe Computer Journalack-nhfbhttp://comjnl.oxfordjournals.org/A. H. Stroud and D. SecrestA multiple-precision floating-point interpretive program for the {Control Data} 1604
@Article{Stroud:1963:MPF,
author = "A. H. Stroud and D. Secrest",
title = "A multiple-precision floating-point interpretive
program for the {Control Data} 1604",
journal = j-COMP-J,
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number = "1",
pages = "62--66",
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bibdate = "Fri Sep 29 08:55:45 MDT 2000",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
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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",
}
kkuU #+!?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,
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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",
}
mvU '#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}.",
}
mwU #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??",
}
""RxZ #)#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
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}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
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}
::_|V '#/=U9K-Em;E=U9mastersthesisfparG-{[#'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 (pD0zV #3-i57=m;1e-i!articlefparith.bibAshenhurst:1964:FEUR. L. AshenhurstFunction Evaluation in Unnormalized AritARyX #1[;;=m;y3g'manualfparith.bibAnonymous:1964:PPFAnonymousPINT: Purdue floating point interpretive system: for the RPC 4000 General Precision electronic computerGeneral Precision, Inc.West Lafayette, IN, USA451964Mon May 06 10:24:31 2002http://www.math.utah.edu/pub/te>uation in Unnormalized Arithmetic",
journal = 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",
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} calculation of the $ 3 - j $, $ 6 - j $ and $ 9 - j $
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journal = j-CACM,
volume = "7",
number = "11",
pages = "657--659",
month = nov,
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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,
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&Lr+>}
@Article{Capps:1988:OAL,
author = "C. David Capps and R. Aaron Falk and Theodore L.
҈*U
@Article{Cappa:1973:AIA,
author = "M. Cappa and V. C. Hamacher",
title = "An Augmj(Q
@Article{Capocelli:1988:EVN,
author = "R. M. Capocelli and R. Giancarlo",
title = ćiS
@Article{Cantor:1962:LEF,
author = "D. Cantor and G. Estrin and R. Turn",
title = K
@Article{Calvetti:1991:REF,
author = "Daniela Calvetti",
title = "Roundoff error "={
@Article{Campbell:1986:SS,
author = "R. A. Campbell",
title = "In Search of a SinH
@Article{Campbell:1986:NSR,
author = "R. A. Campbell",
title = "{NS32000} Square
@Article{Calvert:1936:DDS,
author = "H. R. Calvert",
title = "Decimal Division ofM-
@Article{Callahan:1988:EII,
author = "D. Callahan and J. Cocke and K. Kennedy",
title = Erint), 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)",
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abstract = "Described in this paper is a system of general-purpose
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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
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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",
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}J10782 (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
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ZZY #'+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/doP`~X #177-=m;Ou;# manualfparith.bibBurroughs:1964:BBIBurroughs CorporationBurroughs B5500 Information Processing Systems Reference ManualBurroughs CorporatioM}[ #-'57E;[?c['S articlefparith.bibBrooker:1964:PPSR. A. BrookerA programming package for some general modes of arithmeticj-CACM72119--127feb21964CACMA20001-0782 (print), 1557-7317 (electronic) OR 000Ihs B5500} Information Processing Systems
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}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
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abstract = "In January of 1960, the late Hans J. Maehly completed
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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,
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abstract = "In January of 1960, the late Hans J. Maehly completed
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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,
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bibdate = "Thu Jul 14 06:56:59 MDT 2011",
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acknowledgement = ack-nhfb,
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P{P Y#);=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.jspl1W #/)GC;m;5Kyarticlefparith.i
W #-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.maft of the normalized floating point number
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X#1[;'Em;%M[?bookfparith.bibMcCracken:1964:NMFDaniel D. McCracken and William S. DornNumerical methods and FORTRAN programming, with applications in engineering and sciencepub-WILuxComputer Performance Using Residue
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}zorg/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib2011.07.14 06:56:58 MDThttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038105; http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4038099IEEE Transactions on Electronic Computersresidue arithmetic; residue number systemack-nhfbRoy D. MerrillImproving Digital Computer Performance Using Residue Number Theory
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acknowledgement = ack-nhfb,
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CC9W '#';'97Em;?gmastersthesisfparith.bibMoss:1964:RDCGeorge Joseph Moss, Jr.Recording digital counter with floating point output formatThesis (M.S.)University of MarylandCollege Park, MD, USA1551964Sat Feb 24 15:01:45 MST 1996http://www.math.utah.edu/pub/tex/bib/fparith.bib1996.02.24 15:01:45 MSTack-nhfbGeorge Joseph {Moss, Jr.}Recording digital counter with floating point output format
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cV #'%I!+=K;%IIbookfparith.bibRice:1964:AFVJohn R. RiceThe Approximation of 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
