# bibtab

bibtype: incollection
filename: fparith.bib
label: Kahan:1965:FPO
author: W. Kahan
booktitle: Programmer's Reference Manual
title: The Floating-Point Over / Underflow Trap Routine tt FPTRP
publisher: Institute of Computer Science, University of Toronto
address: Toronto, Ontario, Canada
pages: 497--500
year: 1965
bibdate: Wed Feb 14 19:11:11 2007
bibtimestamp: 2007.02.14 19:11:11 ???
note: Section 4.1.
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawbooktitle: Programmer's Reference Manual
rawnote: Section 4.1.
rawtitle: The Floating-Point Over\slash Underflow Trap Routine {{\tt FPTRP}}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@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 =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Section 4.1.",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Kahan:1965:PFR
author: W. Kahan
title: Pracniques: Further Remarks on Reducing Truncation Errors
journal: j-CACM
volume: 8
number: 1
pages: 40--40
month: jan
monthnumber: 1
year: 1965
CODEN: CACMA2
DOI: https://doi.org/10.1145/363707.363723
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Sep 08 00:18:17 1994
bibtimestamp: 1994.09.08 00:18:17 ???
fjournal: Communications of the ACM
keywords: floating-point arithmetic; truncation errors
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/cacm
rawauthor: W. Kahan
rawtitle: Pracniques: {Further} Remarks on Reducing Truncation Errors
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

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. See improvement cite Ozawa:1993:SAE.

entry:
@Article{Kahan:1965:PFR,
  author =       "W. Kahan",
  title =        "Pracniques: {Further} Remarks on Reducing Truncation
                 Errors",
  journal =      j-CACM,
  volume =       "8",
  number =       "1",
  pages =        "40--40",
  month =        jan,
  year =         "1965",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363707.363723",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 00:18:17 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "floating-point arithmetic; truncation errors",
  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}. See
                 improvement \cite{Ozawa:1993:SAE}.",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 4
year: 1965
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Thu Nov 03 08:47:50 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.11.03 08:47:50 ???
fjournal: Journal of the ACM
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
rawauthor: Herbert Kanner
rawtitle: Number Base Conversion in Significant Digit Arithmetic
entry:
@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 =    "https://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}.",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 4
year: 1965
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Sep 1 10:15:43 1994
bibtimestamp: 1994.09.01 10:15:43 ???
fjournal: Communications of the ACM
keywords: $sqrt (x)$; elementary functions; floating-point arithmetic
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/cacm
rawauthor: R. King
rawtitle: Letter to the {Editor}: On the Double-Precision Square Root Routine
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@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;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions; floating-point
                 arithmetic",
}


bibtype: article
filename: fparith.bib
label: 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
monthnumber: 3
year: 1965
CODEN: CACMA2
DOI: https://doi.org/10.1145/363791.363829
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 68.00
MRnumber: 30\#2709
bibdate: Thu Sep 1 10:15:08 1994
bibtimestamp: 1994.09.01 10:15:08 ???
fjournal: Communications of the ACM
keywords: correct rounding; floating-point arithmetic
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/cacm
rawauthor: E. V. Krishnamurthy
rawtitle: On a Divide-and-Correct Method for Variable Precision Division
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/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://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.

rawabstract:
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.

entry:
@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 =          "https://doi.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/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://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 =  "https://dl.acm.org/loi/cacm",
  keywords =     "correct rounding; floating-point arithmetic",
}


bibtype: techreport
filename: fparith.bib
label: Lederer:1965:FPP
author: E. Lederer
title: Floating-point-Pegasus, FLPPEG
type: ISD-Bericht
number: 12
institution: ISD, Inst. fur Statik u. Dynamik d. Luft- u. Raumfahrtkonstruktionen, Universitat Stuttgart
address: Stuttgart, Germany
pages: 5
year: 1965
bibdate: Thu May 09 09:05:51 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 09:05:51 ???
acknowledgement: ack-nhfb
rawauthor: E. Lederer
rawtitle: Floating-point-Pegasus, {FLPPEG}
entry:
@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",
  address =      "Stuttgart, Germany",
  pages =        "5",
  year =         "1965",
  bibdate =      "Thu May 09 09:05:51 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Lehman:1965:SAT
author: M. Lehman
title: Serial Arithmetic Techniques
crossref: AFIPS:1965:FJC
pages: 715--725
year: 1965
bibdate: Tue Jan 08 23:08:35 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.01.08 23:08:35 ???
acknowledgement: ack-nhfb
rawauthor: M. Lehman
rawtitle: Serial Arithmetic Techniques
entry:
@InProceedings{Lehman:1965:SAT,
  author =       "M. Lehman",
  title =        "Serial Arithmetic Techniques",
  crossref =     "AFIPS:1965:FJC",
  pages =        "715--725",
  year =         "1965",
  bibdate =      "Tue Jan 08 23:08:35 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: mastersthesis
filename: fparith.bib
label: Liddiard:1965:DPF
author: Lawrence Anthony Liddiard
title: Double precision floating point arithmetic
type: Thesis (M.S.)
school: University of Minnesota
pages: various
year: 1965
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Calculators.; Numerical calculations.
acknowledgement: ack-nhfb
rawauthor: Lawrence Anthony Liddiard
rawtitle: Double precision floating point arithmetic
entry:
@MastersThesis{Liddiard:1965:DPF,
  author =       "Lawrence Anthony Liddiard",
  title =        "Double precision floating point arithmetic",
  type =         "Thesis ({M.S.})",
  school =       "University of Minnesota",
  address =      "????",
  pages =        "various",
  year =         "1965",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Calculators.; Numerical calculations.",
}


bibtype: book
filename: fparith.bib
label: Lyusternik:1965:HCE
author: L. A. Lyusternik and O. A. Chervonenkis and A. R. Yanpolski
title: Handbook for Computing Elementary Functions
publisher: pub-PERGAMON
address: pub-PERGAMON:adr
pages: xiii + 251
year: 1965
LCCN: QA221.L513
bibdate: Thu Sep 1 10:13:16 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:13:16 ???
note: Translated from the Russian by G. J. Tee. Translation edited by K. L. Stewart.
acknowledgement: ack-nj
rawauthor: L. A. Lyusternik and O. A. Chervonenkis and A. R. Yanpolski
rawnote: Translated from the Russian by G. J. Tee. Translation edited by K. L. Stewart.
rawtitle: Handbook for Computing Elementary Functions
entry:
@Book{Lyusternik:1965:HCE,
  author =       "L. A. Lyusternik and O. A. Chervonenkis and A. R.
                 Yanpolski",
  title =        "Handbook for Computing Elementary Functions",
  publisher =    pub-PERGAMON,
  address =      pub-PERGAMON:adr,
  pages =        "xiii + 251",
  year =         "1965",
  LCCN =         "QA221.L513",
  bibdate =      "Thu Sep 1 10:13:16 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Translated from the Russian by G. J. Tee. Translation
                 edited by K. L. Stewart.",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Mano:1965:PSB
author: M. Morris Mano
title: Pracniques: Simulation of Boolean functions in a decimal computer
journal: j-CACM
volume: 8
number: 1
pages: 39--40
month: jan
monthnumber: 1
year: 1965
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:58 MST 2005
bibtimestamp: 2005.11.25 18:19:58 MST
note: See remarks cite Dodd:1965:RSB.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: M. Morris Mano
rawnote: See remarks \cite{Dodd:1965:RSB}.
rawtitle: Pracniques: {Simulation} of {Boolean} functions in a decimal computer
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Mano:1965:PSB,
  author =       "M. Morris Mano",
  title =        "Pracniques: {Simulation} of {Boolean} functions in a
                 decimal computer",
  journal =      j-CACM,
  volume =       "8",
  number =       "1",
  pages =        "39--40",
  month =        jan,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:58 MST 2005",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See remarks \cite{Dodd:1965:RSB}.",
  acknowledgement = ack-nhfb,
  checked =      "19940304",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  sjb =          "Describes how to perform Boolean operations by means
                 of arithmetic and conditional transfer operations on a
                 decimal computer lacking any built in logical
                 instructions. See also \cite{Dodd:cacm:65}.",
}


bibtype: article
filename: fparith.bib
label: Martin:1965:SHS
author: A. R. Martin and A. B. Rosenstein
title: A Shiftrix for High-Speed Multiplication
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-14
number: 4
pages: 639--643
month: aug
monthnumber: 8
year: 1965
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1965.264010
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 06:26:39 MDT 2011
bibtimestamp: 2011.07.14 06:26:39 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038521
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: A. R. Martin and A. B. Rosenstein
rawtitle: A Shiftrix for High-Speed Multiplication
entry:
@Article{Martin:1965:SHS,
  author =       "A. R. Martin and A. B. Rosenstein",
  title =        "A Shiftrix for High-Speed Multiplication",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "4",
  pages =        "639--643",
  month =        aug,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264010",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:39 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038521",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: inproceedings
filename: fparith.bib
label: Metropolis:1965:AIE
author: N. Metropolis
title: Analysis of Inherent Errors in Matrix Decomposition Using Unnormalized Arithmetic
crossref: Kalenich:1965:IPP
volume: 2
pages: 441--442
year: 1965
bibdate: Wed Feb 14 19:21:38 2007
bibtimestamp: 2007.02.14 19:21:38 ???
remark: Cited in cite Sterbenz:1974:FPC.
ZMnumber: 0161.35502
acknowledgement: ack-nhfb
rawauthor: N. Metropolis
rawtitle: Analysis of Inherent Errors in Matrix Decomposition Using Unnormalized Arithmetic
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@InProceedings{Metropolis:1965:AIE,
  author =       "N. Metropolis",
  title =        "Analysis of Inherent Errors in Matrix Decomposition
                 Using Unnormalized Arithmetic",
  crossref =     "Kalenich:1965:IPP",
  volume =       "2",
  pages =        "441--442",
  year =         "1965",
  bibdate =      "Wed Feb 14 19:21:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0161.35502",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Metropolis:1965:AUA
author: N. Metropolis
title: Algorithms in unnormalized arithmetic. I. Recurrence relations
journal: j-NUM-MATH
volume: 7
number: 2
pages: 104--112
month: apr
monthnumber: 4
year: 1965
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 68.00
MRnumber: MR0178589 (31 \#2846)
MRreviewer: G. Dahlquist
bibdate: Wed Nov 14 19:04:40 2007
bibtimestamp: 2007.11.14 19:04:40 ???
note: See erratum cite Metropolis:1965:BAU.
fjournal: Numerische Mathematik
ZMnumber: 0128.36301
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: N. Metropolis
rawnote: See erratum \cite{Metropolis:1965:BAU}.
rawtitle: Algorithms in unnormalized arithmetic. {I}. {Recurrence} relations
entry:
@Article{Metropolis:1965:AUA,
  author =       "N. Metropolis",
  title =        "Algorithms in unnormalized arithmetic. {I}.
                 {Recurrence} relations",
  journal =      j-NUM-MATH,
  volume =       "7",
  number =       "2",
  pages =        "104--112",
  month =        apr,
  year =         "1965",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "68.00",
  MRnumber =     "MR0178589 (31 \#2846)",
  MRreviewer =   "G. Dahlquist",
  bibdate =      "Wed Nov 14 19:04:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See erratum \cite{Metropolis:1965:BAU}.",
  ZMnumber =     "0128.36301",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: article
filename: fparith.bib
label: Metropolis:1965:BAU
author: N. Metropolis
title: Berichtigung: Algorithms in unnormalized arithmetic. I. Recurrence relations
journal: j-NUM-MATH
volume: 7
number: 4
pages: 354
month: aug
monthnumber: 8
year: 1965
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: Contributed Item
MRnumber: MR1553943
bibdate: Wed Nov 14 19:04:40 2007
bibtimestamp: 2007.11.14 19:04:40 ???
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: N. Metropolis
rawtitle: Berichtigung: {Algorithms} in unnormalized arithmetic. {I}. {Recurrence} relations
entry:
@Article{Metropolis:1965:BAU,
  author =       "N. Metropolis",
  title =        "Berichtigung: {Algorithms} in unnormalized arithmetic.
                 {I}. {Recurrence} relations",
  journal =      j-NUM-MATH,
  volume =       "7",
  number =       "4",
  pages =        "354",
  month =        aug,
  year =         "1965",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "Contributed Item",
  MRnumber =     "MR1553943",
  bibdate =      "Wed Nov 14 19:04:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: article
filename: fparith.bib
label: Metropolis:1965:RCU
author: N. Metropolis and R. L. Ashenhurst
title: Radix Conversion in an Unnormalized Arithmetic System
journal: j-MATH-COMPUT
volume: 19
number: 91
pages: 435--441
month: jul
monthnumber: 7
year: 1965
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
URL: http://links.jstor.org/sici?sici=0025-5718%28196507%2919%3A91%3C435%3ARCIAUA%3E2.0.CO%3B2-D
fjournal: Mathematics of Computation
ZMnumber: 0146.14607
acknowledgement: ack-nhfb
ajournal: Math. Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: N. Metropolis and R. L. Ashenhurst
rawtitle: Radix Conversion in an Unnormalized Arithmetic System
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database

entry:
@Article{Metropolis:1965:RCU,
  author =       "N. Metropolis and R. L. Ashenhurst",
  title =        "Radix Conversion in an Unnormalized Arithmetic
                 System",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "91",
  pages =        "435--441",
  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 =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  URL =          "http://links.jstor.org/sici?sici=0025-5718%28196507%2919%3A91%3C435%3ARCIAUA%3E2.0.CO%3B2-D",
  ZMnumber =     "0146.14607",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: fparith.bib
label: Metze:1965:MSR
author: Gernot Metze
title: Minimal Square Rooting
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-14
number: 2
pages: 181--185
month: apr
monthnumber: 4
year: 1965
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1965.263963
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 06:26:22 MDT 2011
bibtimestamp: 2011.07.14 06:26:22 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038397
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: Gernot Metze
rawtitle: Minimal Square Rooting
entry:
@Article{Metze:1965:MSR,
  author =       "Gernot Metze",
  title =        "Minimal Square Rooting",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "2",
  pages =        "181--185",
  month =        apr,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.263963",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038397",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: fparith.bib
label: Miller:1965:ASF
author: G. F. Miller
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) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Fri Sep 16 10:22:10 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 10:22:10 ???
fjournal: Numerische Mathematik
acknowledgement: ack-nj
journalURL: http://link.springer.com/journal/211
rawauthor: G. F. Miller
rawtitle: Algorithms for Special Functions {II}
entry:
@Article{Miller:1965:ASF,
  author =       "G. F. Miller",
  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;
                 https://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)",
}


bibtype: article
filename: fparith.bib
label: Moller:1965:NQD
author: Ole Moller
title: Note on Quasi Double-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) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Sat Nov 14 09:14:57 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.11.14 09:14:57 ???
note: See cite Moller:1965:QDP.
acknowledgement: ack-nj
journalURL: http://link.springer.com/journal/10543
rawauthor: Ole M{\o}ller
rawnote: See \cite{Moller:1965:QDP}.
rawtitle: Note on Quasi Double-Precision
entry:
@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",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Sat Nov 14 09:14:57 1998",
  bibsource =    "https://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",
}


bibtype: article
filename: fparith.bib
label: Moller:1965:QDP
author: Ole Moller
title: Quasi Double-Precision in Floating Point Addition
journal: j-NORDISK-TIDSKR-INFORM-BEHAND
volume: 5
number: 1
pages: 37--50
month: mar
monthnumber: 3
year: 1965
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01975722
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65.80
MRnumber: MR0181130 (31 \#5359)
bibdate: Wed Jan 4 18:52:08 MST 2006
bibtimestamp: 2006.01.04 18:52:08 MST
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
keywords: accurate floating-point summation; floating-point arithmetic; rounding errors
acknowledgement: ack-nj
journalURL: http://link.springer.com/journal/10543
rawauthor: Ole M{\o}ller
rawnote: See also \cite{Moller:1965:NQD}.
rawtitle: Quasi Double-Precision in Floating Point Addition
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=5&issue=1; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

remark:
Gives summation error estimate formula `s = fl(a + b); error = (a - s) + b', also discovered independently by cite Kahan:1965:PFR. Extends Gill's earlier fixed-point result cite Gill:1951:PSS.

entry:
@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 =          "https://doi.org/10.1007/BF01975722",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65.80",
  MRnumber =     "MR0181130 (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;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://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:PFR}. Extends Gill's earlier
                 fixed-point result \cite{Gill:1951:PSS}.",
}


bibtype: incollection
filename: fparith.bib
label: Moore:1965:AACa
author: Ramon E. Moore
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: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.06.20 10:51:40 ???
URL: http://interval.louisiana.edu/Moores_early_papers/Moore_in_Rall_V1.pdf
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
rawauthor: Ramon E. Moore
title:
The automatic analysis and control of error in digital computing based on the use of interval numbers

rawtitle:
The automatic analysis and control of error in digital computing based on the use of interval numbers

entry:
@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",
  bookpages =    "????",
  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 =    "https://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,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: incollection
filename: fparith.bib
label: Moore:1965:AACb
author: Ramon E. Moore
crossref: Rall:1965:EDCb
chapter: 2
pages: 103--140
year: 1965
MRclass: 65.80 (65.60)
MRnumber: MR0185839 (32 \#3299)
MRreviewer: T. E. Hull
bibdate: Thu Jun 20 10:51:40 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.06.20 10:51:40 ???
URL: http://interval.louisiana.edu/Moores_early_papers/Moore_in_Rall_V2.pdf
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
rawauthor: Ramon E. Moore
title:
Automatic local coordinate transformations to reduce the growth of error bounds in interval computation of solutions of ordinary differential equations

rawtitle:
Automatic local coordinate transformations to reduce the growth of error bounds in interval computation of solutions of ordinary differential equations

entry:
@InCollection{Moore:1965:AACb,
  author =       "Ramon E. Moore",
  title =        "Automatic local coordinate transformations to reduce
                 the growth of error bounds in interval computation of
                 solutions of ordinary differential equations",
  crossref =     "Rall:1965:EDCb",
  chapter =      "2",
  pages =        "103--140",
  year =         "1965",
  MRclass =      "65.80 (65.60)",
  MRnumber =     "MR0185839 (32 \#3299)",
  MRreviewer =   "T. E. Hull",
  bibdate =      "Thu Jun 20 10:51:40 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://interval.louisiana.edu/Moores_early_papers/Moore_in_Rall_V2.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Morrison:1965:MCC
author: D. R. Morrison
title: A Method for Computing Certain Inverse Functions
journal: j-MATH-TABLES-OTHER-AIDS-COMPUT
volume: 10
pages: 202--208
year: 1965
CODEN: MTTCAS
ISSN: 0891-6837 OR 08916837
bibdate: Thu Sep 1 10:16:10 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:10 ???
fjournal: Mathematical Tables and Other Aids to Computation
acknowledgement: ack-nj
ajournal: Math. Tables Other Aids Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: D. R. Morrison
rawtitle: A Method for Computing Certain Inverse Functions
entry:
@Article{Morrison:1965:MCC,
  author =       "D. R. Morrison",
  title =        "A Method for Computing Certain Inverse Functions",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "10",
  number =       "??",
  pages =        "202--208",
  month =        "????",
  year =         "1965",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibdate =      "Thu Sep 1 10:16:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  ajournal =     "Math. Tables Other Aids Comput.",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: fparith.bib
label: Nathan:1965:CM
author: Amos Nathan
title: The Cascade Multiplier
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-14
number: 2
pages: 243--247
month: apr
monthnumber: 4
year: 1965
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1965.264250
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 06:26:22 MDT 2011
bibtimestamp: 2011.07.14 06:26:22 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038406
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: Amos Nathan
rawtitle: The Cascade Multiplier
entry:
@Article{Nathan:1965:CM,
  author =       "Amos Nathan",
  title =        "The Cascade Multiplier",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "2",
  pages =        "243--247",
  month =        apr,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264250",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038406",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: fparith.bib
label: Penney:1965:BSC
author: Walter Penney
title: A ``Binary'' System for Complex Numbers
journal: j-J-ACM
volume: 12
number: 2
pages: 247--248
month: apr
monthnumber: 4
year: 1965
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Thu Nov 03 08:47:50 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.11.03 08:47:50 ???
fjournal: Journal of the ACM
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
rawauthor: Walter Penney
rawtitle: A {``Binary''} System for Complex Numbers
entry:
@Article{Penney:1965:BSC,
  author =       "Walter Penney",
  title =        "A {``Binary''} System for Complex Numbers",
  journal =      j-J-ACM,
  volume =       "12",
  number =       "2",
  pages =        "247--248",
  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 =    "https://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",
}


bibtype: book
filename: fparith.bib
label: Ralston:1965:FCN
author: Anthony Ralston
title: A first course in numerical analysis
publisher: pub-MCGRAW-HILL
address: pub-MCGRAW-HILL:adr
pages: xix + 578
year: 1965
LCCN: QA297 .R3
bibdate: Fri Aug 20 10:13:32 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.08.20 10:13:32 MDT
series: International series in pure and applied mathematics
remark: See also second edition cite Ralston:1978:FCN,Ralston:2001:FCN. Cited in cite Sterbenz:1974:FPC.
subject: Numerical analysis
acknowledgement: ack-nhfb
rawauthor: Anthony Ralston
rawtitle: A first course in numerical analysis
entry:
@Book{Ralston:1965:FCN,
  author =       "Anthony Ralston",
  title =        "A first course in numerical analysis",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xix + 578",
  year =         "1965",
  LCCN =         "QA297 .R3",
  bibdate =      "Fri Aug 20 10:13:32 MDT 2010",
  bibsource =    "https://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,
  remark =       "See also second edition
                 \cite{Ralston:1978:FCN,Ralston:2001:FCN}. Cited in
                 \cite{Sterbenz:1974:FPC}.",
  subject =      "Numerical analysis",
}


bibtype: article
filename: fparith.bib
label: Riordan:1965:UAT
author: R. H. S. Riordan and R. R. A. Morton
title: The Use of Analog Techniques in Binary Arithmetic Units
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-14
number: 1
pages: 29--35
month: feb
monthnumber: 2
year: 1965
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1965.264051
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 06:26:20 MDT 2011
bibtimestamp: 2011.07.14 06:26:20 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038346
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: R. H. S. Riordan and R. R. A. Morton
rawtitle: The Use of Analog Techniques in Binary Arithmetic Units
entry:
@Article{Riordan:1965:UAT,
  author =       "R. H. S. Riordan and R. R. A. Morton",
  title =        "The Use of Analog Techniques in Binary Arithmetic
                 Units",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "1",
  pages =        "29--35",
  month =        feb,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264051",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038346",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: fparith.bib
label: Ross:1965:RTE
author: D. R. Ross
title: Reducing Truncation Errors Using Cascading Accumulators
journal: j-CACM
volume: 8
number: 1
pages: 32--33
month: jan
monthnumber: 1
year: 1965
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Sun Sep 18 22:55:00 1994
bibtimestamp: 1994.09.18 22:55:00 ???
fjournal: Communications of the ACM
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: D. R. Ross
rawtitle: Reducing Truncation Errors Using Cascading Accumulators
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
When accumulating a large number of quantities as in numerical integration, the sum itself may become much larger than the individual addends. This results in truncation error. Much of this error can be eliminated using cascading accumulators as noted in a recent article by Wolfe. A simpler and slightly more flexible algorithm is presented which deals also with the case of negative addends.

rawabstract:
When accumulating a large number of quantities as in numerical integration, the sum itself may become much larger than the individual addends. This results in truncation error. Much of this error can be eliminated using cascading accumulators as noted in a recent article by Wolfe. A simpler and slightly more flexible algorithm is presented which deals also with the case of negative addends.

entry:
@Article{Ross:1965:RTE,
  author =       "D. R. Ross",
  title =        "Reducing Truncation Errors Using Cascading
                 Accumulators",
  journal =      j-CACM,
  volume =       "8",
  number =       "1",
  pages =        "32--33",
  month =        jan,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sun Sep 18 22:55:00 1994",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "When accumulating a large number of quantities as in
                 numerical integration, the sum itself may become much
                 larger than the individual addends. This results in
                 truncation error. Much of this error can be eliminated
                 using cascading accumulators as noted in a recent
                 article by Wolfe. A simpler and slightly more flexible
                 algorithm is presented which deals also with the case
                 of negative addends.",
  acknowledgement = ack-nhfb,
  checked =      "19940304",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "accurate floating-point summation",
  sjb =          "Refers to \cite{Wolfe:cacm:196,Wilhelm:1977:GMPb}.",
}


bibtype: article
filename: fparith.bib
label: Schreiber:1965:BRB
author: Alvin L. Schreiber
title: Book Review: booktitle A Binary Multiplication (W. C. McGee)
journal: j-SIAM-REVIEW
volume: 7
number: 1
pages: 134--136
year: 1965
CODEN: SIREAD
DOI: https://doi.org/10.1137/1007016
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Thu Mar 27 09:05:20 MDT 2014
bibtimestamp: 2014.03.27 09:05:20 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
onlinedate: January 1965
rawauthor: Alvin L. Schreiber
rawtitle: Book Review: {{\booktitle{A Binary Multiplication}} (W. C. McGee)}
bibsource:
http://epubs.siam.org/toc/siread/7/1; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

entry:
@Article{Schreiber:1965:BRB,
  author =       "Alvin L. Schreiber",
  title =        "Book Review: {{\booktitle{A Binary Multiplication}}
                 (W. C. McGee)}",
  journal =      j-SIAM-REVIEW,
  volume =       "7",
  number =       "1",
  pages =        "134--136",
  month =        "????",
  year =         "1965",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1007016",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:05:20 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/7/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "January 1965",
}


bibtype: article
filename: fparith.bib
label: Smith:1965:ASO
author: Francis J. Smith
journal: j-MATH-COMPUT
volume: 19
number: 89
pages: 33--36
month: apr
monthnumber: 4
year: 1965
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
ajournal: Math. Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: Francis J. Smith
title:
An Algorithm for Summing Orthogonal Polynomial Series and their Derivatives with Applications to Curve-Fitting and Interpolation

bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib; JSTOR database

rawtitle:
An Algorithm for Summing Orthogonal Polynomial Series and their Derivatives with Applications to Curve-Fitting and Interpolation

entry:
@Article{Smith:1965:ASO,
  author =       "Francis J. Smith",
  title =        "An Algorithm for Summing Orthogonal Polynomial Series
                 and their Derivatives with Applications to
                 Curve-Fitting and Interpolation",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "89",
  pages =        "33--36",
  month =        apr,
  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 =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: fparith.bib
label: Specker:1965:CAL
author: W. H. Specker
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-14
number: 1
pages: 85--86
month: feb
monthnumber: 2
year: 1965
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1965.264066
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 06:26:21 MDT 2011
bibtimestamp: 2011.07.14 06:26:21 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038361
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: W. H. Specker
title:
A Class of Algorithms for $ ln x $, $ exp x $, $ sin x $, $ cos x $, $ tan ^-1 x $, and $ cot ^-1 x $

rawtitle:
A Class of Algorithms for $ \ln x $, $ \exp x $, $ \sin x $, $ \cos x $, $ \tan^{-1} x $, and $ \cot^{-1} x $

entry:
@Article{Specker:1965:CAL,
  author =       "W. H. Specker",
  title =        "A Class of Algorithms for $ \ln x $, $ \exp x $, $
                 \sin x $, $ \cos x $, $ \tan^{-1} x $, and $ \cot^{-1}
                 x $",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "1",
  pages =        "85--86",
  month =        feb,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264066",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:21 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038361",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: fparith.bib
label: Swarztrauber:1965:LED
author: P. N. Swarztrauber
title: Letter to the Editor: On the Double-Precision Square Root Routine
journal: j-CACM
volume: 8
number: 4
pages: 202
month: apr
monthnumber: 4
year: 1965
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Wed Aug 31 14:02:19 1994
bibtimestamp: 1994.08.31 14:02:19 ???
fjournal: Communications of the ACM
keywords: $sqrt (x)$; elementary functions; floating-point arithmetic
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: P. N. Swarztrauber
rawtitle: Letter to the {Editor}: On the Double-Precision Square Root Routine
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Swarztrauber:1965:LED,
  author =       "P. N. Swarztrauber",
  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 =      "Wed Aug 31 14:02:19 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions; floating-point
                 arithmetic",
}


bibtype: article
filename: fparith.bib
label: Sweeney:1965:AFP
author: D. W. Sweeney
title: An analysis of floating-point addition
journal: j-IBM-SYS-J
volume: 4
number: 1
pages: 31--42
year: 1965
CODEN: IBMSA7
DOI: https://doi.org/10.1147/sj.41.0031
ISSN: 0018-8670 OR 00188670
bibdate: Thu Sep 15 18:42:42 1994
bibtimestamp: 1994.09.15 18:42:42 ???
note: Reprinted in cite [pp.~317--328]Swartzlander:1990:CAa.
URL: http://www.research.ibm.com/journal/sj/041/ibmsjIVRID.pdf
fjournal: IBM Systems Journal
acknowledgement: ack-nj
rawauthor: D. W. Sweeney
rawnote: Reprinted in \cite[pp.~317--328]{Swartzlander:1990:CAa}.
rawtitle: An analysis of floating-point addition
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ibmsysj.bib

remark:
Page 34, containing a critical table, was originally missing from the PDF file, and this was finally corrected by IBM in November 2008.

entry:
@Article{Sweeney:1965:AFP,
  author =       "D. W. Sweeney",
  title =        "An analysis of floating-point addition",
  journal =      j-IBM-SYS-J,
  volume =       "4",
  number =       "1",
  pages =        "31--42",
  year =         "1965",
  CODEN =        "IBMSA7",
  DOI =          "https://doi.org/10.1147/sj.41.0031",
  ISSN =         "0018-8670",
  bibdate =      "Thu Sep 15 18:42:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmsysj.bib",
  note =         "Reprinted in
                 \cite[pp.~317--328]{Swartzlander:1990:CAa}.",
  URL =          "http://www.research.ibm.com/journal/sj/041/ibmsjIVRID.pdf",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  fjournal =     "IBM Systems Journal",
  remark =       "Page 34, containing a critical table, was originally
                 missing from the PDF file, and this was finally
                 corrected by IBM in November 2008.",
  xxmonth =      "(none)",
}


bibtype: article
filename: fparith.bib
label: Winograd:1965:TRP
author: Shmuel Winograd
title: On the Time Required to Perform Addition
journal: j-J-ACM
volume: 12
number: 2
pages: 277--285
month: apr
monthnumber: 4
year: 1965
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Wed Nov 14 19:04:40 2007
bibtimestamp: 2007.11.14 19:04:40 ???
fjournal: Journal of the ACM
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
rawauthor: Shmuel Winograd
rawtitle: On the Time Required to Perform Addition
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Multi.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Winograd:1965:TRP,
  author =       "Shmuel Winograd",
  title =        "On the Time Required to Perform Addition",
  journal =      j-J-ACM,
  volume =       "12",
  number =       "2",
  pages =        "277--285",
  month =        apr,
  year =         "1965",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Wed Nov 14 19:04:40 2007",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Multi.bib;
                 https://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",
}


bibtype: article
filename: fparith.bib
label: Arango:1966:FCP
author: H. Arango and J. Santos
title: A Fast Carry-Propagation Circuit for Base $3$ Signed Non redundant Arithmetic
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-15
number: 2
pages: 254--255
month: apr
monthnumber: 4
year: 1966
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1966.264311
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 05:46:31 MDT 2011
bibtimestamp: 2011.07.14 05:46:31 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038725
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: H. Arango and J. Santos
rawtitle: A Fast Carry-Propagation Circuit for Base $3$ Signed Non redundant Arithmetic
entry:
@Article{Arango:1966:FCP,
  author =       "H. Arango and J. Santos",
  title =        "A Fast Carry-Propagation Circuit for Base $3$ Signed
                 Non redundant Arithmetic",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-15",
  number =       "2",
  pages =        "254--255",
  month =        apr,
  year =         "1966",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1966.264311",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 05:46:31 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038725",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: fparith.bib
label: Brooker:1966:MFA
author: R. A. Brooker and J. S. Rohl and S. R. Clark
title: The main features of Atlas Autocode
journal: j-COMP-J
volume: 8
number: 4
pages: 303--310
month: jan
monthnumber: 1
year: 1966
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Fri Sep 29 08:56:10 MDT 2000
bibtimestamp: 2000.09.29 08:56:10 MDT
note: See comment cite Clark:1966:CMP.
fjournal: The Computer Journal
acknowledgement: ack-nhfb
journalURL: http://comjnl.oxfordjournals.org/
rawauthor: R. A. Brooker and J. S. Rohl and S. R. Clark
rawnote: See comment \cite{Clark:1966:CMP}.
rawtitle: The main features of {Atlas Autocode}
bibsource:
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/080303.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/303.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/304.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/305.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/306.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/307.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/308.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/309.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/310.tif

entry:
@Article{Brooker:1966:MFA,
  author =       "R. A. Brooker and J. S. Rohl and S. R. Clark",
  title =        "The main features of {Atlas Autocode}",
  journal =      j-COMP-J,
  volume =       "8",
  number =       "4",
  pages =        "303--310",
  month =        jan,
  year =         "1966",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:56:10 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See comment \cite{Clark:1966:CMP}.",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/080303.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/303.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/304.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/305.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/306.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/307.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/308.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/309.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/310.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}


bibtype: mastersthesis
filename: fparith.bib
label: Chang:1966:DHR
author: Henry Kwan-cheung Chang
title: Design of a high rate floating point digital accumulator
type: Thesis (M.S. in Engineering)
school: University of California, Davis
address: Davis, CA, USA
pages: 60
year: 1966
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Dissertations, Academic --- California --- Engineering.
acknowledgement: ack-nhfb
rawauthor: Henry Kwan-cheung Chang
rawtitle: Design of a high rate floating point digital accumulator
entry:
@MastersThesis{Chang:1966:DHR,
  author =       "Henry Kwan-cheung Chang",
  title =        "Design of a high rate floating point digital
                 accumulator",
  type =         "Thesis ({M.S. in Engineering})",
  school =       "University of California, Davis",
  address =      "Davis, CA, USA",
  pages =        "60",
  year =         "1966",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Dissertations, Academic --- California ---
                 Engineering.",
}


bibtype: article
filename: fparith.bib
label: Chartres:1966:ACP
author: Bruce A. Chartres
title: Automatic Controlled Precision Calculations
journal: j-J-ACM
volume: 13
number: 3
pages: 386--403
month: jul
monthnumber: 7
year: 1966
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Fri Nov 28 16:23:06 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 16:23:06 ???
fjournal: Journal of the ACM
acknowledgement: ack-mfc
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
rawauthor: Bruce A. Chartres
rawtitle: Automatic Controlled Precision Calculations
abstract:
Recent developments in computer design and error analysis have made feasible the use of variable precision arithmetic and the preparation of programs that automatically determine their own precision requirements. Such programs enable the user to specify the accuracy he wants, and yield answers guaranteed to lie within the bounds prescribed. A class of such programs, called ``contracting error programs'', is defined in which the precision is determined by prescribing error bounds on the data. A variant of interval arithmetic is defined which enables a limited class of algorithms to be programmed as contracting error programs. A contracting error program for the solution of simultaneous linear equations is described, demonstrating the application of the idea to a wider class of problems.

rawabstract:
Recent developments in computer design and error analysis have made feasible the use of variable precision arithmetic and the preparation of programs that automatically determine their own precision requirements. Such programs enable the user to specify the accuracy he wants, and yield answers guaranteed to lie within the bounds prescribed. A class of such programs, called ``contracting error programs'', is defined in which the precision is determined by prescribing error bounds on the data. A variant of interval arithmetic is defined which enables a limited class of algorithms to be programmed as contracting error programs. A contracting error program for the solution of simultaneous linear equations is described, demonstrating the application of the idea to a wider class of problems.

