# bibtab

bibtype: article
filename: fparith.bib
label: Bemer:1958:MMS
author: Robert W. Bemer
title: A Machine Method for Square-Root Computation
journal: j-CACM
volume: 1
number: 1
pages: 6--7
month: jan
monthnumber: 1
year: 1958
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Sep 15 18:35:46 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 18:35:46 ???
fjournal: Communications of the ACM
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Robert W. Bemer
rawtitle: A Machine Method for Square-Root Computation
entry:
@Article{Bemer:1958:MMS,
  author =       "Robert W. Bemer",
  title =        "A Machine Method for Square-Root Computation",
  journal =      j-CACM,
  volume =       "1",
  number =       "1",
  pages =        "6--7",
  month =        jan,
  year =         "1958",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 15 18:35:46 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: Bemer:1958:SMC
author: R. W. Bemer
title: A Subroutine Method for Calculating Logarithms
journal: j-CACM
volume: 1
number: 5
pages: 5--7
month: may
monthnumber: 5
year: 1958
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Sep 1 10:16:09 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 10:16:09 ???
fjournal: Communications of the ACM
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/cacm
rawauthor: R. W. Bemer
rawtitle: A Subroutine Method for Calculating Logarithms
entry:
@Article{Bemer:1958:SMC,
  author =       "R. W. Bemer",
  title =        "A Subroutine Method for Calculating Logarithms",
  journal =      j-CACM,
  volume =       "1",
  number =       "5",
  pages =        "5--7",
  month =        may,
  year =         "1958",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:16:09 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: Couleur:1958:BBD
author: J. F. Couleur
title: BIDEC --- a Binary-to-Decimal or Decimal-to-Binary Converter
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-7
pages: 313--316
year: 1958
CODEN: IRELAO
ISSN: 0367-9950 OR 03679950
bibdate: Fri Nov 28 16:28:12 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 16:28:12 ???
fjournal: IRE Transactions on Electronic Computers
keywords: decimal floating-point arithmetic
acknowledgement: ack-mfc
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: J. F. Couleur
rawtitle: {BIDEC} --- a Binary-to-Decimal or Decimal-to-Binary Converter
entry:
@Article{Couleur:1958:BBD,
  author =       "J. F. Couleur",
  title =        "{BIDEC} --- a Binary-to-Decimal or Decimal-to-Binary
                 Converter",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-7",
  pages =        "313--316",
  year =         "1958",
  CODEN =        "IRELAO",
  ISSN =         "0367-9950",
  bibdate =      "Fri Nov 28 16:28:12 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Delury:1958:CAN
author: Daniel B. Delury
title: Computation with Approximate Numbers
journal: j-MATH-TEACH
volume: 51
pages: 521--530
month: nov
monthnumber: 11
year: 1958
ISSN: 0025-5769 (print), 2330-0582 (electronic) OR 00255769 (print), 23300582 (electronic)
bibdate: Fri Nov 28 11:47:47 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 11:47:47 ???
fjournal: The Mathematics Teacher
acknowledgement: ack-nhfb
rawauthor: Daniel B. Delury
rawtitle: Computation with Approximate Numbers
entry:
@Article{Delury:1958:CAN,
  author =       "Daniel B. Delury",
  title =        "Computation with Approximate Numbers",
  journal =      j-MATH-TEACH,
  volume =       "51",
  pages =        "521--530",
  month =        nov,
  year =         "1958",
  ISSN =         "0025-5769 (print), 2330-0582 (electronic)",
  bibdate =      "Fri Nov 28 11:47:47 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematics Teacher",
}


bibtype: article
filename: fparith.bib
label: Ershov:1958:PAO
author: Andrei P. Ershov
title: On Programming of Arithmetic Operations
journal: j-CACM
volume: 1
number: 8
pages: 3--6
month: aug
monthnumber: 8
year: 1958
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Wed Jul 14 15:48:21 MDT 2004
bibtimestamp: 2004.07.14 15:48:21 MDT
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Andrei P. Ershov
rawtitle: On Programming of Arithmetic Operations
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Ershov58; http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Ershov:1958:PAO,
  author =       "Andrei P. Ershov",
  title =        "On Programming of Arithmetic Operations",
  journal =      j-CACM,
  volume =       "1",
  number =       "8",
  pages =        "3--6",
  month =        aug,
  year =         "1958",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Jul 14 15:48:21 MDT 2004",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Ershov58;
                 http://portal.acm.org/;
                 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",
  oldlabel =     "Ershov58",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Ershov58",
}


bibtype: article
filename: fparith.bib
label: Gower:1958:NIM
author: J. C. Gower
title: A Note on an Iterative Method for Root Extraction
journal: j-COMP-J
volume: 1
pages: 142--143
year: 1958
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Thu Sep 15 18:36:55 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 18:36:55 ???
fjournal: The Computer Journal
acknowledgement: ack-nj
journalURL: http://comjnl.oxfordjournals.org/
rawauthor: J. C. Gower
rawtitle: A Note on an Iterative Method for Root Extraction
entry:
@Article{Gower:1958:NIM,
  author =       "J. C. Gower",
  title =        "A Note on an Iterative Method for Root Extraction",
  journal =      j-COMP-J,
  volume =       "1",
  pages =        "142--143",
  year =         "1958",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Thu Sep 15 18:36:55 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: Hammer:1958:PST
author: Franz Hammer
journal: Buromarkt
volume: 20
pages: 1023--1025
year: 1958
ISSN: 0007-3148 OR 00073148
ISSNL: 0007-3148 OR 00073148
bibdate: Sat Jul 27 11:05:26 2013
bibtimestamp: 2013.07.27 11:05:26 ???
language: German
acknowledgement: ack-nhfb
rawauthor: Franz Hammer
title:
Nicht Pascal sondern der Tubinger Professor Wilhelm Schickard erfand die Rechenmaschine!. (German) [Not Pascal, but the Tubingen professor William Schickard, invented the calculator!]

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

rawtitle:
{Nicht Pascal sondern der T{\"u}binger Professor Wilhelm Schickard erfand die Rechenmaschine!}. ({German}) [{Not Pascal}, but the {T{\"u}bingen} professor {William Schickard}, invented the calculator!]

entry:
@Article{Hammer:1958:PST,
  author =       "Franz Hammer",
  title =        "{Nicht Pascal sondern der T{\"u}binger Professor
                 Wilhelm Schickard erfand die Rechenmaschine!}.
                 ({German}) [{Not Pascal}, but the {T{\"u}bingen}
                 professor {William Schickard}, invented the
                 calculator!]",
  journal =      "{B{\"u}romarkt}",
  volume =       "20",
  number =       "??",
  pages =        "1023--1025",
  month =        "????",
  year =         "1958",
  ISSN =         "0007-3148",
  ISSN-L =       "0007-3148",
  bibdate =      "Sat Jul 27 11:05:26 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scicontext.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}


bibtype: article
filename: fparith.bib
label: Kogbetliantz:1958:CANa
author: E. G. Kogbetliantz
title: Computation of Arctan $N$ for $ - infty < N < + infty $ Using an Electronic Computer
journal: j-IBM-JRD
volume: 2
number: 1
pages: 43--53
month: jan
monthnumber: 1
year: 1958
CODEN: IBMJAE
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
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: IBM Journal of Research and Development
acknowledgement: ack-nj
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
rawauthor: E. G. Kogbetliantz
rawtitle: Computation of Arctan {$N$} for $ - \infty < {N} < + \infty $ Using an Electronic Computer
entry:
@Article{Kogbetliantz:1958:CANa,
  author =       "E. G. Kogbetliantz",
  title =        "Computation of Arctan {$N$} for $ - \infty < {N} < +
                 \infty $ Using an Electronic Computer",
  journal =      j-IBM-JRD,
  volume =       "2",
  number =       "1",
  pages =        "43--53",
  month =        jan,
  year =         "1958",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  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 =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}