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@Article{Santos:1964:BVB,
author = "J. Santos and H. Arango",
title = "Base $3$ vs Base $2$ Synchronous Arithmetic Units",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "5",
pages = "608--609",
month = oct,
year = "1964",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1964.263734",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:57:04 MDT 2011",
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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 000107tW#+;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://iods for Multiple Precision
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journal = j-CACM,
volume = "7",
number = "8",
pages = "472--474",
month = aug,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:08 1994",
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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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acknowledgement = ack-nj,
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}loating point arithmetic with the residue
number system",
type = "Thesis ({M.S.})",
school = "UCLA - Engineering",
address = "Los Angeles, CA, USA",
pages = "89",
year = "1964",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Congruences and residues.; Electronic digital
computers --- Programming.",
}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,
author = "David Ernest Sweo",
title = "A study of floating point arithmetic with the residue
number system",
type = "Thesis ({M.S.})",
school = "UCLA - Engineering",
address = "Los Angeles, CA, USA",
pages = "89",
year = "1964",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Congruences and residues.; Electronic digital
computers --- Programming.",
}Fast Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "1",
pages = "14--17",
month = feb,
year = "1964",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1964.263830",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:56:56 MDT 2011",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038071",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}/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,
author = "C. S. Wallace",
title = "A Suggestion for a Fast Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "1",
pages = "14--17",
month = feb,
year = "1964",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1964.263830",
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bibdate = "Thu Jul 14 06:56:56 MDT 2011",
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}
3O3sU '#3-!Ew';m;-E!w-#inproceedingsfparY#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), 1V #)#_57=m;?c#_articlefparith.bibWolfe:1964:RTEJ. M. WolfeReducing Trunc%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/bibors by Programming",
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journal = j-CACM,
volume = "7",
number = "6",
pages = "355--356",
month = jun,
year = "1964",
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ISSN = "0001-0782 (print), 1557-7317 (electronic)",
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bibdate = "Thu Sep 08 00:17:16 1994",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
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}volume = "72",
number = "2 (Part 2)",
pages = "47--58",
year = "1965",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "65.80",
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45.",
ZMnumber = "0216.49602",
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keywords = "error estimation; floating-point arithmetic",
}930-0972 (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,
volume = "72",
number = "2 (Part 2)",
pages = "47--58",
year = "1965",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
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MRclass = "65.80",
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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
of Business, University of Chicago, Center for
Mathematical Studies in Business and Economics, number
45.",
ZMnumber = "0216.49602",
acknowledgement = ack-jr,
fjournal = "The American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
keywords = "error estimation; floating-point arithmetic",
}all",
booktitle = "Error in digital computation",
title = "Experimental investigation of unnormalized
arithmetic",
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title = "Techniques for automatic error monitoring and
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TW #'!I57;K;?c!Ikarticlefparith.bibBlum:1965:EAPB. I. BlumAn Extended Arithmetic Packagej-CACM85318--320may51965CACMA20001-0782 (print), 1557-731SW #-'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.bib2011.07.14uU '#3-!Ew';m;-E!w/inproceedingsfpareal-Time Iterative Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "3",
pages = "394--399",
month = jun,
year = "1965",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1965.264145",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:33 MDT 2011",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038457",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
} 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,
volume = "EC-14",
number = "3",
pages = "394--399",
month = jun,
year = "1965",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1965.264145",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:33 MDT 2011",
bibsource = "http://www.computer.org/tc/;
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acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}ckage",
journal = j-CACM,
volume = "8",
number = "5",
pages = "318--320",
month = may,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 8 08:20:53 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
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fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}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",
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",
}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 Eel 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 Scof a Diode Squarer by Applying the
Criterion of Square Root of the Integral of Per Cent
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journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "3",
pages = "456--463",