entry:
@Article{Chartres:1966:ACP,
  author =       "Bruce A. Chartres",
  title =        "Automatic Controlled Precision Calculations",
  journal =      j-J-ACM,
  volume =       "13",
  number =       "3",
  pages =        "386--403",
  month =        jul,
  year =         "1966",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Fri Nov 28 16:23:06 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Recent developments in computer design and error
                 analysis have made feasible the use of variable
                 precision arithmetic and the preparation of programs
                 that automatically determine their own precision
                 requirements. Such programs enable the user to specify
                 the accuracy he wants, and yield answers guaranteed to
                 lie within the bounds prescribed. A class of such
                 programs, called ``contracting error programs'', is
                 defined in which the precision is determined by
                 prescribing error bounds on the data. A variant of
                 interval arithmetic is defined which enables a limited
                 class of algorithms to be programmed as contracting
                 error programs. A contracting error program for the
                 solution of simultaneous linear equations is described,
                 demonstrating the application of the idea to a wider
                 class of problems.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}


bibtype: article
filename: fparith.bib
label: Clark:1966:CMP
author: S. R. Clark and W. F. Lunnon
title: Correspondence: Multiple precision arithmetic (real and complex)
journal: j-COMP-J
volume: 9
number: 2
pages: 174--174
month: aug
monthnumber: 8
year: 1966
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Fri Sep 29 08:56:14 MDT 2000
bibtimestamp: 2000.09.29 08:56:14 MDT
note: See cite Brooker:1966:MFA.
URL: http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_02/tiff/174.tif
fjournal: The Computer Journal
acknowledgement: ack-nhfb
journalURL: http://comjnl.oxfordjournals.org/
rawauthor: S. R. Clark and W. F. Lunnon
rawnote: See \cite{Brooker:1966:MFA}.
rawtitle: Correspondence: Multiple precision arithmetic (real and complex)
bibsource:
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_02/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Clark:1966:CMP,
  author =       "S. R. Clark and W. F. Lunnon",
  title =        "Correspondence: Multiple precision arithmetic (real
                 and complex)",
  journal =      j-COMP-J,
  volume =       "9",
  number =       "2",
  pages =        "174--174",
  month =        aug,
  year =         "1966",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:56:14 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Brooker:1966:MFA}.",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_02/tiff/174.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}


bibtype: article
filename: fparith.bib
label: Clark:1966:MPA
author: S. R. Clark and W. F. Lunnon
title: Multiple precision arithmetic in Atlas Autocode
journal: j-COMP-J
volume: 9
number: 2
pages: 174--174
month: aug
monthnumber: 8
year: 1966
CODEN: CMPJA6
DOI: https://doi.org/10.1093/comjnl/9.2.174
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Dec 4 14:47:36 MST 2012
bibtimestamp: 2012.12.04 14:47:36 MST
URL: http://comjnl.oxfordjournals.org/content/9/2/174.full.pdf+html
fjournal: The Computer Journal
acknowledgement: ack-nhfb
journalURL: http://comjnl.oxfordjournals.org/
rawauthor: S. R. Clark and W. F. Lunnon
rawtitle: Multiple precision arithmetic in {Atlas Autocode}
bibsource:
http://comjnl.oxfordjournals.org/content/9/2.toc; https://www.math.utah.edu/pub/tex/bib/compj1960.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Clark:1966:MPA,
  author =       "S. R. Clark and W. F. Lunnon",
  title =        "Multiple precision arithmetic in {Atlas Autocode}",
  journal =      j-COMP-J,
  volume =       "9",
  number =       "2",
  pages =        "174--174",
  month =        aug,
  year =         "1966",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/9.2.174",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:36 MST 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/9/2.toc;
                 https://www.math.utah.edu/pub/tex/bib/compj1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/9/2/174.full.pdf+html",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}


bibtype: article
filename: fparith.bib
label: Fike:1966:SAS
author: C. T. Fike
title: Starting Approximations for Square Root Calculation on IBM System / 360
journal: j-CACM
volume: 9
number: 4
pages: 297--299
month: apr
monthnumber: 4
year: 1966
CODEN: CACMA2
DOI: https://doi.org/10.1145/365278.365556
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Sep 1 10:15:43 1994
bibtimestamp: 1994.09.01 10:15:43 ???
note: See letter cite Fike:1967:LER.
fjournal: Communications of the ACM
keywords: $sqrt (x)$; elementary functions; IBM S/360
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/cacm
rawauthor: C. T. Fike
rawnote: See letter \cite{Fike:1967:LER}.
rawtitle: Starting Approximations for Square Root Calculation on {IBM System\slash 360}
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Several starting approximations for square root calculation by Newton's method are presented in a form to facilitate their use in IBM System/360 square root routines. These approximations include several for the range [1/16, 1], which is the interval of primary interest on IBM System/360.

rawabstract:
Several starting approximations for square root calculation by Newton's method are presented in a form to facilitate their use in IBM System/360 square root routines. These approximations include several for the range [1/16, 1], which is the interval of primary interest on IBM System/360.

entry:
@Article{Fike:1966:SAS,
  author =       "C. T. Fike",
  title =        "Starting Approximations for Square Root Calculation on
                 {IBM System\slash 360}",
  journal =      j-CACM,
  volume =       "9",
  number =       "4",
  pages =        "297--299",
  month =        apr,
  year =         "1966",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/365278.365556",
  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.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See letter \cite{Fike:1967:LER}.",
  abstract =     "Several starting approximations for square root
                 calculation by Newton's method are presented in a form
                 to facilitate their use in IBM System/360 square root
                 routines. These approximations include several for the
                 range [1/16, 1], which is the interval of primary
                 interest on IBM System/360.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions; IBM S/360",
}


bibtype: article
filename: fparith.bib
label: Filippi:1966:BEE
author: S. Filippi
journal: j-COMPUTING
volume: 1
pages: 127--132
year: 1966
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
bibdate: Fri Sep 16 16:30:40 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:40 ???
fjournal: Computing: Archiv fur informatik und numerik
acknowledgement: ack-nj
journalURL: http://link.springer.com/journal/607
rawauthor: S. Filippi
title:
Die Berechnung einiger elementarer transzendenter Funktionen mit Hilfe des Richardson-Algorithmus toenglish The Computation of Some Elementary Transcendental Functions by Means of the Richardson Algorithm endtoenglish 

rawtitle:
{Die Berechnung einiger elementarer transzendenter Funktionen mit Hilfe des Richardson-Algorithmus} \toenglish {The Computation of Some Elementary Transcendental Functions by Means of the Richardson Algorithm} \endtoenglish

entry:
@Article{Filippi:1966:BEE,
  author =       "S. Filippi",
  title =        "{Die Berechnung einiger elementarer transzendenter
                 Funktionen mit Hilfe des Richardson-Algorithmus}
                 \toenglish {The Computation of Some Elementary
                 Transcendental Functions by Means of the Richardson
                 Algorithm} \endtoenglish",
  journal =      j-COMPUTING,
  volume =       "1",
  number =       "??",
  pages =        "127--132",
  month =        "????",
  year =         "1966",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}


bibtype: article
filename: fparith.bib
label: Flehinger:1966:PRI
author: B. J. Flehinger
title: On the Probability that a Random Integer Has Initial Digit `A'
journal: j-AMER-MATH-MONTHLY
volume: 73
pages: 1056--1061
year: 1966
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Wed Feb 14 18:53:58 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.02.14 18:53:58 ???
fjournal: American Mathematical Monthly
remark: Probably November or December issue; missing from amermathmonthly1960.bib.
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: B. J. Flehinger
rawtitle: On the Probability that a Random Integer Has Initial Digit `{A}'
entry:
@Article{Flehinger:1966:PRI,
  author =       "B. J. Flehinger",
  title =        "On the Probability that a Random Integer Has Initial
                 Digit `{A}'",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "73",
  number =       "??",
  pages =        "1056--1061",
  year =         "1966",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Wed Feb 14 18:53:58 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  remark =       "Probably November or December issue; missing from
                 amermathmonthly1960.bib.",
}


bibtype: article
filename: fparith.bib
label: Flynn:1966:VHS
author: M. J. Flynn
title: Very high-speed computing systems
journal: j-PROC-IEEE
volume: 54
number: 12
pages: 1901--1909
year: 1966
CODEN: IEEPAD
DOI: https://doi.org/10.1109/proc.1966.5273
ISSN: 0018-9219 (print), 1558-2256 (electronic) OR 00189219 (print), 15582256 (electronic)
ISSNL: 0018-9219 OR 00189219
bibdate: Wed Dec 13 08:39:04 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.13 08:39:04 ???
fjournal: Proceedings of the IEEE
keywords: floating-point arithmetic; Goldschmidt division
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5
rawauthor: M. J. Flynn
rawtitle: Very high-speed computing systems
entry:
@Article{Flynn:1966:VHS,
  author =       "M. J. Flynn",
  title =        "Very high-speed computing systems",
  journal =      j-PROC-IEEE,
  volume =       "54",
  number =       "12",
  pages =        "1901--1909",
  year =         "1966",
  CODEN =        "IEEPAD",
  DOI =          "https://doi.org/10.1109/proc.1966.5273",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Wed Dec 13 08:39:04 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  keywords =     "floating-point arithmetic; Goldschmidt division",
}


bibtype: article
filename: fparith.bib
label: Garner:1966:ECA
author: Harvey L. Garner
title: Error Codes for Arithmetic Operations
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-15
number: 5
pages: 763--770
month: oct
monthnumber: 10
year: 1966
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1966.264566
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 05:46:38 MDT 2011
bibtimestamp: 2011.07.14 05:46:38 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038884
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: Harvey L. Garner
rawtitle: Error Codes for Arithmetic Operations
entry:
@Article{Garner:1966:ECA,
  author =       "Harvey L. Garner",
  title =        "Error Codes for Arithmetic Operations",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-15",
  number =       "5",
  pages =        "763--770",
  month =        oct,
  year =         "1966",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1966.264566",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 05:46:38 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038884",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: fparith.bib
label: Grau:1966:BRB
author: A. A. Grau
title: Book Review: booktitle Rounding Errors in Algebraic Processes (J. H. Wilkinson)
journal: j-SIAM-REVIEW
volume: 8
number: 3
pages: 397--398
year: 1966
CODEN: SIREAD
DOI: https://doi.org/10.1137/1008087
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Thu Mar 27 09:05:37 MDT 2014
bibtimestamp: 2014.03.27 09:05:37 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
onlinedate: July 1966
rawauthor: A. A. Grau
rawtitle: Book Review: {{\booktitle{Rounding Errors in Algebraic Processes}} (J. H. Wilkinson)}
bibsource:
http://epubs.siam.org/toc/siread/8/3; https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

entry:
@Article{Grau:1966:BRB,
  author =       "A. A. Grau",
  title =        "Book Review: {{\booktitle{Rounding Errors in Algebraic
                 Processes}} (J. H. Wilkinson)}",
  journal =      j-SIAM-REVIEW,
  volume =       "8",
  number =       "3",
  pages =        "397--398",
  month =        "????",
  year =         "1966",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1008087",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:05:37 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/8/3;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "July 1966",
}


bibtype: article
filename: fparith.bib
label: Gregory:1966:DAU
author: Robert T. Gregory
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-15
number: 2
pages: 255--257
month: apr
monthnumber: 4
year: 1966
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1966.264312
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 05:46:31 MDT 2011
bibtimestamp: 2011.07.14 05:46:31 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038726
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: Robert T. Gregory
title:
On the Design of the Arithmetic Unit of a Fixed-Word-Length Computer from the Standpoint of Computational Accuracy

rawtitle:
On the Design of the Arithmetic Unit of a Fixed-Word-Length Computer from the Standpoint of Computational Accuracy

entry:
@Article{Gregory:1966:DAU,
  author =       "Robert T. Gregory",
  title =        "On the Design of the Arithmetic Unit of a
                 Fixed-Word-Length Computer from the Standpoint of
                 Computational Accuracy",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-15",
  number =       "2",
  pages =        "255--257",
  month =        apr,
  year =         "1966",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1966.264312",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 05:46:31 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038726",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: book
filename: fparith.bib
label: Greve:1966:HLR
author: J. Greve and H. Gumin and E. Hochsteller
publisher: Siemens AG
address: Berlin and Munchen, West Germany
pages: 59
year: 1966
bibdate: Fri Mar 17 08:31:51 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.03.17 08:31:51 ???
keywords: Gottfried Wilhelm Freiherr von Leibnitz
language: German
acknowledgement: ack-nhfb
rawauthor: J. Greve and H. Gumin and E. Hochsteller
title:
Herrn von Leibniz' Rechnung mit Null und Ein. (German) [Mister von Leibniz' calculation with zero and one]

rawtitle:
{Herrn von Leibniz' Rechnung mit Null und Ein}. ({German}) [{Mister von Leibniz'} calculation with zero and one]

entry:
@Book{Greve:1966:HLR,
  author =       "J. Greve and H. Gumin and E. Hochsteller",
  title =        "{Herrn von Leibniz' Rechnung mit Null und Ein}.
                 ({German}) [{Mister von Leibniz'} calculation with zero
                 and one]",
  publisher =    "{Siemens AG}",
  address =      "Berlin and M{\"u}nchen, West Germany",
  pages =        "59",
  year =         "1966",
  bibdate =      "Fri Mar 17 08:31:51 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Gottfried Wilhelm Freiherr von Leibnitz",
  language =     "German",
}


bibtype: inproceedings
filename: fparith.bib
label: Harding:1966:ISF
author: L. J. Harding, Jr.
booktitle: SHARE XXVII, Toronto, Canada, August 1966
title: Idiosyncracies of System / 360 Floating-Point
pages: ??--??
year: 1966
bibdate: Wed Feb 14 19:04:14 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.02.14 19:04:14 ???
acknowledgement: ack-nhfb
rawauthor: L. J. {Harding, Jr.}
rawbooktitle: {SHARE} {XXVII}, Toronto, Canada, August 1966
rawtitle: Idiosyncracies of {System\slash 360} Floating-Point
entry:
@InProceedings{Harding:1966:ISF,
  author =       "L. J. {Harding, Jr.}",
  editor =       "????",
  booktitle =    "{SHARE} {XXVII}, Toronto, Canada, August 1966",
  title =        "Idiosyncracies of {System\slash 360} Floating-Point",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "1966",
  LCCN =         "????",
  bibdate =      "Wed Feb 14 19:04:14 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Harding:1966:MSF
author: L. J. Harding, Jr.
title: Modifications of System / 360 Floating-Point
number: SSD 157, C4470
pages: 11--27
year: 1966
bibdate: Wed Feb 14 19:05:45 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.02.14 19:05:45 ???
acknowledgement: ack-nhfb
howpublished: SHARE Secretarial Distribution
rawauthor: L. J. {Harding, Jr.}
rawtitle: Modifications of {System\slash 360} Floating-Point
entry:
@Misc{Harding:1966:MSF,
  author =       "L. J. {Harding, Jr.}",
  title =        "Modifications of {System\slash 360} Floating-Point",
  number =       "SSD 157, C4470",
  howpublished = "SHARE Secretarial Distribution",
  pages =        "11--27",
  month =        "????",
  year =         "1966",
  bibdate =      "Wed Feb 14 19:05:45 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Henrici:1966:TPM
author: Peter Henrici
title: Test of probabilistic models for the propagation of roundoff errors
journal: j-CACM
volume: 9
number: 6
pages: 409--410
month: jun
monthnumber: 6
year: 1966
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:07 MST 2005
bibtimestamp: 2005.11.25 18:20:07 MST
fjournal: Communications of the ACM
keywords: floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Peter Henrici
rawtitle: Test of probabilistic models for the propagation of roundoff errors
entry:
@Article{Henrici:1966:TPM,
  author =       "Peter Henrici",
  title =        "Test of probabilistic models for the propagation of
                 roundoff errors",
  journal =      j-CACM,
  volume =       "9",
  number =       "6",
  pages =        "409--410",
  month =        jun,
  year =         "1966",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:07 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "floating-point arithmetic; rounding errors",
}


bibtype: article
filename: fparith.bib
label: Hull:1966:TPM
author: T. E. Hull and J. R. Swenson
title: Tests of Probabilistic Models for Propagation of Roundoff Errors
journal: j-CACM
volume: 9
number: 2
pages: 108--113
month: feb
monthnumber: 2
year: 1966
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65.80
MRnumber: 32\#3297
bibdate: Fri Nov 25 18:20:04 MST 2005
bibtimestamp: 2005.11.25 18:20:04 MST
fjournal: Communications of the ACM
keywords: decimal floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: T. E. Hull and J. R. Swenson
rawtitle: Tests of Probabilistic Models for Propagation of Roundoff Errors
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Theory/gvl.bib; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
In any prolonged computation it is generally assumed that the accumulated effect of roundoff errors is in some sense statistical. The purpose of this paper is to give precise descriptions of certain probabilistic models for roundoff error, and then to describe a series of experiments for testing the validity of these models. It is concluded that the models are in general very good. Discrepancies are both rare and mild. The test techniques can also be used to experiment with various types of special arithmetic.

rawabstract:
In any prolonged computation it is generally assumed that the accumulated effect of roundoff errors is in some sense statistical. The purpose of this paper is to give precise descriptions of certain probabilistic models for roundoff error, and then to describe a series of experiments for testing the validity of these models. It is concluded that the models are in general very good. Discrepancies are both rare and mild. The test techniques can also be used to experiment with various types of special arithmetic.

entry:
@Article{Hull:1966:TPM,
  author =       "T. E. Hull and J. R. Swenson",
  title =        "Tests of Probabilistic Models for Propagation of
                 Roundoff Errors",
  journal =      j-CACM,
  volume =       "9",
  number =       "2",
  pages =        "108--113",
  month =        feb,
  year =         "1966",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.80",
  MRnumber =     "32\#3297",
  bibdate =      "Fri Nov 25 18:20:04 MST 2005",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Theory/gvl.bib;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In any prolonged computation it is generally assumed
                 that the accumulated effect of roundoff errors is in
                 some sense statistical. The purpose of this paper is to
                 give precise descriptions of certain probabilistic
                 models for roundoff error, and then to describe a
                 series of experiments for testing the validity of these
                 models. It is concluded that the models are in general
                 very good. Discrepancies are both rare and mild. The
                 test techniques can also be used to experiment with
                 various types of special arithmetic.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "decimal floating-point arithmetic; rounding errors",
}


bibtype: manual
filename: fparith.bib
label: IBM:1966:ISM
title: IBM System / 360 Model 91: Functional Characteristics
publisher: pub-IBM
address: pub-IBM:adr
pages: 108--113
year: 1966
bibdate: Fri Aug 20 09:34:43 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.08.20 09:34:43 ???
note: File No. S360-01, Form A22-6907-2.
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
key: IBM
rawnote: File No. S360-01, Form A22-6907-2.
rawtitle: {IBM System\slash 360 Model 91}: Functional Characteristics
entry:
@Manual{IBM:1966:ISM,
  key =          "IBM",
  title =        "{IBM System\slash 360 Model 91}: Functional
                 Characteristics",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  year =         "1966",
  bibdate =      "Fri Aug 20 09:34:43 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "File No. S360-01, Form A22-6907-2.",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: book
filename: fparith.bib
label: Isaacson:1966:ANM
author: Eugene Isaacson and Herbert Bishop Keller
title: Analysis of numerical methods
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xv + 541
year: 1966
LCCN: QA297 .I8
bibdate: Fri Aug 20 09:37:14 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.08.20 09:37:14 MDT
remark: Cited in cite Sterbenz:1974:FPC. Reprinted in cite Isaacson:1994:ANM.
subject: Numerical analysis
acknowledgement: ack-nhfb
rawauthor: Eugene Isaacson and Herbert Bishop Keller
rawtitle: Analysis of numerical methods
entry:
@Book{Isaacson:1966:ANM,
  author =       "Eugene Isaacson and Herbert Bishop Keller",
  title =        "Analysis of numerical methods",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xv + 541",
  year =         "1966",
  LCCN =         "QA297 .I8",
  bibdate =      "Fri Aug 20 09:37:14 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}. Reprinted in
                 \cite{Isaacson:1994:ANM}.",
  subject =      "Numerical analysis",
}


bibtype: misc
filename: fparith.bib
label: Kahan:1966:ISS
author: W. Kahan
title: 7094 II System Support for Numerical Analysis
pages: 1--54
year: 1966
bibdate: Wed Nov 07 08:39:33 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.07 08:39:33 ???
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
howpublished: SHARE Secretary Distribution 159, C4537
rawauthor: W. Kahan
rawtitle: {7094 II} System Support for Numerical Analysis
entry:
@Misc{Kahan:1966:ISS,
  author =       "W. Kahan",
  title =        "{7094 II} System Support for Numerical Analysis",
  howpublished = "SHARE Secretary Distribution 159, C4537",
  pages =        "1--54",
  year =         "1966",
  bibdate =      "Wed Nov 07 08:39:33 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: incollection
filename: fparith.bib
label: Kogbetliantz:1966:GEF
author: E. G. Kogbetliantz
title: Generation of Elementary Functions
crossref: Ralston:1966:MMD
pages: 7--35
year: 1966
bibdate: Sat Dec 09 14:09:27 1995
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.09 14:09:27 ???
acknowledgement: ack-nj
rawauthor: E. G. Kogbetliantz
rawtitle: Generation of Elementary Functions
entry:
@InCollection{Kogbetliantz:1966:GEF,
  author =       "E. G. Kogbetliantz",
  title =        "Generation of Elementary Functions",
  crossref =     "Ralston:1966:MMD",
  pages =        "7--35",
  year =         "1966",
  bibdate =      "Sat Dec 09 14:09:27 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Kuki:1966:EGS
author: H. Kuki and E. Hanson and J. J. Ortega and J. C. Butcher and P. G. Anderson
title: Evaluation Guidelines SHARE Numerical Analysis Project (N.A.P.)
journal: SHARE Secretary Distribution
volume: SSD 150, part II
number: C4304
pages: 1--42
year: 1966
bibdate: Fri Aug 20 09:45:16 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.08.20 09:45:16 ???
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
rawauthor: H. Kuki and E. Hanson and J. J. Ortega and J. C. Butcher and P. G. Anderson
rawtitle: Evaluation Guidelines {SHARE Numerical Analysis Project (N.A.P.)}
entry:
@Article{Kuki:1966:EGS,
  author =       "H. Kuki and E. Hanson and J. J. Ortega and J. C.
                 Butcher and P. G. Anderson",
  title =        "Evaluation Guidelines {SHARE Numerical Analysis
                 Project (N.A.P.)}",
  journal =      "{SHARE Secretary Distribution}",
  volume =       "SSD 150, part II",
  number =       "C4304",
  pages =        "1--42",
  year =         "1966",
  bibdate =      "Fri Aug 20 09:45:16 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Lam:1966:COG
author: Lay-yong Lam
title: On the Chinese origin of the Galley method of arithmetical division
journal: j-BRITISH-J-HIST-SCI
volume: 3
number: part 1, 9
pages: 66--69
year: 1966
CODEN: BJHSAT
DOI: https://doi.org/10.1017/S0007087400000200
ISSN: 0007-0874 (print), 1474-001X (electronic) OR 00070874 (print), 1474001X (electronic)
ISSNL: 0007-0874 OR 00070874
MRclass: 01.10
MRnumber: 0204243 (34 \#4087)
MRreviewer: I. N. Veselovski{\u\i}
bibdate: Wed Sep 22 18:01:23 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; MathSciNet database
bibtimestamp: 2010.09.22 18:01:23 ???
fjournal: British Journal for the History of Science
keywords: history
ZMnumber: 0143.24202
acknowledgement: ack-nhfb
journalURL: http://journals.cambridge.org/action/displayJournal?jid=BJH
rawauthor: Lay-yong Lam
rawtitle: On the {Chinese} origin of the {Galley} method of arithmetical division
entry:
@Article{Lam:1966:COG,
  author =       "Lay-yong Lam",
  title =        "On the {Chinese} origin of the {Galley} method of
                 arithmetical division",
  journal =      j-BRITISH-J-HIST-SCI,
  volume =       "3",
  number =       "part 1, 9",
  pages =        "66--69",
  year =         "1966",
  CODEN =        "BJHSAT",
  DOI =          "https://doi.org/10.1017/S0007087400000200",
  ISSN =         "0007-0874 (print), 1474-001X (electronic)",
  ISSN-L =       "0007-0874",
  MRclass =      "01.10",
  MRnumber =     "0204243 (34 \#4087)",
  MRreviewer =   "I. N. Veselovski{\u\i}",
  bibdate =      "Wed Sep 22 18:01:23 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  ZMnumber =     "0143.24202",
  acknowledgement = ack-nhfb,
  fjournal =     "British Journal for the History of Science",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=BJH",
  keywords =     "history",
}


bibtype: article
filename: fparith.bib
label: Mancino:1966:MPF
author: O. G. Mancino
title: Multiple precision floating-point conversion from decimal-to-binary and vice versa
journal: j-CACM
volume: 9
number: 5
pages: 347--348
month: may
monthnumber: 5
year: 1966
CODEN: CACMA2
DOI: https://doi.org/10.1145/355592.365635
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:06 MST 2005
bibtimestamp: 2005.11.25 18:20:06 MST
fjournal: Communications of the ACM
keywords: floating-point arithmetic; Multiple precision arithmetic; number base conversion
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: O. G. Mancino
rawtitle: Multiple precision floating-point conversion from decimal-to-binary and vice versa
abstract:
Decimal-to-binary and binary-to-decimal floating-point conversion is often performed by using a table of the powers $ 10^i $ ($i$ a positive integer) for converting from base $ 10$ to base $2$, and by using a table of the coefficients of a polynomial approximation of $ 10^x (0 leq x < 1)$ for converting from base $2$ to base $ 10$. These tables occupy a large storage region in the case of a nonsingle precision conversion. This paper shows that a single small table suffices for a floating-point conversion from decimal to binary, and vice versa, in any useful precision.

rawabstract:
Decimal-to-binary and binary-to-decimal floating-point conversion is often performed by using a table of the powers $ 10^i $ ($i$ a positive integer) for converting from base $ 10$ to base $2$, and by using a table of the coefficients of a polynomial approximation of $ 10^x (0 \leq x < 1)$ for converting from base $2$ to base $ 10$. These tables occupy a large storage region in the case of a nonsingle precision conversion. This paper shows that a single small table suffices for a floating-point conversion from decimal to binary, and vice versa, in any useful precision.

entry:
@Article{Mancino:1966:MPF,
  author =       "O. G. Mancino",
  title =        "Multiple precision floating-point conversion from
                 decimal-to-binary and vice versa",
  journal =      j-CACM,
  volume =       "9",
  number =       "5",
  pages =        "347--348",
  month =        may,
  year =         "1966",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355592.365635",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:06 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Decimal-to-binary and binary-to-decimal floating-point
                 conversion is often performed by using a table of the
                 powers $ 10^i $ ($i$ a positive integer) for converting
                 from base $ 10$ to base $2$, and by using a table of
                 the coefficients of a polynomial approximation of $
                 10^x (0 \leq x < 1)$ for converting from base $2$ to
                 base $ 10$. These tables occupy a large storage region
                 in the case of a nonsingle precision conversion. This
                 paper shows that a single small table suffices for a
                 floating-point conversion from decimal to binary, and
                 vice versa, in any useful precision.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "floating-point arithmetic; Multiple precision
                 arithmetic; number base conversion",
}


bibtype: unpublished
filename: fparith.bib
label: Mazor:1966:FSI
author: Stan Mazor
title: Fairchild Symbol II Decimal Floating Point Unit
pages: 347--348
year: 1966
bibdate: Wed Nov 22 21:18:53 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.11.22 21:18:53 ???
note: Cited in cite [p. 106]Cowlishaw:2003:DFP.
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: Stan Mazor
rawnote: Cited in \cite[p. 106]{Cowlishaw:2003:DFP}.
rawtitle: {Fairchild Symbol II} Decimal Floating Point Unit
entry:
@Unpublished{Mazor:1966:FSI,
  author =       "Stan Mazor",
  title =        "{Fairchild Symbol II} Decimal Floating Point Unit",
  year =         "1966",
  bibdate =      "Wed Nov 22 21:18:53 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Cited in \cite[p. 106]{Cowlishaw:2003:DFP}.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}


bibtype: book
filename: fparith.bib
label: Moore:1966:IA
author: Ramon E. Moore
title: Interval analysis
publisher: pub-PH
address: pub-PH:adr
pages: xi + 145
year: 1966
LCCN: QA297 .M63
bibdate: Sat Feb 14 08:15:54 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.02.14 08:15:54 ???
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
rawauthor: Ramon E. Moore
rawtitle: Interval analysis
entry:
@Book{Moore:1966:IA,
  author =       "Ramon E. Moore",
  title =        "Interval analysis",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xi + 145",
  year =         "1966",
  LCCN =         "QA297 .M63",
  bibdate =      "Sat Feb 14 08:15:54 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Nickel:1966:NFA
author: K. Nickel
title: Uber die Notwendigkeit einer Fehlerschranken- Arithmetik fur Rechenautomaten
journal: j-NUM-MATH
volume: 9
pages: 69--79
year: 1966
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Fri Jan 12 11:37:56 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.01.12 11:37:56 ???
fjournal: Numerische Mathematik
acknowledgement: ack-jr
journalURL: http://link.springer.com/journal/211
rawauthor: K. Nickel
rawtitle: {{\"U}ber die Notwendigkeit einer Fehlerschranken- Arithmetik f{\"u}r Rechenautomaten}
entry:
@Article{Nickel:1966:NFA,
  author =       "K. Nickel",
  title =        "{{\"U}ber die Notwendigkeit einer Fehlerschranken-
                 Arithmetik f{\"u}r Rechenautomaten}",
  journal =      j-NUM-MATH,
  volume =       "9",
  pages =        "69--79",
  year =         "1966",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-jr,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: book
filename: fparith.bib
label: Parker:1966:SNS
author: Francis D. Parker
title: The structure of number systems
publisher: pub-PH
address: pub-PH:adr
pages: xi + 137
year: 1966
LCCN: QA241 .P3; QA241 .P239
bibdate: Fri Nov 9 19:10:47 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; melvyl.cdlib.org:210/CDL90
bibtimestamp: 2007.11.09 19:10:47 MST
series: Teachers' mathematics reference series
subject: Number theory
acknowledgement: ack-nhfb
rawauthor: Francis D. Parker
rawtitle: The structure of number systems
entry:
@Book{Parker:1966:SNS,
  author =       "Francis D. Parker",
  title =        "The structure of number systems",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xi + 137",
  year =         "1966",
  LCCN =         "QA241 .P3; QA241 .P239",
  bibdate =      "Fri Nov 9 19:10:47 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  series =       "Teachers' mathematics reference series",
  acknowledgement = ack-nhfb,
  subject =      "Number theory",
}


bibtype: book
filename: fparith.bib
label: Richards:1966:EDS
author: R. K. (Richard Kohler) Richards
title: Electronic Digital Systems
publisher: pub-WILEY
address: pub-WILEY:adr
pages: ix + 637
year: 1966
LCCN: TK7888.3 .R52
bibdate: Mon Oct 24 05:33:53 MDT 2016
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2016.10.24 05:33:53 MDT
subject: Electronic digital computers
acknowledgement: ack-nhfb
authordates: 1921--
rawauthor: R. K. (Richard Kohler) Richards
rawtitle: Electronic Digital Systems
remark:
According to cite [pp. 168--170]Smiley:2010:MWI, this was the first book to draw attention to the pre-World War II work by John Atanasoff (1903--1995) and Clifford Berry (1918--1963) at Iowa State College of Agricultural and Mechanic Arts (renamed on 4 July 1959 to Iowa State University of Science and Technology), and to name their computer the ABC. Richards is quoted with ``The ancestry of all electronic digital systems appears to be traceable to a computer which will be called the Atanasoff--Berry Computer.'' The book provided important evidence in the priority dispute and courtroom battles over who invented the computer (Atanasoff and Berry versus Mauchly and Eckert). Berry died in unresolved circumstances: suicide or murder?