bibtype: article
filename: fparith.bib
label: Kogbetliantz:1958:CANb
author: E. G. Kogbetliantz
title: Computation of Arcsin $N$ for $ 0 < N < 1 $ Using an Electronic Computer
journal: j-IBM-JRD
volume: 2
number: 3
pages: 218--222
month: jul
monthnumber: 7
year: 1958
CODEN: IBMJAE
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
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: IBM Journal of Research and Development
acknowledgement: ack-nj
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
rawauthor: E. G. Kogbetliantz
rawtitle: Computation of Arcsin {$N$} for $ 0 < {N} < 1 $ Using an Electronic Computer
entry:
@Article{Kogbetliantz:1958:CANb,
  author =       "E. G. Kogbetliantz",
  title =        "Computation of Arcsin {$N$} for $ 0 < {N} < 1 $ Using
                 an Electronic Computer",
  journal =      j-IBM-JRD,
  volume =       "2",
  number =       "3",
  pages =        "218--222",
  month =        jul,
  year =         "1958",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  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 =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}


bibtype: article
filename: fparith.bib
label: Metropolis:1958:SDC
author: N. Metropolis and R. L. Ashenhurst
title: Significant Digit Computer Arithmetic
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-7
number: 4
pages: 265--267
month: dec
monthnumber: 12
year: 1958
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1958.5222657
ISSN: 0367-9950 OR 03679950
bibdate: Wed Feb 14 19:23:38 2007
bibtimestamp: 2007.02.14 19:23:38 ???
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222657
fjournal: IRE Transactions on Electronic Computers
keywords: MANIAC III
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: N. Metropolis and R. L. Ashenhurst
rawtitle: Significant Digit Computer Arithmetic
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib

abstract:
The usual floating point arithmetic makes error analysis difficult. This paper describes an alternative system which offers a means of analyzing floating point calculations more effectively and which also possesses certain advantages from an equipment standpoint.

rawabstract:
The usual floating point arithmetic makes error analysis difficult. This paper describes an alternative system which offers a means of analyzing floating point calculations more effectively and which also possesses certain advantages from an equipment standpoint.

entry:
@Article{Metropolis:1958:SDC,
  author =       "N. Metropolis and R. L. Ashenhurst",
  title =        "Significant Digit Computer Arithmetic",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-7",
  number =       "4",
  pages =        "265--267",
  month =        dec,
  year =         "1958",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1958.5222657",
  ISSN =         "0367-9950",
  bibdate =      "Wed Feb 14 19:23:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222657",
  abstract =     "The usual floating point arithmetic makes error
                 analysis difficult. This paper describes an alternative
                 system which offers a means of analyzing floating point
                 calculations more effectively and which also possesses
                 certain advantages from an equipment standpoint.",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
  keywords =     "MANIAC III",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Robertson:1958:NCDa
author: J. E. Robertson
title: A new class of digital division methods
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-7
number: 3
pages: 88--92
month: sep
monthnumber: 9
year: 1958
CODEN: IRELAO
ISSN: 0367-9950 OR 03679950
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: IRE Transactions on Electronic Computers
acknowledgement: ack-sfo
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: J. E. Robertson
rawtitle: A new class of digital division methods
entry:
@Article{Robertson:1958:NCDa,
  author =       "J. E. Robertson",
  title =        "A new class of digital division methods",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-7",
  number =       "3",
  pages =        "88--92",
  month =        sep,
  year =         "1958",
  CODEN =        "IRELAO",
  ISSN =         "0367-9950",
  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,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Robertson:1958:NCDb
author: James E. Robertson
title: A New Class of Digital Division Methods
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-7
number: 3
pages: 218--222
month: sep
monthnumber: 9
year: 1958
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1958.5222579
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 15:56:43 MDT 2011
bibtimestamp: 2011.07.14 15:56:43 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222579
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: James E. Robertson
rawtitle: A New Class of Digital Division Methods
entry:
@Article{Robertson:1958:NCDb,
  author =       "James E. Robertson",
  title =        "A New Class of Digital Division Methods",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-7",
  number =       "3",
  pages =        "218--222",
  month =        sep,
  year =         "1958",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1958.5222579",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 15:56:43 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=5222579",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Schmid:1958:TFQ
author: Hermann Schmid
title: A Transistorized Four-Quadrant Time-Division Multiplier with an Accuracy of 0.1 Per Cent
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-7
number: 1
pages: 41--47
month: mar
monthnumber: 3
year: 1958
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1958.5222094
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 15:56:43 MDT 2011
bibtimestamp: 2011.07.14 15:56:43 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222094
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: Hermann Schmid
rawtitle: A Transistorized Four-Quadrant Time-Division Multiplier with an Accuracy of 0.1 Per Cent
entry:
@Article{Schmid:1958:TFQ,
  author =       "Hermann Schmid",
  title =        "A Transistorized Four-Quadrant Time-Division
                 Multiplier with an Accuracy of 0.1 Per Cent",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-7",
  number =       "1",
  pages =        "41--47",
  month =        mar,
  year =         "1958",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1958.5222094",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 15:56:43 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=5222094",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Sisson:1958:IDR
author: Roger L. Sisson
title: An Improved Decimal Redundancy Check
journal: j-CACM
volume: 1
number: 5
pages: 10--12
month: may
monthnumber: 5
year: 1958
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 07:22:12 MST 2001
bibtimestamp: 2001.01.22 07:22:12 MST
fjournal: Communications of the ACM
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Roger L. Sisson
rawtitle: An Improved Decimal Redundancy Check
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Sisson58; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
As more emphasis is placed on improving the accuracy of data fed into automatic computing systems, more emphasis will be placed on redundancy checking of predictable fields within the input. Two systems (at least) of checking a field of decimal digits have been proposed. In both of these it is assumed that the field to be checked is all numeric and that the redundancy must be of only one digit.

rawabstract:
As more emphasis is placed on improving the accuracy of data fed into automatic computing systems, more emphasis will be placed on redundancy checking of predictable fields within the input. Two systems (at least) of checking a field of decimal digits have been proposed. In both of these it is assumed that the field to be checked is all numeric and that the redundancy must be of only one digit.

entry:
@Article{Sisson:1958:IDR,
  author =       "Roger L. Sisson",
  title =        "An Improved Decimal Redundancy Check",
  journal =      j-CACM,
  volume =       "1",
  number =       "5",
  pages =        "10--12",
  month =        may,
  year =         "1958",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 07:22:12 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Sisson58;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "As more emphasis is placed on improving the accuracy
                 of data fed into automatic computing systems, more
                 emphasis will be placed on redundancy checking of
                 predictable fields within the input. Two systems (at
                 least) of checking a field of decimal digits have been
                 proposed. In both of these it is assumed that the field
                 to be checked is all numeric and that the redundancy
                 must be of only one digit.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "decimal floating-point arithmetic",
  oldlabel =     "Sisson58",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sisson58",
}


bibtype: article
filename: fparith.bib
label: Tocher:1958:TMD
author: K. D. Tocher
title: Techniques of Multiplication and Division for Automatic Binary Computers
journal: j-QUART-J-MECH-APPLIED-MATH
volume: 11
number: 3
pages: 364--384
year: 1958
CODEN: QJMMAV
ISSN: 0033-5614 (print), 1464-3855 (electronic) OR 00335614 (print), 14643855 (electronic)
ISSNL: 0033-5614 OR 00335614
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: Quarterly Journal of Mechanics and Applied Mathematics
acknowledgement: ack-sfo
journalURL: http://qjmam.oxfordjournals.org/content/by/year
rawauthor: K. D. Tocher
rawtitle: Techniques of Multiplication and Division for Automatic Binary Computers
entry:
@Article{Tocher:1958:TMD,
  author =       "K. D. Tocher",
  title =        "Techniques of Multiplication and Division for
                 Automatic Binary Computers",
  journal =      j-QUART-J-MECH-APPLIED-MATH,
  volume =       "11",
  number =       "3",
  pages =        "364--384",
  month =        "????",
  year =         "1958",
  CODEN =        "QJMMAV",
  ISSN =         "0033-5614 (print), 1464-3855 (electronic)",
  ISSN-L =       "0033-5614",
  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,
  fjournal =     "Quarterly Journal of Mechanics and Applied
                 Mathematics",
  journal-URL =  "http://qjmam.oxfordjournals.org/content/by/year",
}