month = jun,
year = "1965",
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} Applying the Criterion of Square Root of the Integral of Per Cent Error Squared
@Article{Deiters:1965:ODD,
author = "Robert M. Deiters",
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volume = "EC-14",
number = "3",
pages = "456--463",
month = jun,
year = "1965",
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ISSN = "0367-7508",
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038465",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
%%OY #-/u=a7E;_/uearticlefparith.bibDeiters:1965:ODDRobert M. DeitersOptimum Design of a Diode Squarer by Applying the Criterion of Square Root of the Integral of Per Cent Error 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 by of {Boolean} Functions",
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abstract = "Recently M. Morris Mano presented a method for
performing Boolean OR, AND and NOT operations by means
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decimal computer lacking builtin logical
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journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "Boolean operations; decimal arithmetic",
sjb = "Commenting on \cite{Mano:1965:PSB}.",
}
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author = "George G. Dodd",
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journal = j-CACM,
volume = "8",
number = "8",
pages = "517--517",
month = aug,
year = "1965",
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ISSN = "0001-0782 (print), 1557-7317 (electronic)",
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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}.",
}
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fjournal = "IBM Technical Disclosure Bulletin",
}
u U #)#=7=m;O#=articlefparith.bibEarle:1965:LCSJ. G. EarleLatched Carry-Save Adderj-IBM-TDB7909--910mar31965IBMTAA0018-8689 OR 00188689Fri Nov 09 10:49:36 2007http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.11.09 10:49:36 ???IBM Technical Disclosure Bulletinack-nhfbJ. G. EarleLatched Carry-Save Adder
@Article{Earle:1965:LCS,
author = "J. G. Earle",
title = "Latched Carry-Save Adder",
journal = j-IBM-TDB,
volume = "7",
number = "??",
pages = "909--910",
month = mar,
year = "1965",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Fri Nov 09 10:49:36 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
}nd arithmetic",
crossref = "Alt:1965:AC",
volume = "6",
pages = "131--194",
year = "1965",
bibdate = "Sat May 18 14:18:19 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}!
?"Y #+%=a7EU;__%#articlefparith=!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",
volume = "6",
pages = "131--194",
year = "1965",
bibdate = "Sat May 18 14:18:19 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}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",
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}".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
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author = "H. L. Garner",
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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",
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http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
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acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
keywords = "residue arithmetic; residue number system",
}mputer Arithmetic",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "4",
pages = "670--670",
month = aug,
year = "1965",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1965.264031",
ISSN = "0367-7508",
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@Article{Hammel:1965:RLC,
author = "D. Hammel",
title = "{R65-54} The Logic of Computer Arithmetic",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "4",
pages = "670--670",
month = aug,
year = "1965",
CODEN = "IEECA8",
DOI = "http://dx.doi.org/10.1109/PGEC.1965.264031",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:40 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
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URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038535",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
FGF[&[ #))57=a;?c)qarticlefparH%Z#-I=a7E ;_'Icarticlefparith.bibHamming:1965:NLBR. W. Hamming and W. L. MammelA Note on the Location of the Binary Point in a Computin&$Y #-/++O57E;S'c/7Carticlefparith.bibHammer:1965:BRBaPreston C. HammerBook Review: booktitle Experimenta-#W #+[=a7E;__yarticlefparith.bibHammel:1965:RLCD. HammelR65-54 The Logic of Computer Arithmeticj-IEEE-TRANS-ELEC-COMPUTEC-144670--670aug81965IEECA8http://dx.doi.org/10.1109/PGEC.1965.2640310367-7508 OR 03677508Thu Jul 14 06:26:40 MDT 2011http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetrd Computing and Mathematics}} by N. C.
Metropolis; A. H. Taub; John Todd; C. B. Tompkins}",
journal = j-TECHNOMETRICS,
volume = "7",
number = "1",
pages = "82--82",
month = feb,
year = "1965",
CODEN = "TCMTA2",
DOI = "http://dx.doi.org/10.2307/1266139",
ISSN = "0040-1706 (print), 1537-2723 (electronic)",
ISSN-L = "0040-1706",
bibdate = "Sat Jun 21 13:17:45 MDT 2014",
bibsource = "http://www.jstor.org/journals/00401706.html;
http://www.jstor.org/stable/i254241;
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fjournal = "Technometrics",
journal-URL = "http://www.jstor.org/journals/00401706.html",
}$l Arithmetic, High Speed Computing and Mathematics by N. C. Metropolis; A. H. Taub; John Todd; C. B. Tompkinsj-TECHNOMETRICS7182--82feb21965TCMTA2http://dx.doi.org/10.2307/12661390040-1706 (print), 1537-2723 (electronic) OR 00401706 (print), 15372723 (electronic)0040-1706 OR 00401706Sat Jun 21 13:17:45 MDT 2014http://www.jstor.org/journals/00401706.html; http://www.jstor.org/stable/i254241; http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/technometrics1960.bib2014.06.21 13:17:45 MDThttp://www.jstor.org/stable/1266139Technometricsack-nhfbhttp://www.jstor.org/journals/00401706.htmlPreston C. HammerBook Review: {{\booktitle{Experimental Arithmetic, High Speed Computing and Mathematics}} by N. C. Metropolis; A. H. Taub; John Todd; C. B. Tompkins}
@Article{Hammer:1965:BRBa,
author = "Preston C. Hammer",
title = "Book Review: {{\booktitle{Experimental Arithmetic,
High Speed Computing and Mathematics}} by N. C.