TOC:
1: History and Introduction / 1 2: Theory of Digital Systems / 50 3: The Stored-Program Concept / 109 4: Automatic Programming / 293 5: Digital Data Transmission / 362 6: Combined Analog and Digital Techniques / 451 7: Telephone and Message Switching Systems / 481 8: The Relationship between Thinking and Digital Systems / 519 9: Miscellaneous Digital Systems / 541 10: Digital System Reliability / 571 11: The Automatic Design of Digital Systems / 610 Index / 631

rawTOC:
1: History and Introduction / 1 \\ 2: Theory of Digital Systems / 50 \\ 3: The Stored-Program Concept / 109 \\ 4: Automatic Programming / 293 \\ 5: Digital Data Transmission / 362 \\ 6: Combined Analog and Digital Techniques / 451 \\ 7: Telephone and Message Switching Systems / 481 \\ 8: The Relationship between Thinking and Digital Systems / 519 \\ 9: Miscellaneous Digital Systems / 541 \\ 10: Digital System Reliability / 571 \\ 11: The Automatic Design of Digital Systems / 610 \\ Index / 631

entry:
@Book{Richards:1966:EDS,
  author =       "R. K. (Richard Kohler) Richards",
  title =        "Electronic Digital Systems",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "ix + 637",
  year =         "1966",
  LCCN =         "TK7888.3 .R52",
  bibdate =      "Mon Oct 24 05:33:53 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1921--",
  remark =       "According to \cite[pp. 168--170]{Smiley:2010:MWI},
                 this was the first book to draw attention to the
                 pre-World War II work by John Atanasoff (1903--1995)
                 and Clifford Berry (1918--1963) at Iowa State College
                 of Agricultural and Mechanic Arts (renamed on 4 July
                 1959 to Iowa State University of Science and
                 Technology), and to name their computer the ABC.
                 Richards is quoted with ``The ancestry of all
                 electronic digital systems appears to be traceable to a
                 computer which will be called the Atanasoff--Berry
                 Computer.'' The book provided important evidence in the
                 priority dispute and courtroom battles over who
                 invented the computer (Atanasoff and Berry versus
                 Mauchly and Eckert). Berry died in unresolved
                 circumstances: suicide or murder?",
  subject =      "Electronic digital computers",
  tableofcontents = "1: History and Introduction / 1 \\
                 2: Theory of Digital Systems / 50 \\
                 3: The Stored-Program Concept / 109 \\
                 4: Automatic Programming / 293 \\
                 5: Digital Data Transmission / 362 \\
                 6: Combined Analog and Digital Techniques / 451 \\
                 7: Telephone and Message Switching Systems / 481 \\
                 8: The Relationship between Thinking and Digital
                 Systems / 519 \\
                 9: Miscellaneous Digital Systems / 541 \\
                 10: Digital System Reliability / 571 \\
                 11: The Automatic Design of Digital Systems / 610 \\
                 Index / 631",
}


bibtype: article
filename: fparith.bib
label: Saidan:1966:EEA
author: A. S. Saidan
journal: j-ISIS
volume: 57
number: 4
pages: 475--490
month: Winter
year: 1966
CODEN: ISISA4
ISSN: 0021-1753 (print), 1545-6994 (electronic) OR 00211753 (print), 15456994 (electronic)
ISSNL: 0021-1753 OR 00211753
bibdate: Tue Jul 30 21:22:16 MDT 2013
bibtimestamp: 2013.07.30 21:22:16 MDT
URL: http://www.jstor.org/stable/228518
fjournal: Isis
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journal/isis
rawauthor: A. S. Saidan
title:
The Earliest Extant Arabic Arithmetic: booktitle Kitab al-Fusul fi al Hisab al-Hindi of Abu al-Hasan, Ahmad ibn Ibrahim al-Uqlidisi

bibsource:
http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i211145; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/isis1960.bib

rawtitle:
The Earliest Extant {Arabic} Arithmetic: {{\booktitle{Kitab al-Fusul fi al Hisab al-Hindi}}} of {Abu al-Hasan, Ahmad ibn Ibrahim al-Uqlidisi}

entry:
@Article{Saidan:1966:EEA,
  author =       "A. S. Saidan",
  title =        "The Earliest Extant {Arabic} Arithmetic:
                 {{\booktitle{Kitab al-Fusul fi al Hisab al-Hindi}}} of
                 {Abu al-Hasan, Ahmad ibn Ibrahim al-Uqlidisi}",
  journal =      j-ISIS,
  volume =       "57",
  number =       "4",
  pages =        "475--490",
  month =        "Winter",
  year =         "1966",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:22:16 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i211145;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1960.bib",
  URL =          "http://www.jstor.org/stable/228518",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}


bibtype: article
filename: fparith.bib
label: Smith:1966:CP
author: John Smith
title: The Challenge of Pi
journal: j-IEEE-SPECTRUM
volume: 3
number: 10
pages: 5--5
month: oct
monthnumber: 10
year: 1966
CODEN: IEESAM
DOI: https://doi.org/10.1109/MSPEC.1966.5217340
ISSN: 0018-9235 (print), 1939-9340 (electronic) OR 00189235 (print), 19399340 (electronic)
ISSNL: 0018-9235 OR 00189235
bibdate: Wed Jan 15 08:45:04 2020
bibtimestamp: 2020.01.15 08:45:04 ???
fjournal: IEEE Spectrum
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6
rawauthor: John Smith
rawtitle: The Challenge of {Pi}
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib; https://www.math.utah.edu/pub/tex/bib/pi.bib

keywords:
Computer errors; Digital arithmetic; Educational institutions; Hardware; Physics computing; Power engineering computing; Programming profession; Registers; Testing; Upper bound

remark:
Report of a computation of $ pi $ to 17,935 places using base-1,000,000 arithmetic. A footnote reports ``The AIL result to 17,940 places was identical with the reference to 17,935 places. Reference: D. Shanks and J. W. Wrench, Jr., `Calculation of Pi to 100,000 Decimals', Mathematics of Computation, January 1962, Vol. 16, No. 77, pp. 67--99.''

entry:
@Article{Smith:1966:CP,
  author =       "John Smith",
  title =        "The Challenge of {Pi}",
  journal =      j-IEEE-SPECTRUM,
  volume =       "3",
  number =       "10",
  pages =        "5--5",
  month =        oct,
  year =         "1966",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.1966.5217340",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Wed Jan 15 08:45:04 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "Computer errors; Digital arithmetic; Educational
                 institutions; Hardware; Physics computing; Power
                 engineering computing; Programming profession;
                 Registers; Testing; Upper bound",
  remark =       "Report of a computation of $ \pi $ to 17,935 places
                 using base-1,000,000 arithmetic. A footnote reports
                 ``The AIL result to 17,940 places was identical with
                 the reference to 17,935 places. Reference: D. Shanks
                 and J. W. Wrench, Jr., `Calculation of Pi to 100,000
                 Decimals', Mathematics of Computation, January 1962,
                 Vol. 16, No. 77, pp. 67--99.''",
}


bibtype: article
filename: fparith.bib
label: Spielberg:1966:CEU
author: K. Spielberg
title: Computation of $ e^x $ with the use of large tables
journal: j-IBM-SYS-J
volume: 5
number: 2
pages: 102--114
year: 1966
CODEN: IBMSA7
ISSN: 0018-8670 OR 00188670
bibdate: Thu Sep 15 18:43:03 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.15 18:43:03 ???
fjournal: IBM Systems Journal
acknowledgement: ack-nj
rawauthor: K. Spielberg
rawtitle: Computation of $ e^x $ with the use of large tables
entry:
@Article{Spielberg:1966:CEU,
  author =       "K. Spielberg",
  title =        "Computation of $ e^x $ with the use of large tables",
  journal =      j-IBM-SYS-J,
  volume =       "5",
  number =       "2",
  pages =        "102--114",
  year =         "1966",
  CODEN =        "IBMSA7",
  ISSN =         "0018-8670",
  bibdate =      "Thu Sep 15 18:43:03 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Systems Journal",
  xxmonth =      "(none)",
}


bibtype: article
filename: fparith.bib
label: Tienari:1966:SPM
author: M. Tienari and V. Suokonautio
title: A Set of Procedures Making Real Arithmetic of Unlimited Accuracy Possible Within Algol 60
journal: j-NORDISK-TIDSKR-INFORM-BEHAND
volume: 6
number: 4
pages: 332--338
month: jul
monthnumber: 7
year: 1966
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01966093
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Mon Sep 12 08:07:38 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.12 08:07:38 ???
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=6&issue=4&spage=332
acknowledgement: ack-nj
journalURL: http://link.springer.com/journal/10543
rawauthor: M. Tienari and V. Suokonautio
rawtitle: A Set of Procedures Making Real Arithmetic of Unlimited Accuracy Possible Within {Algol 60}
entry:
@Article{Tienari:1966:SPM,
  author =       "M. Tienari and V. Suokonautio",
  title =        "A Set of Procedures Making Real Arithmetic of
                 Unlimited Accuracy Possible Within {Algol 60}",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "6",
  number =       "4",
  pages =        "332--338",
  month =        jul,
  year =         "1966",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01966093",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Mon Sep 12 08:07:38 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=6&issue=4&spage=332",
  acknowledgement = ack-nj,
  journal-URL =  "http://link.springer.com/journal/10543",
}


bibtype: article
filename: fparith.bib
label: vanWijngaarden:1966:NAI
author: A. van Wijngaarden
title: Numerical Analysis as an Independent Science
journal: j-NORDISK-TIDSKR-INFORM-BEHAND
volume: 6
number: 1
pages: 66--81
month: mar
monthnumber: 3
year: 1966
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01939551
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 18:52:09 MST 2006
bibtimestamp: 2006.01.04 18:52:09 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=6&issue=1&spage=66
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: A. {van Wijngaarden}
rawtitle: Numerical Analysis as an Independent Science
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=6&issue=1; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
The paper describes how a number of well-known mathematical concepts ought to be modified in order to make sense within the scope of numerical analysis. It is also shown how obvious difficulties can be overcome in a logical way. All algorithms suggested are given as ALGOL procedures.

rawabstract:
The paper describes how a number of well-known mathematical concepts ought to be modified in order to make sense within the scope of numerical analysis. It is also shown how obvious difficulties can be overcome in a logical way. All algorithms suggested are given as ALGOL procedures.

entry:
@Article{vanWijngaarden:1966:NAI,
  author =       "A. {van Wijngaarden}",
  title =        "Numerical Analysis as an Independent Science",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "6",
  number =       "1",
  pages =        "66--81",
  month =        mar,
  year =         "1966",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01939551",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:09 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=6&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=6&issue=1&spage=66",
  abstract =     "The paper describes how a number of well-known
                 mathematical concepts ought to be modified in order to
                 make sense within the scope of numerical analysis. It
                 is also shown how obvious difficulties can be overcome
                 in a logical way. All algorithms suggested are given as
                 ALGOL procedures.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Watson:1966:SCC
author: R. W. Watson and C. W. Hastings
title: Self-Checked Computation using Residue Arithmetic
journal: j-PROC-IEEE
volume: 54
number: 12
pages: 1920--1931
month: dec
monthnumber: 12
year: 1966
CODEN: IEEPAD
ISSN: 0018-9219 (print), 1558-2256 (electronic) OR 00189219 (print), 15582256 (electronic)
ISSNL: 0018-9219 OR 00189219
bibdate: Fri Nov 09 19:37:52 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:37:52 ???
fjournal: Proceedings of the IEEE
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5
rawauthor: R. W. Watson and C. W. Hastings
rawtitle: Self-Checked Computation using Residue Arithmetic
entry:
@Article{Watson:1966:SCC,
  author =       "R. W. Watson and C. W. Hastings",
  title =        "Self-Checked Computation using Residue Arithmetic",
  journal =      j-PROC-IEEE,
  volume =       "54",
  number =       "12",
  pages =        "1920--1931",
  month =        dec,
  year =         "1966",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Fri Nov 09 19:37:52 2007",
  bibsource =    "https://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",
}


bibtype: article
filename: fparith.bib
label: Whitney:1966:PCR
author: D. E. Whitney
title: Propagation and control of roundoff error in the matrix exponential method
journal: j-PROC-IEEE
volume: 54
number: 10
pages: 1483--1484
month: oct
monthnumber: 10
year: 1966
CODEN: IEEPAD
ISSN: 0018-9219 (print), 1558-2256 (electronic) OR 00189219 (print), 15582256 (electronic)
ISSNL: 0018-9219 OR 00189219
bibdate: Sat Jul 16 11:25:06 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:06 MDT
fjournal: Proceedings of the IEEE
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5
rawauthor: D. E. Whitney
rawtitle: Propagation and control of roundoff error in the matrix exponential method
entry:
@Article{Whitney:1966:PCR,
  author =       "D. E. Whitney",
  title =        "Propagation and control of roundoff error in the
                 matrix exponential method",
  journal =      j-PROC-IEEE,
  volume =       "54",
  number =       "10",
  pages =        "1483--1484",
  month =        oct,
  year =         "1966",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://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",
}


bibtype: techreport
filename: fparith.bib
label: Wiegel:1966:MBA
author: R. E. Wiegel
title: Methods of Binary Addition
type: Technical report
number: 195
institution: Department of Computer Science, University of Illinois
address: Urbana, IL, USA
pages: 1483--1484
month: feb
monthnumber: 2
year: 1966
bibdate: Fri Nov 09 19:40:18 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:40:18 ???
acknowledgement: ack-nhfb
rawauthor: R. E. Wiegel
rawtitle: Methods of Binary Addition
entry:
@TechReport{Wiegel:1966:MBA,
  author =       "R. E. Wiegel",
  title =        "Methods of Binary Addition",
  type =         "Technical report",
  number =       "195",
  institution =  "Department of Computer Science, University of
                 Illinois",
  address =      "Urbana, IL, USA",
  month =        feb,
  year =         "1966",
  bibdate =      "Fri Nov 09 19:40:18 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Adams:1967:SCP
author: Duane A. Adams
title: A stopping criterion for polynomial root finding
journal: j-CACM
volume: 10
number: 10
pages: 655--658
month: oct
monthnumber: 10
year: 1967
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65.50
MRnumber: 39\#2314
bibdate: Fri Nov 25 18:20:15 MST 2005
bibtimestamp: 2005.11.25 18:20:15 MST
fjournal: Communications of the ACM
keywords: floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Duane A. Adams
rawtitle: A stopping criterion for polynomial root finding
abstract:
When searching for the root of a polynomial, it is generally difficult to know just when to accept a number as an adequate approximation to the root. In this paper an algorithm is presented which allows one to terminate the iteration process on the basis of calculated bounds for the roundoff error which occurs in evaluating the polynomial. This stopping criterion has been tested on numerous examples and has been found to serve as a satisfactory means for accepting a complex number as a zero of a real polynomial.

rawabstract:
When searching for the root of a polynomial, it is generally difficult to know just when to accept a number as an adequate approximation to the root. In this paper an algorithm is presented which allows one to terminate the iteration process on the basis of calculated bounds for the roundoff error which occurs in evaluating the polynomial. This stopping criterion has been tested on numerous examples and has been found to serve as a satisfactory means for accepting a complex number as a zero of a real polynomial.

entry:
@Article{Adams:1967:SCP,
  author =       "Duane A. Adams",
  title =        "A stopping criterion for polynomial root finding",
  journal =      j-CACM,
  volume =       "10",
  number =       "10",
  pages =        "655--658",
  month =        oct,
  year =         "1967",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.50",
  MRnumber =     "39\#2314",
  bibdate =      "Fri Nov 25 18:20:15 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "When searching for the root of a polynomial, it is
                 generally difficult to know just when to accept a
                 number as an adequate approximation to the root. In
                 this paper an algorithm is presented which allows one
                 to terminate the iteration process on the basis of
                 calculated bounds for the roundoff error which occurs
                 in evaluating the polynomial. This stopping criterion
                 has been tested on numerous examples and has been found
                 to serve as a satisfactory means for accepting a
                 complex number as a zero of a real polynomial.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "floating-point arithmetic; rounding errors",
}


bibtype: article
filename: fparith.bib
label: Anderson:1967:ISMb
author: S. F. Anderson and J. G. Earle and R. E. Goldschmidt and D. M. Powers
title: The IBM System / 360 Model 91: Floating-point execution unit
journal: j-IBM-JRD
volume: 11
number: 1
pages: 34--53
month: jan
monthnumber: 1
year: 1967
CODEN: IBMJAE
DOI: https://doi.org/10.1147/rd.111.0034
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
bibdate: Tue Sep 11 15:36:09 MDT 2012
bibtimestamp: 2012.09.11 15:36:09 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392016
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
bookURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
rawauthor: S. F. Anderson and J. G. Earle and R. E. Goldschmidt and D. M. Powers
rawtitle: The {IBM System\slash 360 Model 91}: Floating-point execution unit
bibsource:
http://www.research.ibm.com/journal/; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib

abstract:
The principal requirement for the Model 91 floating-point execution unit was that it be designed to support the instruction-issuing rate of the processor. The chosen solution was to develop separate, instruction-oriented algorithms for the add, multiply, and divide functions. Linked together by the floating-point instruction unit, the multiple execution units provide concurrent instruction execution at the burst rate of one instruction per cycle.

rawabstract:
The principal requirement for the Model 91 floating-point execution unit was that it be designed to support the instruction-issuing rate of the processor. The chosen solution was to develop separate, instruction-oriented algorithms for the add, multiply, and divide functions. Linked together by the floating-point instruction unit, the multiple execution units provide concurrent instruction execution at the burst rate of one instruction per cycle.

entry:
@Article{Anderson:1967:ISMb,
  author =       "S. F. Anderson and J. G. Earle and R. E. Goldschmidt
                 and D. M. Powers",
  title =        "The {IBM System\slash 360 Model 91}: Floating-point
                 execution unit",
  journal =      j-IBM-JRD,
  volume =       "11",
  number =       "1",
  pages =        "34--53",
  month =        jan,
  year =         "1967",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.111.0034",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Tue Sep 11 15:36:09 MDT 2012",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392016",
  abstract =     "The principal requirement for the Model 91
                 floating-point execution unit was that it be designed
                 to support the instruction-issuing rate of the
                 processor. The chosen solution was to develop separate,
                 instruction-oriented algorithms for the add, multiply,
                 and divide functions. Linked together by the
                 floating-point instruction unit, the multiple execution
                 units provide concurrent instruction execution at the
                 burst rate of one instruction per cycle.",
  acknowledgement = ack-nhfb # "\slash " # ack-nj,
  book-URL =     "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}


bibtype: techreport
filename: fparith.bib
label: Clark:1967:PSF
author: N. A. Clark and W. J. Cody and K. E. Hillstrom and E. A. Thieleker
title: Performance Statistics of the FORTRAN IV (H) Library for the IBM System / 360
type: Technical Report
number: ANL-7231
institution: inst-ANL
address: inst-ANL:adr
pages: 34--53
year: 1967
bibdate: Fri Aug 20 08:47:24 2010
bibtimestamp: 2010.08.20 08:47:24 ???
note: Reprinted in SHARE Secretary Distribution, SDD 169, C4473, pp. 12 46.
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
rawauthor: N. A. Clark and W. J. Cody and K. E. Hillstrom and E. A. Thieleker
rawnote: Reprinted in SHARE Secretary Distribution, SDD 169, C4473, pp. 12 46.
rawtitle: Performance Statistics of the {FORTRAN IV (H)} Library for the {IBM System\slash 360}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@TechReport{Clark:1967:PSF,
  author =       "N. A. Clark and W. J. Cody and K. E. Hillstrom and E.
                 A. Thieleker",
  title =        "Performance Statistics of the {FORTRAN IV (H)} Library
                 for the {IBM System\slash 360}",
  type =         "Technical Report",
  number =       "ANL-7231",
  institution =  inst-ANL,
  address =      inst-ANL:adr,
  year =         "1967",
  bibdate =      "Fri Aug 20 08:47:24 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in SHARE Secretary Distribution, SDD 169,
                 C4473, pp. 12 46.",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Cody:1967:CFI
author: W. J. Cody
title: Critique of the FORTRAN IV (H) Library for the IBM System / 360
journal: SHARE Secretary Distribution
volume: SSD 169
number: C4473
pages: 4--11
year: 1967
bibdate: Fri Aug 20 08:52:04 2010
bibtimestamp: 2010.08.20 08:52:04 ???
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
rawauthor: W. J. Cody
rawtitle: Critique of the {FORTRAN IV (H)} Library for the {IBM System\slash 360}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Cody:1967:CFI,
  author =       "W. J. Cody",
  title =        "Critique of the {FORTRAN IV (H)} Library for the {IBM
                 System\slash 360}",
  journal =      "{SHARE Secretary Distribution}",
  volume =       "SSD 169",
  number =       "C4473",
  pages =        "4--11",
  year =         "1967",
  bibdate =      "Fri Aug 20 08:52:04 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: inproceedings
filename: fparith.bib
label: Cody:1967:IMD
author: W. J. Cody
title: The influence of machine design on numerical algorithms
crossref: AFIPS:1967:ACP
pages: 305--309
year: 1967
bibdate: Sat Sep 24 00:18:32 1994
bibtimestamp: 1994.09.24 00:18:32 ???
acknowledgement: ack-nhfb
rawauthor: W. J. Cody
rawtitle: The influence of machine design on numerical algorithms
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@InProceedings{Cody:1967:IMD,
  author =       "W. J. Cody",
  title =        "The influence of machine design on numerical
                 algorithms",
  crossref =     "AFIPS:1967:ACP",
  pages =        "305--309",
  year =         "1967",
  bibdate =      "Sat Sep 24 00:18:32 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Cody:1967:LEA
author: William J. Cody, Jr.
title: Letter to the Editor: Another Aspect of Economical Polynomials
journal: j-CACM
volume: 10
number: 9
pages: 531--531
month: sep
monthnumber: 9
year: 1967
CODEN: CACMA2
DOI: https://doi.org/10.1145/363566.363577
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Nov 17 10:20:03 1994
bibtimestamp: 1994.11.17 10:20:03 ???
note: See cite Fike:1967:MEP.
fjournal: Communications of the ACM
keywords: floating-point arithmetic
acknowledgement: ack-wjc
journalURL: https://dl.acm.org/loi/cacm
rawauthor: William J. {Cody, Jr.}
rawnote: See \cite{Fike:1967:MEP}.
rawtitle: Letter to the {Editor}: Another Aspect of Economical Polynomials
bibsource:
http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
In his paper ``Methods of Evaluating Polynomial Approximations in Function Evaluation Routines'' [Comm. ACM 10, (March 1967)], C. T. Fike fails to discuss one very important aspect of the ``economical'' methods for polynomials. Since these evaluation methods involve a decreased number of arithmetic operations over the usual Horner's method (or at least replace a multiplication by an addition) the implication is that they are faster to execute. Dr. Fike points out that these methods can be poorly conditioned for particular polynomials, thus requiring extended precision or fixed-point arithmetic to maintain accuracy and costing more in time than Horner's method. But even if we assume the methods are well conditioned, the need to store away and retrieve intermediate results in some machines with only one floating-point arithmetic register can wipe out the time savings effected by a reduction in the number of arithmetic operations. On many of today's high-performance computers the time required to store away and retrieve a result is about the same as the time required for a floating-point addition. It is no longer sufficient to estimate the efficiency of a method by a count of arithmetic operations alone.

rawabstract:
In his paper ``Methods of Evaluating Polynomial Approximations in Function Evaluation Routines'' [Comm. ACM 10, (March 1967)], C. T. Fike fails to discuss one very important aspect of the ``economical'' methods for polynomials. Since these evaluation methods involve a decreased number of arithmetic operations over the usual Horner's method (or at least replace a multiplication by an addition) the implication is that they are faster to execute. Dr. Fike points out that these methods can be poorly conditioned for particular polynomials, thus requiring extended precision or fixed-point arithmetic to maintain accuracy and costing more in time than Horner's method. But even if we assume the methods are well conditioned, the need to store away and retrieve intermediate results in some machines with only one floating-point arithmetic register can wipe out the time savings effected by a reduction in the number of arithmetic operations. On many of today's high-performance computers the time required to store away and retrieve a result is about the same as the time required for a floating-point addition. It is no longer sufficient to estimate the efficiency of a method by a count of arithmetic operations alone.

entry:
@Article{Cody:1967:LEA,
  author =       "William J. {Cody, Jr.}",
  title =        "Letter to the {Editor}: Another Aspect of Economical
                 Polynomials",
  journal =      j-CACM,
  volume =       "10",
  number =       "9",
  pages =        "531--531",
  month =        sep,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363566.363577",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Nov 17 10:20:03 1994",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Fike:1967:MEP}.",
  abstract =     "In his paper ``Methods of Evaluating Polynomial
                 Approximations in Function Evaluation Routines'' [Comm.
                 ACM 10, (March 1967)], C. T. Fike fails to discuss one
                 very important aspect of the ``economical'' methods for
                 polynomials. Since these evaluation methods involve a
                 decreased number of arithmetic operations over the
                 usual Horner's method (or at least replace a
                 multiplication by an addition) the implication is that
                 they are faster to execute. Dr. Fike points out that
                 these methods can be poorly conditioned for particular
                 polynomials, thus requiring extended precision or
                 fixed-point arithmetic to maintain accuracy and costing
                 more in time than Horner's method. But even if we
                 assume the methods are well conditioned, the need to
                 store away and retrieve intermediate results in some
                 machines with only one floating-point arithmetic
                 register can wipe out the time savings effected by a
                 reduction in the number of arithmetic operations. On
                 many of today's high-performance computers the time
                 required to store away and retrieve a result is about
                 the same as the time required for a floating-point
                 addition. It is no longer sufficient to estimate the
                 efficiency of a method by a count of arithmetic
                 operations alone.",
  acknowledgement = ack-wjc # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Crisansan-Zverca:1967:PED
author: Mariana Crisan-Zverca
title: Pseudo-operations of an electronic digital machine with floating point. (Romanian)
journal: j-STUD-CERCET-MAT
volume: 19
pages: 1413--1424
year: 1967
ISSN: 0039-4068, 0567-6401 OR 00394068, 05676401
MRclass: 68.00
MRnumber: 40\#3753
bibdate: Fri Dec 8 08:24:14 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:14 ???
fjournal: Studii si cercetari Matematice
acknowledgement: ack-nhfb
rawauthor: Mariana Cri{\c{s}}an-Zverca
rawtitle: Pseudo-operations of an electronic digital machine with floating point. ({Romanian})
entry:
@Article{Crisansan-Zverca:1967:PED,
  author =       "Mariana Cri{\c{s}}an-Zverca",
  title =        "Pseudo-operations of an electronic digital machine
                 with floating point. ({Romanian})",
  journal =      j-STUD-CERCET-MAT,
  volume =       "19",
  pages =        "1413--1424",
  year =         "1967",
  ISSN =         "0039-4068, 0567-6401",
  MRclass =      "68.00",
  MRnumber =     "40\#3753",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Studii {\c{s}}i cercet{\u{a}}ri Matematice",
}


bibtype: article
filename: fparith.bib
label: Curry:1967:ART
author: E. Curry
title: The analysis of round-off and truncation errors in a hybrid control system
journal: j-IEEE-TRANS-AUTOMAT-CONTR
volume: 12
number: 5
pages: 601--604
month: oct
monthnumber: 10
year: 1967
CODEN: IETAA9
ISSN: 0018-9286 (print), 1558-2523 (electronic) OR 00189286 (print), 15582523 (electronic)
ISSNL: 0018-9286 OR 00189286
bibdate: Sat Jul 16 11:25:03 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 11:25:03 MDT
fjournal: IEEE Transactions on Automatic Control
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9
rawauthor: E. Curry
rawtitle: The analysis of round-off and truncation errors in a hybrid control system
entry:
@Article{Curry:1967:ART,
  author =       "E. Curry",
  title =        "The analysis of round-off and truncation errors in a
                 hybrid control system",
  journal =      j-IEEE-TRANS-AUTOMAT-CONTR,
  volume =       "12",
  number =       "5",
  pages =        "601--604",
  month =        oct,
  year =         "1967",
  CODEN =        "IETAA9",
  ISSN =         "0018-9286 (print), 1558-2523 (electronic)",
  ISSN-L =       "0018-9286",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Automatic Control",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
  summary =      "The round-off and truncation errors of a
                 digital-analog (hybrid) servo system are studied in
                 terms of the least upper bound and second moment, or
                 variance. The study was applied to the azimuth function
                 of a guided missile launcher system and a \ldots{}",
}


bibtype: article
filename: fparith.bib
label: DeRegt:1967:NRA
author: M. P. DeRegt
title: Negative radix arithmetic
journal: j-COMP-DESIGN
volume: 6
pages: 52--63
month: may
monthnumber: 5
year: 1967
CODEN: CMPDAM
ISSN: 0010-4566 OR 00104566
bibdate: Thu Nov 06 06:07:24 2014
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2014.11.06 06:07:24 ???
fjournal: Computer Design
keywords: negative base
acknowledgement: ack-nhfb
rawauthor: M. P. DeRegt
rawtitle: Negative radix arithmetic
entry:
@Article{DeRegt:1967:NRA,
  author =       "M. P. DeRegt",
  title =        "Negative radix arithmetic",
  journal =      j-COMP-DESIGN,
  volume =       "6",
  number =       "??",
  pages =        "52--63",
  month =        may,
  year =         "1967",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  bibdate =      "Thu Nov 06 06:07:24 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Design",
  keywords =     "negative base",
}


bibtype: article
filename: fparith.bib
label: Ferrari:1967:DMU
author: Domenico Ferrari
title: A Division Method Using a Parallel Multiplier
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-16
number: 2
pages: 224--226
month: apr
monthnumber: 4
year: 1967
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1967.264580
ISSN: 0367-7508 OR 03677508
bibdate: Wed Jul 13 21:15:02 MDT 2011
bibtimestamp: 2011.07.13 21:15:02 MDT
note: See correction cite Ferrari:1969:CDM.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039036
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: Domenico Ferrari
rawnote: See correction \cite{Ferrari:1969:CDM}.
rawtitle: A Division Method Using a Parallel Multiplier
abstract:
The use of a parallel multiplier for performing high-speed binary division requires that an algorithm be devised that obtains the quotient by means of multiplications and additions. Furthermore, its hardware implementation must be as simple and as fast as possible. A suitable algorithm, which applies to a first approximation to the reciprocal of the divisor, has already been proposed [1]. A similar algorithm is presented in this paper. The comparison between the two methods for equal numbers of multiplications shows that the latter is more accurate. Conversely, a given accuracy can often be obtained with a higher speed. The generation of a piecewise-linear initial approximation is also discussed.

rawabstract:
The use of a parallel multiplier for performing high-speed binary division requires that an algorithm be devised that obtains the quotient by means of multiplications and additions. Furthermore, its hardware implementation must be as simple and as fast as possible. A suitable algorithm, which applies to a first approximation to the reciprocal of the divisor, has already been proposed [1]. A similar algorithm is presented in this paper. The comparison between the two methods for equal numbers of multiplications shows that the latter is more accurate. Conversely, a given accuracy can often be obtained with a higher speed. The generation of a piecewise-linear initial approximation is also discussed.

entry:
@Article{Ferrari:1967:DMU,
  author =       "Domenico Ferrari",
  title =        "A Division Method Using a Parallel Multiplier",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-16",
  number =       "2",
  pages =        "224--226",
  month =        apr,
  year =         "1967",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264580",
  ISSN =         "0367-7508",
  bibdate =      "Wed Jul 13 21:15:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  note =         "See correction \cite{Ferrari:1969:CDM}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039036",
  abstract =     "The use of a parallel multiplier for performing
                 high-speed binary division requires that an algorithm
                 be devised that obtains the quotient by means of
                 multiplications and additions. Furthermore, its
                 hardware implementation must be as simple and as fast
                 as possible. A suitable algorithm, which applies to a
                 first approximation to the reciprocal of the divisor,
                 has already been proposed [1]. A similar algorithm is
                 presented in this paper. The comparison between the two
                 methods for equal numbers of multiplications shows that
                 the latter is more accurate. Conversely, a given
                 accuracy can often be obtained with a higher speed. The
                 generation of a piecewise-linear initial approximation
                 is also discussed.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: fparith.bib
label: Fike:1967:LER
author: C. T. Fike
title: Letter to the Editor: A rational approximation optimal by Moursund's criterion
journal: j-CACM
volume: 10
number: 11
pages: 683--684
month: nov
monthnumber: 11
year: 1967
CODEN: CACMA2
DOI: https://doi.org/10.1145/363790.363795
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:16 MST 2005
bibtimestamp: 2005.11.25 18:20:16 MST
note: See cite Moursund:1967:OSV,Fike:1966:SAS
fjournal: Communications of the ACM
keywords: elementary function; square root
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: C. T. Fike
rawnote: See \cite{Moursund:1967:OSV,Fike:1966:SAS}
rawtitle: Letter to the {Editor}: {A} rational approximation optimal by {Moursund}'s criterion
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

remark:
Gives a starting value for $ sqrt x $ ($x$ on $ [1 / 16, 1]$) of $ R*(x) = 1.68212586 - 1.28977371 / (x + 0.84106293)$, with an error of $ 2^-12.496$.

entry:
@Article{Fike:1967:LER,
  author =       "C. T. Fike",
  title =        "Letter to the {Editor}: {A} rational approximation
                 optimal by {Moursund}'s criterion",
  journal =      j-CACM,
  volume =       "10",
  number =       "11",
  pages =        "683--684",
  month =        nov,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363790.363795",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:16 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Moursund:1967:OSV,Fike:1966:SAS}",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "elementary function; square root",
  remark =       "Gives a starting value for $ \sqrt {x} $ ($x$ on $ [1
                 / 16, 1]$) of $ R*(x) = 1.68212586 - 1.28977371 / (x +
                 0.84106293)$, with an error of $ 2^{-12.496}$.",
}


bibtype: article
filename: fparith.bib
label: Fike:1967:MEP
author: C. T. Fike
title: Methods of Evaluating Polynomial Approximations in Function Evaluation Routines
journal: j-CACM
volume: 10
number: 3
pages: 175--178
month: mar
monthnumber: 3
year: 1967
CODEN: CACMA2
DOI: https://doi.org/10.1145/363162.363200
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:12 MST 2005
bibtimestamp: 2005.11.25 18:20:12 MST
note: See remark on efficiency cite Cody:1967:LEA.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: C. T. Fike
rawnote: See remark on efficiency \cite{Cody:1967:LEA}.
rawtitle: Methods of Evaluating Polynomial Approximations in Function Evaluation Routines
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
The method of nested multiplication is commonly used in function evaluation routines to evaluate approximation polynomials. New polynomial evaluation methods have been developed in recent years which require fewer multiplications than nested multiplication and may therefore be preferable for use in function evaluation routines. Although some of these methods do not appear to be practically useful because of rounding-error difficulties, several methods of evaluating low-degree polynomials have been found to be satisfactory. Three such methods are described and illustrated.

rawabstract:
The method of nested multiplication is commonly used in function evaluation routines to evaluate approximation polynomials. New polynomial evaluation methods have been developed in recent years which require fewer multiplications than nested multiplication and may therefore be preferable for use in function evaluation routines. Although some of these methods do not appear to be practically useful because of rounding-error difficulties, several methods of evaluating low-degree polynomials have been found to be satisfactory. Three such methods are described and illustrated.

entry:
@Article{Fike:1967:MEP,
  author =       "C. T. Fike",
  title =        "Methods of Evaluating Polynomial Approximations in
                 Function Evaluation Routines",
  journal =      j-CACM,
  volume =       "10",
  number =       "3",
  pages =        "175--178",
  month =        mar,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363162.363200",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:12 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See remark on efficiency \cite{Cody:1967:LEA}.",
  abstract =     "The method of nested multiplication is commonly used
                 in function evaluation routines to evaluate
                 approximation polynomials. New polynomial evaluation
                 methods have been developed in recent years which
                 require fewer multiplications than nested
                 multiplication and may therefore be preferable for use
                 in function evaluation routines. Although some of these
                 methods do not appear to be practically useful because
                 of rounding-error difficulties, several methods of
                 evaluating low-degree polynomials have been found to be
                 satisfactory. Three such methods are described and
                 illustrated.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: article
filename: fparith.bib
label: Fike:1967:RAO
author: C. T. Fike
title: A Rational Approximation Optimal by Moursund's Criterion (letter to the editor)
journal: j-CACM
volume: 10
number: 11
pages: 683--684
month: nov
monthnumber: 11
year: 1967
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Sep 1 10:15:43 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:43 ???
fjournal: Communications of the ACM
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/cacm
rawauthor: C. T. Fike
rawtitle: A Rational Approximation Optimal by {Moursund}'s Criterion (letter to the editor)
entry:
@Article{Fike:1967:RAO,
  author =       "C. T. Fike",
  title =        "A Rational Approximation Optimal by {Moursund}'s
                 Criterion (letter to the editor)",
  journal =      j-CACM,
  volume =       "10",
  number =       "11",
  pages =        "683--684",
  month =        nov,
  year =         "1967",
  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;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: article
filename: fparith.bib
label: Filho:1967:AGF
author: A. M. S. Filho and G. Schwachheim
title: Algorithm 309: Gamma Function with Arbitrary Precision
journal: j-CACM
volume: 10
number: 8
pages: 511--512
month: aug
monthnumber: 8
year: 1967
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Sep 1 10:16:10 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:10 ???
fjournal: Communications of the ACM
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/cacm
rawauthor: A. M. S. Filho and G. Schwachheim
rawtitle: Algorithm 309: Gamma Function with Arbitrary Precision
entry:
@Article{Filho:1967:AGF,
  author =       "A. M. S. Filho and G. Schwachheim",
  title =        "Algorithm 309: Gamma Function with Arbitrary
                 Precision",
  journal =      j-CACM,
  volume =       "10",
  number =       "8",
  pages =        "511--512",
  month =        aug,
  year =         "1967",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:16:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: book
filename: fparith.bib
label: Forsythe:1967:CSL
author: George E. Forsythe and Cleve B. Moler
title: Computer Solution of Linear Algebraic Systems
publisher: pub-PH
address: pub-PH:adr
pages: xi + 148
year: 1967
LCCN: QA297 .F57 1967
MRclass: 65.35
MRnumber: MR0219223 (36 \#2306)
MRreviewer: N. Gastinel
bibdate: Tue May 25 08:52:32 2010
bibtimestamp: 2010.05.25 08:52:32 ???
keywords: numerical analysis; software
remark: Translated to Russian (1969), Japanese (1969), and German (1971). Cited in cite Sterbenz:1974:FPC.
subject: numerical analysis; data processing; matrices
ZMnumber: 0154.40401
acknowledgement: ack-nhfb
rawauthor: George E. Forsythe and Cleve B. Moler
rawtitle: Computer Solution of Linear Algebraic Systems
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib; https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib

TOC:
Reader's background and purpose of book Vector and matrix norms Diagonal form of a matrix under orthogonal equivalence Proof of diagonal-form theorem Types of computational problems in linear algebra Types of matrices encountered impractical problems Sources of computational problems of linear algebra Condition of a linear system Gaussian elimination and LU decomposition Need for interchanging rows Scaling equations and unknowns The Crout and Doolittle variants Iterative improvement Computing the determinant Nearly singular matrices Algol 60 program Fortran, extended Algol, and PL/1 programs Matrix inversion An example: Hilbert matrices Floating-point round-off analysis Rounding error in Gaussian elimination Convergence of iterative improvement Positive definite matrices; band matrices Iterative methods for solving linear systems Nonlinear systems of equations

rawTOC:
Reader's background and purpose of book \\ Vector and matrix norms \\ Diagonal form of a matrix under orthogonal equivalence \\ Proof of diagonal-form theorem \\ Types of computational problems in linear algebra \\ Types of matrices encountered impractical problems \\ Sources of computational problems of linear algebra \\ Condition of a linear system \\ Gaussian elimination and LU decomposition \\ Need for interchanging rows \\ Scaling equations and unknowns \\ The Crout and Doolittle variants \\ Iterative improvement \\ Computing the determinant \\ Nearly singular matrices \\ Algol 60 program \\ Fortran, extended Algol, and PL/1 programs \\ Matrix inversion \\ An example: Hilbert matrices \\ Floating-point round-off analysis \\ Rounding error in Gaussian elimination \\ Convergence of iterative improvement \\ Positive definite matrices; band matrices \\ Iterative methods for solving linear systems \\ Nonlinear systems of equations

entry:
@Book{Forsythe:1967:CSL,
  author =       "George E. Forsythe and Cleve B. Moler",
  title =        "Computer Solution of Linear Algebraic Systems",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xi + 148",
  year =         "1967",
  LCCN =         "QA297 .F57 1967",
  MRclass =      "65.35",
  MRnumber =     "MR0219223 (36 \#2306)",
  MRreviewer =   "N. Gastinel",
  bibdate =      "Tue May 25 08:52:32 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/gvl.bib",
  ZMnumber =     "0154.40401",
  acknowledgement = ack-nhfb,
  keywords =     "numerical analysis; software",
  remark =       "Translated to Russian (1969), Japanese (1969), and
                 German (1971). Cited in \cite{Sterbenz:1974:FPC}.",
  subject =      "numerical analysis; data processing; matrices",
  tableofcontents = "Reader's background and purpose of book \\
                 Vector and matrix norms \\
                 Diagonal form of a matrix under orthogonal equivalence
                 \\
                 Proof of diagonal-form theorem \\
                 Types of computational problems in linear algebra \\
                 Types of matrices encountered impractical problems \\
                 Sources of computational problems of linear algebra \\
                 Condition of a linear system \\
                 Gaussian elimination and LU decomposition \\
                 Need for interchanging rows \\
                 Scaling equations and unknowns \\
                 The Crout and Doolittle variants \\
                 Iterative improvement \\
                 Computing the determinant \\
                 Nearly singular matrices \\
                 Algol 60 program \\
                 Fortran, extended Algol, and PL/1 programs \\
                 Matrix inversion \\
                 An example: Hilbert matrices \\
                 Floating-point round-off analysis \\
                 Rounding error in Gaussian elimination \\
                 Convergence of iterative improvement \\
                 Positive definite matrices; band matrices \\
                 Iterative methods for solving linear systems \\
                 Nonlinear systems of equations",
}


bibtype: article
filename: fparith.bib
label: Freeman:1967:CMS
author: Herbert Freeman
title: Calculation of Mean Shift for a Binary Multiplier Using $2$, $3$, or $4$ Bits at a Time
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-16
number: 6
pages: 864--866
month: dec
monthnumber: 12
year: 1967
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1967.264752
ISSN: 0367-7508 OR 03677508
bibdate: Wed Jul 13 21:15:06 MDT 2011
bibtimestamp: 2011.07.13 21:15:06 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039205
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: Herbert Freeman
rawtitle: Calculation of Mean Shift for a Binary Multiplier Using $2$, $3$, or $4$ Bits at a Time
entry:
@Article{Freeman:1967:CMS,
  author =       "Herbert Freeman",
  title =        "Calculation of Mean Shift for a Binary Multiplier
                 Using $2$, $3$, or $4$ Bits at a Time",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-16",
  number =       "6",
  pages =        "864--866",
  month =        dec,
  year =         "1967",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264752",
  ISSN =         "0367-7508",
  bibdate =      "Wed Jul 13 21:15:06 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039205",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: fparith.bib
label: Freiman:1967:CDU
author: C. V. Freiman and others
title: Composite Division Unit
journal: j-IBM-TDB
volume: 9
number: 8
pages: 994--995
month: jan
monthnumber: 1
year: 1967
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Tue Jan 08 22:40:53 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.01.08 22:40:53 ???
fjournal: IBM Technical Disclosure Bulletin
acknowledgement: ack-nhfb
rawauthor: C. V. Freiman and others
rawtitle: Composite Division Unit
entry:
@Article{Freiman:1967:CDU,
  author =       "C. V. Freiman and others",
  title =        "Composite Division Unit",
  journal =      j-IBM-TDB,
  volume =       "9",
  number =       "8",
  pages =        "994--995",
  month =        jan,
  year =         "1967",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Tue Jan 08 22:40:53 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Technical Disclosure Bulletin",
}


bibtype: article
filename: fparith.bib
label: Friedland:1967:AAV
author: Paul Friedland
title: Algorithm 312: Absolute Value and Square Root of a Complex Number
journal: j-CACM
volume: 10
number: 10
pages: 665--665
month: oct
monthnumber: 10
year: 1967
CODEN: CACMA2
DOI: https://doi.org/10.1145/363717.363780
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:15 MST 2005
bibtimestamp: 2005.11.25 18:20:15 MST
fjournal: Communications of the ACM
keywords: $abs (z)$; $sqrt (z)$; elementary functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Paul Friedland
rawtitle: {Algorithm 312}: {Absolute} Value and Square Root of a Complex Number
entry:
@Article{Friedland:1967:AAV,
  author =       "Paul Friedland",
  title =        "{Algorithm 312}: {Absolute} Value and Square Root of a
                 Complex Number",
  journal =      j-CACM,
  volume =       "10",
  number =       "10",
  pages =        "665--665",
  month =        oct,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363717.363780",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:15 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\abs(z)$; $\sqrt(z)$; elementary functions",
}


bibtype: article
filename: fparith.bib
label: Goldberg:1967:BED
author: I. Bennett Goldberg
title: $ 27 $ Bits Are Not Enough For $8$-Digit Accuracy
journal: j-CACM
volume: 10
number: 2
pages: 105--106
month: feb
monthnumber: 2
year: 1967
CODEN: CACMA2
DOI: https://doi.org/10.1145/363067.363112
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:11 MST 2005
bibtimestamp: 2005.11.25 18:20:11 MST
fjournal: Communications of the ACM
keywords: decimal floating-point arithmetic
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/cacm
rawauthor: I. Bennett Goldberg
rawtitle: $ 27 $ Bits Are Not Enough For $8$-Digit Accuracy
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
From the inequality $ 10^8 < 2^27 $, we are likely to conclude that we can represent 8-digit decimal floating-point numbers accurately by 27-bit [binary] floating-point numbers. However, we need 28 significant bits to represent some 8-digit numbers accurately. In general, we can show that if $ 10^p < 2^q - 1 $, then $q$ significant bits are always enough for $p$-digit decimal accuracy. Finally, we can define a compact 27-bit floating-point representation that will give 28 significant bits, for numbers of practical importance.

rawabstract:
From the inequality $ 10^8 < 2^{27} $, we are likely to conclude that we can represent 8-digit decimal floating-point numbers accurately by 27-bit [binary] floating-point numbers. However, we need 28 significant bits to represent some 8-digit numbers accurately. In general, we can show that if $ 10^p < 2^{q - 1} $, then $q$ significant bits are always enough for $p$-digit decimal accuracy. Finally, we can define a compact 27-bit floating-point representation that will give 28 significant bits, for numbers of practical importance.

entry:
@Article{Goldberg:1967:BED,
  author =       "I. Bennett Goldberg",
  title =        "$ 27 $ Bits Are Not Enough For $8$-Digit Accuracy",
  journal =      j-CACM,
  volume =       "10",
  number =       "2",
  pages =        "105--106",
  month =        feb,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363067.363112",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:11 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "From the inequality $ 10^8 < 2^{27} $, we are likely
                 to conclude that we can represent 8-digit decimal
                 floating-point numbers accurately by 27-bit [binary]
                 floating-point numbers. However, we need 28 significant
                 bits to represent some 8-digit numbers accurately. In
                 general, we can show that if $ 10^p < 2^{q - 1} $, then
                 $q$ significant bits are always enough for $p$-digit
                 decimal accuracy. Finally, we can define a compact
                 27-bit floating-point representation that will give 28
                 significant bits, for numbers of practical
                 importance.",
  acknowledgement = ack-nj # " and " # ack-mfc # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "decimal floating-point arithmetic",
  received =     "August 1966 (revised October 1966)",
}


bibtype: book
filename: fparith.bib
label: Gschwind:1967:DDC
author: H. W. Gschwind
title: Design of Digital Computers: An Introduction
publisher: pub-SV
address: pub-SV:adr
pages: viii + 530
year: 1967
LCCN: TK7888.3 .G72
bibdate: Fri Nov 09 18:56:39 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 18:56:39 ???
acknowledgement: ack-nhfb
rawauthor: H. W. Gschwind
rawtitle: Design of Digital Computers: An Introduction
entry:
@Book{Gschwind:1967:DDC,
  author =       "H. W. Gschwind",
  title =        "Design of Digital Computers: An Introduction",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 530",
  year =         "1967",
  LCCN =         "TK7888.3 .G72",
  bibdate =      "Fri Nov 09 18:56:39 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Hertz:1967:CHF
author: Theodore M. Hertz
title: Computer Having Floating Point Multiplication
pages: viii + 530
day: 14
month: feb
monthnumber: 2
year: 1967
bibdate: Sat Mar 24 06:05:12 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2018.03.24 06:05:12 ???
note: Filed 1 October 1962.
acknowledgement: ack-nhfb
howpublished: US Patent 3,304,417.
rawauthor: Theodore M. Hertz
rawnote: Filed 1 October 1962.
rawtitle: Computer Having Floating Point Multiplication
URL:
https://patentimages.storage.googleapis.com/47/86/c8/897ec6540ff584/US3304417.pdf; https://patents.google.com/patent/US3304417

abstract:
Prior art digital computers utilized fixed point arithmetic processes in executing computer operations. In performing fixed point arithmetic processes a computer assumes the binary point (analogous to a decimal point) to be between the sign of a number and the most significant digit of the number. Thus the number is considered to have an absolute value of less than one. As explained in patent application filed September 24, 1962, Serial No. 225,676, now abandoned, for a ``Computer Having Floating Point Addition and Floating Point Subtraction'' invented by me, in order to execute fixed point addition and subtraction operations, numbers to be operated upon by a computer must first be appropriately scaled prior to computation in order to obtain the scaling of the numbers is accomplished prior to entering them into the computer or by shifting them through programming afterwards. Fixed point multiplication needs to have numbers scale prior to performing computations with them. In multiplication, shifting of the result through programming is desirable in order to prevent loss of significant portions which should be retained for use in later computations. Particularly is it true where after a multiplication operation has been performed, the product must be added or subtracted from or with other numbers, in which case scaling would first have to be done before the additional computation could be made.

rawabstract:
Prior art digital computers utilized fixed point arithmetic processes in executing computer operations. In performing fixed point arithmetic processes a computer assumes the binary point (analogous to a decimal point) to be between the sign of a number and the most significant digit of the number. Thus the number is considered to have an absolute value of less than one. As explained in patent application filed September 24, 1962, Serial No. 225,676, now abandoned, for a ``Computer Having Floating Point Addition and Floating Point Subtraction'' invented by me, in order to execute fixed point addition and subtraction operations, numbers to be operated upon by a computer must first be appropriately scaled prior to computation in order to obtain the scaling of the numbers is accomplished prior to entering them into the computer or by shifting them through programming afterwards. Fixed point multiplication needs to have numbers scale prior to performing computations with them. In multiplication, shifting of the result through programming is desirable in order to prevent loss of significant portions which should be retained for use in later computations. Particularly is it true where after a multiplication operation has been performed, the product must be added or subtracted from or with other numbers, in which case scaling would first have to be done before the additional computation could be made.

entry:
@Misc{Hertz:1967:CHF,
  author =       "Theodore M. Hertz",
  title =        "Computer Having Floating Point Multiplication",
  howpublished = "US Patent 3,304,417.",
  day =          "14",
  month =        feb,
  year =         "1967",
  bibdate =      "Sat Mar 24 06:05:12 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Filed 1 October 1962.",
  URL =          "https://patentimages.storage.googleapis.com/47/86/c8/897ec6540ff584/US3304417.pdf;
                 https://patents.google.com/patent/US3304417",
  abstract =     "Prior art digital computers utilized fixed point
                 arithmetic processes in executing computer operations.
                 In performing fixed point arithmetic processes a
                 computer assumes the binary point (analogous to a
                 decimal point) to be between the sign of a number and
                 the most significant digit of the number. Thus the
                 number is considered to have an absolute value of less
                 than one. As explained in patent application filed
                 September 24, 1962, Serial No. 225,676, now abandoned,
                 for a ``Computer Having Floating Point Addition and
                 Floating Point Subtraction'' invented by me, in order
                 to execute fixed point addition and subtraction
                 operations, numbers to be operated upon by a computer
                 must first be appropriately scaled prior to computation
                 in order to obtain the scaling of the numbers is
                 accomplished prior to entering them into the computer
                 or by shifting them through programming afterwards.
                 Fixed point multiplication needs to have numbers scale
                 prior to performing computations with them. In
                 multiplication, shifting of the result through
                 programming is desirable in order to prevent loss of
                 significant portions which should be retained for use
                 in later computations. Particularly is it true where
                 after a multiplication operation has been performed,
                 the product must be added or subtracted from or with
                 other numbers, in which case scaling would first have
                 to be done before the additional computation could be
                 made.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Howell:1967:MPA
author: K. M. Howell
title: Multiple precision arithmetic techniques
journal: j-COMP-J
volume: 9
number: 4
pages: 383--387
month: feb
monthnumber: 2
year: 1967
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Fri Sep 29 08:56:19 MDT 2000
bibtimestamp: 2000.09.29 08:56:19 MDT
fjournal: The Computer Journal
acknowledgement: ack-nhfb
journalURL: http://comjnl.oxfordjournals.org/
rawauthor: K. M. Howell
rawtitle: Multiple precision arithmetic techniques
bibsource:
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/090383.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/383.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/384.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/385.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/386.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/387.tif

entry:
@Article{Howell:1967:MPA,
  author =       "K. M. Howell",
  title =        "Multiple precision arithmetic techniques",
  journal =      j-COMP-J,
  volume =       "9",
  number =       "4",
  pages =        "383--387",
  month =        feb,
  year =         "1967",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:56:19 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/090383.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/383.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/384.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/385.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/386.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/387.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}


bibtype: article
filename: fparith.bib
label: Jarden:1967:EAL
author: Dov Jarden
journal: j-FIB-QUART
volume: 5
number: 3
pages: 280--??
month: oct
monthnumber: 10
year: 1967
CODEN: FIBQAU
ISSN: 0015-0517 OR 00150517
ISSNL: 0015-0517 OR 00150517
bibdate: Thu Oct 20 18:04:54 MDT 2011
bibtimestamp: 2011.10.20 18:04:54 MDT
URL: http://www.fq.math.ca/Scanned/5-3/jarden1.pdf
fjournal: The Fibonacci Quarterly. Official Organ of the Fibonacci Association
acknowledgement: ack-nhfb
ajournal: Fib. Quart
journalURL: http://www.fq.math.ca/
rawauthor: Dov Jarden
title:
Existence of Arbitrarily Long Sequences of Consecutive Members in Arithmetic Progressions Divisible by Arbitrarily Many Different Primes

bibsource:
http://www.fq.math.ca/5-3.html; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawtitle:
Existence of Arbitrarily Long Sequences of Consecutive Members in Arithmetic Progressions Divisible by Arbitrarily Many Different Primes

entry:
@Article{Jarden:1967:EAL,
  author =       "Dov Jarden",
  title =        "Existence of Arbitrarily Long Sequences of Consecutive
                 Members in Arithmetic Progressions Divisible by
                 Arbitrarily Many Different Primes",
  journal =      j-FIB-QUART,
  volume =       "5",
  number =       "3",
  pages =        "280--??",
  month =        oct,
  year =         "1967",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:04:54 MDT 2011",
  bibsource =    "http://www.fq.math.ca/5-3.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/5-3/jarden1.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}


bibtype: article
filename: fparith.bib
label: Krishnamurthy:1967:NRD
author: E. V. Krishnamurthy and S. K. Nandi
title: On the Normalization Requirement of Divisor in Divide-and-Correct Methods
journal: j-CACM
volume: 10
number: 12
pages: 809--813
month: dec
monthnumber: 12
year: 1967
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Sep 1 10:15:08 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:08 ???
fjournal: Communications of the ACM
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/cacm
rawauthor: E. V. Krishnamurthy and S. K. Nandi
rawtitle: On the Normalization Requirement of Divisor in Divide-and-Correct Methods
entry:
@Article{Krishnamurthy:1967:NRD,
  author =       "E. V. Krishnamurthy and S. K. Nandi",
  title =        "On the Normalization Requirement of Divisor in
                 Divide-and-Correct Methods",
  journal =      j-CACM,
  volume =       "10",
  number =       "12",
  pages =        "809--813",
  month =        dec,
  year =         "1967",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: article
filename: fparith.bib
label: Kuki:1967:CAE
author: H. Kuki
title: Comments on the ANL Evaluation of the OS / 360 FORTRAN Math Function Library
journal: SHARE Secretary Distribution
volume: SSD 169
number: C4773
pages: 47--53
year: 1967
bibdate: Fri Aug 20 09:42:04 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.08.20 09:42:04 ???
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
rawauthor: H. Kuki
rawtitle: Comments on the {ANL} Evaluation of the {OS\slash 360 FORTRAN} Math Function Library
entry:
@Article{Kuki:1967:CAE,
  author =       "H. Kuki",
  title =        "Comments on the {ANL} Evaluation of the {OS\slash 360
                 FORTRAN} Math Function Library",
  journal =      "{SHARE Secretary Distribution}",
  volume =       "SSD 169",
  number =       "C4773",
  pages =        "47--53",
  year =         "1967",
  bibdate =      "Fri Aug 20 09:42:04 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Lewis:1967:CFP
author: H. R. Lewis, Jr. and E. J. Stovall, Jr.
journal: j-MATH-COMPUT
volume: 21
number: 98
pages: 157--161
month: apr
monthnumber: 4
year: 1967
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
ajournal: Math. Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: H. R. {Lewis, Jr.} and E. J. {Stovall, Jr.}
title:
Comments on a Floating-Point Version of Nordsieck's Scheme for the Numerical Integration of Differential Equations

rawtitle:
Comments on a Floating-Point Version of {Nordsieck}'s Scheme for the Numerical Integration of Differential Equations

entry:
@Article{Lewis:1967:CFP,
  author =       "H. R. {Lewis, Jr.} and E. J. {Stovall, Jr.}",
  title =        "Comments on a Floating-Point Version of {Nordsieck}'s
                 Scheme for the Numerical Integration of Differential
                 Equations",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "98",
  pages =        "157--161",
  month =        apr,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: fparith.bib
label: Long:1967:LAS
author: C. T. Long and J. H. Jordan
title: A Limited Arithmetic on Simple Continued Fractions
journal: j-FIB-QUART
volume: 5
number: 2
pages: 113--128
month: apr
monthnumber: 4
year: 1967
CODEN: FIBQAU
ISSN: 0015-0517 OR 00150517
ISSNL: 0015-0517 OR 00150517
bibdate: Thu Oct 20 18:04:52 MDT 2011
bibtimestamp: 2011.10.20 18:04:52 MDT
URL: http://www.fq.math.ca/Scanned/5-2/long.pdf
fjournal: The Fibonacci Quarterly. Official Organ of the Fibonacci Association
acknowledgement: ack-nhfb
ajournal: Fib. Quart
journalURL: http://www.fq.math.ca/
rawauthor: C. T. Long and J. H. Jordan
rawtitle: A Limited Arithmetic on Simple Continued Fractions
bibsource:
http://www.fq.math.ca/5-2.html; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Long:1967:LAS,
  author =       "C. T. Long and J. H. Jordan",
  title =        "A Limited Arithmetic on Simple Continued Fractions",
  journal =      j-FIB-QUART,
  volume =       "5",
  number =       "2",
  pages =        "113--128",
  month =        apr,
  year =         "1967",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:04:52 MDT 2011",
  bibsource =    "http://www.fq.math.ca/5-2.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/5-2/long.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}


bibtype: article
filename: fparith.bib
label: Mandelbaum:1967:CLS
author: David Mandelbaum
title: A Comparison of Linear Sequential Circuits and Arithmetic Sequences
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-16
number: 2
pages: 151--157
month: apr
monthnumber: 4
year: 1967
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1967.264810
ISSN: 0367-7508 OR 03677508
bibdate: Wed Jul 13 21:15:01 MDT 2011
bibtimestamp: 2011.07.13 21:15:01 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039022
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: David Mandelbaum
rawtitle: A Comparison of Linear Sequential Circuits and Arithmetic Sequences
entry:
@Article{Mandelbaum:1967:CLS,
  author =       "David Mandelbaum",
  title =        "A Comparison of Linear Sequential Circuits and
                 Arithmetic Sequences",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-16",
  number =       "2",
  pages =        "151--157",
  month =        apr,
  year =         "1967",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810",
  ISSN =         "0367-7508",
  bibdate =      "Wed Jul 13 21:15:01 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039022",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: fparith.bib
label: Massell:1967:RAP
author: E. Massell
title: R67-41 An Analog Photoresistive Multiplier
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-16
number: 3
pages: 380--380
month: jun
monthnumber: 6
year: 1967
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1967.264730
ISSN: 0367-7508 OR 03677508
bibdate: Wed Jul 13 21:15:03 MDT 2011
bibtimestamp: 2011.07.13 21:15:03 MDT
note: See comment cite Azgapetian:1968:CAP.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039094
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: E. Massell
rawnote: See comment \cite{Azgapetian:1968:CAP}.
rawtitle: {R67-41} An Analog Photoresistive Multiplier
entry:
@Article{Massell:1967:RAP,
  author =       "E. Massell",
  title =        "{R67-41} An Analog Photoresistive Multiplier",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-16",
  number =       "3",
  pages =        "380--380",
  month =        jun,
  year =         "1967",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264730",
  ISSN =         "0367-7508",
  bibdate =      "Wed Jul 13 21:15:03 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  note =         "See comment \cite{Azgapetian:1968:CAP}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039094",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: inproceedings
filename: fparith.bib
label: Matula:1967:BCM
author: David W. Matula
booktitle: Proceedings of the AFIPS 1967 Spring Joint Computer Conference
title: Base Conversion Mappings
volume: 30
publisher: pub-AFIPS
address: pub-AFIPS:adr
pages: 311--318
year: 1967
bibdate: Wed Feb 14 19:18:24 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.02.14 19:18:24 ???
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
rawauthor: David W. Matula
rawbooktitle: {Proceedings of the AFIPS 1967 Spring Joint Computer Conference}
rawtitle: Base Conversion Mappings
entry:
@InProceedings{Matula:1967:BCM,
  author =       "David W. Matula",
  booktitle =    "{Proceedings of the AFIPS 1967 Spring Joint Computer
                 Conference}",
  title =        "Base Conversion Mappings",
  volume =       "30",
  publisher =    pub-AFIPS,
  address =      pub-AFIPS:adr,
  pages =        "311--318",
  year =         "1967",
  bibdate =      "Wed Feb 14 19:18:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: book
filename: fparith.bib
label: McCalla:1967:INM
author: Thomas Richard McCalla
title: Introduction to Numerical Methods and Fortran Programming
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xiii + 359
month: jan
monthnumber: 1
year: 1967
ISBN: 0-471-58125-9 OR 0471581259
ISBN13: 978-0-471-58125-3 OR 9780471581253
LCCN: QA297 .M25
bibdate: Sat Sep 27 17:58:26 MDT 1997
bibtimestamp: 1997.09.27 17:58:26 MDT
URL: http://www.cbooks.com/sqlnut/SP/search/gtsumt?source=&isbn=0471581259
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
rawauthor: Thomas Richard McCalla
rawtitle: Introduction to Numerical Methods and {Fortran} Programming
bibsource:
http://www.amazon.com/exec/obidos/ISBN=0471581259/wholesaleproductA/; http://www.cbooks.com/; https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager

keywords:
Electronic digital computers --- Programming.; FORTRAN (Computer program language); Numerical analysis.

entry:
@Book{McCalla:1967:INM,
  author =       "Thomas Richard McCalla",
  title =        "Introduction to Numerical Methods and {Fortran}
                 Programming",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiii + 359",
  month =        jan,
  year =         "1967",
  ISBN =         "0-471-58125-9",
  ISBN-13 =      "978-0-471-58125-3",
  LCCN =         "QA297 .M25",
  bibdate =      "Sat Sep 27 17:58:26 MDT 1997",
  bibsource =    "http://www.amazon.com/exec/obidos/ISBN=0471581259/wholesaleproductA/;
                 http://www.cbooks.com/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$27.95",
  URL =          "http://www.cbooks.com/sqlnut/SP/search/gtsumt?source=&isbn=0471581259",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming.; FORTRAN
                 (Computer program language); Numerical analysis.",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: McKeeman:1967:RER
author: W. M. McKeeman
title: Representation Error for Real Numbers in Binary Computer Arithmetic
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-16
number: 5
pages: 682--683
month: oct
monthnumber: 10
year: 1967
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1967.264781
ISSN: 0367-7508 OR 03677508
bibdate: Wed Jul 13 21:15:05 MDT 2011
bibtimestamp: 2011.07.13 21:15:05 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039164
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: W. M. McKeeman
rawtitle: Representation Error for Real Numbers in Binary Computer Arithmetic
abstract:
Real numbers can be represented in a binary computer by the form $ i cdot B^e $ where $i$ is the integer part, $B$ the base, and $e$ the exponent. The accuracy of the representation will depend upon the number of bits allocated to the integer part and exponent part as well as what base is chosen. If $ L(i) $ and $ L(e) $ are the number of bits allocated to the magnitudes of the integer and exponent parts and we define $ I = 2^L(i) $ and $ E = 2^L(e) $, the exponent range is given by $ B^pm E $, the maximum relative representation error is given by $ B / 2 I $, and the average relative representation error is given by $ (B - 1) / (4 I ln B) $. The formulas provide quantitative comparison for the effectiveness of alternative formats for real number representations.

remark:
McKeeman discusses the maximum and average relative errors in binary (with and without a hidden bit), octal, and hexadecimal bases for floating-point arithmetic with a 48-bit computer word. Errors are smallest with binary and a hidden bit.

rawabstract:
Real numbers can be represented in a binary computer by the form $ i \cdot B^e $ where $i$ is the integer part, $B$ the base, and $e$ the exponent. The accuracy of the representation will depend upon the number of bits allocated to the integer part and exponent part as well as what base is chosen. If $ L(i) $ and $ L(e) $ are the number of bits allocated to the magnitudes of the integer and exponent parts and we define $ I = 2^{L(i)} $ and $ E = 2^{L(e)} $, the exponent range is given by $ B^{\pm E} $, the maximum relative representation error is given by $ B / 2 I $, and the average relative representation error is given by $ (B - 1) / (4 I \ln B) $. The formulas provide quantitative comparison for the effectiveness of alternative formats for real number representations.

entry:
@Article{McKeeman:1967:RER,
  author =       "W. M. McKeeman",
  title =        "Representation Error for Real Numbers in Binary
                 Computer Arithmetic",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-16",
  number =       "5",
  pages =        "682--683",
  month =        oct,
  year =         "1967",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264781",
  ISSN =         "0367-7508",
  bibdate =      "Wed Jul 13 21:15:05 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039164",
  abstract =     "Real numbers can be represented in a binary computer
                 by the form $ i \cdot B^e $ where $i$ is the integer
                 part, $B$ the base, and $e$ the exponent. The accuracy
                 of the representation will depend upon the number of
                 bits allocated to the integer part and exponent part as
                 well as what base is chosen. If $ L(i) $ and $ L(e) $
                 are the number of bits allocated to the magnitudes of
                 the integer and exponent parts and we define $ I =
                 2^{L(i)} $ and $ E = 2^{L(e)} $, the exponent range is
                 given by $ B^{\pm E} $, the maximum relative
                 representation error is given by $ B / 2 I $, and the
                 average relative representation error is given by $ (B
                 - 1) / (4 I \ln B) $. The formulas provide quantitative
                 comparison for the effectiveness of alternative formats
                 for real number representations.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
  remark =       "McKeeman discusses the maximum and average relative
                 errors in binary (with and without a hidden bit),
                 octal, and hexadecimal bases for floating-point
                 arithmetic with a 48-bit computer word. Errors are
                 smallest with binary and a hidden bit.",
}


bibtype: article
filename: fparith.bib
label: Menzel:1967:AUA
author: M. Menzel and N. Metropolis
title: Algorithms in unnormalized arithmetic. II. Unrestricted polynomial evaluation
journal: j-NUM-MATH
volume: 10
number: 5
pages: 451--462
month: nov
monthnumber: 11
year: 1967
CODEN: NUMMA7
DOI: https://doi.org/10.1007/BF02162878
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 65.80
MRnumber: MR0255093 (40 \#8300)
bibdate: Wed Nov 14 19:04:40 2007
bibtimestamp: 2007.11.14 19:04:40 ???
fjournal: Numerische Mathematik
ZMnumber: 0225.65059
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: M. Menzel and N. Metropolis
rawtitle: Algorithms in unnormalized arithmetic. {II}. {Unrestricted} polynomial evaluation
entry:
@Article{Menzel:1967:AUA,
  author =       "M. Menzel and N. Metropolis",
  title =        "Algorithms in unnormalized arithmetic. {II}.
                 {Unrestricted} polynomial evaluation",
  journal =      j-NUM-MATH,
  volume =       "10",
  number =       "5",
  pages =        "451--462",
  month =        nov,
  year =         "1967",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF02162878",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.80",
  MRnumber =     "MR0255093 (40 \#8300)",
  bibdate =      "Wed Nov 14 19:04:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0225.65059",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: book
filename: fparith.bib
label: Minsky:1967:CFI
author: Marvin Lee Minsky
title: Computation: Finite and Infinite Machines
publisher: pub-PH
address: pub-PH:adr
pages: xvii + 317
year: 1967
LCCN: QA267 .M55
bibdate: Thu Oct 17 06:05:56 2019
bibtimestamp: 2019.10.17 06:05:56 ???
acknowledgement: ack-nhfb
authordates: 1927--2016
rawauthor: Marvin Lee Minsky
rawtitle: Computation: Finite and Infinite Machines
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

TOC:
Physical machines and their abstract counterparts Part 1: Finite-state machines Neural networks. Automata made up of parts The memories of events in finite-state machines Part 2: Infinite machines Computability, effective procedures, and algorithms. Infinite machines Turing machines Universal Turing machines Limitations of effective computability: some problems not solvable by instruction-obeying machines The computable real numbers The relations between Turing machines and recursive functions Models similar to digital computers Part 3: Symbol-manipulation systems and computability The symbol-manipulation systems of post Post's normal-form theorem Very simple bases for computability Solutions to selected problems

rawTOC:
Physical machines and their abstract counterparts \\ Part 1: Finite-state machines \\ Neural networks. Automata made up of parts \\ The memories of events in finite-state machines \\ Part 2: Infinite machines \\ Computability, effective procedures, and algorithms. Infinite machines \\ Turing machines \\ Universal Turing machines \\ Limitations of effective computability: some problems not solvable by instruction-obeying machines \\ The computable real numbers \\ The relations between Turing machines and recursive functions \\ Models similar to digital computers \\ Part 3: Symbol-manipulation systems and computability \\ The symbol-manipulation systems of post \\ Post's normal-form theorem \\ Very simple bases for computability \\ Solutions to selected problems

entry:
@Book{Minsky:1967:CFI,
  author =       "Marvin Lee Minsky",
  title =        "Computation: Finite and Infinite Machines",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xvii + 317",
  year =         "1967",
  LCCN =         "QA267 .M55",
  bibdate =      "Thu Oct 17 06:05:56 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1927--2016",
  tableofcontents = "Physical machines and their abstract counterparts
                 \\
                 Part 1: Finite-state machines \\
                 Neural networks. Automata made up of parts \\
                 The memories of events in finite-state machines \\
                 Part 2: Infinite machines \\
                 Computability, effective procedures, and algorithms.
                 Infinite machines \\
                 Turing machines \\
                 Universal Turing machines \\
                 Limitations of effective computability: some problems
                 not solvable by instruction-obeying machines \\
                 The computable real numbers \\
                 The relations between Turing machines and recursive
                 functions \\
                 Models similar to digital computers \\
                 Part 3: Symbol-manipulation systems and computability
                 \\
                 The symbol-manipulation systems of post \\
                 Post's normal-form theorem \\
                 Very simple bases for computability \\
                 Solutions to selected problems",
}


bibtype: article
filename: fparith.bib
label: Moler:1967:IRF
author: C. B. Moler
title: Iterative Refinement in Floating Point
journal: j-J-ACM
volume: 14
number: 2
pages: 316--321
month: apr
monthnumber: 4
year: 1967
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Tue Nov 1 09:43:17 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.11.01 09:43:17 ???
fjournal: Journal of the ACM
keywords: ir, nla, lud, iterative refinement
acknowledgement: ack-nj
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
rawauthor: C. B. Moler
rawtitle: Iterative Refinement in Floating Point
entry:
@Article{Moler:1967:IRF,
  author =       "C. B. Moler",
  title =        "Iterative Refinement in Floating Point",
  journal =      j-J-ACM,
  volume =       "14",
  number =       "2",
  pages =        "316--321",
  month =        apr,
  year =         "1967",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Tue Nov 1 09:43:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  keywords =     "ir, nla, lud, iterative refinement",
}


bibtype: article
filename: fparith.bib
label: Mosteller:1967:DSR
author: Frederick Mosteller and Cleo Youtz and Douglas Zahn
title: The Distribution of Sums of Rounded Percentages
journal: j-DEMOGRAPHY
volume: 4
number: 2
pages: 850--858
month: jun
monthnumber: 6
year: 1967
ISSN: 0070-3370 (print), 1533-7790 (electronic) OR 00703370 (print), 15337790 (electronic)
ISSNL: 0070-3370 OR 00703370
bibdate: Thu Nov 24 08:03:16 2011
bibtimestamp: 2011.11.24 08:03:16 ???
note: See cite Diaconis:1979:RP for further work.
fjournal: Demography
acknowledgement: ack-nhfb
rawauthor: Frederick Mosteller and Cleo Youtz and Douglas Zahn
rawnote: See \cite{Diaconis:1979:RP} for further work.
rawtitle: The Distribution of Sums of Rounded Percentages
bibsource:
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://muse.jhu.edu/journals/dem/; http://www.biomedsearch.com/nih/Distribution-Sums-Rounded-Percentages/21318695.html; http://www.jstor.org/stable/2060324

abstract:
When percentages are computed for counts in several categories or for several positive measurements0 each taken as a fraction of their sum, the rounded percentages often fail to add to 100 percent. We investigate how frequently this failure occurs and what the distributions of sums of rounded percentages are for (1) an empirical set of data, (2) the multinomial distribution in small samples, (3) spacings between points dropped on an interval --- the broken-stick model; and (4) for simulation for several categories. The several methods produce similar distributions.We find that the probability that the sum of rounded percentages adds to exactly 100 percent is certain for two categories, about three-fourths for three categories, about two-thirds for four categories, and about [Formula: see text] for larger numbers of categories, c, on the average when categories are not improbable.

rawabstract:
When percentages are computed for counts in several categories or for several positive measurements0 each taken as a fraction of their sum, the rounded percentages often fail to add to 100 percent. We investigate how frequently this failure occurs and what the distributions of sums of rounded percentages are for (1) an empirical set of data, (2) the multinomial distribution in small samples, (3) spacings between points dropped on an interval --- the broken-stick model; and (4) for simulation for several categories. The several methods produce similar distributions.We find that the probability that the sum of rounded percentages adds to exactly 100 percent is certain for two categories, about three-fourths for three categories, about two-thirds for four categories, and about [Formula: see text] for larger numbers of categories, c, on the average when categories are not improbable.

entry:
@Article{Mosteller:1967:DSR,
  author =       "Frederick Mosteller and Cleo Youtz and Douglas Zahn",
  title =        "The Distribution of Sums of Rounded Percentages",
  journal =      j-DEMOGRAPHY,
  volume =       "4",
  number =       "2",
  pages =        "850--858",
  month =        jun,
  year =         "1967",
  CODEN =        "????",
  ISSN =         "0070-3370 (print), 1533-7790 (electronic)",
  ISSN-L =       "0070-3370",
  bibdate =      "Thu Nov 24 08:03:16 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Diaconis:1979:RP} for further work.",
  URL =          "http://muse.jhu.edu/journals/dem/;
                 http://www.biomedsearch.com/nih/Distribution-Sums-Rounded-Percentages/21318695.html;
                 http://www.jstor.org/stable/2060324",
  abstract =     "When percentages are computed for counts in several
                 categories or for several positive measurements0 each
                 taken as a fraction of their sum, the rounded
                 percentages often fail to add to 100 percent. We
                 investigate how frequently this failure occurs and what
                 the distributions of sums of rounded percentages are
                 for (1) an empirical set of data, (2) the multinomial
                 distribution in small samples, (3) spacings between
                 points dropped on an interval --- the broken-stick
                 model; and (4) for simulation for several categories.
                 The several methods produce similar distributions.We
                 find that the probability that the sum of rounded
                 percentages adds to exactly 100 percent is certain for
                 two categories, about three-fourths for three
                 categories, about two-thirds for four categories, and
                 about [Formula: see text] for larger numbers of
                 categories, c, on the average when categories are not
                 improbable.",
  acknowledgement = ack-nhfb,
  fjournal =     "Demography",
  pubmedid =     "21318695",
}


bibtype: article
filename: fparith.bib
label: Moursund:1967:OSV
author: David G. Moursund
title: Optimal starting values for Newton--Raphson calculation of $ sqrt x $
journal: j-CACM
volume: 10
number: 7
pages: 430--432
month: jul
monthnumber: 7
year: 1967
CODEN: CACMA2
DOI: https://doi.org/10.1145/363427.363454
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65.25
MRnumber: 39\#2297
bibdate: Thu Sep 1 10:15:43 1994
bibtimestamp: 1994.09.01 10:15:43 ???
note: See letter cite Fike:1967:LER.
fjournal: Communications of the ACM
keywords: $sqrt (x)$; elementary functions
remark: Title of article has incorrect $ sqrt (x^1 / 2) $: the article discusses computation of tt sqrt(x).
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/cacm
rawauthor: David G. Moursund
rawnote: See letter \cite{Fike:1967:LER}.
rawtitle: Optimal starting values for {Newton--Raphson} calculation of $ \sqrt {x} $
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
The problem of obtaining starting values for the Newton-Raphson calculation of $ sqrt x $ on a digital computer is considered. It is shown that the conventionally used best uniform approximations to $ sqrt x $ do not provide optimal starting values. The problem of obtaining optimal starting values is stated, and several basic results are proved. A table of optimal polynomial starting values is given.