bibtype: article
filename: fparith.bib
label: Wadey:1958:TSR
author: W. G. Wadey
title: Two Square-Root Approximations
journal: j-CACM
volume: 1
number: 11
pages: 13--14
month: nov
monthnumber: 11
year: 1958
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Wed Jul 14 15:48:22 MDT 2004
bibtimestamp: 2004.07.14 15:48:22 MDT
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: W. G. Wadey
rawtitle: Two Square-Root Approximations
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Wadey58; http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Wadey:1958:TSR,
  author =       "W. G. Wadey",
  title =        "Two Square-Root Approximations",
  journal =      j-CACM,
  volume =       "1",
  number =       "11",
  pages =        "13--14",
  month =        nov,
  year =         "1958",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Jul 14 15:48:22 MDT 2004",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Wadey58;
                 http://portal.acm.org/;
                 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",
  oldlabel =     "Wadey58",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Wadey58",
}


bibtype: article
filename: fparith.bib
label: Ashenhurst:1959:UFP
author: Robert L. Ashenhurst and Nicholas Metropolis
title: Unnormalized Floating Point Arithmetic
journal: j-J-ACM
volume: 6
number: 3
pages: 415--428
month: jul
monthnumber: 7
year: 1959
CODEN: JACOAH
DOI: https://doi.org/10.1145/320986.320996
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
MRclass: 68.00
MRnumber: MR0105833 (21 \#4568)
MRreviewer: H. H. Goldstine
bibdate: Fri Dec 08 13:06:24 1995
bibtimestamp: 1995.12.08 13:06:24 ???
fjournal: Journal of the Association for Computing Machinery
ZMnumber: 0121.12102
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
rawauthor: Robert L. Ashenhurst and Nicholas Metropolis
rawtitle: Unnormalized Floating Point Arithmetic
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jacm.bib

abstract:
Algorithms for floating point computer arithmetic are described, in which fractional parts are not subject to the usual normalization convention. These algorithms give results in a form which furnishes some indication of their degree of precision. An analysis of one-stage error propagation is developed for each operation; a suggested statistical model for long-run error propagation is also set forth.

rawabstract:
Algorithms for floating point computer arithmetic are described, in which fractional parts are not subject to the usual normalization convention. These algorithms give results in a form which furnishes some indication of their degree of precision. An analysis of one-stage error propagation is developed for each operation; a suggested statistical model for long-run error propagation is also set forth.

entry:
@Article{Ashenhurst:1959:UFP,
  author =       "Robert L. Ashenhurst and Nicholas Metropolis",
  title =        "Unnormalized Floating Point Arithmetic",
  journal =      j-J-ACM,
  volume =       "6",
  number =       "3",
  pages =        "415--428",
  month =        jul,
  year =         "1959",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/320986.320996",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "68.00",
  MRnumber =     "MR0105833 (21 \#4568)",
  MRreviewer =   "H. H. Goldstine",
  bibdate =      "Fri Dec 08 13:06:24 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jacm.bib",
  ZMnumber =     "0121.12102",
  abstract =     "Algorithms for floating point computer arithmetic are
                 described, in which fractional parts are not subject to
                 the usual normalization convention. These algorithms
                 give results in a form which furnishes some indication
                 of their degree of precision. An analysis of one-stage
                 error propagation is developed for each operation; a
                 suggested statistical model for long-run error
                 propagation is also set forth.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}


bibtype: article
filename: fparith.bib
label: Buchholz:1959:FFC
author: Wilfried Buchholz
title: Fingers or Fists? (The Choice of Decimal or Binary Representation)
journal: j-CACM
volume: 2
number: 12
pages: 3--11
year: 1959
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 06:28:45 MST 2001
bibtimestamp: 2001.01.22 06:28:45 MST
fjournal: Communications of the ACM
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Wilfried Buchholz
rawtitle: Fingers or Fists? (The Choice of Decimal or Binary Representation)
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Buchholz59; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Buchholz:1959:FFC,
  author =       "Wilfried Buchholz",
  title =        "Fingers or Fists? (The Choice of Decimal or Binary
                 Representation)",
  journal =      j-CACM,
  volume =       "2",
  number =       "12",
  pages =        "3--11",
  month =        "????",
  year =         "1959",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:28:45 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Buchholz59;
                 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 =     "decimal floating-point arithmetic",
  oldlabel =     "Buchholz59",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Buchholz59",
  xxnote =       "Check author first name: article has W. Buchholz; I
                 think it should be Werner, not Wilfried.",
}


bibtype: article
filename: fparith.bib
label: Carr:1959:EAF
author: John W. Carr III
title: Error Analysis in Floating Point Arithmetic
journal: j-CACM
volume: 2
number: 5
pages: 10--15
month: may
monthnumber: 5
year: 1959
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Wed Jul 14 15:48:23 MDT 2004
bibtimestamp: 2004.07.14 15:48:23 MDT
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: John W. {Carr III}
rawtitle: Error Analysis in Floating Point Arithmetic
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Carr59a; http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Carr:1959:EAF,
  author =       "John W. {Carr III}",
  title =        "Error Analysis in Floating Point Arithmetic",
  journal =      j-CACM,
  volume =       "2",
  number =       "5",
  pages =        "10--15",
  month =        may,
  year =         "1959",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Jul 14 15:48:23 MDT 2004",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Carr59a;
                 http://portal.acm.org/;
                 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",
  oldlabel =     "Carr59a",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Carr59a",
}


bibtype: incollection
filename: fparith.bib
label: Carr:1959:PC
author: John W. Carr III
editor: Eugene M. Grabbe and Simon Ramo and Dean E. Wooldridge
booktitle: Handbook of Automation, Computation, and Control
title: Programming and Coding
publisher: pub-WILEY
address: pub-WILEY:adr
pages: 10--15
year: 1959
LCCN: TJ213 .G72
bibdate: Fri Aug 20 08:41:16 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.08.20 08:41:16 ???
note: Chapter 2.
subject: automation; mathematics; computers; operations research
acknowledgement: ack-nhfb
rawauthor: John W. {Carr III}
rawbooktitle: Handbook of Automation, Computation, and Control
raweditor: Eugene M. Grabbe and Simon Ramo and Dean E. Wooldridge
rawnote: Chapter 2.
rawtitle: Programming and Coding
remark:
1958--1961: Volume 1. Control fundamentals. Volume 2. Computers and data processing. Volume 3. Systems and components. Cited in cite Sterbenz:1974:FPC.