Metropolis; A. H. Taub; John Todd; C. B. Tompkins}",
journal = j-TECHNOMETRICS,
volume = "7",
number = "1",
pages = "82--82",
month = feb,
year = "1965",
CODEN = "TCMTA2",
DOI = "http://dx.doi.org/10.2307/1266139",
ISSN = "0040-1706 (print), 1537-2723 (electronic)",
ISSN-L = "0040-1706",
bibdate = "Sat Jun 21 13:17:45 MDT 2014",
bibsource = "http://www.jstor.org/journals/00401706.html;
http://www.jstor.org/stable/i254241;
http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/technometrics1960.bib",
URL = "http://www.jstor.org/stable/1266139",
acknowledgement = ack-nhfb,
fjournal = "Technometrics",
journal-URL = "http://www.jstor.org/journals/00401706.html",
}Note on the Location of the Binary Point in a
Computing Machine",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
pages = "260--261",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "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/;
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http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=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.",
}%
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Stack",
journal = j-COMP-J,
vocg 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 would 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,
author = "R. W. Hamming and W. L. Mammel",
title = "A Note on the Location of the Binary Point in a
Computing Machine",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
pages = "260--261",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "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.",
}sion Floating-Point Arithmetic
with 132-Bit Numbers",
journal = j-CACM,
volume = "8",
number = "3",
pages = "175--177",
month = mar,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00",
MRnumber = "30\#2707",
bibdate = "Fri Dec 08 14:32:51 1995",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In a recent paper, Gregory and Raney described a
technique for double-precision floating-point
arithmetic. A similar technique can be developed for
triple-precision floating-point arithmetic and its is
the purpose of this note to describe this technique.
Only the multiplication and the division algorithms are
described, since the addition-subtraction algorithm can
be obtained by a trivial modification of the algorithm
in Gregory's and Raney's paper.",
acknowledgement = ack-nhfb,
checked = "19940404",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}&ith.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 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.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
with 132-Bit Numbers",
journal = j-CACM,
volume = "8",
number = "3",
pages = "175--177",
month = mar,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00",
MRnumber = "30\#2707",
bibdate = "Fri Dec 08 14:32:51 1995",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In a recent paper, Gregory and Raney described a
technique for double-precision floating-point
arithmetic. A similar technique can be developed for
triple-precision floating-point arithmetic and its is
the purpose of this note to describe this technique.
Only the multiplication and the division algorithms are
described, since the addition-subtraction algorithm can
be obtained by a trivial modification of the algorithm
in Gregory's and Raney's paper.",
acknowledgement = ack-nhfb,
checked = "19940404",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}ration of Square Roots on a Computer with
Rapid Multiplication Compared with Division (in
{Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "19",
number = "91",
pages = "497--500",
month = jul,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}'ication Compared with Division (in {Technical Notes and Short Papers})
@Article{James:1965:GSR,
author = "Wendy James and P. Jarratt",
title = "The Generation of Square Roots on a Computer with
Rapid Multiplication Compared with Division (in
{Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "19",
number = "91",
pages = "497--500",
month = jul,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR
database",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
'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 Multiple 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}.",
}(14 19:11:11 2007http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib2007.02.14 19:11:11 ???Section 4.1.Cited in cite Sterbenz:1974:FPC.ack-nhfbW. KahanProgrammer's Reference ManualSection 4.1.The Floating-Point Over\slash Underflow Trap Routine {{\tt FPTRP}}
@InCollection{Kahan:1965:FPO,
author = "W. Kahan",
booktitle = "Programmer's Reference Manual",
title = "The Floating-Point Over\slash Underflow Trap Routine
{{\tt FPTRP}}",
publisher = "Institute of Computer Science, University of Toronto",
address = "Toronto, Ontario, Canada",
year = "1965",
LCCN = "????",
bibdate = "Wed Feb 14 19:11:11 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Section 4.1.",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
7(W %#)Gu==s;%MG%incollectionfparith.bibKahan:1965:FPOW. KahanProgrammer's Reference ManualThe Floating-Point Over / Underflow Trap Routine tt FPTRPInstitute of Computer Science, University of TorontoToronto, Ontario, Canada497--5001965Wed Feb g Truncation Errors",
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",
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}.",
})fm?idx=J79W. KahanFurther Remarks on Reducing Truncation Errors
@Article{Kahan:1965:FRR,
author = "W. Kahan",
title = "Further Remarks on Reducing Truncation Errors",
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",
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 (e͍.)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",
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}.",
}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;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$\sqrt(x)$; elementary functions; floating-point
arithmetic",
}+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
Root Routine",
journal = j-CACM,
volume = "8",
number = "4",
pages = "202",
month = apr,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "$\sqrt(x)$; elementary functions; floating-point
arithmetic",
}
T+Z #'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;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Described in this paper is a divide-and-correct method
for variable precision division in digital computers.