rawabstract:
The problem of obtaining starting values for the Newton-Raphson calculation of $ \sqrt {x} $ on a digital computer is considered. It is shown that the conventionally used best uniform approximations to $ \sqrt {x} $ do not provide optimal starting values. The problem of obtaining optimal starting values is stated, and several basic results are proved. A table of optimal polynomial starting values is given.

entry:
@Article{Moursund:1967:OSV,
  author =       "David G. Moursund",
  title =        "Optimal starting values for {Newton--Raphson}
                 calculation of $ \sqrt {x} $",
  journal =      j-CACM,
  volume =       "10",
  number =       "7",
  pages =        "430--432",
  month =        jul,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363427.363454",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.25",
  MRnumber =     "39\#2297",
  bibdate =      "Thu Sep 1 10:15:43 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See letter \cite{Fike:1967:LER}.",
  abstract =     "The problem of obtaining starting values for the
                 Newton-Raphson calculation of $ \sqrt {x} $ on a
                 digital computer is considered. It is shown that the
                 conventionally used best uniform approximations to $
                 \sqrt {x} $ do not provide optimal starting values. The
                 problem of obtaining optimal starting values is stated,
                 and several basic results are proved. A table of
                 optimal polynomial starting values is given.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions",
  remark =       "Title of article has incorrect $ \sqrt (x^{1 / 2}) $:
                 the article discusses computation of {\tt sqrt(x)}.",
}


bibtype: article
filename: fparith.bib
label: Nandi:1967:STD
author: Salil K. Nandi and E. V. Krishnamurthy
title: A simple technique for digital division
journal: j-CACM
volume: 10
number: 5
pages: 299--301
month: may
monthnumber: 5
year: 1967
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:13 MST 2005
bibtimestamp: 2005.11.25 18:20:13 MST
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Salil K. Nandi and E. V. Krishnamurthy
rawtitle: A simple technique for digital division
entry:
@Article{Nandi:1967:STD,
  author =       "Salil K. Nandi and E. V. Krishnamurthy",
  title =        "A simple technique for digital division",
  journal =      j-CACM,
  volume =       "10",
  number =       "5",
  pages =        "299--301",
  month =        may,
  year =         "1967",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:13 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: article
filename: fparith.bib
label: Sandberg:1967:FPR
author: I. W. Sandberg
title: Floating-Point-Roundoff Accumulation in Digital-Filter Realizations
journal: j-BELL-SYST-TECH-J
volume: 46
number: 8
pages: 1775--1791
month: oct
monthnumber: 10
year: 1967
CODEN: BSTJAN
ISSN: 0005-8580 OR 00058580
bibdate: Tue Nov 9 11:15:55 MST 2010
bibtimestamp: 2010.11.09 11:15:55 MST
URL: http://bstj.bell-labs.com/BSTJ/images/Vol46/bstj46-8-1775.pdf
fjournal: The Bell System Technical Journal
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/
rawauthor: I. W. Sandberg
rawtitle: Floating-Point-Roundoff Accumulation in Digital-Filter Realizations
bibsource:
http://bstj.bell-labs.com/oldfiles/year.1967/BSTJ.1967.4608.html; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
In this paper, several results are presented concerning the effects of roundoff in the floating-point realization of a general discrete filter governed ideally by a stable difference equation of the formpar $$ w_n = sum _k = 0^M b_k x_n - k - sum k = 1^N a_k w_n - k, qquad n geq N qquad (1) $$ par in which $ w_n $ and $ x_n $ are output and input sequences, respectively.par In particular, for a large class of filters it is proved that there is a function $ f(K) $ with $ f(K) to 0 $ as $ K to infty $ and a constant $c$, both dependent on the $ b_k $, the $ a_k $, the order in which the products on the right side of (1) are summed in the machine, and $t$, the number of bits allotted to the mantissa, such thatpar $$ langle e rangle _K leq c langle y rangle _K + f(K) $$ par for all $ K geq N $, in which, with the computed output sequence of the realized filter,par $$ langle y rangle _K = left (frac 1K + 1 sum _n = 0^K |y_n|^2 right )^1 / 2 $$ par andpar $$ langle e rangle _K = left (frac 1K + 1 sum _n = 0^K |w_n - y_n|^2 right )^1 / 2 $$ par Bounds on $ f(K) $ and $c$ are given that are not difficult to evaluate, and which, in many realistic cases, are informative. For example, for the second-order bandpass filter:par $$ w_n = x_n - a_1 w_n - 1 - a_2 w_n - 2, qquad n geq 2 qquad (2) $$ par with $ a_1 $ and $ a_2 $ chosen so that its poles arc at approximately $ pm 45^circ $ and at distance approximately (but not less than) $ 0.001 $ from the unit circle, we find that $c$, an upper bound on the ``asymptotic output error-to-signal ratio'', is not greater than $ 0.58 times 10^-4 $, assuming that $ t = 27 $, that the terms on the right side of (2) are summed in the machine in the order indicated (from right to left), and that the $ x_n $ in (2) are machine numbers. If the $ x_n $ are not machine numbers, and hence must be quantized before processing, then $ c leq 0.76 times 10^-4 $.par In addition to error bounds, an inequality is derived which, if satisfied, rules out certain types of generally undesirable behavior such as self-sustained output limit cycles due to roundoff effects. This inequality is satisfied for the example described above.

rawabstract:
In this paper, several results are presented concerning the effects of roundoff in the floating-point realization of a general discrete filter governed ideally by a stable difference equation of the form\par $$ w_n = \sum_{k = 0}^M b_k x_{n - k} - \sum {k = 1}^N a_k w_{n - k}, \qquad n \geq N \qquad (1) $$ \par in which $ \{ w_n \} $ and $ \{ x_n \} $ are output and input sequences, respectively.\par In particular, for a large class of filters it is proved that there is a function $ f(K) $ with $ f(K) \to 0 $ as $ K \to \infty $ and a constant $c$, both dependent on the $ b_k $, the $ a_k $, the order in which the products on the right side of (1) are summed in the machine, and $t$, the number of bits allotted to the mantissa, such that\par $$ \langle e \rangle_K \leq c \langle y \rangle_K + f(K) $$ \par for all $ K \geq N $, in which, with the computed output sequence of the realized filter,\par $$ \langle y \rangle_K = \left (\frac {1}{K + 1} \sum_{n = 0}^K |y_n|^2 \right)^{1 / 2} $$ \par and\par $$ \langle e \rangle_K = \left (\frac {1}{K + 1} \sum_{n = 0}^K |w_n - y_n|^2 \right)^{1 / 2} $$ \par Bounds on $ f(K) $ and $c$ are given that are not difficult to evaluate, and which, in many realistic cases, are informative. For example, for the second-order bandpass filter:\par $$ w_n = x_n - a_1 w_{n - 1} - a_2 w_{n - 2}, \qquad n \geq 2 \qquad (2) $$ \par with $ a_1 $ and $ a_2 $ chosen so that its poles arc at approximately $ \pm 45^\circ $ and at distance approximately (but not less than) $ 0.001 $ from the unit circle, we find that $c$, an upper bound on the ``asymptotic output error-to-signal ratio'', is not greater than $ 0.58 \times 10^{-4} $, assuming that $ t = 27 $, that the terms on the right side of (2) are summed in the machine in the order indicated (from right to left), and that the $ x_n $ in (2) are machine numbers. If the $ x_n $ are not machine numbers, and hence must be quantized before processing, then $ c \leq 0.76 \times 10^{-4} $.\par In addition to error bounds, an inequality is derived which, if satisfied, rules out certain types of generally undesirable behavior such as self-sustained output limit cycles due to roundoff effects. This inequality is satisfied for the example described above.

entry:
@Article{Sandberg:1967:FPR,
  author =       "I. W. Sandberg",
  title =        "Floating-Point-Roundoff Accumulation in Digital-Filter
                 Realizations",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "46",
  number =       "8",
  pages =        "1775--1791",
  month =        oct,
  year =         "1967",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  bibdate =      "Tue Nov 9 11:15:55 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1967/BSTJ.1967.4608.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol46/bstj46-8-1775.pdf",
  abstract =     "In this paper, several results are presented
                 concerning the effects of roundoff in the
                 floating-point realization of a general discrete filter
                 governed ideally by a stable difference equation of the
                 form\par

                  $$ w_n = \sum_{k = 0}^M b_k x_{n - k} - \sum {k = 1}^N
                 a_k w_{n - k}, \qquad n \geq N \qquad (1) $$ \par

                 in which $ \{ w_n \} $ and $ \{ x_n \} $ are output and
                 input sequences, respectively.\par

                 In particular, for a large class of filters it is
                 proved that there is a function $ f(K) $ with $ f(K)
                 \to 0 $ as $ K \to \infty $ and a constant $c$, both
                 dependent on the $ b_k $, the $ a_k $, the order in
                 which the products on the right side of (1) are summed
                 in the machine, and $t$, the number of bits allotted to
                 the mantissa, such that\par

                  $$ \langle e \rangle_K \leq c \langle y \rangle_K +
                 f(K) $$ \par

                 for all $ K \geq N $, in which, with the computed
                 output sequence of the realized filter,\par

                  $$ \langle y \rangle_K = \left (\frac {1}{K + 1}
                 \sum_{n = 0}^K |y_n|^2 \right)^{1 / 2} $$ \par

                 and\par

                  $$ \langle e \rangle_K = \left (\frac {1}{K + 1}
                 \sum_{n = 0}^K |w_n - y_n|^2 \right)^{1 / 2} $$
                 \par

                 Bounds on $ f(K) $ and $c$ are given that are not
                 difficult to evaluate, and which, in many realistic
                 cases, are informative. For example, for the
                 second-order bandpass filter:\par

                  $$ w_n = x_n - a_1 w_{n - 1} - a_2 w_{n - 2}, \qquad n
                 \geq 2 \qquad (2) $$ \par

                 with $ a_1 $ and $ a_2 $ chosen so that its poles arc
                 at approximately $ \pm 45^\circ $ and at distance
                 approximately (but not less than) $ 0.001 $ from the
                 unit circle, we find that $c$, an upper bound on the
                 ``asymptotic output error-to-signal ratio'', is not
                 greater than $ 0.58 \times 10^{-4} $, assuming that $ t
                 = 27 $, that the terms on the right side of (2) are
                 summed in the machine in the order indicated (from
                 right to left), and that the $ x_n $ in (2) are machine
                 numbers. If the $ x_n $ are not machine numbers, and
                 hence must be quantized before processing, then $ c
                 \leq 0.76 \times 10^{-4} $.\par

                 In addition to error bounds, an inequality is derived
                 which, if satisfied, rules out certain types of
                 generally undesirable behavior such as self-sustained
                 output limit cycles due to roundoff effects. This
                 inequality is satisfied for the example described
                 above.",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}


bibtype: article
filename: fparith.bib
label: Sasaki:1967:ASR
author: Akio Sasaki
title: Addition and Subtraction in the Residue Number System
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-16
number: 2
pages: 157--164
month: apr
monthnumber: 4
year: 1967
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1967.264811
ISSN: 0367-7508 OR 03677508
bibdate: Wed Jul 13 21:15:01 MDT 2011
bibtimestamp: 2011.07.13 21:15:01 MDT
fjournal: IEEE Transactions on Electronic Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: Akio Sasaki
rawtitle: Addition and Subtraction in the Residue Number System
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039023; http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4039015

entry:
@Article{Sasaki:1967:ASR,
  author =       "Akio Sasaki",
  title =        "Addition and Subtraction in the Residue Number
                 System",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-16",
  number =       "2",
  pages =        "157--164",
  month =        apr,
  year =         "1967",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264811",
  ISSN =         "0367-7508",
  bibdate =      "Wed Jul 13 21:15:01 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039023;
                 http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4039015",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Improved residue expression and new arithmetic
                 algorithms for addition and subtraction are proposed.
                 In the proposed system positive and negative integers
                 of any magnitude can be handled regardless of the
                 particular choice of the set of relatively \ldots{}",
}


bibtype: book
filename: fparith.bib
label: Szabo:1967:RAA
author: Nicholas S. Szabo and Richard I. Tanaka
title: Residue arithmetic and its applications to computer technology
publisher: pub-MCGRAW-HILL
address: pub-MCGRAW-HILL:adr
pages: xvi + 236
year: 1967
LCCN: QA247.35 .S95
bibdate: Fri Jun 24 16:02:00 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2005.06.24 16:02:00 MDT
series: McGraw-Hill series in information processing and computers
remark: Based on the authors' Report on residue (modular) arithmetic survey.
subject: Modular arithmetic; Algorithms; Computer programming
acknowledgement: ack-nhfb
rawauthor: Nicholas S. Szab{\'o} and Richard I. Tanaka
rawtitle: Residue arithmetic and its applications to computer technology
entry:
@Book{Szabo:1967:RAA,
  author =       "Nicholas S. Szab{\'o} and Richard I. Tanaka",
  title =        "Residue arithmetic and its applications to computer
                 technology",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xvi + 236",
  year =         "1967",
  LCCN =         "QA247.35 .S95",
  bibdate =      "Fri Jun 24 16:02:00 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "McGraw-Hill series in information processing and
                 computers",
  acknowledgement = ack-nhfb,
  remark =       "Based on the authors' Report on residue (modular)
                 arithmetic survey.",
  subject =      "Modular arithmetic; Algorithms; Computer programming",
}


bibtype: article
filename: fparith.bib
label: Tomasulo:1967:EAE
author: R. M. Tomasulo
title: An Efficient Algorithm for Exploiting Multiple Arithmetic Units
journal: j-IBM-JRD
volume: 11
number: 1
pages: 25--33
month: jan
monthnumber: 1
year: 1967
CODEN: IBMJAE
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
bibdate: Fri Aug 26 10:27:10 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.08.26 10:27:10 ???
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
rawauthor: R. M. Tomasulo
rawtitle: An Efficient Algorithm for Exploiting Multiple Arithmetic Units
entry:
@Article{Tomasulo:1967:EAE,
  author =       "R. M. Tomasulo",
  title =        "An Efficient Algorithm for Exploiting Multiple
                 Arithmetic Units",
  journal =      j-IBM-JRD,
  volume =       "11",
  number =       "1",
  pages =        "25--33",
  month =        jan,
  year =         "1967",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Fri Aug 26 10:27:10 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}


bibtype: book
filename: fparith.bib
label: Wilkinson:1967:BZW
author: J. H. Wilkinson
title: Bledy Zaokraglen w Procesach Algebraicznych. (Polish) [Rounding errors in algebraic Processes]
publisher: PWW
address: Warszawa, Poland
year: 1967
bibdate: Thu Aug 25 09:28:02 2011
bibtimestamp: 2011.08.25 09:28:02 ???
note: Polish translation of cite Wilkinson:1963:REA
language: Polish
acknowledgement: ack-nhfb
rawauthor: J. H. Wilkinson
rawnote: Polish translation of \cite{Wilkinson:1963:REA}
rawtitle:
Bledy Zaokragle{\'n} w Procesach Algebraicznych. ({Polish}) [{Rounding} errors in algebraic Processes]

entry:
@Book{Wilkinson:1967:BZW,
  author =       "J. H. Wilkinson",
  title =        "Bledy Zaokragle{\'n} w Procesach Algebraicznych.
                 ({Polish}) [{Rounding} errors in algebraic Processes]",
  publisher =    "PWW",
  address =      "Warszawa, Poland",
  pages =        "????",
  year =         "1967",
  bibdate =      "Thu Aug 25 09:28:02 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Polish translation of \cite{Wilkinson:1963:REA}",
  acknowledgement = ack-nhfb,
  language =     "Polish",
}


bibtype: article
filename: fparith.bib
label: Winograd:1967:TRP
author: Shmuel Winograd
title: On the Time Required to Perform Multiplication
journal: j-J-ACM
volume: 14
number: 4
pages: 793--802
month: oct
monthnumber: 10
year: 1967
CODEN: JACOAH
DOI: https://doi.org/10.1145/321420.321438
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Sat Feb 8 10:29:30 2020
bibtimestamp: 2020.02.08 10:29:30 ???
fjournal: Journal of the ACM
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
rawauthor: Shmuel Winograd
rawtitle: On the Time Required to Perform Multiplication
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Multi.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Winograd:1967:TRP,
  author =       "Shmuel Winograd",
  title =        "On the Time Required to Perform Multiplication",
  journal =      j-J-ACM,
  volume =       "14",
  number =       "4",
  pages =        "793--802",
  month =        oct,
  year =         "1967",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/321420.321438",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Sat Feb 8 10:29:30 2020",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Multi.bib;
                 https://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",
}


bibtype: article
filename: fparith.bib
label: Yarbrough:1967:PCC
author: Lynn Yarbrough
title: Precision calculations of $e$ and $ pi $ constants
journal: j-CACM
volume: 10
number: 9
pages: 537--537
month: sep
monthnumber: 9
year: 1967
CODEN: CACMA2
DOI: https://doi.org/10.1145/363566.363578
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:15 MST 2005
bibtimestamp: 2005.11.25 18:20:15 MST
fjournal: Communications of the ACM
keywords: floating-point arithmetic; number base conversion
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Lynn Yarbrough
rawtitle: Precision calculations of $e$ and $ \pi $ constants
bibsource:
http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

remark:
Gives decimal, octal, and hexadecimal values of $e$ and $ pi $ to 100 digits, and notes ``The difficulty arises because assemblers and compilers are hardly ever designed to convert decimal constants to a precision of more than a dozen or so digits. Thus, if calculations to greater precision are to be done, constants usually must be input in octal or other binary-derived representation.''. Cited in cite Sterbenz:1974:FPC.

entry:
@Article{Yarbrough:1967:PCC,
  author =       "Lynn Yarbrough",
  title =        "Precision calculations of $e$ and $ \pi $ constants",
  journal =      j-CACM,
  volume =       "10",
  number =       "9",
  pages =        "537--537",
  month =        sep,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363566.363578",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:15 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "floating-point arithmetic; number base conversion",
  remark =       "Gives decimal, octal, and hexadecimal values of $e$
                 and $ \pi $ to 100 digits, and notes ``The difficulty
                 arises because assemblers and compilers are hardly ever
                 designed to convert decimal constants to a precision of
                 more than a dozen or so digits. Thus, if calculations
                 to greater precision are to be done, constants usually
                 must be input in octal or other binary-derived
                 representation.''. Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Atkins:1968:HRD
author: D. E. Atkins
title: Higher-radix division using estimates of the divisor and partial remainders
journal: j-IEEE-TRANS-COMPUT
volume: C-17
number: 10
pages: 925--934
month: oct
monthnumber: 10
year: 1968
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1968.226439
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Thu Apr 2 08:38:35 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.04.02 08:38:35 ???
fjournal: IEEE Transactions on Computers
acknowledgement: ack-sfo
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. E. Atkins
rawtitle: Higher-radix division using estimates of the divisor and partial remainders
entry:
@Article{Atkins:1968:HRD,
  author =       "D. E. Atkins",
  title =        "Higher-radix division using estimates of the divisor
                 and partial remainders",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-17",
  number =       "10",
  pages =        "925--934",
  month =        oct,
  year =         "1968",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1968.226439",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: techreport
filename: fparith.bib
label: Azen:1968:DMS
author: S. Azen and S. Derr
title: On the Distribution of the Most Significant Hexadecimal Digit
type: Technical Report
number: RM 5496 PR
institution: Rand Report
address: Santa Monica, CA, USA
pages: 925--934
year: 1968
bibdate: Wed Feb 14 17:22:53 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.02.14 17:22:53 ???
acknowledgement: ack-nhfb
rawauthor: S. Azen and S. Derr
rawtitle: On the Distribution of the Most Significant Hexadecimal Digit
entry:
@TechReport{Azen:1968:DMS,
  author =       "S. Azen and S. Derr",
  title =        "On the Distribution of the Most Significant
                 Hexadecimal Digit",
  type =         "Technical Report",
  number =       "RM 5496 PR",
  institution =  "Rand Report",
  address =      "Santa Monica, CA, USA",
  year =         "1968",
  bibdate =      "Wed Feb 14 17:22:53 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Azgapetian:1968:CAP
author: V. Azgapetian
title: Comment on ``An Analog Photoresistive Multiplier''
journal: j-IEEE-TRANS-COMPUT
volume: C-17
number: 2
pages: 188--188
month: feb
monthnumber: 2
year: 1968
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1968.229083
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 17:40:47 MDT 2011
bibtimestamp: 2011.07.13 17:40:47 MDT
note: See cite Massell:1967:RAP.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687312
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: V. Azgapetian
rawnote: See \cite{Massell:1967:RAP}.
rawtitle: Comment on {``An Analog Photoresistive Multiplier''}
entry:
@Article{Azgapetian:1968:CAP,
  author =       "V. Azgapetian",
  title =        "Comment on {``An Analog Photoresistive Multiplier''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-17",
  number =       "2",
  pages =        "188--188",
  month =        feb,
  year =         "1968",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1968.229083",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 17:40:47 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  note =         "See \cite{Massell:1967:RAP}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687312",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Brennan:1968:FTA
author: J. F. Brennan
title: The Fastest Time of Addition and Multiplication
journal: IBM Research Reports
volume: 4
number: 1
pages: ??--??
year: 1968
bibdate: Fri Nov 09 10:43:37 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 10:43:37 ???
acknowledgement: ack-nhfb
rawauthor: J. F. Brennan
rawtitle: The Fastest Time of Addition and Multiplication
entry:
@Article{Brennan:1968:FTA,
  author =       "J. F. Brennan",
  title =        "The Fastest Time of Addition and Multiplication",
  journal =      "IBM Research Reports",
  volume =       "4",
  number =       "1",
  pages =        "??--??",
  month =        "????",
  year =         "1968",
  bibdate =      "Fri Nov 09 10:43:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Dietmeyer:1968:GPI
author: D. L. Dietmeyer and J. R. Duley
title: Generating prime implicants via ternary encoding and decimal arithmetic
journal: j-CACM
volume: 11
number: 7
pages: 520--523
month: jul
monthnumber: 7
year: 1968
CODEN: CACMA2
DOI: https://doi.org/10.1145/363397.363565
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Aug 07 17:25:16 2008
bibtimestamp: 2008.08.07 17:25:16 ???
fjournal: Communications of the ACM
keywords: cubical complexes; extremal; minimization; prime implicants; switching function; ternary encoding
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: D. L. Dietmeyer and J. R. Duley
rawtitle: Generating prime implicants via ternary encoding and decimal arithmetic
abstract:
Decimal arithmetic, ternary encoding of cubes, and topological considerations are used in an algorithm to obtain the extremals and prime implicants of Boolean functions. The algorithm, which has been programmed in the FORTRAN language, generally requires less memory than other minimization procedures, and treats DON'T CARE terms in an efficient manner.

rawabstract:
Decimal arithmetic, ternary encoding of cubes, and topological considerations are used in an algorithm to obtain the extremals and prime implicants of Boolean functions. The algorithm, which has been programmed in the FORTRAN language, generally requires less memory than other minimization procedures, and treats DON'T CARE terms in an efficient manner.

entry:
@Article{Dietmeyer:1968:GPI,
  author =       "D. L. Dietmeyer and J. R. Duley",
  title =        "Generating prime implicants via ternary encoding and
                 decimal arithmetic",
  journal =      j-CACM,
  volume =       "11",
  number =       "7",
  pages =        "520--523",
  month =        jul,
  year =         "1968",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363397.363565",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Aug 07 17:25:16 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Decimal arithmetic, ternary encoding of cubes, and
                 topological considerations are used in an algorithm to
                 obtain the extremals and prime implicants of Boolean
                 functions. The algorithm, which has been programmed in
                 the FORTRAN language, generally requires less memory
                 than other minimization procedures, and treats DON'T
                 CARE terms in an efficient manner.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "cubical complexes; extremal; minimization; prime
                 implicants; switching function; ternary encoding",
}


bibtype: article
filename: fparith.bib
label: Elliott:1968:EAA
author: David Elliott
title: Error analysis of an algorithm for summing certain finite series
journal: j-J-AUSTRALIAN-MATH-SOC
volume: 8
number: 2
pages: 213--221
month: may
monthnumber: 5
year: 1968
CODEN: JAUMAX
DOI: https://doi.org/10.1017/s1446788700005267
ISSN: 0004-9735 (print), 2059-9234 (electronic) OR 00049735 (print), 20599234 (electronic)
ISSNL: 0004-9735 OR 00049735
MRclass: 65.25
MRnumber: 0230452
MRreviewer: U. C. Guha
bibdate: Fri Feb 9 15:20:35 2018
bibtimestamp: 2018.02.09 15:20:35 ???
fjournal: Journal of the Australian Mathematical Society
acknowledgement: ack-nhfb
rawauthor: David Elliott
rawtitle: Error analysis of an algorithm for summing certain finite series
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

remark:
Analysis of Clenshaw algorithm for Chebyshev summation cite Clenshaw:1955:NSC, and report of region of instability of that procedure

entry:
@Article{Elliott:1968:EAA,
  author =       "David Elliott",
  title =        "Error analysis of an algorithm for summing certain
                 finite series",
  journal =      j-J-AUSTRALIAN-MATH-SOC,
  volume =       "8",
  number =       "2",
  pages =        "213--221",
  month =        may,
  year =         "1968",
  CODEN =        "JAUMAX",
  DOI =          "https://doi.org/10.1017/s1446788700005267",
  ISSN =         "0004-9735 (print), 2059-9234 (electronic)",
  ISSN-L =       "0004-9735",
  MRclass =      "65.25",
  MRnumber =     "0230452",
  MRreviewer =   "U. C. Guha",
  bibdate =      "Fri Feb 9 15:20:35 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Australian Mathematical Society",
  remark =       "Analysis of Clenshaw algorithm for Chebyshev summation
                 \cite{Clenshaw:1955:NSC}, and report of region of
                 instability of that procedure",
}


bibtype: book
filename: fparith.bib
label: Fike:1968:CEM
author: C. T. Fike
title: Computer Evaluation of Mathematical Functions
publisher: pub-PH
address: pub-PH:adr
pages: xii + 227
year: 1968
LCCN: QA297 .F5
bibdate: Thu Sep 1 10:12:51 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:12:51 ???
acknowledgement: ack-nj
rawauthor: C. T. Fike
rawtitle: Computer Evaluation of Mathematical Functions
entry:
@Book{Fike:1968:CEM,
  author =       "C. T. Fike",
  title =        "Computer Evaluation of Mathematical Functions",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xii + 227",
  year =         "1968",
  LCCN =         "QA297 .F5",
  bibdate =      "Thu Sep 1 10:12:51 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Fraser:1968:AUA
author: M. Fraser and N. Metropolis
title: Algorithms in unnormalized arithmetic. III. Matrix inversion
journal: j-NUM-MATH
volume: 12
number: 5
pages: 416--428
month: dec
monthnumber: 12
year: 1968
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 65.80
MRnumber: MR0255094 (40 \#8301)
bibdate: Wed Nov 14 19:04:40 2007
bibtimestamp: 2007.11.14 19:04:40 ???
fjournal: Numerische Mathematik
ZMnumber: 0184.37503
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: M. Fraser and N. Metropolis
rawtitle: Algorithms in unnormalized arithmetic. {III}. {Matrix} inversion
entry:
@Article{Fraser:1968:AUA,
  author =       "M. Fraser and N. Metropolis",
  title =        "Algorithms in unnormalized arithmetic. {III}. {Matrix}
                 inversion",
  journal =      j-NUM-MATH,
  volume =       "12",
  number =       "5",
  pages =        "416--428",
  month =        dec,
  year =         "1968",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.80",
  MRnumber =     "MR0255094 (40 \#8301)",
  bibdate =      "Wed Nov 14 19:04:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0184.37503",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: article
filename: fparith.bib
label: Harman:1968:ADI
author: M. G. Harman
title: An Attempt to Design an Improved Multiplication System
journal: j-IEEE-TRANS-COMPUT
volume: C-17
number: 11
pages: 1090--1090
month: nov
monthnumber: 11
year: 1968
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1968.226864
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 17:40:51 MDT 2011
bibtimestamp: 2011.07.13 17:40:51 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687268
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. G. Harman
rawtitle: An Attempt to Design an Improved Multiplication System
entry:
@Article{Harman:1968:ADI,
  author =       "M. G. Harman",
  title =        "An Attempt to Design an Improved Multiplication
                 System",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-17",
  number =       "11",
  pages =        "1090--1090",
  month =        nov,
  year =         "1968",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1968.226864",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 17:40:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687268",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: book
filename: fparith.bib
label: Hart:1968:CAa
title: Computer Approximations
publisher: pub-R-E-KRIEGER
address: pub-R-E-KRIEGER:adr
pages: x + 343
year: 1968
ISBN: 0-88275-642-7 OR 0882756427
ISBN13: 978-0-88275-642-4 OR 9780882756424
LCCN: QA 297 C64 1978
bibdate: Tue Dec 14 22:55:11 1993
bibtimestamp: 1993.12.14 22:55:11 ???
note: Reprinted 1978 with corrections.
acknowledgement: ack-nhfb
rawnote: Reprinted 1978 with corrections.
rawtitle: Computer Approximations
author:
John F. Hart and E. W. Cheney and Charles L. Lawson and Hans J. Maehly and Charles K. Mesztenyi and John R. Rice and Henry G. Thatcher, Jr. and Christoph Witzgall

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib

TOC:
1: The Design of a Function Subroutine / 1 1.1 Introduction / 1 1.2 General Considerations in Writing a Function Subroutine / 2 1.3 Relation of the Function Subroutine to the Computer System / 3 1.4 The Three Main Types of Function Subroutine / 4 1.5 Special Programming Techniques / 7 1.6 Subroutine Errors / 7 1.7 Final Steps / 9 2: General Methods of Computing Functions / 10 2.1 Introduction / 10 2.2 Application of Infinite Expansions / 11 2.3 Recurrence and Difference Relations / 23 2.4 Iterative Techniques / 27 2.5 Integral Representations / 28 2.6 Differential Equations / 29 2.7 Tabular Data / 32 2.8 Convergence Acceleration / 33 3: Least Maximum Approximations / 42 3.1 Introduction / 42 3.2 Properties of Least Maximum Approximations / 43 3.3 Nearly Least Maximum Approximations / 46 3.4 Rational Approximation / 51 3.5 Segmented Approximation / 54 3.6 Computation of the Tables / 55 4: The Choice and Application of Approximations / 58 4.1 Introduction / 5 8 4.2 Domain Considerations / 58 4.3 Machine Considerations / 62 4.4 Conditioning of Approximations / 65 4.5 Polynomial Forms / 67 4.6 Rational Forms / 73 4.7 Transformation Algorithms / 78 5: Description and Use of the Tables / 82 5.1 Introduction / 22 5.2 Function Notes / 82 5.3 Accuracy of the Coefficients / 83 5.4 How to Use the Tables / 86 5.5 Preparation of the Tables / 88 6: Function Notes / 89 6.1 Square Root, Cube Root / 89 6.2 Exponential and Hyperbolic Functions / 96 6.3 The Logarithm Function / 105 6.4 Trigonometric Functions / 112 6.5 The Inverse Trigonometric Functions / 120 6.6 The Gamma Function and Its Logarithm / 130 6.7 The Error Function / 136 6.8 Bessel Functions / 141 6.9 Complete Elliptic Integrals / 150 7: Tables of Coefficients / 155 Appendix A: Conversion Algorithms / 307 Appendix B: Bibliography of Approximations / 313 Appendix C: Decimal and Octal Constants / 333 References / 336 Index / 341

rawauthor:
John F. Hart and E. W. Cheney and Charles L. Lawson and Hans J. Maehly and Charles K. Mesztenyi and John R. Rice and Henry G. {Thatcher, Jr.} and Christoph Witzgall

shortTOC:
1: The Design of a Function Subroutine / 1 2: General Methods of Computing Functions / 10 3: Least Maximum Approximations / 42 4: The Choice and Application of Approximations / 58 5: Description and Use of the Tables / 82 6: Function Notes / 89 7: Tables of Coefficients / 155 Appendix A: Conversion Algorithms / 307 Appendix B: Bibliography of Approximations / 313 Appendix C: Decimal and Octal Constants / 333 References / 336 Index / 341

rawshortTOC:
1: The Design of a Function Subroutine / 1 \\ 2: General Methods of Computing Functions / 10 \\ 3: Least Maximum Approximations / 42 \\ 4: The Choice and Application of Approximations / 58 \\ 5: Description and Use of the Tables / 82 \\ 6: Function Notes / 89 \\ 7: Tables of Coefficients / 155 \\ Appendix A: Conversion Algorithms / 307 \\ Appendix B: Bibliography of Approximations / 313 \\ Appendix C: Decimal and Octal Constants / 333 \\ References / 336 \\ Index / 341

rawTOC:
1: The Design of a Function Subroutine / 1 \\ 1.1 Introduction / 1 \\ 1.2 General Considerations in Writing a Function Subroutine / 2 \\ 1.3 Relation of the Function Subroutine to the Computer System / 3 \\ 1.4 The Three Main Types of Function Subroutine / 4 \\ 1.5 Special Programming Techniques / 7 \\ 1.6 Subroutine Errors / 7 \\ 1.7 Final Steps / 9 \\ 2: General Methods of Computing Functions / 10 \\ 2.1 Introduction / 10 \\ 2.2 Application of Infinite Expansions / 11 \\ 2.3 Recurrence and Difference Relations / 23 \\ 2.4 Iterative Techniques / 27 \\ 2.5 Integral Representations / 28 \\ 2.6 Differential Equations / 29 \\ 2.7 Tabular Data / 32 \\ 2.8 Convergence Acceleration / 33 \\ 3: Least Maximum Approximations / 42 \\ 3.1 Introduction / 42 \\ 3.2 Properties of Least Maximum Approximations / 43 \\ 3.3 Nearly Least Maximum Approximations / 46 \\ 3.4 Rational Approximation / 51 \\ 3.5 Segmented Approximation / 54 \\ 3.6 Computation of the Tables / 55 \\ 4: The Choice and Application of Approximations / 58 \\ 4.1 Introduction / 5 8 \\ 4.2 Domain Considerations / 58 \\ 4.3 Machine Considerations / 62 \\ 4.4 Conditioning of Approximations / 65 \\ 4.5 Polynomial Forms / 67 \\ 4.6 Rational Forms / 73 \\ 4.7 Transformation Algorithms / 78 \\ 5: Description and Use of the Tables / 82 \\ 5.1 Introduction / 22 \\ 5.2 Function Notes / 82 \\ 5.3 Accuracy of the Coefficients / 83 \\ 5.4 How to Use the Tables / 86 \\ 5.5 Preparation of the Tables / 88 \\ 6: Function Notes / 89 \\ 6.1 Square Root, Cube Root / 89 \\ 6.2 Exponential and Hyperbolic Functions / 96 \\ 6.3 The Logarithm Function / 105 \\ 6.4 Trigonometric Functions / 112 \\ 6.5 The Inverse Trigonometric Functions / 120 \\ 6.6 The Gamma Function and Its Logarithm / 130 \\ 6.7 The Error Function / 136 \\ 6.8 Bessel Functions / 141 \\ 6.9 Complete Elliptic Integrals / 150 \\ 7: Tables of Coefficients / 155 \\ Appendix A: Conversion Algorithms / 307 \\ Appendix B: Bibliography of Approximations / 313 \\ Appendix C: Decimal and Octal Constants / 333 \\ References / 336 \\ Index / 341

entry:
@Book{Hart:1968:CAa,
  author =       "John F. Hart and E. W. Cheney and Charles L. Lawson
                 and Hans J. Maehly and Charles K. Mesztenyi and John R.
                 Rice and Henry G. {Thatcher, Jr.} and Christoph
                 Witzgall",
  title =        "Computer Approximations",
  publisher =    pub-R-E-KRIEGER,
  address =      pub-R-E-KRIEGER:adr,
  pages =        "x + 343",
  year =         "1968",
  ISBN =         "0-88275-642-7",
  ISBN-13 =      "978-0-88275-642-4",
  LCCN =         "QA 297 C64 1978",
  bibdate =      "Tue Dec 14 22:55:11 1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "Reprinted 1978 with corrections.",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "1: The Design of a Function Subroutine / 1 \\
                 2: General Methods of Computing Functions / 10 \\
                 3: Least Maximum Approximations / 42 \\
                 4: The Choice and Application of Approximations / 58
                 \\
                 5: Description and Use of the Tables / 82 \\
                 6: Function Notes / 89 \\
                 7: Tables of Coefficients / 155 \\
                 Appendix A: Conversion Algorithms / 307 \\
                 Appendix B: Bibliography of Approximations / 313 \\
                 Appendix C: Decimal and Octal Constants / 333 \\
                 References / 336 \\
                 Index / 341",
  tableofcontents = "1: The Design of a Function Subroutine / 1 \\
                 1.1 Introduction / 1 \\
                 1.2 General Considerations in Writing a Function
                 Subroutine / 2 \\
                 1.3 Relation of the Function Subroutine to the Computer
                 System / 3 \\
                 1.4 The Three Main Types of Function Subroutine / 4 \\
                 1.5 Special Programming Techniques / 7 \\
                 1.6 Subroutine Errors / 7 \\
                 1.7 Final Steps / 9 \\
                 2: General Methods of Computing Functions / 10 \\
                 2.1 Introduction / 10 \\
                 2.2 Application of Infinite Expansions / 11 \\
                 2.3 Recurrence and Difference Relations / 23 \\
                 2.4 Iterative Techniques / 27 \\
                 2.5 Integral Representations / 28 \\
                 2.6 Differential Equations / 29 \\
                 2.7 Tabular Data / 32 \\
                 2.8 Convergence Acceleration / 33 \\
                 3: Least Maximum Approximations / 42 \\
                 3.1 Introduction / 42 \\
                 3.2 Properties of Least Maximum Approximations / 43 \\
                 3.3 Nearly Least Maximum Approximations / 46 \\
                 3.4 Rational Approximation / 51 \\
                 3.5 Segmented Approximation / 54 \\
                 3.6 Computation of the Tables / 55 \\
                 4: The Choice and Application of Approximations / 58
                 \\
                 4.1 Introduction / 5 8 \\
                 4.2 Domain Considerations / 58 \\
                 4.3 Machine Considerations / 62 \\
                 4.4 Conditioning of Approximations / 65 \\
                 4.5 Polynomial Forms / 67 \\
                 4.6 Rational Forms / 73 \\
                 4.7 Transformation Algorithms / 78 \\
                 5: Description and Use of the Tables / 82 \\
                 5.1 Introduction / 22 \\
                 5.2 Function Notes / 82 \\
                 5.3 Accuracy of the Coefficients / 83 \\
                 5.4 How to Use the Tables / 86 \\
                 5.5 Preparation of the Tables / 88 \\
                 6: Function Notes / 89 \\
                 6.1 Square Root, Cube Root / 89 \\
                 6.2 Exponential and Hyperbolic Functions / 96 \\
                 6.3 The Logarithm Function / 105 \\
                 6.4 Trigonometric Functions / 112 \\
                 6.5 The Inverse Trigonometric Functions / 120 \\
                 6.6 The Gamma Function and Its Logarithm / 130 \\
                 6.7 The Error Function / 136 \\
                 6.8 Bessel Functions / 141 \\
                 6.9 Complete Elliptic Integrals / 150 \\
                 7: Tables of Coefficients / 155 \\
                 Appendix A: Conversion Algorithms / 307 \\
                 Appendix B: Bibliography of Approximations / 313 \\
                 Appendix C: Decimal and Octal Constants / 333 \\
                 References / 336 \\
                 Index / 341",
}


bibtype: book
filename: fparith.bib
label: Hart:1968:CAb
title: Computer Approximations
publisher: pub-WILEY
address: pub-WILEY:adr
pages: x + 343
year: 1968
ISBN: 0-471-35630-1 OR 0471356301
ISBN13: 978-0-471-35630-1 OR 9780471356301
LCCN: QA297 .C64
bibdate: Sat Jan 14 14:53:06 2006
bibtimestamp: 2006.01.14 14:53:06 ???
series: The SIAM series in applied mathematics
acknowledgement: ack-nhfb
rawtitle: Computer Approximations
author:
John F. Hart and E. W. Cheney and Charles L. Lawson and Hans J. Maehly and Charles K. Mesztenyi and John R. Rice and Henry G. Thatcher, Jr. and Christoph Witzgall