entry:
@InCollection{Carr:1959:PC,
  author =       "John W. {Carr III}",
  editor =       "Eugene M. Grabbe and Simon Ramo and Dean E.
                 Wooldridge",
  booktitle =    "Handbook of Automation, Computation, and Control",
  title =        "Programming and Coding",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  bookpages =    "????",
  year =         "1959",
  LCCN =         "TJ213 .G72",
  bibdate =      "Fri Aug 20 08:41:16 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Chapter 2.",
  acknowledgement = ack-nhfb,
  remark =       "1958--1961: Volume 1. Control fundamentals. Volume 2.
                 Computers and data processing. Volume 3. Systems and
                 components. Cited in \cite{Sterbenz:1974:FPC}.",
  subject =      "automation; mathematics; computers; operations
                 research",
}


bibtype: article
filename: fparith.bib
label: Daggett:1959:DBC
author: D. H. Daggett
title: Decimal-Binary Conversions in CORDIC
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-8
number: 5
pages: 335--339
month: sep
monthnumber: 9
year: 1959
CODEN: IRELAO
ISSN: 0367-9950 OR 03679950
bibdate: Thu Sep 08 08:14:00 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.08 08:14:00 ???
fjournal: IRE Transactions on Electronic Computers
keywords: decimal floating-point arithmetic
acknowledgement: ack-nj
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: D. H. Daggett
rawtitle: Decimal-Binary Conversions in {CORDIC}
entry:
@Article{Daggett:1959:DBC,
  author =       "D. H. Daggett",
  title =        "Decimal-Binary Conversions in {CORDIC}",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-8",
  number =       "5",
  pages =        "335--339",
  month =        sep,
  year =         "1959",
  CODEN =        "IRELAO",
  ISSN =         "0367-9950",
  bibdate =      "Thu Sep 08 08:14:00 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Ercoli:1959:BAD
author: Paolo Ercoli and Roberto Vacca
title: Binary Arithmetic for Discretely Variable Word Length in a Serial Computer
journal: j-CACM
volume: 2
number: 4
pages: 13--15
month: apr
monthnumber: 4
year: 1959
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Wed Jul 14 15:48:22 MDT 2004
bibtimestamp: 2004.07.14 15:48:22 MDT
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Paolo Ercoli and Roberto Vacca
rawtitle: Binary Arithmetic for Discretely Variable Word Length in a Serial Computer
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#ErcoliV59; http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Ercoli:1959:BAD,
  author =       "Paolo Ercoli and Roberto Vacca",
  title =        "Binary Arithmetic for Discretely Variable Word Length
                 in a Serial Computer",
  journal =      j-CACM,
  volume =       "2",
  number =       "4",
  pages =        "13--15",
  month =        apr,
  year =         "1959",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Jul 14 15:48:22 MDT 2004",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#ErcoliV59;
                 http://portal.acm.org/;
                 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",
  oldlabel =     "ErcoliV59",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/ErcoliV59",
}


bibtype: article
filename: fparith.bib
label: Forsythe:1959:RNR
author: George E. Forsythe
title: Reprint of a Note on Rounding-Off Errors
journal: j-SIAM-REVIEW
volume: 1
number: 1
pages: 66--67
month: jan
monthnumber: 1
year: 1959
CODEN: SIREAD
DOI: https://doi.org/10.1137/1001011
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
MRclass: 65.00
MRnumber: MR0099119 (20 \#5563)
bibdate: Thu Mar 27 09:04:24 MDT 2014
bibtimestamp: 2014.03.27 09:04:24 MDT
fjournal: SIAM Review
keywords: numerical analysis; random rounding-off procedure
ZMnumber: 0168.14002
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
onlinedate: January 1959
rawauthor: George E. Forsythe
rawtitle: Reprint of a Note on Rounding-Off Errors
bibsource:
http://epubs.siam.org/toc/siread/1/1; https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.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/siamreview.bib

remark:
From a footnote on the cover page: ``This note was written in June 1950 at the National Bureau of Standards, Los Angeles, and a few copies were distributed in multilithed form by that organization as an appendix to a reproduction of a well-known article by Rademacher [1]. The note was abstracted in Math. Reviews, Vol. 12 (1951), p. 208. Because he receives frequent requests for copies of the note, which are unavailable, the author has asked the editors to reprint it in essentially its original form.''

entry:
@Article{Forsythe:1959:RNR,
  author =       "George E. Forsythe",
  title =        "Reprint of a Note on Rounding-Off Errors",
  journal =      j-SIAM-REVIEW,
  volume =       "1",
  number =       "1",
  pages =        "66--67",
  month =        jan,
  year =         "1959",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1001011",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "65.00",
  MRnumber =     "MR0099119 (20 \#5563)",
  bibdate =      "Thu Mar 27 09:04:24 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/1/1;
                 https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.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/siamreview.bib",
  ZMnumber =     "0168.14002",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  keywords =     "numerical analysis; random rounding-off procedure",
  onlinedate =   "January 1959",
  received =     "7 February 1958",
  remark =       "From a footnote on the cover page: ``This note was
                 written in June 1950 at the National Bureau of
                 Standards, Los Angeles, and a few copies were
                 distributed in multilithed form by that organization as
                 an appendix to a reproduction of a well-known article
                 by Rademacher [1]. The note was abstracted in Math.
                 Reviews, Vol. 12 (1951), p. 208. Because he receives
                 frequent requests for copies of the note, which are
                 unavailable, the author has asked the editors to
                 reprint it in essentially its original form.''",
}


bibtype: article
filename: fparith.bib
label: Garner:1959:RMS
author: Harvey L. Garner
title: A Ring Model for the Study of Multiplication for Complement Codes
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-8
number: 1
pages: 25--30
month: mar
monthnumber: 3
year: 1959
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1959.5222757
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 15:56:44 MDT 2011
bibtimestamp: 2011.07.14 15:56:44 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222757
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: Harvey L. Garner
rawtitle: A Ring Model for the Study of Multiplication for Complement Codes
entry:
@Article{Garner:1959:RMS,
  author =       "Harvey L. Garner",
  title =        "A Ring Model for the Study of Multiplication for
                 Complement Codes",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-8",
  number =       "1",
  pages =        "25--30",
  month =        mar,
  year =         "1959",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1959.5222757",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 15:56:44 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=5222757",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Garner:1959:RNS
author: Harvey L. Garner
title: The Residue Number System
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-8
number: 2
pages: 140--147
month: jun
monthnumber: 6
year: 1959
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1959.5219515
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 15:56:44 MDT 2011
bibtimestamp: 2011.07.14 15:56:44 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219515
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: Harvey L. Garner
rawtitle: The Residue Number System
entry:
@Article{Garner:1959:RNS,
  author =       "Harvey L. Garner",
  title =        "The Residue Number System",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-8",
  number =       "2",
  pages =        "140--147",
  month =        jun,
  year =         "1959",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1959.5219515",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 15:56:44 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=5219515",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: inproceedings
filename: fparith.bib
label: Gray:1959:NFP
author: H. L. Gray and C. Harrison
booktitle: Proceedings of the Eastern Joint Computer Conference, Boston, MA, December 1--3, 1959
title: Normalized floating-point arithmetic with an index of significance
volume: 16
publisher: pub-AFIPS
address: pub-AFIPS:adr
pages: 244--248
year: 1959
LCCN: TK7885.A1 J6
bibdate: Tue Oct 09 09:43:31 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.10.09 09:43:31 ???
acknowledgement: ack-nhfb
rawauthor: H. L. Gray and C. Harrison
rawbooktitle: Proceedings of the Eastern Joint Computer Conference, Boston, {MA}, December 1--3, 1959
rawtitle: Normalized floating-point arithmetic with an index of significance
entry:
@InProceedings{Gray:1959:NFP,
  author =       "H. L. Gray and C. Harrison",
  booktitle =    "Proceedings of the Eastern Joint Computer Conference,
                 Boston, {MA}, December 1--3, 1959",
  title =        "Normalized floating-point arithmetic with an index of
                 significance",
  volume =       "16",
  publisher =    pub-AFIPS,
  address =      pub-AFIPS:adr,
  pages =        "244--248",
  year =         "1959",
  LCCN =         "TK7885.A1 J6",
  bibdate =      "Tue Oct 09 09:43:31 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: fparith.bib
label: Henrici:1959:TES
author: Peter Henrici
booktitle: Proceedings of the International Conference on Information Processing, UNESCO
pages: 36--43
year: 1959
bibdate: Fri Aug 20 09:11:32 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.08.20 09:11:32 ???
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
rawauthor: Peter Henrici
rawbooktitle: Proceedings of the International Conference on Information Processing, {UNESCO}
title:
Theoretical and Experimental Studies on the Accumulation of Error in the Numerical Solution of Initial Value Problems for Systems of Ordinary Differential Equations