Unlike the earlier methods of Stein and Pope, the
present method uses a suitably rounded form of the
normalized divisor for getting an estimate of the
quotient characters. This result is a correction of at
most plus or minus one to the estimate, to obtain the
exact quotient character. It is believed that this
method will be widely applicable for division
operations in variable word-length character-oriented
machines.",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "floating-point arithmetic",
}, 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,
author = "E. V. Krishnamurthy",
title = "On a Divide-and-Correct Method for Variable Precision
Division",
journal = j-CACM,
volume = "8",
number = "3",
pages = "179--181",
month = mar,
year = "1965",
CODEN = "CACMA2",
DOI = "http://doi.acm.org/10.1145/363791.363829",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
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MRclass = "68.00",
MRnumber = "30\#2709",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Described in this paper is a divide-and-correct method
for variable precision division in digital computers.
Unlike the earlier methods of Stein and Pope, the
present method uses a suitably rounded form of the
normalized divisor for getting an estimate of the
quotient characters. This result is a correction of at
most plus or minus one to the estimate, to obtain the
exact quotient character. It is believed that this
method will be widely applicable for division
operations in variable word-length character-oriented
machines.",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "floating-point arithmetic",
}
%%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.
Raumfahrtkonstruktionen, Universit{\"a}t Stuttgart",
address = "Stuttgart, Germany",
pages = "5",
year = "1965",
bibdate = "Thu May 09 09:05:51 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}-
--O-V !#-!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}
@TechReport{Lederer:1965:FPP,
author = "E. Lederer",
title = "Floating-point-Pegasus, {FLPPEG}",
type = "{ISD-Bericht}",
number = "12",
institution = "ISD, Inst. f{\"u}r Statik u. Dynamik d. Luft- u.
Raumfahrtkonstruktionen, Universit{\"a}t Stuttgart",
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bibdate = "Thu May 09 09:05:51 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}Techniques",
crossref = "AFIPS:1965:FJC",
pages = "715--725",
year = "1965",
bibdate = "Tue Jan 08 23:08:35 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}.