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

rawauthor:
John F. Hart and E. W. Cheney and Charles L. Lawson and Hans J. Maehly and Charles K. Mesztenyi and John R. Rice and Henry G. {Thatcher, Jr.} and Christoph Witzgall

entry:
@Book{Hart:1968:CAb,
  author =       "John F. Hart and E. W. Cheney and Charles L. Lawson
                 and Hans J. Maehly and Charles K. Mesztenyi and John R.
                 Rice and Henry G. {Thatcher, Jr.} and Christoph
                 Witzgall",
  title =        "Computer Approximations",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "x + 343",
  year =         "1968",
  ISBN =         "0-471-35630-1",
  ISBN-13 =      "978-0-471-35630-1",
  LCCN =         "QA297 .C64",
  bibdate =      "Sat Jan 14 14:53:06 2006",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "The SIAM series in applied mathematics",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: IBM:1968:ISP
author: IBM Corporation
title: IBM System / 360 Principles of Operation
publisher: pub-IBM
address: pub-IBM:adr
edition: Eighth
pages: 175
year: 1968
LCCN: QA76.8.I12 I59 1968
bibdate: Wed Sep 14 23:12:39 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.14 23:12:39 ???
acknowledgement: ack-nhfb
rawauthor: {IBM Corporation}
rawtitle: {IBM System}\slash 360 Principles of Operation
entry:
@Book{IBM:1968:ISP,
  author =       "{IBM Corporation}",
  title =        "{IBM System}\slash 360 Principles of Operation",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  edition =      "Eighth",
  pages =        "175",
  year =         "1968",
  LCCN =         "QA76.8.I12 I59 1968",
  bibdate =      "Wed Sep 14 23:12:39 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: fparith.bib
label: Kahan:1968:ISS
author: W. Kahan
title: 7094-II system support for numerical analysis
pages: 175
year: 1968
bibdate: Mon Sep 16 16:14:28 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.09.16 16:14:28 ???
acknowledgement: ack-nhfb
howpublished: SHARE Secretarial Distribution SSD-159.
rawauthor: W. Kahan
rawtitle: {7094-II} system support for numerical analysis
entry:
@Misc{Kahan:1968:ISS,
  author =       "W. Kahan",
  title =        "{7094-II} system support for numerical analysis",
  howpublished = "SHARE Secretarial Distribution SSD-159.",
  year =         "1968",
  bibdate =      "Mon Sep 16 16:14:28 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Kaneko:1968:PSA
author: T. Kaneko and B. Liu
title: Round-off error of floating-point digital filters
crossref: Anonymous:1968:PSA
pages: 219--227
year: 1968
MRclass: 65.80
MRnumber: 41\#7878
bibdate: Fri Dec 8 08:24:14 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:14 ???
acknowledgement: ack-nhfb
rawauthor: T. Kaneko and B. Liu
rawtitle: Round-off error of floating-point digital filters
entry:
@InProceedings{Kaneko:1968:PSA,
  author =       "T. Kaneko and B. Liu",
  title =        "Round-off error of floating-point digital filters",
  crossref =     "Anonymous:1968:PSA",
  pages =        "219--227",
  year =         "1968",
  MRclass =      "65.80",
  MRnumber =     "41\#7878",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Matula:1968:BCT
author: David W. Matula
title: The Base Conversion Theorem
journal: j-PROC-AM-MATH-SOC
volume: 19
number: 3
pages: 716--723
month: jun
monthnumber: 6
year: 1968
CODEN: PAMYAR
DOI: https://doi.org/10.1090/s0002-9939-1968-0234908-9
ISSN: 0002-9939 (print), 1088-6826 (electronic) OR 00029939 (print), 10886826 (electronic)
ISSNL: 0002-9939 OR 00029939
bibdate: Fri Apr 21 07:26:39 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2000.04.21 07:26:39 ???
fjournal: Proceedings of the American Mathematical Society
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/journals/proc
rawauthor: David W. Matula
rawtitle: The Base Conversion Theorem
abstract:
A demonstration that, in converting numbers from base $ beta $ to base $ nu $, where $ beta ^i neq nu ^j $ for any positive integers $ i, j $, a one-to-one mapping exists only if $ nu ^m - 1 geq beta ^n - 1 $. Here $m$ is the number of digits in base $ nu $ and $n$ that in base $ beta $.par The implications of this result are discussed in the author's earlier paper [Proc. Amer. Fed. Information Processing Soc. 30 (1967), 311--318].

rawabstract:
A demonstration that, in converting numbers from base $ \beta $ to base $ \nu $, where $ \beta^i \neq \nu^j $ for any positive integers $ i, j $, a one-to-one mapping exists only if $ \nu^{m - 1} \geq \beta^n - 1 $. Here $m$ is the number of digits in base $ \nu $ and $n$ that in base $ \beta $.\par The implications of this result are discussed in the author's earlier paper [Proc. Amer. Fed. Information Processing Soc. 30 (1967), 311--318].

entry:
@Article{Matula:1968:BCT,
  author =       "David W. Matula",
  title =        "The Base Conversion Theorem",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "19",
  number =       "3",
  pages =        "716--723",
  month =        jun,
  year =         "1968",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.1090/s0002-9939-1968-0234908-9",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  bibdate =      "Fri Apr 21 07:26:39 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A demonstration that, in converting numbers from base
                 $ \beta $ to base $ \nu $, where $ \beta^i \neq \nu^j $
                 for any positive integers $ i, j $, a one-to-one
                 mapping exists only if $ \nu^{m - 1} \geq \beta^n - 1
                 $. Here $m$ is the number of digits in base $ \nu $ and
                 $n$ that in base $ \beta $.\par

                 The implications of this result are discussed in the
                 author's earlier paper [Proc. Amer. Fed. Information
                 Processing Soc. 30 (1967), 311--318].",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
  received =     "9 February 1967",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Matula:1968:C
author: David W. Matula
title: In-and-out conversions
journal: j-CACM
volume: 11
number: 1
pages: 47--50
month: jan
monthnumber: 1
year: 1968
CODEN: CACMA2
DOI: https://doi.org/10.1145/362851.362887
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65.80
MRnumber: 39\#2360
bibdate: Fri Nov 25 18:20:17 MST 2005
bibtimestamp: 2005.11.25 18:20:17 MST
note: See also cite Goldberg:1967:BED,Matula:1968:BCT
fjournal: Communications of the ACM
keywords: floating-point numbers; number base conversion; rounding error; significance; truncation error
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: David W. Matula
rawnote: See also \cite{Goldberg:1967:BED,Matula:1968:BCT}
rawtitle: In-and-out conversions
abstract:
By an in-and-out conversion we mean that a floating-point number in one base is converted into a floating-point number in another base and then converted back to a floating-point number in the original base. For all combinations of rounding and truncation conversions the question is considered of how many significant digits are needed in the intermediate base to allow such in-and-out conversions to return the original number (when possible), or at least significant digit.

rawabstract:
By an in-and-out conversion we mean that a floating-point number in one base is converted into a floating-point number in another base and then converted back to a floating-point number in the original base. For all combinations of rounding and truncation conversions the question is considered of how many significant digits are needed in the intermediate base to allow such in-and-out conversions to return the original number (when possible), or at least significant digit.

entry:
@Article{Matula:1968:C,
  author =       "David W. Matula",
  title =        "In-and-out conversions",
  journal =      j-CACM,
  volume =       "11",
  number =       "1",
  pages =        "47--50",
  month =        jan,
  year =         "1968",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/362851.362887",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.80",
  MRnumber =     "39\#2360",
  bibdate =      "Fri Nov 25 18:20:17 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also \cite{Goldberg:1967:BED,Matula:1968:BCT}",
  abstract =     "By an in-and-out conversion we mean that a
                 floating-point number in one base is converted into a
                 floating-point number in another base and then
                 converted back to a floating-point number in the
                 original base. For all combinations of rounding and
                 truncation conversions the question is considered of
                 how many significant digits are needed in the
                 intermediate base to allow such in-and-out conversions
                 to return the original number (when possible), or at
                 least significant digit.",
  acknowledgement = ack-nhfb # "\slash " # ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "floating-point numbers; number base conversion;
                 rounding error; significance; truncation error",
  received =     "April 1967 (revised August 1967)",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Metropolis:1968:ANA
author: N. Metropolis
title: Algorithms in un-normalized arithmetic: Polynomial evaluation and matrix decomposition
journal: Colloques internationaux, Centre National de la Recherche Scientifique, Paris
volume: 165
pages: 293--303
year: 1968
bibdate: Wed Nov 14 19:04:40 2007
bibtimestamp: 2007.11.14 19:04:40 ???
ZMnumber: 0207.15804
acknowledgement: ack-nhfb
rawauthor: N. Metropolis
rawtitle: Algorithms in un-normalized arithmetic: Polynomial evaluation and matrix decomposition
entry:
@Article{Metropolis:1968:ANA,
  author =       "N. Metropolis",
  title =        "Algorithms in un-normalized arithmetic: Polynomial
                 evaluation and matrix decomposition",
  journal =      "Colloques internationaux, Centre National de la
                 Recherche Scientifique, Paris",
  volume =       "165",
  pages =        "293--303",
  year =         "1968",
  bibdate =      "Wed Nov 14 19:04:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0207.15804",
  acknowledgement = ack-nhfb,
  classmath =    "*65H05 (Single nonlinear equations (numerical
                 methods)) 65F05 (Direct methods for linear systems)",
}


bibtype: article
filename: fparith.bib
label: Nathan:1968:IVS
author: A. Nathan and J. Molcho
title: Improved Voltage Selector and Cascade Multiplier Circuits
journal: j-IEEE-TRANS-COMPUT
volume: C-17
number: 4
pages: 380--382
month: apr
monthnumber: 4
year: 1968
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1968.229386
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 17:40:48 MDT 2011
bibtimestamp: 2011.07.13 17:40:48 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687350
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: A. Nathan and J. Molcho
rawtitle: Improved Voltage Selector and Cascade Multiplier Circuits
entry:
@Article{Nathan:1968:IVS,
  author =       "A. Nathan and J. Molcho",
  title =        "Improved Voltage Selector and Cascade Multiplier
                 Circuits",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-17",
  number =       "4",
  pages =        "380--382",
  month =        apr,
  year =         "1968",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1968.229386",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 17:40:48 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687350",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Nickel:1968:EBC
author: K. Nickel
booktitle: Proceedings of the IFIP Congress
title: Error Bounds and Computer Arithmetic
publisher: pub-NORTH-HOLLAND
address: pub-NORTH-HOLLAND:adr
pages: 54--60
year: 1968
bibdate: Fri Aug 20 10:09:47 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.08.20 10:09:47 ???
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
rawauthor: K. Nickel
rawbooktitle: Proceedings of the {IFIP} Congress
rawtitle: Error Bounds and Computer Arithmetic
entry:
@InProceedings{Nickel:1968:EBC,
  author =       "K. Nickel",
  booktitle =    "Proceedings of the {IFIP} Congress",
  title =        "Error Bounds and Computer Arithmetic",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "54--60",
  year =         "1968",
  LCCN =         "????",
  bibdate =      "Fri Aug 20 10:09:47 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Nievergelt:1968:CCP
author: J. Nievergelt
title: Computers and computing --- Past present Future
journal: j-IEEE-SPECTRUM
volume: 5
number: 1
pages: 57--61
month: jan
monthnumber: 1
year: 1968
CODEN: IEESAM
DOI: https://doi.org/10.1109/MSPEC.1968.5215633
ISSN: 0018-9235 (print), 1939-9340 (electronic) OR 00189235 (print), 19399340 (electronic)
ISSNL: 0018-9235 OR 00189235
bibdate: Wed Jan 15 09:30:58 2020
bibtimestamp: 2020.01.15 09:30:58 ???
fjournal: IEEE Spectrum
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6
rawauthor: J. Nievergelt
rawtitle: Computers and computing --- Past present Future
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib

keywords:
Computer science; Concurrent computing; Digital arithmetic; Hardware; History; Instruments; Maintenance; Manufacturing; Programming; Relays

entry:
@Article{Nievergelt:1968:CCP,
  author =       "J. Nievergelt",
  title =        "Computers and computing --- Past present Future",
  journal =      j-IEEE-SPECTRUM,
  volume =       "5",
  number =       "1",
  pages =        "57--61",
  month =        jan,
  year =         "1968",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.1968.5215633",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Wed Jan 15 09:30:58 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "Computer science; Concurrent computing; Digital
                 arithmetic; Hardware; History; Instruments;
                 Maintenance; Manufacturing; Programming; Relays",
}


bibtype: article
filename: fparith.bib
label: Padegs:1968:SAS
author: A. Padegs
journal: j-IBM-SYS-J
volume: 7
number: 1
pages: 22--29
year: 1968
CODEN: IBMSA7
ISSN: 0018-8670 OR 00188670
bibdate: Tue Mar 19 17:38:46 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.03.19 17:38:46 ???
fjournal: IBM Systems Journal
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
rawauthor: A. Padegs
title:
Structural aspects of the SYSTEM / 360 Model 85, Part III: Extensions to floating-point architecture

rawtitle:
Structural aspects of the {SYSTEM\slash 360 Model 85}, Part {III}: Extensions to floating-point architecture

entry:
@Article{Padegs:1968:SAS,
  author =       "A. Padegs",
  title =        "Structural aspects of the {SYSTEM\slash 360 Model 85},
                 Part {III}: Extensions to floating-point architecture",
  journal =      j-IBM-SYS-J,
  volume =       "7",
  number =       "1",
  pages =        "22--29",
  year =         "1968",
  CODEN =        "IBMSA7",
  ISSN =         "0018-8670",
  bibdate =      "Tue Mar 19 17:38:46 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Systems Journal",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Phillips:1968:EME
author: G. M. Phillips
title: Estimate of the maximum error in best polynomial approximations
journal: j-COMP-J
volume: 11
pages: 110--111
year: 1968
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Thu Sep 15 18:39:47 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.15 18:39:47 ???
fjournal: The Computer Journal
acknowledgement: ack-nj
journalURL: http://comjnl.oxfordjournals.org/
rawauthor: G. M. Phillips
rawtitle: Estimate of the maximum error in best polynomial approximations
entry:
@Article{Phillips:1968:EME,
  author =       "G. M. Phillips",
  title =        "Estimate of the maximum error in best polynomial
                 approximations",
  journal =      j-COMP-J,
  volume =       "11",
  pages =        "110--111",
  year =         "1968",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Thu Sep 15 18:39:47 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  xxmonth =      "(none)",
  xxnumber =     "(none)",
}


bibtype: article
filename: fparith.bib
label: Rao:1968:ECL
author: T. R. N. Rao
title: Error-Checking Logic for Arithmetic-Type Operations of a Processor
journal: j-IEEE-TRANS-COMPUT
volume: C-17
number: 9
pages: 845--849
month: sep
monthnumber: 9
year: 1968
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1968.229144
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 17:40:50 MDT 2011
bibtimestamp: 2011.07.13 17:40:50 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687471
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: T. R. N. Rao
rawtitle: Error-Checking Logic for Arithmetic-Type Operations of a Processor
entry:
@Article{Rao:1968:ECL,
  author =       "T. R. N. Rao",
  title =        "Error-Checking Logic for Arithmetic-Type Operations of
                 a Processor",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-17",
  number =       "9",
  pages =        "845--849",
  month =        sep,
  year =         "1968",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1968.229144",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 17:40:50 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687471",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: techreport
filename: fparith.bib
label: Ross:1968:UMF
author: Richard D. Ross
title: University of Mississippi floating point subroutines (UMFS)
institution: Computer Center, University of Mississippi
address: University
pages: 31
year: 1968
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Electronic data processing.
remark: Cover title.
acknowledgement: ack-nhfb
rawauthor: Richard D. Ross
rawtitle: {University of Mississippi} floating point subroutines ({UMFS})
entry:
@TechReport{Ross:1968:UMF,
  author =       "Richard D. Ross",
  title =        "{University of Mississippi} floating point subroutines
                 ({UMFS})",
  institution =  "Computer Center, University of Mississippi",
  address =      "University",
  pages =        "31",
  year =         "1968",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic data processing.",
  remark =       "Cover title.",
}


bibtype: article
filename: fparith.bib
label: Sasaki:1968:BIA
author: A. Sasaki
title: The Basis for Implementation of Additive Operations in the Residue Number System
journal: j-IEEE-TRANS-COMPUT
volume: C-17
number: 11
pages: 1066--1073
month: nov
monthnumber: 11
year: 1968
CODEN: ITCOB4
DOI: https://doi.org/10.1109/PGEC.1967.264810; https://doi.org/10.1109/TC.1968.226466
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 17:40:51 MDT 2011
bibtimestamp: 2011.07.13 17:40:51 MDT
fjournal: IEEE Transactions on Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: A. Sasaki
rawtitle: The Basis for Implementation of Additive Operations in the Residue Number System
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687264; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35582

entry:
@Article{Sasaki:1968:BIA,
  author =       "A. Sasaki",
  title =        "The Basis for Implementation of Additive Operations in
                 the Residue Number System",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-17",
  number =       "11",
  pages =        "1066--1073",
  month =        nov,
  year =         "1968",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810;
                 https://doi.org/10.1109/TC.1968.226466",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 17:40:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687264;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35582",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new residue number system algebra has been
                 previously proposed by the author. The algebra has
                 solved an essential theoretical barrier in the residue
                 number system and has enabled one to pursue additive
                 operations in the residue \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Schmookler:1968:HSB
author: M. S. Schmookler
title: High Speed Binary to Decimal Conversion
journal: j-IEEE-TRANS-COMPUT
volume: C-17
pages: 506--508
year: 1968
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1968.226913
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Fri Nov 28 19:09:15 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 19:09:15 ???
fjournal: IEEE Transactions on Computers
keywords: decimal floating-point arithmetic
acknowledgement: ack-mfc
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. S. Schmookler
rawtitle: High Speed Binary to Decimal Conversion
abstract:
This note describes several methods of performing fast, efficient, binary-to-decimal conversion. With a modest amount of circuitry, an order of magnitude speed improvement can is obtained. This achievement offers a unique advantage to general-purpose computers requiring special hardware to translate between binary and decimal numbering systems.

rawabstract:
This note describes several methods of performing fast, efficient, binary-to-decimal conversion. With a modest amount of circuitry, an order of magnitude speed improvement can is obtained. This achievement offers a unique advantage to general-purpose computers requiring special hardware to translate between binary and decimal numbering systems.

entry:
@Article{Schmookler:1968:HSB,
  author =       "M. S. Schmookler",
  title =        "High Speed Binary to Decimal Conversion",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-17",
  pages =        "506--508",
  year =         "1968",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1968.226913",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 28 19:09:15 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This note describes several methods of performing
                 fast, efficient, binary-to-decimal conversion. With a
                 modest amount of circuitry, an order of magnitude speed
                 improvement can is obtained. This achievement offers a
                 unique advantage to general-purpose computers requiring
                 special hardware to translate between binary and
                 decimal numbering systems.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: book
filename: fparith.bib
label: Scott:1968:OET
author: Theodore G. Scott
title: Ordinateurs electroniques, techniques de programmation: Computer programming techniques
publisher: Tournai, Ed. Gamma
address: Paris, France
pages: 662
year: 1968
bibdate: Thu May 09 09:52:34 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 09:52:34 ???
note: Cinq volumes. Version francaise de Juliette Charbonneau-Kohiyama.
acknowledgement: ack-nhfb
rawauthor: Th{\'e}odore G. Scott
rawnote: Cinq volumes. Version fran{\c{c}}aise de Juliette Charbonneau-Kohiyama.
rawtitle: Ordinateurs {\'e}lectroniques, techniques de programmation: Computer programming techniques
entry:
@Book{Scott:1968:OET,
  author =       "Th{\'e}odore G. Scott",
  title =        "Ordinateurs {\'e}lectroniques, techniques de
                 programmation: Computer programming techniques",
  publisher =    "Tournai, Ed. Gamma",
  address =      "Paris, France",
  pages =        "662",
  year =         "1968",
  bibdate =      "Thu May 09 09:52:34 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Cinq volumes. Version fran{\c{c}}aise de Juliette
                 Charbonneau-Kohiyama.",
  acknowledgement = ack-nhfb,
  contents =     "1. Pr{\'e}sentation du Tutac. Etude du registre - base
                 et de ses fonctions. Le registre base. - 2. Les sous
                 programmes. L'entr{\'e}e. La sorite. - 3. La bande
                 magn{\'e}tique. La d{\'e}tection des erreurs. - 4. Les
                 calculs en virgule flottante. L'{\'e}dition des
                 programmes. - 5. La programmation symbolique. Le
                 language Cobol. Fortran et Algol",
}


bibtype: manual
filename: fparith.bib
label: Smith:1968:CC
author: Smith, Robert E. (Robert Elijah)
title: Competence course
organization: Control Data Corp.
address: Minneapolis, MN, USA
pages: vi + 296
year: 1968
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Smith, Robert E. (Robert Elijah)
rawtitle: Competence course
keywords:
Electronic digital computers --- Programming.; Floating-point arithmetic.; FORTRAN (Computer program language)

remark:
``Computer programming using FORTRAN and card inputs without key punching!'' Cover title: Competence course, FORTRAN computer programming. At head of title: School computer-use plan.

entry:
@Manual{Smith:1968:CC,
  author =       "Smith, Robert E. (Robert Elijah)",
  title =        "Competence course",
  organization = "Control Data Corp.",
  address =      "Minneapolis, MN, USA",
  pages =        "vi + 296",
  year =         "1968",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming.;
                 Floating-point arithmetic.; FORTRAN (Computer program
                 language)",
  remark =       "``Computer programming using FORTRAN and card inputs
                 without key punching!'' Cover title: Competence course,
                 FORTRAN computer programming. At head of title: School
                 computer-use plan.",
}


bibtype: book
filename: fparith.bib
label: Stuart:1968:FP
author: Fredric Stuart
title: Fortran programming
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xix + 353
year: 1968
ISBN: 0-471-83477-7 OR 0471834777
ISBN13: 978-0-471-83477-9 OR 9780471834779
LCCN: QA76.5 .S8
bibdate: Sat Jan 27 13:40:57 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.01.27 13:40:57 MST
keywords: Electronic digital computers --- Programming.; Fortran (Computer program language)
remark: Cited in cite Sterbenz:1974:FPC, but given year 1969.
acknowledgement: ack-nhfb
rawauthor: Fredric Stuart
rawtitle: {Fortran} programming
entry:
@Book{Stuart:1968:FP,
  author =       "Fredric Stuart",
  title =        "{Fortran} programming",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xix + 353",
  year =         "1968",
  ISBN =         "0-471-83477-7",
  ISBN-13 =      "978-0-471-83477-9",
  LCCN =         "QA76.5 .S8",
  bibdate =      "Sat Jan 27 13:40:57 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming.;
                 {Fortran} (Computer program language)",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}, but given year
                 1969.",
}


bibtype: article
filename: fparith.bib
label: Tung:1968:DAS
author: Chin Tung
title: A Division Algorithm for Signed-Digit Arithmetic
journal: j-IEEE-TRANS-COMPUT
volume: C-17
number: 9
pages: 887--889
month: sep
monthnumber: 9
year: 1968
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.1968.229150
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 17:40:50 MDT 2011
bibtimestamp: 2011.07.13 17:40:50 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687477
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Chin Tung
rawtitle: A Division Algorithm for Signed-Digit Arithmetic
entry:
@Article{Tung:1968:DAS,
  author =       "Chin Tung",
  title =        "A Division Algorithm for Signed-Digit Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-17",
  number =       "9",
  pages =        "887--889",
  month =        sep,
  year =         "1968",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1968.229150",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 17:40:50 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687477",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Urabe:1968:RED
author: Minoru Urabe
title: Roundoff Error Distribution in Fixed-Point Multiplication and a Remark about the Rounding Rule
journal: j-SIAM-J-NUMER-ANAL
volume: 5
number: 2
pages: 202--210
month: jun
monthnumber: 6
year: 1968
CODEN: SJNAAM
ISSN: 0036-1429 (print), 1095-7170 (electronic) OR 00361429 (print), 10957170 (electronic)
ISSNL: 0036-1429 OR 00361429
bibdate: Fri Oct 16 06:57:22 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database
bibtimestamp: 1998.10.16 06:57:22 MDT
fjournal: SIAM Journal on Numerical Analysis
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sinum
rawauthor: Minoru Urabe
rawtitle: Roundoff Error Distribution in Fixed-Point Multiplication and a Remark about the Rounding Rule
entry:
@Article{Urabe:1968:RED,
  author =       "Minoru Urabe",
  title =        "Roundoff Error Distribution in Fixed-Point
                 Multiplication and a Remark about the Rounding Rule",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "5",
  number =       "2",
  pages =        "202--210",
  month =        jun,
  year =         "1968",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: techreport
filename: fparith.bib
label: Veltkamp:1968:APV
author: G. W. Veltkamp
type: Technical report
number: 22
institution: RC-Informatie, Technishe Hogeschool Eindhoven
address: Eindhoven, The Netherlands
pages: 202--210
year: 1968
bibdate: Tue Dec 26 14:53:03 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.12.26 14:53:03 ???
language: Dutch
acknowledgement: ack-nhfb
rawauthor: G. W. Veltkamp
title:
ALGOL procedures voor het berekenen van een inwendig product in dubbele precisie. (Dutch) [ALGOL procedures for calculating an inner product in double precision]

rawtitle:
{ALGOL} procedures voor het berekenen van een inwendig product in dubbele precisie. ({Dutch}) [{ALGOL} procedures for calculating an inner product in double precision]

entry:
@TechReport{Veltkamp:1968:APV,
  author =       "G. W. Veltkamp",
  title =        "{ALGOL} procedures voor het berekenen van een inwendig
                 product in dubbele precisie. ({Dutch}) [{ALGOL}
                 procedures for calculating an inner product in double
                 precision]",
  type =         "Technical report",
  number =       "22",
  institution =  "RC-Informatie, Technishe Hogeschool Eindhoven",
  address =      "Eindhoven, The Netherlands",
  year =         "1968",
  bibdate =      "Tue Dec 26 14:53:03 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Dutch",
}


bibtype: article
filename: fparith.bib
label: Vitenko:1968:OAA
author: I. V. Viten'ko
title: Optimal algorithms for addition and multiplication on machines with floating point. (Russian)
journal: Z. Vycisl. Mat. i Mat. Fiz
volume: 8
pages: 1076--1084
year: 1968
MRnumber: 40\#2250
bibdate: Sat Dec 16 16:45:14 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.16 16:45:14 ???
language: Russian
acknowledgement: ack-nhfb
reviewer: J. Kuntzmann
rawauthor: {\=I}. V. V{\=\i}ten'{k}o
rawtitle: Optimal algorithms for addition and multiplication on machines with floating point. ({Russian})
entry:
@Article{Vitenko:1968:OAA,
  author =       "{\=I}. V. V{\=\i}ten'{k}o",
  title =        "Optimal algorithms for addition and multiplication on
                 machines with floating point. ({Russian})",
  journal =      "{\v{Z}}. Vy{\v{c}}isl. Mat. i Mat. Fiz",
  volume =       "8",
  pages =        "1076--1084",
  year =         "1968",
  MRnumber =     "40\#2250",
  bibdate =      "Sat Dec 16 16:45:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
  reviewer =     "J. Kuntzmann",
}


bibtype: techreport
filename: fparith.bib
label: Yohe:1968:CPA
author: J. M. Yohe
title: Computer Programming for Accuracy
type: MRC Technical Summary Report
number: 866
institution: inst-MRC-WISCONSIN
address: inst-MRC-WISCONSIN:adr
pages: 1076--1084
month: apr
monthnumber: 4
year: 1968
bibdate: Sun Dec 30 21:42:55 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.12.30 21:42:55 ???
acknowledgement: ack-nhfb
rawauthor: J. M. Yohe
rawtitle: Computer Programming for Accuracy
abstract:
In most computations, it is tacitly assumed that the results produced by the program are 'accurate enough'. This assumption is not always valid. In this report, we discuss several possible sources of error in digital computation, and we list several steps which can be taken to guard against some types of error and determine an upper bound for the effects of other types. We illustrate these techniques with our experience in writing a program to locate zeros of the Riemann zeta function.

rawabstract:
In most computations, it is tacitly assumed that the results produced by the program are 'accurate enough'. This assumption is not always valid. In this report, we discuss several possible sources of error in digital computation, and we list several steps which can be taken to guard against some types of error and determine an upper bound for the effects of other types. We illustrate these techniques with our experience in writing a program to locate zeros of the Riemann zeta function.

entry:
@TechReport{Yohe:1968:CPA,
  author =       "J. M. Yohe",
  title =        "Computer Programming for Accuracy",
  type =         "{MRC} Technical Summary Report",
  number =       "866",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  month =        apr,
  year =         "1968",
  bibdate =      "Sun Dec 30 21:42:55 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In most computations, it is tacitly assumed that the
                 results produced by the program are 'accurate enough'.
                 This assumption is not always valid. In this report, we
                 discuss several possible sources of error in digital
                 computation, and we list several steps which can be
                 taken to guard against some types of error and
                 determine an upper bound for the effects of other
                 types. We illustrate these techniques with our
                 experience in writing a program to locate zeros of the
                 Riemann zeta function.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Anonymous:1969:VPD
author: Anonymous
title: Video Probability Distributions
journal: j-IEEE-SPECTRUM
volume: 6
number: 4
pages: 5--5
month: apr
monthnumber: 4
year: 1969
CODEN: IEESAM
DOI: https://doi.org/10.1109/MSPEC.1969.5214042
ISSN: 1939-9340 OR 19399340
ISSNL: 0018-9235 OR 00189235
bibdate: Wed Jan 15 11:58:06 2020
bibtimestamp: 2020.01.15 11:58:06 ???
fjournal: IEEE Spectrum
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6
rawauthor: Anonymous
rawtitle: Video Probability Distributions
bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib

keywords:
Arithmetic; Circuit noise; Detectors; Distribution functions; Gaussian noise; Probability distribution; Signal to noise ratio; Tail; Testing; Voltage

entry:
@Article{Anonymous:1969:VPD,
  author =       "Anonymous",
  title =        "Video Probability Distributions",
  journal =      j-IEEE-SPECTRUM,
  volume =       "6",
  number =       "4",
  pages =        "5--5",
  month =        apr,
  year =         "1969",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.1969.5214042",
  ISSN =         "1939-9340",
  ISSN-L =       "0018-9235",
  bibdate =      "Wed Jan 15 11:58:06 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "Arithmetic; Circuit noise; Detectors; Distribution
                 functions; Gaussian noise; Probability distribution;
                 Signal to noise ratio; Tail; Testing; Voltage",
}


bibtype: inproceedings
filename: fparith.bib
label: Babuska:1969:NSM
author: Ivo Babuska
title: Numerical stability in mathematical analysis
crossref: Morrell:1969:IPP
pages: 11--23
year: 1969
bibdate: Tue Nov 22 05:36:22 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.11.22 05:36:22 ???
keywords: accurate floating-point summation
acknowledgement: ack-nhfb
rawauthor: Ivo Babu{\v{s}}ka
rawtitle: Numerical stability in mathematical analysis
entry:
@InProceedings{Babuska:1969:NSM,
  author =       "Ivo Babu{\v{s}}ka",
  title =        "Numerical stability in mathematical analysis",
  crossref =     "Morrell:1969:IPP",
  pages =        "11--23",
  year =         "1969",
  bibdate =      "Tue Nov 22 05:36:22 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}


bibtype: article
filename: fparith.bib
label: Banerji:1969:SDR
author: D. K. Banerji and J. A. Brzozowski
title: Sign Detection in Residue Number Systems
journal: j-IEEE-TRANS-COMPUT
volume: C-18
number: 4
pages: 313--320
month: apr
monthnumber: 4
year: 1969
CODEN: ITCOB4
DOI: https://doi.org/10.1109/PGEC.1967.264810; https://doi.org/10.1109/T-C.1969.222658
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 16:55:18 MDT 2011
bibtimestamp: 2011.07.13 16:55:18 MDT
fjournal: IEEE Transactions on Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. K. Banerji and J. A. Brzozowski
rawtitle: Sign Detection in Residue Number Systems
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671251; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35034

abstract:
This paper is concerned with the sign detection problem in residue number systems. The proposed solution is applicable only to nonredundant systems. It is shown that under rather general conditions an explicit, closed formula for the sign function can be obtained. In a special case, when one of the moduli is $2$, the sign function becomes an EXCLUSIVE-OR function. A sign detection algorithm is proposed and methods of implementing the algorithm are presented.

rawabstract:
This paper is concerned with the sign detection problem in residue number systems. The proposed solution is applicable only to nonredundant systems. It is shown that under rather general conditions an explicit, closed formula for the sign function can be obtained. In a special case, when one of the moduli is $2$, the sign function becomes an EXCLUSIVE-OR function. A sign detection algorithm is proposed and methods of implementing the algorithm are presented.

entry:
@Article{Banerji:1969:SDR,
  author =       "D. K. Banerji and J. A. Brzozowski",
  title =        "Sign Detection in Residue Number Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-18",
  number =       "4",
  pages =        "313--320",
  month =        apr,
  year =         "1969",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810;
                 https://doi.org/10.1109/T-C.1969.222658",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 16:55:18 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671251;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35034",
  abstract =     "This paper is concerned with the sign detection
                 problem in residue number systems. The proposed
                 solution is applicable only to nonredundant systems. It
                 is shown that under rather general conditions an
                 explicit, closed formula for the sign function can be
                 obtained. In a special case, when one of the moduli is
                 $2$, the sign function becomes an EXCLUSIVE-OR
                 function. A sign detection algorithm is proposed and
                 methods of implementing the algorithm are presented.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
}


bibtype: manual
filename: fparith.bib
label: BrinchHansen:1969:RCR
author: Per Brinch Hansen
title: RC-4000 Computer Reference Manual
number: RCSL No: 55-D1
organization: A/S Regnecentralen
address: Copenhagen, Denmark
pages: 85
month: jun
monthnumber: 6
year: 1969
bibdate: Sat Mar 09 14:14:25 2019
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2019.03.09 14:14:25 ???
acknowledgement: ack-nhfb
rawauthor: Per {Brinch Hansen}
rawtitle: {RC-4000 Computer} Reference Manual
URL:
http://bitsavers.org/pdf/regnecentralen/RC_4000_Reference_Manual_Jun69.pdf; https://www.math.utah.edu/~beebe/RC-4000

remark:
The RC-4000 has a 24-bit word, and supplies 12-bit and 24-bit integer arithmetic, and 48-bit floating-point arithmetic. The latter has a signed 36-bit normalized two's-complement binary fraction stored at the left of a double word, followed by a 12-bit two's-complement signed exponent. The representable range is therefore [-0x1p-2049, +0x1p2047), or about [-1.547e-617, 1.615e+161]. The sign, and zero value, can be determined by examining only the first word. Its floating-point arithmetic can exactly represent 35-bit integer arithmetic.