rawtitle:
Theoretical and Experimental Studies on the Accumulation of Error in the Numerical Solution of Initial Value Problems for Systems of Ordinary Differential Equations

entry:
@InProceedings{Henrici:1959:TES,
  author =       "Peter Henrici",
  editor =       "????",
  booktitle =    "Proceedings of the International Conference on
                 Information Processing, {UNESCO}",
  title =        "Theoretical and Experimental Studies on the
                 Accumulation of Error in the Numerical Solution of
                 Initial Value Problems for Systems of Ordinary
                 Differential Equations",
  publisher =    "????",
  address =      "????",
  pages =        "36--43",
  year =         "1959",
  LCCN =         "????",
  bibdate =      "Fri Aug 20 09:11:32 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: Kogbetliantz:1959:CSC
author: E. G. Kogbetliantz
title: Computation of $ sin N $, $ cos N $, and $M$ th Root of $N$ Using an Electronic Computer
journal: j-IBM-JRD
volume: 3
number: 2
pages: 147--152
month: apr
monthnumber: 4
year: 1959
CODEN: IBMJAE
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
bibdate: Thu Sep 1 10:15:56 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 10:15:56 ???
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nj
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
rawauthor: E. G. Kogbetliantz
rawtitle: Computation of $ \sin {N} $, $ \cos {N} $, and {$M$ th} Root of {$N$} Using an Electronic Computer
entry:
@Article{Kogbetliantz:1959:CSC,
  author =       "E. G. Kogbetliantz",
  title =        "Computation of $ \sin {N} $, $ \cos {N} $, and {$M$
                 th} Root of {$N$} Using an Electronic Computer",
  journal =      j-IBM-JRD,
  volume =       "3",
  number =       "2",
  pages =        "147--152",
  month =        apr,
  year =         "1959",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Thu Sep 1 10:15:56 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 Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}


bibtype: article
filename: fparith.bib
label: Lucal:1959:AOD
author: Harold M. Lucal
title: Arithmetic Operations for Digital Computers Using a Modified Reflected Binary Code
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-8
number: 4
pages: 449--458
month: dec
monthnumber: 12
year: 1959
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1959.5222057
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 15:56:45 MDT 2011
bibtimestamp: 2011.07.14 15:56:45 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222057
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: Harold M. Lucal
rawtitle: Arithmetic Operations for Digital Computers Using a Modified Reflected Binary Code
entry:
@Article{Lucal:1959:AOD,
  author =       "Harold M. Lucal",
  title =        "Arithmetic Operations for Digital Computers Using a
                 Modified Reflected Binary Code",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-8",
  number =       "4",
  pages =        "449--458",
  month =        dec,
  year =         "1959",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1959.5222057",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 15:56:45 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=5222057",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Muller:1959:CMG
author: Mervin E. Muller
title: A Comparison of Methods for Generating Normal Deviates on Digital Computers
journal: j-J-ACM
volume: 6
number: 3
pages: 376--383
month: jul
monthnumber: 7
year: 1959
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Tue Nov 1 09:33:26 1994
bibtimestamp: 1994.11.01 09:33:26 ???
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: Mervin E. Muller
rawtitle: A Comparison of Methods for Generating Normal Deviates on Digital Computers
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Muller:1959:CMG,
  author =       "Mervin E. Muller",
  title =        "A Comparison of Methods for Generating Normal Deviates
                 on Digital Computers",
  journal =      j-J-ACM,
  volume =       "6",
  number =       "3",
  pages =        "376--383",
  month =        jul,
  year =         "1959",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Tue Nov 1 09:33:26 1994",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  descriptors =  "RVG",
  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: Pawlak:1959:EDC
author: Z. Pawlak
title: An electronic digital computer based on the `$ - 2 $' system
journal: Bull. Acad. Pol. Sci., Ser. Sci. Tech.
volume: 7
pages: 713--722
year: 1959
bibdate: Thu Nov 06 05:58:31 2014
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2014.11.06 05:58:31 ???
keywords: negative base
acknowledgement: ack-nhfb
rawauthor: Z. Pawlak
rawtitle: An electronic digital computer based on the `$ - 2 $' system
entry:
@Article{Pawlak:1959:EDC,
  author =       "Z. Pawlak",
  title =        "An electronic digital computer based on the `$ - 2 $'
                 system",
  journal =      "Bull. Acad. Pol. Sci., Ser. Sci. Tech.",
  volume =       "7",
  number =       "??",
  pages =        "713--722",
  month =        "????",
  year =         "1959",
  bibdate =      "Thu Nov 06 05:58:31 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "negative base",
}


bibtype: article
filename: fparith.bib
label: Pfeiffer:1959:FQM
author: Paul E. Pfeiffer
title: A Four-Quadrant Multiplier Using Triangular Waves, Diodes, Resistors, and Operational Amplifiers
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-8
number: 2
pages: 222--227
month: jun
monthnumber: 6
year: 1959
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1959.5219526
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 15:56:45 MDT 2011
bibtimestamp: 2011.07.14 15:56:45 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219526
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: Paul E. Pfeiffer
rawtitle: A Four-Quadrant Multiplier Using Triangular Waves, Diodes, Resistors, and Operational Amplifiers
entry:
@Article{Pfeiffer:1959:FQM,
  author =       "Paul E. Pfeiffer",
  title =        "A Four-Quadrant Multiplier Using Triangular Waves,
                 Diodes, Resistors, and Operational Amplifiers",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-8",
  number =       "2",
  pages =        "222--227",
  month =        jun,
  year =         "1959",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1959.5219526",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 15:56:45 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=5219526",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Rothstein:1959:RBN
author: Jerome Rothstein
title: Residues of Binary Numbers Modulo Three
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-8
number: 2
pages: 229--229
month: jun
monthnumber: 6
year: 1959
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1959.5219529
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 15:56:45 MDT 2011
bibtimestamp: 2011.07.14 15:56:45 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219529
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: Jerome Rothstein
rawtitle: Residues of Binary Numbers Modulo Three
entry:
@Article{Rothstein:1959:RBN,
  author =       "Jerome Rothstein",
  title =        "Residues of Binary Numbers Modulo Three",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-8",
  number =       "2",
  pages =        "229--229",
  month =        jun,
  year =         "1959",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1959.5219529",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 15:56:45 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=5219529",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Sarafyan:1959:NMC
author: Diran Sarafyan
title: A New Method of Computation of Square Roots Without Using Division
journal: j-CACM
volume: 2
number: 11
pages: 23--24
month: nov
monthnumber: 11
year: 1959
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Wed Jul 14 15:48:24 MDT 2004
bibtimestamp: 2004.07.14 15:48:24 MDT
note: See comments cite Traub:1960:CNM.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Diran Sarafyan
rawnote: See comments \cite{Traub:1960:CNM}.
rawtitle: A New Method of Computation of Square Roots Without Using Division
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sarafyan59; http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Sarafyan:1959:NMC,
  author =       "Diran Sarafyan",
  title =        "A New Method of Computation of Square Roots Without
                 Using Division",
  journal =      j-CACM,
  volume =       "2",
  number =       "11",
  pages =        "23--24",
  month =        nov,
  year =         "1959",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Jul 14 15:48:24 MDT 2004",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sarafyan59;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See comments \cite{Traub:1960:CNM}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Sarafyan59",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sarafyan59",
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bibtype: article
filename: fparith.bib
label: Sheridan:1959:ATC
author: Peter B. Sheridan
title: The Arithmetic Translator Compiler of the IBM FORTRAN Automatic Coding System
journal: j-CACM
volume: 2
number: 2
pages: 9--21
month: feb
monthnumber: 2
year: 1959
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Wed Jul 14 15:48:22 MDT 2004
bibtimestamp: 2004.07.14 15:48:22 MDT
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Peter B. Sheridan
rawtitle: The Arithmetic Translator Compiler of the {IBM FORTRAN Automatic Coding System}
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sheridan59; http://ei.cs.vt.edu/~cs4304/bibliography.html; http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Sheridan:1959:ATC,
  author =       "Peter B. Sheridan",
  title =        "The Arithmetic Translator Compiler of the {IBM FORTRAN
                 Automatic Coding System}",
  journal =      j-CACM,
  volume =       "2",
  number =       "2",
  pages =        "9--21",
  month =        feb,
  year =         "1959",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Jul 14 15:48:22 MDT 2004",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sheridan59;
                 http://ei.cs.vt.edu/~cs4304/bibliography.html;
                 http://portal.acm.org/;
                 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",
  oldlabel =     "Sheridan59",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sheridan59",
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bibtype: article
filename: fparith.bib
label: Strachey:1959:TSR
author: C. Strachey
title: On taking the square root of a complex number
journal: j-COMP-J
volume: 2
number: 2
pages: 89--89
month: jul
monthnumber: 7
year: 1959
CODEN: CMPJA6
DOI: https://doi.org/10.1093/comjnl/2.2.89
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Fri Sep 29 08:55:11 MDT 2000
bibtimestamp: 2000.09.29 08:55:11 MDT
fjournal: The Computer Journal
acknowledgement: ack-nhfb
journalURL: http://comjnl.oxfordjournals.org/
rawauthor: C. Strachey
rawtitle: On taking the square root of a complex number
bibsource:
http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/020089.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/tiff/89.tif