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,
author = "M. Lehman",
title = "Serial Arithmetic Techniques",
crossref = "AFIPS:1965:FJC",
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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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crossref = "Kalenich:1965:IPP",
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pages = "441--442",
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@Article{Prince:1984:SFP,
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@Article{Metropolis:1965:RCU,
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title = "Algorithms for Special Functions {II}",
journal = j-NUM-MATH,
volume = "7",
pages = "194--196",
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Sep 16 10:22:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
xxmonth = "(none)",
xxnumber = "(none)",
}-Precision",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "5",
number = "4",
pages = "251--255",
year = "1965",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Sat Nov 14 09:14:57 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Moller:1965:QDP}.",
acknowledgement = ack-nj # " and " # ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
}91--2551965BITTEL, NBITAB0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)0006-3835 OR 00063835Sat Nov 14 09:14:57 1998http://www.math.utah.edu/pub/tex/bib/fparith.bib1998.11.14 09:14:57 ???See cite Moller:1965:QDP.ack-njhttp://link.springer.com/journal/10543Ole M{\o}llerSee \cite{Moller:1965:QDP}.Note on Quasi Double-Precision
@Article{Moller:1965:NQD,
author = "Ole M{\o}ller",
title = "Note on Quasi Double-Precision",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "5",
number = "4",
pages = "251--255",
year = "1965",
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journal-URL = "http://link.springer.com/journal/10543",
}on in Floating Point Addition",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "5",
number = "1",
pages = "37--50",
month = mar,
year = "1965",
CODEN = "BITTEL, NBITAB",
DOI = "http://dx.doi.org/10.1007/BF01975722",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65.80",
MRnumber = "31\#5359",
bibdate = "Wed Jan 4 18:52:08 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=5&issue=1;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Moller:1965:NQD}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=5&issue=1&spage=37",
acknowledgement = ack-nj # " and " # ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "accurate floating-point summation; floating-point
arithmetic; rounding errors",
remark = "Gives summation error estimate formula `s = fl(a + b);
error = (a - s) + b', also discovered independently by
\cite{Kahan:1965:FRR}. Extends Gill's earlier
fixed-point result \cite{Gill:1951:PSS}.",
}:b2006.01.04 18:52:08 MSTSee also cite Moller:1965:NQD.http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=5&issue=1&spage=37accurate floating-point summation; floating-point arithmetic; rounding errorsGives summation error estimate formula `s = fl(a + b); error = (a - s) + b', also discovered independently by cite Kahan:1965:FRR. Extends Gill's earlier fixed-point result cite Gill:1951:PSS.ack-njhttp://link.springer.com/journal/10543Ole M{\o}llerSee also \cite{Moller:1965:NQD}.Quasi Double-Precision in Floating Point Addition
@Article{Moller:1965:QDP,
author = "Ole M{\o}ller",
title = "Quasi Double-Precision in Floating Point Addition",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "5",
number = "1",
pages = "37--50",
month = mar,
year = "1965",
CODEN = "BITTEL, NBITAB",
DOI = "http://dx.doi.org/10.1007/BF01975722",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65.80",
MRnumber = "31\#5359",
bibdate = "Wed Jan 4 18:52:08 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=5&issue=1;
http://www.math.utah.edu/pub/tex/bib/bit.bib;
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note = "See also \cite{Moller:1965:NQD}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=5&issue=1&spage=37",
acknowledgement = ack-nj # " and " # ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "accurate floating-point summation; floating-point
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remark = "Gives summation error estimate formula `s = fl(a + b);
error = (a - s) + b', also discovered independently by
\cite{Kahan:1965:FRR}. Extends Gill's earlier
fixed-point result \cite{Gill:1951:PSS}.",
}
33Y;X %#+)W)'5!=m;M)WQFincollectionfparith.bibMoore:1965:AACaRamon E. MooreThe automatic analysis and control of error in digital computing based on the use of interval numbersRall:1965:EDCa261--130196565.61 (65.80)MR0176614 (31 \#886)T. E. HullThu Jun 20 10:51:40 2002http://www.matX:Z #+!oI)U57C;II'
Y'Mo'articlefparith.bibMoller:1965:QDPOle MollerQuasi Double-Precision in Floating Point Additionj-NORDISK-TIDSKR-INFORM-BEHAND5137--50mar31965BITTEL, NBITABhttp://dx.doi.org/10.1007/BF019757220006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)0006-3835 OR 0006383565.8031\#5359Wed Jan 4 18:52:08 MST 2006http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=5&issue=1; http://www.math.utah.edu/pub/tex/bib/bit.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bianalysis and control of error in digital
computing based on the use of interval numbers",
crossref = "Rall:1965:EDCa",
chapter = "2",
pages = "61--130",
year = "1965",
MRclass = "65.61 (65.80)",
MRnumber = "MR0176614 (31 \#886)",
MRreviewer = "T. E. Hull",
bibdate = "Thu Jun 20 10:51:40 2002",
bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://interval.louisiana.edu/Moores_early_papers/Moore_in_Rall_V1.pdf",
acknowledgement = ack-nhfb,
bookpages = "????",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
};h.utah.edu/pub/tex/bib/fparith.bib2002.06.20 10:51:40 ???http://interval.louisiana.edu/Moores_early_papers/Moore_in_Rall_V1.pdfCited in cite Sterbenz:1974:FPC.ack-nhfbRamon E. MooreThe automatic analysis and control of error in digital computing based on the use of interval numbers
@InCollection{Moore:1965:AACa,
author = "Ramon E. Moore",
title = "The automatic analysis and control of error in digital
computing based on the use of interval numbers",
crossref = "Rall:1965:EDCa",
chapter = "2",
~~