TOC:
1. RC 4000 Specifications / 9 2. Design Considerations / 11 2.1. Word Length / 11 2.2. Register Structure / 11 2.3. Address Modification / 11 2.4. Monitor Control / 12 2.5. Input/Output Control / 13 3. Data and Instruction Formats / 15 3.1. Data Formats / 15 3.2. Storage Addressing / 15 3.3. Working Registers / 16 3.4. Instruction Format / 17 3.5. Address Modify Instruction / 18 4. Integer Arithmetic / 19 4.1. Number Representation / 19 4.2. Byte Arithmetic / 19 4.3. Multiplication and Division / 20 4.4. Overflow and Carry Indication / 21 5. Floating-Point Arithmetic / 22 5.1. Number Representation / 22 5.2. Arithmetic Operations / 23 5.3. Normalization and Rounding / 23 5.4. Precision Modes / 24 5.5. Underflow, Overflow, and Non-Normalized Operands / 25 5.6. Number Conversion / 26 5.7. Exact Arithmetic with Floating-Point Instructions / 26 6. Protection System / 28 6.1. Storage Protection / 28 6.2. Privileged Instructions / 29 6.3. Summary of Protection System / 29 6.4. An Example of Protected Areas / 30 7. Interruption System / 32 7.1. Interruption Logic / 32 7.2. Interruption Conditions / 33 8. Low-Speed Data Channel / 35 8.1. Main Characteristics / 35 8.2. Input/Output Instruction / 35 8.3. Channel Operation / 36 8.4. Disconnected and Busy Indication / 37 8.5. Device Commands / 37 8.6. Read / 37 8.7. Sense / 37 8.8. Write / 38 8.9. Control / 39 8.10. Summary of Low-Speed Channel / 39 9. High-Speed Data Channel / 41 10. Standard Peripheral Devices / 43 10.1. Console Devices / 43 10.2. Interval Timer / 43 11. Operator Control Panel / 44 11.1. Indicators and Control Keys / 44 11.2. Machine Errors / 44 11.3. Reset Control / 44 11.4. Start Control / 45 11.5. Autoload Control / 45 11.6. Local/Remote Indication / 46 12. Technical Control Panel / 47 12.1. Operating Modes / 47 12.2. Instruction Step Keys / 47 12.3. Register Setting and Display / 47 12.4. Microinstruction Selection and Display / 48 12.5. Parity Control / 48 13. Instruction Set / 49 14. Definition of Instructions / 51 14.1. Algol Notation / 51 14.2. Register Structure / 51 14.3. Elementary Operations / 54 14.4. Control Panel Functions / 55 14.5. Instruction Fetch Cycle / 55 14.6. Protection Procedures / 56 14.7. Arithmetic Procedures / 57 14.8. Instruction Execution / 58 Appendix / 79 A.1. Reserved Storage Locations / 79 A.2. Numeric Instruction Codes / 80 A.3. Instruction Execution Times / 81 Index / 83

rawTOC:
1. RC 4000 Specifications / 9 \\ 2. Design Considerations / 11 \\ 2.1. Word Length / 11 \\ 2.2. Register Structure / 11 \\ 2.3. Address Modification / 11 \\ 2.4. Monitor Control / 12 \\ 2.5. Input/Output Control / 13 \\ 3. Data and Instruction Formats / 15 \\ 3.1. Data Formats / 15 \\ 3.2. Storage Addressing / 15 \\ 3.3. Working Registers / 16 \\ 3.4. Instruction Format / 17 \\ 3.5. Address Modify Instruction / 18 \\ 4. Integer Arithmetic / 19 \\ 4.1. Number Representation / 19 \\ 4.2. Byte Arithmetic / 19 \\ 4.3. Multiplication and Division / 20 \\ 4.4. Overflow and Carry Indication / 21 \\ 5. Floating-Point Arithmetic / 22 \\ 5.1. Number Representation / 22 \\ 5.2. Arithmetic Operations / 23 \\ 5.3. Normalization and Rounding / 23 \\ 5.4. Precision Modes / 24 \\ 5.5. Underflow, Overflow, and Non-Normalized Operands / 25 \\ 5.6. Number Conversion / 26 \\ 5.7. Exact Arithmetic with Floating-Point Instructions / 26 \\ 6. Protection System / 28 \\ 6.1. Storage Protection / 28 \\ 6.2. Privileged Instructions / 29 \\ 6.3. Summary of Protection System / 29 \\ 6.4. An Example of Protected Areas / 30 \\ 7. Interruption System / 32 \\ 7.1. Interruption Logic / 32 \\ 7.2. Interruption Conditions / 33 \\ 8. Low-Speed Data Channel / 35 \\ 8.1. Main Characteristics / 35 \\ 8.2. Input/Output Instruction / 35 \\ 8.3. Channel Operation / 36 \\ 8.4. Disconnected and Busy Indication / 37 \\ 8.5. Device Commands / 37 \\ 8.6. Read / 37 \\ 8.7. Sense / 37 \\ 8.8. Write / 38 \\ 8.9. Control / 39 \\ 8.10. Summary of Low-Speed Channel / 39 \\ 9. High-Speed Data Channel / 41 \\ 10. Standard Peripheral Devices / 43 \\ 10.1. Console Devices / 43 \\ 10.2. Interval Timer / 43 \\ 11. Operator Control Panel / 44 \\ 11.1. Indicators and Control Keys / 44 \\ 11.2. Machine Errors / 44 \\ 11.3. Reset Control / 44 \\ 11.4. Start Control / 45 \\ 11.5. Autoload Control / 45 \\ 11.6. Local/Remote Indication / 46 \\ 12. Technical Control Panel / 47 \\ 12.1. Operating Modes / 47 \\ 12.2. Instruction Step Keys / 47 \\ 12.3. Register Setting and Display / 47 \\ 12.4. Microinstruction Selection and Display / 48 \\ 12.5. Parity Control / 48 \\ 13. Instruction Set / 49 \\ 14. Definition of Instructions / 51 \\ 14.1. Algol Notation / 51 \\ 14.2. Register Structure / 51 \\ 14.3. Elementary Operations / 54 \\ 14.4. Control Panel Functions / 55 \\ 14.5. Instruction Fetch Cycle / 55 \\ 14.6. Protection Procedures / 56 \\ 14.7. Arithmetic Procedures / 57 \\ 14.8. Instruction Execution / 58 \\ Appendix / 79 \\ A.1. Reserved Storage Locations / 79 \\ A.2. Numeric Instruction Codes / 80 \\ A.3. Instruction Execution Times / 81 \\ Index / 83

entry:
@Manual{BrinchHansen:1969:RCR,
  author =       "Per {Brinch Hansen}",
  title =        "{RC-4000 Computer} Reference Manual",
  number =       "RCSL No: 55-D1",
  organization = "A/S Regnecentralen",
  address =      "Copenhagen, Denmark",
  pages =        "85",
  month =        jun,
  year =         "1969",
  bibdate =      "Sat Mar 09 14:14:25 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bitsavers.org/pdf/regnecentralen/RC_4000_Reference_Manual_Jun69.pdf;
                 https://www.math.utah.edu/~beebe/RC-4000",
  acknowledgement = ack-nhfb,
  remark =       "The RC-4000 has a 24-bit word, and supplies 12-bit and
                 24-bit integer arithmetic, and 48-bit floating-point
                 arithmetic. The latter has a signed 36-bit normalized
                 two's-complement binary fraction stored at the left of
                 a double word, followed by a 12-bit two's-complement
                 signed exponent. The representable range is therefore
                 [-0x1p-2049, +0x1p2047), or about [-1.547e-617,
                 1.615e+161]. The sign, and zero value, can be
                 determined by examining only the first word. Its
                 floating-point arithmetic can exactly represent 35-bit
                 integer arithmetic.",
  tableofcontents = "1. RC 4000 Specifications / 9 \\
                 2. Design Considerations / 11 \\
                 2.1. Word Length / 11 \\
                 2.2. Register Structure / 11 \\
                 2.3. Address Modification / 11 \\
                 2.4. Monitor Control / 12 \\
                 2.5. Input/Output Control / 13 \\
                 3. Data and Instruction Formats / 15 \\
                 3.1. Data Formats / 15 \\
                 3.2. Storage Addressing / 15 \\
                 3.3. Working Registers / 16 \\
                 3.4. Instruction Format / 17 \\
                 3.5. Address Modify Instruction / 18 \\
                 4. Integer Arithmetic / 19 \\
                 4.1. Number Representation / 19 \\
                 4.2. Byte Arithmetic / 19 \\
                 4.3. Multiplication and Division / 20 \\
                 4.4. Overflow and Carry Indication / 21 \\
                 5. Floating-Point Arithmetic / 22 \\
                 5.1. Number Representation / 22 \\
                 5.2. Arithmetic Operations / 23 \\
                 5.3. Normalization and Rounding / 23 \\
                 5.4. Precision Modes / 24 \\
                 5.5. Underflow, Overflow, and Non-Normalized Operands /
                 25 \\
                 5.6. Number Conversion / 26 \\
                 5.7. Exact Arithmetic with Floating-Point Instructions
                 / 26 \\
                 6. Protection System / 28 \\
                 6.1. Storage Protection / 28 \\
                 6.2. Privileged Instructions / 29 \\
                 6.3. Summary of Protection System / 29 \\
                 6.4. An Example of Protected Areas / 30 \\
                 7. Interruption System / 32 \\
                 7.1. Interruption Logic / 32 \\
                 7.2. Interruption Conditions / 33 \\
                 8. Low-Speed Data Channel / 35 \\
                 8.1. Main Characteristics / 35 \\
                 8.2. Input/Output Instruction / 35 \\
                 8.3. Channel Operation / 36 \\
                 8.4. Disconnected and Busy Indication / 37 \\
                 8.5. Device Commands / 37 \\
                 8.6. Read / 37 \\
                 8.7. Sense / 37 \\
                 8.8. Write / 38 \\
                 8.9. Control / 39 \\
                 8.10. Summary of Low-Speed Channel / 39 \\
                 9. High-Speed Data Channel / 41 \\
                 10. Standard Peripheral Devices / 43 \\
                 10.1. Console Devices / 43 \\
                 10.2. Interval Timer / 43 \\
                 11. Operator Control Panel / 44 \\
                 11.1. Indicators and Control Keys / 44 \\
                 11.2. Machine Errors / 44 \\
                 11.3. Reset Control / 44 \\
                 11.4. Start Control / 45 \\
                 11.5. Autoload Control / 45 \\
                 11.6. Local/Remote Indication / 46 \\
                 12. Technical Control Panel / 47 \\
                 12.1. Operating Modes / 47 \\
                 12.2. Instruction Step Keys / 47 \\
                 12.3. Register Setting and Display / 47 \\
                 12.4. Microinstruction Selection and Display / 48 \\
                 12.5. Parity Control / 48 \\
                 13. Instruction Set / 49 \\
                 14. Definition of Instructions / 51 \\
                 14.1. Algol Notation / 51 \\
                 14.2. Register Structure / 51 \\
                 14.3. Elementary Operations / 54 \\
                 14.4. Control Panel Functions / 55 \\
                 14.5. Instruction Fetch Cycle / 55 \\
                 14.6. Protection Procedures / 56 \\
                 14.7. Arithmetic Procedures / 57 \\
                 14.8. Instruction Execution / 58 \\
                 Appendix / 79 \\
                 A.1. Reserved Storage Locations / 79 \\
                 A.2. Numeric Instruction Codes / 80 \\
                 A.3. Instruction Execution Times / 81 \\
                 Index / 83",
}


bibtype: article
filename: fparith.bib
label: Brown:1969:CB
author: W. S. Brown and P. L. Richman
title: The Choice of Base
journal: j-CACM
volume: 12
number: 10
pages: 560--561
month: oct
monthnumber: 10
year: 1969
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 68.00
MRnumber: 43\#5755
bibdate: Mon Mar 24 21:38:51 MST 1997
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1997.03.24 21:38:51 MST
fjournal: Communications of the ACM
keywords: accuracy; base choice; digital arithmetic; floating-point; number representations
acknowledgement: ack-nj
classcodes: C5230 (Digital arithmetic methods)
corpsource: Bell Telephone Labs. Inc., Murray Hill, NJ, USA
journalURL: https://dl.acm.org/loi/cacm
rawauthor: W. S. Brown and P. L. Richman
rawtitle: The Choice of Base
abstract:
A digital computer is considered, whose memory words are composed of $N$ $r$-state devices plus two sign bits (two state devices). The choice of base $ beta $ for the internal representation floating-point numbers on such a computer is discussed. It is shown that in a certain sense $ beta = r $ is best.

rawabstract:
A digital computer is considered, whose memory words are composed of $N$ $r$-state devices plus two sign bits (two state devices). The choice of base $ \beta $ for the internal representation floating-point numbers on such a computer is discussed. It is shown that in a certain sense $ \beta = r $ is best.

entry:
@Article{Brown:1969:CB,
  author =       "W. S. Brown and P. L. Richman",
  title =        "The Choice of Base",
  journal =      j-CACM,
  volume =       "12",
  number =       "10",
  pages =        "560--561",
  month =        oct,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "68.00",
  MRnumber =     "43\#5755",
  bibdate =      "Mon Mar 24 21:38:51 MST 1997",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A digital computer is considered, whose memory words
                 are composed of $N$ $r$-state devices plus two sign
                 bits (two state devices). The choice of base $ \beta $
                 for the internal representation floating-point numbers
                 on such a computer is discussed. It is shown that in a
                 certain sense $ \beta = r $ is best.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Bell Telephone Labs. Inc., Murray Hill, NJ, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "accuracy; base choice; digital arithmetic;
                 floating-point; number representations",
}


bibtype: inproceedings
filename: fparith.bib
label: Clark:1969:SCE
author: N. W. Clark and W. J. Cody
title: Self-contained exponentiation
crossref: AFIPS:1969:ACPb
volume: 35
pages: 701--706
year: 1969
bibdate: Thu Sep 1 10:16:10 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:16:10 ???
acknowledgement: ack-nj
rawauthor: N. W. Clark and W. J. Cody
rawtitle: Self-contained exponentiation
entry:
@InProceedings{Clark:1969:SCE,
  author =       "N. W. Clark and W. J. Cody",
  title =        "Self-contained exponentiation",
  crossref =     "AFIPS:1969:ACPb",
  volume =       "35",
  pages =        "701--706",
  year =         "1969",
  bibdate =      "Thu Sep 1 10:16:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: inproceedings
filename: fparith.bib
label: Cody:1969:PTF
author: W. J. Cody
title: Performance testing of function subroutines
crossref: AFIPS:1969:ACPa
volume: 34
pages: 759--763
year: 1969
bibdate: Thu Sep 1 10:15:07 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:07 ???
acknowledgement: ack-nj
rawauthor: W. J. Cody
rawtitle: Performance testing of function subroutines
entry:
@InProceedings{Cody:1969:PTF,
  author =       "W. J. Cody",
  title =        "Performance testing of function subroutines",
  crossref =     "AFIPS:1969:ACPa",
  volume =       "34",
  pages =        "759--763",
  year =         "1969",
  bibdate =      "Thu Sep 1 10:15:07 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: article
filename: fparith.bib
label: Duke:1969:DFP
author: K. A. Duke
title: Decimal Floating Point Processor
journal: j-IBM-TDB
volume: 11-69
pages: 862--862
month: nov
monthnumber: 11
year: 1969
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Fri Nov 28 11:29:48 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 11:29:48 ???
fjournal: IBM Technical Disclosure Bulletin
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: K. A. Duke
rawtitle: Decimal Floating Point Processor
remark:
Decimal arithmetic with unnormalized binary integers of unspecified length for coefficient and exponent.

entry:
@Article{Duke:1969:DFP,
  author =       "K. A. Duke",
  title =        "Decimal Floating Point Processor",
  journal =      j-IBM-TDB,
  volume =       "11-69",
  pages =        "862--862",
  month =        nov,
  year =         "1969",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Fri Nov 28 11:29:48 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Technical Disclosure Bulletin",
  keywords =     "decimal floating-point arithmetic",
  remark =       "Decimal arithmetic with unnormalized binary integers
                 of unspecified length for coefficient and exponent.",
}


bibtype: mastersthesis
filename: fparith.bib
label: Duncan:1969:FFA
author: Daniel D. A. Duncan
title: FLOP: a floating-point arithmetic package
type: Thesis (M.S.)
school: University of Southwestern Louisiana
address: Lafayette, LA, USA
pages: 108
year: 1969
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Daniel D. A. Duncan
rawtitle: {FLOP}: a floating-point arithmetic package
keywords:
Algorithms.; Arithmetic --- Foundations.; FLOP (Computer program language).; Transformations (Mathematics).

entry:
@MastersThesis{Duncan:1969:FFA,
  author =       "Daniel D. A. Duncan",
  title =        "{FLOP}: a floating-point arithmetic package",
  type =         "Thesis ({M.S.})",
  school =       "University of Southwestern Louisiana",
  address =      "Lafayette, LA, USA",
  pages =        "108",
  year =         "1969",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithms.; Arithmetic --- Foundations.; FLOP
                 (Computer program language).; Transformations
                 (Mathematics).",
}


bibtype: article
filename: fparith.bib
label: Dunworth:1969:ECB
author: A. Dunworth and J. I. Roche
title: The Error Characteristics of the Binary Rate Multiplier
journal: j-IEEE-TRANS-COMPUT
volume: C-18
number: 8
pages: 741--745
month: aug
monthnumber: 8
year: 1969
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1969.222757
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 16:55:20 MDT 2011
bibtimestamp: 2011.07.13 16:55:20 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671350
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: A. Dunworth and J. I. Roche
rawtitle: The Error Characteristics of the Binary Rate Multiplier
entry:
@Article{Dunworth:1969:ECB,
  author =       "A. Dunworth and J. I. Roche",
  title =        "The Error Characteristics of the Binary Rate
                 Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-18",
  number =       "8",
  pages =        "741--745",
  month =        aug,
  year =         "1969",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1969.222757",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 16:55:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671350",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: techreport
filename: fparith.bib
label: Ehrman:1969:SFP
author: J. R. Ehrman
title: A Study of Floating-Point Conversions in Some OS / 360 Components
number: SDD 196, C5207
institution: SHARE Secretary Distribution
pages: 1--6
year: 1969
bibdate: Wed Feb 14 18:50:19 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.02.14 18:50:19 ???
acknowledgement: ack-nhfb
rawauthor: J. R. Ehrman
rawtitle: A Study of Floating-Point Conversions in Some {OS\slash 360} Components
entry:
@TechReport{Ehrman:1969:SFP,
  author =       "J. R. Ehrman",
  title =        "A Study of Floating-Point Conversions in Some
                 {OS\slash 360} Components",
  number =       "SDD 196, C5207",
  institution =  "SHARE Secretary Distribution",
  address =      "????",
  pages =        "1--6",
  year =         "1969",
  bibdate =      "Wed Feb 14 18:50:19 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Fenstad:1969:NSM
author: Jens Erik Fenstad
title: Non-standard models for arithmetic and analysis
journal: j-LECT-NOTES-MATH
volume: 118
pages: 30--47
year: 1969
CODEN: LNMAA2
DOI: https://doi.org/10.1007/BFb0060250
ISBN: 3-540-04907-X (print), 3-540-36246-0 (e-book) OR 354004907X (print), 3540362460 (ebook)
ISSN: 0075-8434 (print), 1617-9692 (electronic) OR 00758434 (print), 16179692 (electronic)
ISSNL: 0075-8434 OR 00758434
bibdate: Thu May 8 17:39:14 MDT 2014
bibtimestamp: 2014.05.08 17:39:14 MDT
URL: http://link.springer.com/chapter/10.1007/BFb0060250/
fjournal: Lecture Notes in Mathematics
acknowledgement: ack-nhfb
bookDOI: https://doi.org/10.1007/BFb0060247
bookURL: http://www.springerlink.com/content/978-3-540-36246-3
journalURL: http://link.springer.com/bookseries/304
rawauthor: Jens Erik Fenstad
rawtitle: Non-standard models for arithmetic and analysis
ISBN13:
978-3-540-04907-4 (print), 978-3-540-36246-3 (e-book) OR 9783540049074 (print), 9783540362463 (ebook)

bibsource:
https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/lnm1960.bib

entry:
@Article{Fenstad:1969:NSM,
  author =       "Jens Erik Fenstad",
  title =        "Non-standard models for arithmetic and analysis",
  journal =      j-LECT-NOTES-MATH,
  volume =       "118",
  pages =        "30--47",
  year =         "1969",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/BFb0060250",
  ISBN =         "3-540-04907-X (print), 3-540-36246-0 (e-book)",
  ISBN-13 =      "978-3-540-04907-4 (print), 978-3-540-36246-3
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  bibdate =      "Thu May 8 17:39:14 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm1960.bib",
  URL =          "http://link.springer.com/chapter/10.1007/BFb0060250/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/BFb0060247",
  book-URL =     "http://www.springerlink.com/content/978-3-540-36246-3",
  fjournal =     "Lecture Notes in Mathematics",
  journal-URL =  "http://link.springer.com/bookseries/304",
}


bibtype: article
filename: fparith.bib
label: Fenwick:1969:BMO
author: P. M. Fenwick
title: Binary Multiplication with Overlapped Addition Cycles
journal: j-IEEE-TRANS-COMPUT
volume: C-18
number: 1
pages: 71--74
month: jan
monthnumber: 1
year: 1969
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1969.222527
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 16:55:17 MDT 2011
bibtimestamp: 2011.07.13 16:55:17 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671120
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: P. M. Fenwick
rawtitle: Binary Multiplication with Overlapped Addition Cycles
entry:
@Article{Fenwick:1969:BMO,
  author =       "P. M. Fenwick",
  title =        "Binary Multiplication with Overlapped Addition
                 Cycles",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-18",
  number =       "1",
  pages =        "71--74",
  month =        jan,
  year =         "1969",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1969.222527",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 16:55:17 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671120",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: Ferrari:1969:CDM
author: D. Ferrari
title: Correction to ``A Division Method Using a Parallel Multiplier''
journal: j-IEEE-TRANS-COMPUT
volume: C-18
number: 10
pages: 960--960
month: oct
monthnumber: 10
year: 1969
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1969.222555
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 16:55:21 MDT 2011
bibtimestamp: 2011.07.13 16:55:21 MDT
note: See cite Ferrari:1967:DMU.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671148
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: D. Ferrari
rawnote: See \cite{Ferrari:1967:DMU}.
rawtitle: Correction to {``A Division Method Using a Parallel Multiplier''}
entry:
@Article{Ferrari:1969:CDM,
  author =       "D. Ferrari",
  title =        "Correction to {``A Division Method Using a Parallel
                 Multiplier''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-18",
  number =       "10",
  pages =        "960--960",
  month =        oct,
  year =         "1969",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1969.222555",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 16:55:21 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  note =         "See \cite{Ferrari:1967:DMU}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671148",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: inproceedings
filename: fparith.bib
label: Field:1969:OFP
author: J. A. Field
title: Optimizing floating-point arithmetic via post addition shift probabilities
crossref: AFIPS:1969:ACPa
pages: 597--??
year: 1969
bibdate: Tue Oct 09 07:54:02 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.10.09 07:54:02 ???
acknowledgement: ack-nhfb
rawauthor: J. A. Field
rawtitle: Optimizing floating-point arithmetic via post addition shift probabilities
entry:
@InProceedings{Field:1969:OFP,
  author =       "J. A. Field",
  title =        "Optimizing floating-point arithmetic via post addition
                 shift probabilities",
  crossref =     "AFIPS:1969:ACPa",
  pages =        "597--??",
  year =         "1969",
  bibdate =      "Tue Oct 09 07:54:02 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Flores:1969:BRB
author: Ivan Flores
journal: j-SIAM-REVIEW
volume: 11
number: 1
pages: 103--104
year: 1969
CODEN: SIREAD
DOI: https://doi.org/10.1137/1011027
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Thu Mar 27 09:06:04 MDT 2014
bibtimestamp: 2014.03.27 09:06:04 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
onlinedate: January 1969
rawauthor: Ivan Flores
title:
Book Review: booktitle Residue Arithmetic and Its Application to Computer Technology (Nicholas S. Szabo and Richard I. Tanaka)

bibsource:
http://epubs.siam.org/toc/siread/11/1; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

rawtitle:
Book Review: {{\booktitle{Residue Arithmetic and Its Application to Computer Technology}} (Nicholas S. Szabo and Richard I. Tanaka)}

entry:
@Article{Flores:1969:BRB,
  author =       "Ivan Flores",
  title =        "Book Review: {{\booktitle{Residue Arithmetic and Its
                 Application to Computer Technology}} (Nicholas S. Szabo
                 and Richard I. Tanaka)}",
  journal =      j-SIAM-REVIEW,
  volume =       "11",
  number =       "1",
  pages =        "103--104",
  month =        "????",
  year =         "1969",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1011027",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:06:04 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/11/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "January 1969",
}


bibtype: book
filename: fparith.bib
label: Froberg:1969:INA
author: Carl Erik Froberg
title: Introduction to numerical analysis
publisher: pub-AW
address: pub-AW:adr
edition: Second
pages: xii + 433
year: 1969
LCCN: QA297 .F6813 1969
bibdate: Fri Aug 20 09:03:07 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.08.20 09:03:07 MDT
remark: Translation of Swedish original em Larobok i numerisk analys. Cited in cite Sterbenz:1974:FPC.
subject: Numerical analysis
acknowledgement: ack-nhfb
rawauthor: Carl Erik Fr{\"o}berg
rawtitle: Introduction to numerical analysis
entry:
@Book{Froberg:1969:INA,
  author =       "Carl Erik Fr{\"o}berg",
  title =        "Introduction to numerical analysis",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Second",
  pages =        "xii + 433",
  year =         "1969",
  LCCN =         "QA297 .F6813 1969",
  bibdate =      "Fri Aug 20 09:03:07 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "Translation of Swedish original {\em L{\"a}robok i
                 numerisk analys}. Cited in \cite{Sterbenz:1974:FPC}.",
  subject =      "Numerical analysis",
}


bibtype: phdthesis
filename: fparith.bib
label: Glaser:1969:HMN
author: Anton Glaser
title: History of Modern Numeration Systems
type: Educat.D. thesis
school: Temple University
address: Philadelphia, PA, USA
pages: 261
year: 1969
bibdate: Fri Mar 17 08:18:07 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2023.03.17 08:18:07 ???
note: See subsequent books cite Glaser:1971:HBO,Glaser:1981:HBO.
URL: https://www.proquest.com/pqdtglobal/docview/302503306/A48758ED17C34A1APQ/1
remark: ProQuest dissertation number 7016666.
acknowledgement: ack-nhfb
rawauthor: Anton Glaser
rawnote: See subsequent books \cite{Glaser:1971:HBO,Glaser:1981:HBO}.
rawtitle: History of Modern Numeration Systems
entry:
@PhdThesis{Glaser:1969:HMN,
  author =       "Anton Glaser",
  title =        "History of Modern Numeration Systems",
  type =         "{Educat.D.} thesis",
  school =       "Temple University",
  address =      "Philadelphia, PA, USA",
  pages =        "261",
  year =         "1969",
  bibdate =      "Fri Mar 17 08:18:07 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See subsequent books
                 \cite{Glaser:1971:HBO,Glaser:1981:HBO}.",
  URL =          "https://www.proquest.com/pqdtglobal/docview/302503306/A48758ED17C34A1APQ/1",
  acknowledgement = ack-nhfb,
  remark =       "ProQuest dissertation number 7016666.",
}


bibtype: article
filename: fparith.bib
label: Hammersley:1969:NAP
author: P. Hammersley
title: Note on Algorithm 34: Procedures for the Basic Arithmetical Operations in Multi-Length Working
journal: j-COMP-J
volume: 12
number: 1
pages: 102--103
month: feb
monthnumber: 2
year: 1969
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Fri Sep 29 08:51:33 MDT 2000
bibtimestamp: 2000.09.29 08:51:33 MDT
fjournal: The Computer Journal
acknowledgement: ack-nhfb
journalURL: http://comjnl.oxfordjournals.org/
rawauthor: P. Hammersley
rawtitle: Note on {Algorithm 34}: Procedures for the Basic Arithmetical Operations in Multi-Length Working
bibsource:
http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_01/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_01/tiff/102.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_01/tiff/103.tif

entry:
@Article{Hammersley:1969:NAP,
  author =       "P. Hammersley",
  title =        "Note on {Algorithm 34}: Procedures for the Basic
                 Arithmetical Operations in Multi-Length Working",
  journal =      j-COMP-J,
  volume =       "12",
  number =       "1",
  pages =        "102--103",
  month =        feb,
  year =         "1969",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:51:33 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_01/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_01/tiff/102.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_01/tiff/103.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}


bibtype: article
filename: fparith.bib
label: Holzwarth:1969:VBB
author: A. Holzwarth
journal: j-COMPUTING
volume: 4
number: 2
pages: 168--177
year: 1969
CODEN: CMPTA2
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
bibdate: Fri Sep 16 16:30:41 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 16:30:41 ???
fjournal: Computing: Archiv fur informatik und numerik
language: German
acknowledgement: ack-nj
affiliation: Tubingen, West Germany
journalURL: http://link.springer.com/journal/607
rawauthor: A. Holzwarth
title:
Ein Verfahren zur Bestimmung bester Tschebyscheff- Approximationen der Quadratwurzelfunktion toenglish A Method for Determination of Best Chebyshev Approximations to the Square Root Function endtoenglish 

rawtitle:
{Ein Verfahren zur Bestimmung bester Tscheb\-y\-scheff- Ap\-prox\-i\-ma\-tion\-en der Quadratwurzelfunktion} \toenglish {A Method for Determination of Best Chebyshev Approximations to the Square Root Function} \endtoenglish

entry:
@Article{Holzwarth:1969:VBB,
  author =       "A. Holzwarth",
  title =        "{Ein Verfahren zur Bestimmung bester
                 Tscheb\-y\-scheff- Ap\-prox\-i\-ma\-tion\-en der
                 Quadratwurzelfunktion} \toenglish {A Method for
                 Determination of Best Chebyshev Approximations to the
                 Square Root Function} \endtoenglish",
  journal =      j-COMPUTING,
  volume =       "4",
  number =       "2",
  pages =        "168--177",
  year =         "1969",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  affiliation =  "T{\"u}bingen, West Germany",
  classification = "C4130",
  description =  "Chebyshev approximation; numerical analysis",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  language =     "German",
}


bibtype: article
filename: fparith.bib
label: Howell:1969:ASLa
author: Jo Ann Howell and Robert T. Gregory
title: An algorithm for solving linear algebraic equations using residue arithmetic. I
journal: j-BIT
volume: 9
pages: 200--224
year: 1969
CODEN: BITTEL, NBITAB
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65.35
MRnumber: MR0261775 (41 \#6388a)
bibdate: Thu Nov 8 14:50:15 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:15 ???
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Jo Ann Howell and Robert T. Gregory
rawtitle: An algorithm for solving linear algebraic equations using residue arithmetic. {I}
entry:
@Article{Howell:1969:ASLa,
  author =       "Jo Ann Howell and Robert T. Gregory",
  title =        "An algorithm for solving linear algebraic equations
                 using residue arithmetic. {I}",
  journal =      j-BIT,
  volume =       "9",
  pages =        "200--224",
  year =         "1969",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65.35",
  MRnumber =     "MR0261775 (41 \#6388a)",
  bibdate =      "Thu Nov 8 14:50:15 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}


bibtype: article
filename: fparith.bib
label: Howell:1969:ASLb
author: Jo Ann Howell and Robert T. Gregory
title: An algorithm for solving linear algebraic equations using residue arithmetic. II
journal: j-BIT
volume: 9
pages: 324--337
year: 1969
CODEN: BITTEL, NBITAB
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65.35
MRnumber: MR0261776 (41 \#6388b)
MRreviewer: J. Legras
bibdate: Thu Nov 8 14:50:18 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:50:18 ???
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Jo Ann Howell and Robert T. Gregory
rawtitle: An algorithm for solving linear algebraic equations using residue arithmetic. {II}
entry:
@Article{Howell:1969:ASLb,
  author =       "Jo Ann Howell and Robert T. Gregory",
  title =        "An algorithm for solving linear algebraic equations
                 using residue arithmetic. {II}",
  journal =      j-BIT,
  volume =       "9",
  pages =        "324--337",
  year =         "1969",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65.35",
  MRnumber =     "MR0261776 (41 \#6388b)",
  MRreviewer =   "J. Legras",
  bibdate =      "Thu Nov 8 14:50:18 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}


bibtype: mastersthesis
filename: fparith.bib
label: Huey:1969:DFP
author: Ben Milton Huey
title: Design of a floating point processor for the PDP-9 computer
type: Thesis (M.S. - Electrical Engineering)
school: University of Arizona
address: Tucson, AZ, USA
pages: 175
year: 1969
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Computer storage devices.; Hybrid computers.
acknowledgement: ack-nhfb
rawauthor: Ben Milton Huey
rawtitle: Design of a floating point processor for the {PDP-9} computer
entry:
@MastersThesis{Huey:1969:DFP,
  author =       "Ben Milton Huey",
  title =        "Design of a floating point processor for the {PDP-9}
                 computer",
  type =         "Thesis ({M.S. - Electrical Engineering})",
  school =       "University of Arizona",
  address =      "Tucson, AZ, USA",
  pages =        "175",
  year =         "1969",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer storage devices.; Hybrid computers.",
}


bibtype: article
filename: fparith.bib
label: Huttenhoff:1969:AUC
author: J. H. Huttenhoff and R. R. Shively
title: Arithmetic Unit of a Computing Element in a Global, Highly Parallel Computer
journal: j-IEEE-TRANS-COMPUT
volume: C-18
number: 8
pages: 695--698
month: aug
monthnumber: 8
year: 1969
CODEN: ITCOB4
DOI: https://doi.org/10.1109/T-C.1969.222751
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 13 16:55:20 MDT 2011
bibtimestamp: 2011.07.13 16:55:20 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671344
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. H. Huttenhoff and R. R. Shively
rawtitle: Arithmetic Unit of a Computing Element in a Global, Highly Parallel Computer
entry:
@Article{Huttenhoff:1969:AUC,
  author =       "J. H. Huttenhoff and R. R. Shively",
  title =        "Arithmetic Unit of a Computing Element in a Global,
                 Highly Parallel Computer",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-18",
  number =       "8",
  pages =        "695--698",
  month =        aug,
  year =         "1969",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1969.222751",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 16:55:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671344",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: fparith.bib
label: King:1969:LEN
author: Richard F. King and David L. Phillips
title: The Logarithmic Error and Newton's Method for the Square Root
journal: j-CACM
volume: 12
number: 2
pages: 87--88
month: feb
monthnumber: 2
year: 1969
CODEN: CACMA2
DOI: https://doi.org/10.1145/362848.362861
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65.50
MRnumber: 44\#2333
bibdate: Fri Nov 25 18:20:24 MST 2005
bibtimestamp: 2005.11.25 18:20:24 MST
fjournal: Communications of the ACM
keywords: $sqrt (x)$; elementary functions; function evaluation; iterative methods
acknowledgement: ack-nj
classcodes: C4120 (Functional analysis)
corpsource: Argonne Nat. Lab., Argonne, IL, USA
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Richard F. King and David L. Phillips
rawtitle: The Logarithmic Error and {Newton}'s Method for the Square Root
abstract:
The problem of obtaining optimal starting values for the calculation of the square root using Newton's method is considered. It has been pointed out elsewhere that if relative error is used as the measure of goodness of fit, optimal results are not obtained when the initial approximation is a best fit. It is shown here that if, instead, the so-called logarithmic error is used, then a best initial fit is optimal for both types of error. Moreover, use of the logarithmic error appears to simplify the problem of determining the optimal initial approximation.