entry:
@Article{Strachey:1959:TSR,
  author =       "C. Strachey",
  title =        "On taking the square root of a complex number",
  journal =      j-COMP-J,
  volume =       "2",
  number =       "2",
  pages =        "89--89",
  month =        jul,
  year =         "1959",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/2.2.89",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:55:11 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/020089.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/tiff/89.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}


bibtype: article
filename: fparith.bib
label: Taranto:1959:BCF
author: Donald Taranto
title: Binary Conversion, with Fixed Decimal Precision, of a Decimal Fraction
journal: j-CACM
volume: 2
number: 7
pages: 27--27
month: jul
monthnumber: 7
year: 1959
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Jan 22 07:25:37 MST 2001
bibtimestamp: 2001.01.22 07:25:37 MST
fjournal: Communications of the ACM
keywords: decimal floating-point arithmetic
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Donald Taranto
rawtitle: Binary Conversion, with Fixed Decimal Precision, of a Decimal Fraction
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Taranto59; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
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  author =       "Donald Taranto",
  title =        "Binary Conversion, with Fixed Decimal Precision, of a
                 Decimal Fraction",
  journal =      j-CACM,
  volume =       "2",
  number =       "7",
  pages =        "27--27",
  month =        jul,
  year =         "1959",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 07:25:37 MST 2001",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Taranto59;
                 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 =     "decimal floating-point arithmetic",
  oldlabel =     "Taranto59",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Taranto59",
}


bibtype: article
filename: fparith.bib
label: Volder:1959:CTC
author: J. E. Volder
title: The CORDIC Trigonometric Computing Technique
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-8
number: 5
pages: 330--334
month: sep
monthnumber: 9
year: 1959
CODEN: IRELAO
ISSN: 0367-9950 OR 03679950
bibdate: Thu Sep 1 10:15:31 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 10:15:31 ???
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nj
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: J. E. Volder
rawtitle: The {CORDIC} Trigonometric Computing Technique
entry:
@Article{Volder:1959:CTC,
  author =       "J. E. Volder",
  title =        "The {CORDIC} Trigonometric Computing Technique",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-8",
  number =       "5",
  pages =        "330--334",
  month =        sep,
  year =         "1959",
  CODEN =        "IRELAO",
  ISSN =         "0367-9950",
  bibdate =      "Thu Sep 1 10:15:31 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 =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Wensley:1959:CNA
author: J. H. Wensley
title: A Class of Non-Analytical Iterative Processes
journal: j-COMP-J
volume: 1
number: 4
pages: 163--167
month: jan
monthnumber: 1
year: 1959
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Fri Sep 29 08:55:07 MDT 2000
bibtimestamp: 2000.09.29 08:55:07 MDT
fjournal: The Computer Journal
acknowledgement: ack-nhfb
journalURL: http://comjnl.oxfordjournals.org/
rawauthor: J. H. Wensley
rawtitle: A Class of Non-Analytical Iterative Processes
bibsource:
Compiler/semantics.bib; http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/010163.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/163.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/164.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/165.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/166.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/167.tif

entry:
@Article{Wensley:1959:CNA,
  author =       "J. H. Wensley",
  title =        "A Class of Non-Analytical Iterative Processes",
  journal =      j-COMP-J,
  volume =       "1",
  number =       "4",
  pages =        "163--167",
  month =        jan,
  year =         "1959",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:55:07 MDT 2000",
  bibsource =    "Compiler/semantics.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/010163.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/163.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/164.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/165.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/166.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/167.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}


bibtype: article
filename: fparith.bib
label: Wilkinson:1959:EZIa
author: J. H. Wilkinson
title: The evaluation of the zeros of ill-conditioned polynomials. I
journal: j-NUM-MATH
volume: 1
pages: 150--166
month: dec
monthnumber: 12
year: 1959
CODEN: NUMMA7
DOI: https://doi.org/10.1007/BF01386381
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 65.00
MRnumber: MR0109435 (22 \#321)
MRreviewer: H. Rutishauser
bibdate: Mon Oct 18 01:28:20 MDT 1999
bibtimestamp: 1999.10.18 01:28:20 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: J. H. Wilkinson
rawtitle: The evaluation of the zeros of ill-conditioned polynomials. {I}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Wilkinson:1959:EZIa,
  author =       "J. H. Wilkinson",
  title =        "The evaluation of the zeros of ill-conditioned
                 polynomials. {I}",
  journal =      j-NUM-MATH,
  volume =       "1",
  pages =        "150--166",
  month =        dec,
  year =         "1959",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01386381",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.00",
  MRnumber =     "MR0109435 (22 \#321)",
  MRreviewer =   "H. Rutishauser",
  bibdate =      "Mon Oct 18 01:28:20 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.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: Wilkinson:1959:EZIb
author: J. H. Wilkinson
title: The evaluation of the zeros of ill-conditioned polynomials. II
journal: j-NUM-MATH
volume: 1
pages: 167--180
month: dec
monthnumber: 12
year: 1959
CODEN: NUMMA7
DOI: https://doi.org/10.1007/BF01386382
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 65.00
MRnumber: MR0109435 (22 \#321)
MRreviewer: H. Rutishauser
bibdate: Mon Oct 18 01:28:20 MDT 1999
bibtimestamp: 1999.10.18 01:28:20 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: J. H. Wilkinson
rawtitle: The evaluation of the zeros of ill-conditioned polynomials. {II}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Wilkinson:1959:EZIb,
  author =       "J. H. Wilkinson",
  title =        "The evaluation of the zeros of ill-conditioned
                 polynomials. {II}",
  journal =      j-NUM-MATH,
  volume =       "1",
  pages =        "167--180",
  month =        dec,
  year =         "1959",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01386382",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.00",
  MRnumber =     "MR0109435 (22 \#321)",
  MRreviewer =   "H. Rutishauser",
  bibdate =      "Mon Oct 18 01:28:20 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.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: mastersthesis
filename: fparith.bib
label: Young:1959:SSM
author: John Mackay Young
title: A study of some methods of numerical integration using floating point arithmetic
type: Thesis (M.S. in Mathematics)
school: Texas A.&M. College
address: College Station, TX, USA
pages: 50
year: 1959
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: John Mackay Young
rawtitle: A study of some methods of numerical integration using floating point arithmetic
entry:
@MastersThesis{Young:1959:SSM,
  author =       "John Mackay Young",
  title =        "A study of some methods of numerical integration using
                 floating point arithmetic",
  type =         "Thesis ({M.S. in Mathematics})",
  school =       "Texas A.\&M. College",
  address =      "College Station, TX, USA",
  pages =        "50",
  year =         "1959",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Bockstaele:1960:NFA
author: P. Bockstaele
title: Notes on the First Arithmetics Printed in Dutch and English
journal: j-ISIS
volume: 51
number: 3
pages: 315--321
month: sep
monthnumber: 9
year: 1960
CODEN: ISISA4
ISSN: 0021-1753 (print), 1545-6994 (electronic) OR 00211753 (print), 15456994 (electronic)
ISSNL: 0021-1753 OR 00211753
bibdate: Tue Jul 30 21:28:03 MDT 2013
bibtimestamp: 2013.07.30 21:28:03 MDT
URL: http://www.jstor.org/stable/226510
fjournal: Isis
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journal/isis
rawauthor: P. Bockstaele
rawtitle: Notes on the First Arithmetics Printed in {Dutch} and {English}
bibsource:
http://www.jstor.org/action/showPublication?journalCode=isis; http://www.jstor.org/stable/i302265; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/isis1960.bib

entry:
@Article{Bockstaele:1960:NFA,
  author =       "P. Bockstaele",
  title =        "Notes on the First Arithmetics Printed in {Dutch} and
                 {English}",
  journal =      j-ISIS,
  volume =       "51",
  number =       "3",
  pages =        "315--321",
  month =        sep,
  year =         "1960",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:28:03 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i302265;
                 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/226510",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}


bibtype: article
filename: fparith.bib
label: Brown:1960:EDC
author: David T. Brown
title: Error Detecting and Correcting Binary Codes for Arithmetic Operations
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-9
number: 3
pages: 333--337
month: sep
monthnumber: 9
year: 1960
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1960.5219855
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 15:34:12 MDT 2011
bibtimestamp: 2011.07.14 15:34:12 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219855
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: David T. Brown
rawtitle: Error Detecting and Correcting Binary Codes for Arithmetic Operations
entry:
@Article{Brown:1960:EDC,
  author =       "David T. Brown",
  title =        "Error Detecting and Correcting Binary Codes for
                 Arithmetic Operations",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-9",
  number =       "3",
  pages =        "333--337",
  month =        sep,
  year =         "1960",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1960.5219855",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 15:34:12 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=5219855",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Cohen:1960:EAF
author: Eckford Cohen
title: The elementary arithmetical functions
journal: j-SCRIPTA-MATH
volume: 25
pages: 221--228
year: 1960
ISSN: 0036-9713 OR 00369713
ISSNL: 0036-9713 OR 00369713
MRclass: 10.00
MRnumber: 118694
MRreviewer: H. Bergstr{\"{o}}m
bibdate: Thu Oct 26 11:15:25 2023
bibtimestamp: 2023.10.26 11:15:25 ???
ZMnumber: 0116.27101
acknowledgement: ack-nhfb
ajournal: Scripta Math.
rawauthor: Eckford Cohen
rawtitle: The elementary arithmetical functions
entry:
@Article{Cohen:1960:EAF,
  author =       "Eckford Cohen",
  title =        "The elementary arithmetical functions",
  journal =      j-SCRIPTA-MATH,
  volume =       "25",
  number =       "??",
  pages =        "221--228",
  month =        "????",
  year =         "1960",
  ISSN =         "0036-9713",
  ISSN-L =       "0036-9713",
  MRclass =      "10.00",
  MRnumber =     "118694",
  MRreviewer =   "H. Bergstr{\"{o}}m",
  bibdate =      "Thu Oct 26 11:15:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
  ZMnumber =     "0116.27101",
  acknowledgement = ack-nhfb,
  ajournal =     "Scripta Math.",
  fjournal =     "Scripta Mathematica: A Quarterly Journal Devoted to
                 the Philosophy, History, and Expository Treatment of
                 Mathematics",
  xxpages =      "221--227",
  ZBmath =       "3189455",
}


bibtype: article
filename: fparith.bib
label: Croy:1960:IAD
author: John E. Croy
title: Improved Arrangement of a Decimal Multiplier
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-9
number: 2
pages: 263--263
month: jun
monthnumber: 6
year: 1960
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1960.5219830
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 15:34:11 MDT 2011
bibtimestamp: 2011.07.14 15:34:11 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219830
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: John E. Croy
rawtitle: Improved Arrangement of a Decimal Multiplier
entry:
@Article{Croy:1960:IAD,
  author =       "John E. Croy",
  title =        "Improved Arrangement of a Decimal Multiplier",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-9",
  number =       "2",
  pages =        "263--263",
  month =        jun,
  year =         "1960",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1960.5219830",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 15:34:11 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
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  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219830",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Ercoli:1960:LEE
author: Paolo Ercoli
title: Letter to the Editor: Errors Due to Overflow in Arithmetic Operations
journal: j-CACM
volume: 3
number: 12
pages: A9--A9
month: dec
monthnumber: 12
year: 1960
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:29 MST 2005
bibtimestamp: 2005.11.25 18:19:29 MST
note: See cite Ercoli:1957:EDO.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Paolo Ercoli
rawnote: See \cite{Ercoli:1957:EDO}.
rawtitle: Letter to the {Editor}: {Errors} Due to Overflow in Arithmetic Operations
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

entry:
@Article{Ercoli:1960:LEE,
  author =       "Paolo Ercoli",
  title =        "Letter to the {Editor}: {Errors} Due to Overflow in
                 Arithmetic Operations",
  journal =      j-CACM,
  volume =       "3",
  number =       "12",
  pages =        "A9--A9",
  month =        dec,
  year =         "1960",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:29 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",
  note =         "See \cite{Ercoli:1957:EDO}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: article
filename: fparith.bib
label: Gurzi:1960:HSM
author: Fred Gurzi
title: A High-Speed Multiplication Process for Digital Computers
journal: j-CACM
volume: 3
number: 4
pages: 241--245
month: apr
monthnumber: 4
year: 1960
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:26 MST 2005
bibtimestamp: 2005.11.25 18:19:26 MST
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Fred Gurzi
rawtitle: A High-Speed Multiplication Process for Digital Computers
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Gurzi60; 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{Gurzi:1960:HSM,
  author =       "Fred Gurzi",
  title =        "A High-Speed Multiplication Process for Digital
                 Computers",
  journal =      j-CACM,
  volume =       "3",
  number =       "4",
  pages =        "241--245",
  month =        apr,
  year =         "1960",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:26 MST 2005",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Gurzi60;
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  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Gurzi60",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Gurzi60",
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bibtype: techreport
filename: fparith.bib
label: Jensen:1960:CIF
author: B. A. Jensen
type: Group report
number: 30G-0009
institution: Massachusetts Institute of Technology, Lincoln Laboratory
address: Lexington, MA, USA
pages: 7
year: 1960
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: Trigonometrical functions --- Computer programs.
remark: Cover title. ``Millstone Hill Radar Station.'' ``1 November 1960.'' Air Force Contract
acknowledgement: ack-nhfb
rawauthor: B. A. Jensen
title:
Coding instructions for floating point trigonometric, inverse trigonometric hyperbolic and exponential functions

rawtitle:
Coding instructions for floating point trigonometric, inverse trigonometric hyperbolic and exponential functions

entry:
@TechReport{Jensen:1960:CIF,
  author =       "B. A. Jensen",
  title =        "Coding instructions for floating point trigonometric,
                 inverse trigonometric hyperbolic and exponential
                 functions",
  type =         "Group report",
  number =       "30G-0009",
  institution =  "Massachusetts Institute of Technology, Lincoln
                 Laboratory",
  address =      "Lexington, MA, USA",
  pages =        "7",
  year =         "1960",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Trigonometrical functions --- Computer programs.",
  remark =       "Cover title. ``Millstone Hill Radar Station.'' ``1
                 November 1960.'' Air Force Contract",
}


bibtype: article
filename: fparith.bib
label: Kanner:1960:NUA
author: Herbert Kanner
title: A Note on the Use of the Abacus in Number Conversion
journal: j-CACM
volume: 3
number: 3
pages: 167--167
month: mar
monthnumber: 3
year: 1960
CODEN: CACMA2
DOI: https://doi.org/10.1145/367149.367166
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:26 MST 2005
bibtimestamp: 2005.11.25 18:19:26 MST
fjournal: Communications of the ACM
keywords: number base conversion
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Herbert Kanner
rawtitle: A Note on the Use of the Abacus in Number Conversion
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Kanner60; 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:
Conversion of integers in both directions between the base ten and any desired base can be accomplished with remarkable simplicity by use of the abacus. In fact, the conversion procedures are far more cumbersome on the electric desk calculator, for reasons which will be apparent.

rawabstract:
Conversion of integers in both directions between the base ten and any desired base can be accomplished with remarkable simplicity by use of the abacus. In fact, the conversion procedures are far more cumbersome on the electric desk calculator, for reasons which will be apparent.