rawabstract:
The problem of obtaining optimal starting values for the calculation of the square root using Newton's method is considered. It has been pointed out elsewhere that if relative error is used as the measure of goodness of fit, optimal results are not obtained when the initial approximation is a best fit. It is shown here that if, instead, the so-called logarithmic error is used, then a best initial fit is optimal for both types of error. Moreover, use of the logarithmic error appears to simplify the problem of determining the optimal initial approximation.

entry:
@Article{King:1969:LEN,
  author =       "Richard F. King and David L. Phillips",
  title =        "The Logarithmic Error and {Newton}'s Method for the
                 Square Root",
  journal =      j-CACM,
  volume =       "12",
  number =       "2",
  pages =        "87--88",
  month =        feb,
  year =         "1969",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/362848.362861",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.50",
  MRnumber =     "44\#2333",
  bibdate =      "Fri Nov 25 18:20:24 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The problem of obtaining optimal starting values for
                 the calculation of the square root using Newton's
                 method is considered. It has been pointed out elsewhere
                 that if relative error is used as the measure of
                 goodness of fit, optimal results are not obtained when
                 the initial approximation is a best fit. It is shown
                 here that if, instead, the so-called logarithmic error
                 is used, then a best initial fit is optimal for both
                 types of error. Moreover, use of the logarithmic error
                 appears to simplify the problem of determining the
                 optimal initial approximation.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C4120 (Functional analysis)",
  corpsource =   "Argonne Nat. Lab., Argonne, IL, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions; function evaluation;
                 iterative methods",
}


bibtype: article
filename: fparith.bib
label: Kirsch:1969:ACA
author: Arnold Kirsch
title: An analysis of commercial arithmetic
journal: j-EDUC-STUD-MATH
volume: 1
number: 3
pages: 300--311
month: jan
monthnumber: 1
year: 1969
CODEN: EDSMAN
DOI: https://doi.org/10.1007/BF00558315
ISSN: 0013-1954 (print), 1573-0816 (electronic) OR 00131954 (print), 15730816 (electronic)
ISSNL: 0013-1954 OR 00131954
bibdate: Sat Jan 14 17:12:11 MST 2017
bibtimestamp: 2017.01.14 17:12:11 MST
URL: http://link.springer.com/accesspage/article/10.1007/BF00558315
fjournal: Educational Studies in Mathematics
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10649
rawauthor: Arnold Kirsch
rawtitle: An analysis of commercial arithmetic
bibsource:
https://www.math.utah.edu/pub/tex/bib/educstudmath.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Kirsch:1969:ACA,
  author =       "Arnold Kirsch",
  title =        "An analysis of commercial arithmetic",
  journal =      j-EDUC-STUD-MATH,
  volume =       "1",
  number =       "3",
  pages =        "300--311",
  month =        jan,
  year =         "1969",
  CODEN =        "EDSMAN",
  DOI =          "https://doi.org/10.1007/BF00558315",
  ISSN =         "0013-1954 (print), 1573-0816 (electronic)",
  ISSN-L =       "0013-1954",
  bibdate =      "Sat Jan 14 17:12:11 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/educstudmath.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer.com/accesspage/article/10.1007/BF00558315",
  acknowledgement = ack-nhfb,
  fjournal =     "Educational Studies in Mathematics",
  journal-URL =  "http://link.springer.com/journal/10649",
}


bibtype: mastersthesis
filename: fparith.bib
label: Knight:1969:FPS
author: Douglas Wayne Knight
title: A floating point software package in BCD format for small, fixed word length, digital computers
type: Thesis (M.S.)
school: Arizona State University, Electrical Engineering
address: Tempe, AZ, USA
pages: 151
year: 1969
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
acknowledgement: ack-nhfb
rawauthor: Douglas Wayne Knight
rawtitle: A floating point software package in {BCD} format for small, fixed word length, digital computers
entry:
@MastersThesis{Knight:1969:FPS,
  author =       "Douglas Wayne Knight",
  title =        "A floating point software package in {BCD} format for
                 small, fixed word length, digital computers",
  type =         "Thesis ({M.S.})",
  school =       "Arizona State University, Electrical Engineering",
  address =      "Tempe, AZ, USA",
  pages =        "151",
  year =         "1969",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Knuth:1969:SA
author: Donald E. Knuth
title: Seminumerical Algorithms
volume: 2
publisher: pub-AW
address: pub-AW:adr
pages: xi + 624
year: 1969
ISBN: 0-201-03802-1 OR 0201038021
ISBN13: 978-0-201-03802-6 OR 9780201038026
LCCN: QA76.5 .K57
MRclass: 68.00 (65.00)
MRnumber: 44 \#3531
MRreviewer: M. Muller
bibdate: Wed Dec 15 15:47:38 1993
bibtimestamp: 1993.12.15 15:47:38 ???
series: The Art of Computer Programming
remark: Benford's Law is discussed on pp. 219--229. Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
rawauthor: Donald E. Knuth
rawtitle: Seminumerical Algorithms
bibsource:
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/cryptography.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib

TOC:
3: Random Numbers 3.1. Introduction / 1 3.2. Generating Uniform Random Numbers / 9 3.2.1. The Linear Congruential Method / 9 3.2.1.1. Choice of modulus / 11 3.2.1.2. Choice of multiplier / 15 3.2.1.3. Potency / 21 3.2.2. Other Methods / 25 3.3. Statistical Tests / 34 3.3.1. General Test Procedures for Studying Random Data / 35 3.3.2. Empirical Tests / 54 *3.3.3. Theoretical Tests / 69 3.3.4. The Spectral Test / 82 3.4. Other Types of Random Quantities / 100 3.4.1. Numerical Distributions / 101 3.4.2. Random Sampling and Shuffling / 121 *3.5. What is a Random Sequence? / 127 3.6. Summary / 155 4: Arithmetic 4.1. Positional Number Systems / 162 4.2. Floating-Point Arithmetic / 180 4.2.1. Single-Precision Calculations / 180 4.2.2. Accuracy of Floating-Point Arithmetic / 195 *4.2.3. Double-Precision Calculations / 210 4.2.4. Statistical Distribution / 218 4.3. Multiple-Precision Arithmetic / 229 4.3.1. The Classical Algorithms / 229 *4.3.2. Modular Arithmetic / 248 *4.3.3. How Fast Can We Multiply? / 258 4.4. Radix Conversion / 280 4.5. Rational Arithmetic / 290 4.5.1. Fractions / 290 4.5.2. The Greatest Common Divisor / 293 *4.5.3. Analysis of Euclid's Algorithm / 316 4.5.4. Factoring into Primes / 339 4.6. Polynomial Arithmetic / 360 4.6.1. Division of Polynomials / 363 *4.6.2. Factorization of Polynomials / 381 4.6.3. Evaluation of Powers / 398 4.6.4. Evaluation of Polynomials / 422 *4.7. Manipulation of Power Series / 444 Answers to Exercises / 452 Appendix A: MIX / 565 1. Description of MIX / 565 2. The MIX Assembly Language / 584 Appendix B: Tables of Numerical Quantities / 596 1. Fundamental Constants (decimal) / 596 2. Fundamental Constants (octal) / 597 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers / 598 Appendix C: Index to Notations / 600 Index and Glossary / 605

rawTOC:
3: Random Numbers \\ 3.1. Introduction / 1 \\ 3.2. Generating Uniform Random Numbers / 9 \\ 3.2.1. The Linear Congruential Method / 9 \\ 3.2.1.1. Choice of modulus / 11 \\ 3.2.1.2. Choice of multiplier / 15 \\ 3.2.1.3. Potency / 21 \\ 3.2.2. Other Methods / 25 \\ 3.3. Statistical Tests / 34 \\ 3.3.1. General Test Procedures for Studying Random Data / 35 \\ 3.3.2. Empirical Tests / 54 \\ *3.3.3. Theoretical Tests / 69 \\ 3.3.4. The Spectral Test / 82 \\ 3.4. Other Types of Random Quantities / 100 \\ 3.4.1. Numerical Distributions / 101 \\ 3.4.2. Random Sampling and Shuffling / 121 \\ *3.5. What is a Random Sequence? / 127 \\ 3.6. Summary / 155 \\ 4: Arithmetic \\ 4.1. Positional Number Systems / 162 \\ 4.2. Floating-Point Arithmetic / 180 \\ 4.2.1. Single-Precision Calculations / 180 \\ 4.2.2. Accuracy of Floating-Point Arithmetic / 195 \\ *4.2.3. Double-Precision Calculations / 210 \\ 4.2.4. Statistical Distribution / 218 \\ 4.3. Multiple-Precision Arithmetic / 229 \\ 4.3.1. The Classical Algorithms / 229 \\ *4.3.2. Modular Arithmetic / 248 \\ *4.3.3. How Fast Can We Multiply? / 258 \\ 4.4. Radix Conversion / 280 \\ 4.5. Rational Arithmetic / 290 \\ 4.5.1. Fractions / 290 \\ 4.5.2. The Greatest Common Divisor / 293 \\ *4.5.3. Analysis of Euclid's Algorithm / 316 \\ 4.5.4. Factoring into Primes / 339 \\ 4.6. Polynomial Arithmetic / 360 \\ 4.6.1. Division of Polynomials / 363 \\ *4.6.2. Factorization of Polynomials / 381 \\ 4.6.3. Evaluation of Powers / 398 \\ 4.6.4. Evaluation of Polynomials / 422 \\ *4.7. Manipulation of Power Series / 444 \\ Answers to Exercises / 452 \\ Appendix A: MIX / 565 \\ 1. Description of MIX / 565 \\ 2. The MIX Assembly Language / 584 \\ Appendix B: Tables of Numerical Quantities / 596 \\ 1. Fundamental Constants (decimal) / 596 \\ 2. Fundamental Constants (octal) / 597 \\ 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers / 598 \\ Appendix C: Index to Notations / 600 \\ Index and Glossary / 605

entry:
@Book{Knuth:1969:SA,
  author =       "Donald E. Knuth",
  title =        "Seminumerical Algorithms",
  volume =       "2",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xi + 624",
  year =         "1969",
  ISBN =         "0-201-03802-1",
  ISBN-13 =      "978-0-201-03802-6",
  LCCN =         "QA76.5 .K57",
  MRclass =      "68.00 (65.00)",
  MRnumber =     "44 \#3531",
  MRreviewer =   "M. Muller",
  bibdate =      "Wed Dec 15 15:47:38 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptography.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$19.75",
  series =       "The Art of Computer Programming",
  acknowledgement = ack-nhfb,
  remark =       "Benford's Law is discussed on pp. 219--229. Cited in
                 \cite{Sterbenz:1974:FPC}.",
  tableofcontents = "3: Random Numbers \\
                 3.1. Introduction / 1 \\
                 3.2. Generating Uniform Random Numbers / 9 \\
                 3.2.1. The Linear Congruential Method / 9 \\
                 3.2.1.1. Choice of modulus / 11 \\
                 3.2.1.2. Choice of multiplier / 15 \\
                 3.2.1.3. Potency / 21 \\
                 3.2.2. Other Methods / 25 \\
                 3.3. Statistical Tests / 34 \\
                 3.3.1. General Test Procedures for Studying Random Data
                 / 35 \\
                 3.3.2. Empirical Tests / 54 \\
                 *3.3.3. Theoretical Tests / 69 \\
                 3.3.4. The Spectral Test / 82 \\
                 3.4. Other Types of Random Quantities / 100 \\
                 3.4.1. Numerical Distributions / 101 \\
                 3.4.2. Random Sampling and Shuffling / 121 \\
                 *3.5. What is a Random Sequence? / 127 \\
                 3.6. Summary / 155 \\
                 4: Arithmetic \\
                 4.1. Positional Number Systems / 162 \\
                 4.2. Floating-Point Arithmetic / 180 \\
                 4.2.1. Single-Precision Calculations / 180 \\
                 4.2.2. Accuracy of Floating-Point Arithmetic / 195 \\
                 *4.2.3. Double-Precision Calculations / 210 \\
                 4.2.4. Statistical Distribution / 218 \\
                 4.3. Multiple-Precision Arithmetic / 229 \\
                 4.3.1. The Classical Algorithms / 229 \\
                 *4.3.2. Modular Arithmetic / 248 \\
                 *4.3.3. How Fast Can We Multiply? / 258 \\
                 4.4. Radix Conversion / 280 \\
                 4.5. Rational Arithmetic / 290 \\
                 4.5.1. Fractions / 290 \\
                 4.5.2. The Greatest Common Divisor / 293 \\
                 *4.5.3. Analysis of Euclid's Algorithm / 316 \\
                 4.5.4. Factoring into Primes / 339 \\
                 4.6. Polynomial Arithmetic / 360 \\
                 4.6.1. Division of Polynomials / 363 \\
                 *4.6.2. Factorization of Polynomials / 381 \\
                 4.6.3. Evaluation of Powers / 398 \\
                 4.6.4. Evaluation of Polynomials / 422 \\
                 *4.7. Manipulation of Power Series / 444 \\
                 Answers to Exercises / 452 \\
                 Appendix A: MIX / 565 \\
                 1. Description of MIX / 565 \\
                 2. The MIX Assembly Language / 584 \\
                 Appendix B: Tables of Numerical Quantities / 596 \\
                 1. Fundamental Constants (decimal) / 596 \\
                 2. Fundamental Constants (octal) / 597 \\
                 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
                 Numbers / 598 \\
                 Appendix C: Index to Notations / 600 \\
                 Index and Glossary / 605",
  xxyear =       "{\noopsort{1968c}}1969",
}


bibtype: book
filename: fparith.bib
label: Knuth:ACP69-2
author: Donald E. Knuth
title: Seminumerical Algorithms
volume: 2
publisher: pub-AW
address: pub-AW:adr
pages: xi + 624
year: 1969
ISBN: 0-201-03802-1 OR 0201038021
ISBN13: 978-0-201-03802-6 OR 9780201038026
LCCN: QA76.5 .K57
MRclass: 68.00 (65.00)
MRnumber: 44 \#3531
MRreviewer: M. Muller
bibdate: Wed Dec 15 15:47:38 1993
bibtimestamp: 1993.12.15 15:47:38 ???
series: The Art of Computer Programming
remark: Benford's Law is discussed on pp. 219--229.
acknowledgement: ack-nhfb
rawauthor: Donald E. Knuth
rawtitle: Seminumerical Algorithms
bibsource:
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/cryptography.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib

TOC:
3: Random Numbers 3.1. Introduction / 1 3.2. Generating Uniform Random Numbers / 9 3.2.1. The Linear Congruential Method / 9 3.2.1.1. Choice of modulus / 11 3.2.1.2. Choice of multiplier / 15 3.2.1.3. Potency / 21 3.2.2. Other Methods / 25 3.3. Statistical Tests / 34 3.3.1. General Test Procedures for Studying Random Data / 35 3.3.2. Empirical Tests / 54 *3.3.3. Theoretical Tests / 69 3.3.4. The Spectral Test / 82 3.4. Other Types of Random Quantities / 100 3.4.1. Numerical Distributions / 101 3.4.2. Random Sampling and Shuffling / 121 *3.5. What is a Random Sequence? / 127 3.6. Summary / 155 4: Arithmetic 4.1. Positional Number Systems / 162 4.2. Floating-Point Arithmetic / 180 4.2.1. Single-Precision Calculations / 180 4.2.2. Accuracy of Floating-Point Arithmetic / 195 *4.2.3. Double-Precision Calculations / 210 4.2.4. Statistical Distribution / 218 4.3. Multiple-Precision Arithmetic / 229 4.3.1. The Classical Algorithms / 229 *4.3.2. Modular Arithmetic / 248 *4.3.3. How Fast Can We Multiply? / 258 4.4. Radix Conversion / 280 4.5. Rational Arithmetic / 290 4.5.1. Fractions / 290 4.5.2. The Greatest Common Divisor / 293 *4.5.3. Analysis of Euclid's Algorithm / 316 4.5.4. Factoring into Primes / 339 4.6. Polynomial Arithmetic / 360 4.6.1. Division of Polynomials / 363 *4.6.2. Factorization of Polynomials / 381 4.6.3. Evaluation of Powers / 398 4.6.4. Evaluation of Polynomials / 422 *4.7. Manipulation of Power Series / 444 Answers to Exercises / 452 Appendix A: MIX / 565 1. Description of MIX / 565 2. The MIX Assembly Language / 584 Appendix B: Tables of Numerical Quantities / 596 1. Fundamental Constants (decimal) / 596 2. Fundamental Constants (octal) / 597 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers / 598 Appendix C: Index to Notations / 600 Index and Glossary / 605

rawTOC:
3: Random Numbers \\ 3.1. Introduction / 1 \\ 3.2. Generating Uniform Random Numbers / 9 \\ 3.2.1. The Linear Congruential Method / 9 \\ 3.2.1.1. Choice of modulus / 11 \\ 3.2.1.2. Choice of multiplier / 15 \\ 3.2.1.3. Potency / 21 \\ 3.2.2. Other Methods / 25 \\ 3.3. Statistical Tests / 34 \\ 3.3.1. General Test Procedures for Studying Random Data / 35 \\ 3.3.2. Empirical Tests / 54 \\ *3.3.3. Theoretical Tests / 69 \\ 3.3.4. The Spectral Test / 82 \\ 3.4. Other Types of Random Quantities / 100 \\ 3.4.1. Numerical Distributions / 101 \\ 3.4.2. Random Sampling and Shuffling / 121 \\ *3.5. What is a Random Sequence? / 127 \\ 3.6. Summary / 155 \\ 4: Arithmetic \\ 4.1. Positional Number Systems / 162 \\ 4.2. Floating-Point Arithmetic / 180 \\ 4.2.1. Single-Precision Calculations / 180 \\ 4.2.2. Accuracy of Floating-Point Arithmetic / 195 \\ *4.2.3. Double-Precision Calculations / 210 \\ 4.2.4. Statistical Distribution / 218 \\ 4.3. Multiple-Precision Arithmetic / 229 \\ 4.3.1. The Classical Algorithms / 229 \\ *4.3.2. Modular Arithmetic / 248 \\ *4.3.3. How Fast Can We Multiply? / 258 \\ 4.4. Radix Conversion / 280 \\ 4.5. Rational Arithmetic / 290 \\ 4.5.1. Fractions / 290 \\ 4.5.2. The Greatest Common Divisor / 293 \\ *4.5.3. Analysis of Euclid's Algorithm / 316 \\ 4.5.4. Factoring into Primes / 339 \\ 4.6. Polynomial Arithmetic / 360 \\ 4.6.1. Division of Polynomials / 363 \\ *4.6.2. Factorization of Polynomials / 381 \\ 4.6.3. Evaluation of Powers / 398 \\ 4.6.4. Evaluation of Polynomials / 422 \\ *4.7. Manipulation of Power Series / 444 \\ Answers to Exercises / 452 \\ Appendix A: MIX / 565 \\ 1. Description of MIX / 565 \\ 2. The MIX Assembly Language / 584 \\ Appendix B: Tables of Numerical Quantities / 596 \\ 1. Fundamental Constants (decimal) / 596 \\ 2. Fundamental Constants (octal) / 597 \\ 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers / 598 \\ Appendix C: Index to Notations / 600 \\ Index and Glossary / 605

entry:
@Book{Knuth:ACP69-2,
  author =       "Donald E. Knuth",
  title =        "Seminumerical Algorithms",
  volume =       "2",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xi + 624",
  year =         "1969",
  ISBN =         "0-201-03802-1",
  ISBN-13 =      "978-0-201-03802-6",
  LCCN =         "QA76.5 .K57",
  MRclass =      "68.00 (65.00)",
  MRnumber =     "44 \#3531",
  MRreviewer =   "M. Muller",
  bibdate =      "Wed Dec 15 15:47:38 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptography.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$19.75",
  series =       "The Art of Computer Programming",
  acknowledgement = ack-nhfb,
  remark =       "Benford's Law is discussed on pp. 219--229.",
  tableofcontents = "3: Random Numbers \\
                 3.1. Introduction / 1 \\
                 3.2. Generating Uniform Random Numbers / 9 \\
                 3.2.1. The Linear Congruential Method / 9 \\
                 3.2.1.1. Choice of modulus / 11 \\
                 3.2.1.2. Choice of multiplier / 15 \\
                 3.2.1.3. Potency / 21 \\
                 3.2.2. Other Methods / 25 \\
                 3.3. Statistical Tests / 34 \\
                 3.3.1. General Test Procedures for Studying Random Data
                 / 35 \\
                 3.3.2. Empirical Tests / 54 \\
                 *3.3.3. Theoretical Tests / 69 \\
                 3.3.4. The Spectral Test / 82 \\
                 3.4. Other Types of Random Quantities / 100 \\
                 3.4.1. Numerical Distributions / 101 \\
                 3.4.2. Random Sampling and Shuffling / 121 \\
                 *3.5. What is a Random Sequence? / 127 \\
                 3.6. Summary / 155 \\
                 4: Arithmetic \\
                 4.1. Positional Number Systems / 162 \\
                 4.2. Floating-Point Arithmetic / 180 \\
                 4.2.1. Single-Precision Calculations / 180 \\
                 4.2.2. Accuracy of Floating-Point Arithmetic / 195 \\
                 *4.2.3. Double-Precision Calculations / 210 \\
                 4.2.4. Statistical Distribution / 218 \\
                 4.3. Multiple-Precision Arithmetic / 229 \\
                 4.3.1. The Classical Algorithms / 229 \\
                 *4.3.2. Modular Arithmetic / 248 \\
                 *4.3.3. How Fast Can We Multiply? / 258 \\
                 4.4. Radix Conversion / 280 \\
                 4.5. Rational Arithmetic / 290 \\
                 4.5.1. Fractions / 290 \\
                 4.5.2. The Greatest Common Divisor / 293 \\
                 *4.5.3. Analysis of Euclid's Algorithm / 316 \\
                 4.5.4. Factoring into Primes / 339 \\
                 4.6. Polynomial Arithmetic / 360 \\
                 4.6.1. Division of Polynomials / 363 \\
                 *4.6.2. Factorization of Polynomials / 381 \\
                 4.6.3. Evaluation of Powers / 398 \\
                 4.6.4. Evaluation of Polynomials / 422 \\
                 *4.7. Manipulation of Power Series / 444 \\
                 Answers to Exercises / 452 \\
                 Appendix A: MIX / 565 \\
                 1. Description of MIX / 565 \\
                 2. The MIX Assembly Language / 584 \\
                 Appendix B: Tables of Numerical Quantities / 596 \\
                 1. Fundamental Constants (decimal) / 596 \\
                 2. Fundamental Constants (octal) / 597 \\
                 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
                 Numbers / 598 \\
                 Appendix C: Index to Notations / 600 \\
                 Index and Glossary / 605",
  xxyear =       "{\noopsort{1968c}}1969",
}


bibtype: article
filename: fparith.bib
label: Linhardt:1969:DDT
author: R. J. Linhardt and H. S. Miller
title: Digit-by-Digit Transcendental-Function Computation
journal: j-RCA-REV
volume: 30
number: 2
pages: 209--247
month: jun
monthnumber: 6
year: 1969
CODEN: RCARCI
ISSN: 0033-6831 OR 00336831
bibdate: Fri Sep 16 10:31:06 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 10:31:06 ???
fjournal: RCA review
acknowledgement: ack-nj
rawauthor: R. J. Linhardt and H. S. Miller
rawtitle: Digit-by-Digit Transcendental-Function Computation
entry:
@Article{Linhardt:1969:DDT,
  author =       "R. J. Linhardt and H. S. Miller",
  title =        "Digit-by-Digit Transcendental-Function Computation",
  journal =      j-RCA-REV,
  volume =       "30",
  number =       "2",
  pages =        "209--247",
  month =        jun,
  year =         "1969",
  CODEN =        "RCARCI",
  ISSN =         "0033-6831",
  bibdate =      "Fri Sep 16 10:31:06 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "RCA review",
}


bibtype: article
filename: fparith.bib
label: Liu:1969:EAD
author: B. Liu and T. Kaneko
title: Error analysis of digital filters realized with floating-point arithmetic
journal: j-PROC-IEEE
volume: 57
number: 10
pages: 1735--1747
month: oct
monthnumber: 10
year: 1969
CODEN: IEEPAD
ISSN: 0018-9219 (print), 1558-2256 (electronic) OR 00189219 (print), 15582256 (electronic)
ISSNL: 0018-9219 OR 00189219
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 08:40:52 MDT
note: See correction cite Liu:1970:CEA.
fjournal: Proceedings of the IEEE
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5
rawauthor: B. Liu and T. Kaneko
rawnote: See correction \cite{Liu:1970:CEA}.
rawtitle: Error analysis of digital filters realized with floating-point arithmetic
entry:
@Article{Liu:1969:EAD,
  author =       "B. Liu and T. Kaneko",
  title =        "Error analysis of digital filters realized with
                 floating-point arithmetic",
  journal =      j-PROC-IEEE,
  volume =       "57",
  number =       "10",
  pages =        "1735--1747",
  month =        oct,
  year =         "1969",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See correction \cite{Liu:1970:CEA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  summary =      "This paper calculates the error at the output of a
                 digital filter using floating-point arithmetic
                 operations due to roundoff accumulation and input
                 quantization. Expressions are derived for the mean
                 square error for each of the three canonical forms
                 \ldots{}",
}


bibtype: inproceedings
filename: fparith.bib
label: Matula:1969:TAM
author: David W. Matula
title: Towards an Abstract Mathematical Theory of Floating-Point Arithmetic
crossref: AFIPS:1969:ACPa
pages: 765--772
year: 1969
bibdate: Fri Oct 19 23:01:32 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.10.19 23:01:32 ???
acknowledgement: ack-nhfb
rawauthor: David W. Matula
rawtitle: Towards an Abstract Mathematical Theory of Floating-Point Arithmetic
entry:
@InProceedings{Matula:1969:TAM,
  author =       "David W. Matula",
  title =        "Towards an Abstract Mathematical Theory of
                 Floating-Point Arithmetic",
  crossref =     "AFIPS:1969:ACPa",
  pages =        "765--772",
  year =         "1969",
  bibdate =      "Fri Oct 19 23:01:32 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Posnov:1969:FPR
author: N. N. Posnov and M. K. Buza and V. K. Kravcov
title: The floating point in a residue class number system. (Russian)
journal: Vestnik Beloruss. Gos. Univ. Ser. I
volume: 3
pages: 21--27
year: 1969
MRclass: 10A10
MRnumber: 45 3303e
bibdate: Fri Dec 8 08:24:14 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:14 ???
language: Russian
acknowledgement: ack-nhfb
reviewer: J. B. Roberts
rawauthor: N. N. Posnov and M. K. Buza and V. K. Kravcov
rawtitle: The floating point in a residue class number system. ({Russian})
entry:
@Article{Posnov:1969:FPR,
  author =       "N. N. Posnov and M. K. Buza and V. K. Kravcov",
  title =        "The floating point in a residue class number system.
                 ({Russian})",
  journal =      "Vestnik Beloruss. Gos. Univ. Ser. I",
  volume =       "3",
  pages =        "21--27",
  year =         "1969",
  MRclass =      "10A10",
  MRnumber =     "45 3303e",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
  reviewer =     "J. B. Roberts",
}


bibtype: book
filename: fparith.bib
label: Rice:1969:AFV
author: John R. Rice
title: The Approximation of Functions
volume: 2
publisher: pub-AW
address: pub-AW:adr
pages: various
year: 1969
LCCN: QA221 .R5 V.1-2
bibdate: Fri Dec 08 13:02:54 1995
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 13:02:54 ???
acknowledgement: ack-nj
rawauthor: John R. Rice
rawtitle: The Approximation of Functions
entry:
@Book{Rice:1969:AFV,
  author =       "John R. Rice",
  title =        "The Approximation of Functions",
  volume =       "2",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "various",
  year =         "1969",
  LCCN =         "QA221 .R5 V.1-2",
  bibdate =      "Fri Dec 08 13:02:54 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}


bibtype: techreport
filename: fparith.bib
label: Rigby:1969:DFP
author: G. W. Rigby
title: To draw a floating point number on the graph plotter(PRP 2)
type: Group Research report
institution: British Steel Corporation
address: London, UK
pages: various
year: 1969
bibdate: Thu May 09 08:32:48 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.09 08:32:48 ???
acknowledgement: ack-nhfb
rawauthor: G. W. Rigby
rawtitle: To draw a floating point number on the graph plotter({PRP 2})
entry:
@TechReport{Rigby:1969:DFP,
  author =       "G. W. Rigby",
  title =        "To draw a floating point number on the graph
                 plotter({PRP 2})",
  type =         "Group Research report",
  institution =  "British Steel Corporation",
  address =      "London, UK",
  year =         "1969",
  bibdate =      "Thu May 09 08:32:48 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Rosen:1969:ECH
author: Saul Rosen
title: Electronic Computers: a Historical Survey
journal: j-COMP-SURV
volume: 1
number: 1
pages: 7--36
month: mar
monthnumber: 3
year: 1969
CODEN: CMSVAN
DOI: https://doi.org/10.1145/356540.356543
ISSN: 0010-4892 OR 00104892
ISSNL: 0360-0300 OR 03600300
bibdate: Mon Sep 19 18:18:44 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.19 18:18:44 ???
fjournal: ACM Computing Surveys
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J204
rawauthor: Saul Rosen
rawtitle: Electronic Computers: a Historical Survey
abstract:
The first large scale electronic computers were built in connection with university projects sponsored by government military and research organizations. Many established companies, as well as new companies, entered the computer field during the first generation, 1947-1959, in which the vacuum tube was almost universally used as the active component in the implementation of computer logic. The second generation was characterized by the transistorized computers that began to appear in 1959. Some of the computers built then and since are considered super computers; they attempt to go to the limit of current technology in terms of size, speed, and logical complexity. From 1965 onward, most new computers belong to a third generation, which features integrated circuit technology and multiprocessor multiprogramming systems.

keywords:
computer history; electronic computers; magnetic drum computers; super computers; time-sharing; transistorized computers; university computer projects; vacuum tube computers

rawabstract:
The first large scale electronic computers were built in connection with university projects sponsored by government military and research organizations. Many established companies, as well as new companies, entered the computer field during the first generation, 1947-1959, in which the vacuum tube was almost universally used as the active component in the implementation of computer logic. The second generation was characterized by the transistorized computers that began to appear in 1959. Some of the computers built then and since are considered super computers; they attempt to go to the limit of current technology in terms of size, speed, and logical complexity. From 1965 onward, most new computers belong to a third generation, which features integrated circuit technology and multiprocessor multiprogramming systems.

entry:
@Article{Rosen:1969:ECH,
  author =       "Saul Rosen",
  title =        "Electronic Computers: a Historical Survey",
  journal =      j-COMP-SURV,
  volume =       "1",
  number =       "1",
  pages =        "7--36",
  month =        mar,
  year =         "1969",
  CODEN =        "CMSVAN",
  DOI =          "https://doi.org/10.1145/356540.356543",
  ISSN =         "0010-4892",
  ISSN-L =       "0360-0300",
  bibdate =      "Mon Sep 19 18:18:44 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The first large scale electronic computers were built
                 in connection with university projects sponsored by
                 government military and research organizations. Many
                 established companies, as well as new companies,
                 entered the computer field during the first generation,
                 1947-1959, in which the vacuum tube was almost
                 universally used as the active component in the
                 implementation of computer logic. The second generation
                 was characterized by the transistorized computers that
                 began to appear in 1959. Some of the computers built
                 then and since are considered super computers; they
                 attempt to go to the limit of current technology in
                 terms of size, speed, and logical complexity. From 1965
                 onward, most new computers belong to a third
                 generation, which features integrated circuit
                 technology and multiprocessor multiprogramming
                 systems.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
  keywords =     "computer history; electronic computers; magnetic drum
                 computers; super computers; time-sharing;
                 transistorized computers; university computer projects;
                 vacuum tube computers",
}


bibtype: article
filename: fparith.bib
label: S:1969:BRQ
author: D. S.
journal: j-MATH-COMPUT
volume: 23
number: 107
pages: 679--679
month: jul
monthnumber: 7
year: 1969
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Mar 20 13:34:21 2007
bibtimestamp: 2007.03.20 13:34:21 ???
URL: http://links.jstor.org/sici?sici=0025-5718%28196907%2923%3A107%3C679%3ASROI2T%3E2.0.CO%3B2-C
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
ajournal: Math. Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: D. S.
title:
Book Review: em Square Roots of Integers $2$ to $ 15 $ in Various Bases $2$ to $ 10 $: $ 88062 $ Binary Digits or Equivalent by W. A. Beyer, N. Metropolis, and J. R. Neergaard

rawtitle:
Book Review: {{\em Square Roots of Integers $2$ to $ 15 $ in Various Bases $2$ to $ 10 $: $ 88062 $ Binary Digits or Equivalent} by W. A. Beyer, N. Metropolis, and J. R. Neergaard}

entry:
@Article{S:1969:BRQ,
  author =       "D. S.",
  title =        "Book Review: {{\em Square Roots of Integers $2$ to $
                 15 $ in Various Bases $2$ to $ 10 $: $ 88062 $ Binary
                 Digits or Equivalent} by W. A. Beyer, N. Metropolis,
                 and J. R. Neergaard}",
  journal =      j-MATH-COMPUT,
  volume =       "23",
  number =       "107",
  pages =        "679--679",
  month =        jul,
  year =         "1969",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Mar 20 13:34:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://links.jstor.org/sici?sici=0025-5718%28196907%2923%3A107%3C679%3ASROI2T%3E2.0.CO%3B2-C",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