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  author =       "Herbert Kanner",
  title =        "A Note on the Use of the Abacus in Number Conversion",
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  volume =       "3",
  number =       "3",
  pages =        "167--167",
  month =        mar,
  year =         "1960",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/367149.367166",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:26 MST 2005",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Kanner60;
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                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Conversion of integers in both directions between the
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                 apparent.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
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  oldlabel =     "Kanner60",
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bibtype: article
filename: fparith.bib
label: Knuth:1960:INS
author: Donald E. Knuth
title: An Imaginary Number System
journal: j-CACM
volume: 3
number: 4
pages: 245--247
month: apr
monthnumber: 4
year: 1960
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65.99
MRnumber: 23\#B554
MRreviewer: C. B. Haselgrove
bibdate: Fri Nov 25 18:19:26 MST 2005
bibtimestamp: 2005.11.25 18:19:26 MST
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Donald E. Knuth
rawtitle: An Imaginary Number System
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Knuth60; 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; MathSciNet database

note:
Errata, sl Communications of the ACM bf 4 (August 1961), 355 cite Knuth:1961:EIN. See cite Nadler:1961:DSR for extension to division and square root.

abstract:
For centuries the decimal number system reigned supreme, except, perhaps, among the Mayan Indians, until the advent of digital computers brought the binary and octal systems into the limelight. This paper introduces another number system which may prove useful for manipulating complex numbers on machines.

rawabstract:
For centuries the decimal number system reigned supreme, except, perhaps, among the Mayan Indians, until the advent of digital computers brought the binary and octal systems into the limelight. This paper introduces another number system which may prove useful for manipulating complex numbers on machines.

rawnote:
Errata, {\sl Commun\-i\-ca\-tions of the ACM\/ \bf 4} (August 1961), 355 \cite{Knuth:1961:EIN}. See \cite{Nadler:1961:DSR} for extension to division and square root.

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  author =       "Donald E. Knuth",
  title =        "An Imaginary Number System",
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  number =       "4",
  pages =        "245--247",
  month =        apr,
  year =         "1960",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.99",
  MRnumber =     "23\#B554",
  MRreviewer =   "C. B. Haselgrove",
  bibdate =      "Fri Nov 25 18:19:26 MST 2005",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Knuth60;
                 http://www.acm.org/pubs/contents/journals/cacm/;
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                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  note =         "Errata, {\sl Commun\-i\-ca\-tions of the ACM\/ \bf 4}
                 (August 1961), 355 \cite{Knuth:1961:EIN}. See
                 \cite{Nadler:1961:DSR} for extension to division and
                 square root.",
  abstract =     "For centuries the decimal number system reigned
                 supreme, except, perhaps, among the Mayan Indians,
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                 for manipulating complex numbers on machines.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Knuth60",
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bibtype: article
filename: fparith.bib
label: Lowan:1960:PREa
author: Arnold N. Lowan
title: On the Propagation of Round-Off Errors in the Numerical Integration of the Heat Equation
journal: j-MATH-COMPUT
volume: 14
number: 70
pages: 139--146
month: apr
monthnumber: 4
year: 1960
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: Arnold N. Lowan
rawtitle: On the Propagation of Round-Off Errors in the Numerical Integration of the Heat Equation
entry:
@Article{Lowan:1960:PREa,
  author =       "Arnold N. Lowan",
  title =        "On the Propagation of Round-Off Errors in the
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  journal =      j-MATH-COMPUT,
  volume =       "14",
  number =       "70",
  pages =        "139--146",
  month =        apr,
  year =         "1960",
  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: Lowan:1960:PREb
author: Arnold N. Lowan
title: On the Propagation of Round-Off Errors in the Numerical Treatment of the Wave Equation
journal: j-MATH-COMPUT
volume: 14
number: 71
pages: 223--228
month: jul
monthnumber: 7
year: 1960
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: Arnold N. Lowan
rawtitle: On the Propagation of Round-Off Errors in the Numerical Treatment of the Wave Equation
entry:
@Article{Lowan:1960:PREb,
  author =       "Arnold N. Lowan",
  title =        "On the Propagation of Round-Off Errors in the
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  journal =      j-MATH-COMPUT,
  volume =       "14",
  number =       "71",
  pages =        "223--228",
  month =        jul,
  year =         "1960",
  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: Pawlak:1960:ODC
author: Z. Pawlak
title: The organization of a digital computer based on the `$ - 2 $' system
journal: Bull. Acad. Pol. Sci., Ser. Tech. Sci.
volume: 8
pages: 253--258
year: 1960
bibdate: Thu Nov 06 06:00:08 2014
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2014.11.06 06:00:08 ???
keywords: negative base
acknowledgement: ack-nhfb
rawauthor: Z. Pawlak
rawtitle: The organization of a digital computer based on the `$ - 2 $' system
entry:
@Article{Pawlak:1960:ODC,
  author =       "Z. Pawlak",
  title =        "The organization of a digital computer based on the `$
                 - 2 $' system",
  journal =      "Bull. Acad. Pol. Sci., Ser. Tech. Sci.",
  volume =       "8",
  number =       "??",
  pages =        "253--258",
  month =        "????",
  year =         "1960",
  bibdate =      "Thu Nov 06 06:00:08 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "negative base",
}


bibtype: article
filename: fparith.bib
label: Perlin:1960:HPC
author: I. E. Perlin and J. R. Garrett
journal: j-MATH-COMPUT
volume: 14
number: 71
pages: 270--274
month: jul
monthnumber: 7
year: 1960
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-nj
ajournal: Math. Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: I. E. Perlin and J. R. Garrett
title:
High Precision Calculation of $ operatorname Arcsin x $, $ operatorname Arccos x $, and $ operatorname Arctan x $ (in Technical Notes and Short Papers)

bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database

rawtitle:
High Precision Calculation of $ \operatorname {Arcsin} x $, $ \operatorname {Arccos} x $, and $ \operatorname {Arctan} x $ (in {Technical Notes and Short Papers})

entry:
@Article{Perlin:1960:HPC,
  author =       "I. E. Perlin and J. R. Garrett",
  title =        "High Precision Calculation of $ \operatorname {Arcsin}
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                 {Arctan} x $ (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "14",
  number =       "71",
  pages =        "270--274",
  month =        jul,
  year =         "1960",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: fparith.bib
label: Perry:1960:CBF
author: C. Perry
title: Conversion between floating point representations
journal: j-CACM
volume: 3
pages: 270--274
year: 1960
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 352.68.00
MRnumber: 22\#8714
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: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: C. Perry
rawtitle: Conversion between floating point representations
entry:
@Article{Perry:1960:CBF,
  author =       "C. Perry",
  title =        "Conversion between floating point representations",
  journal =      j-CACM,
  volume =       "3",
  year =         "1960",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "352.68.00",
  MRnumber =     "22\#8714",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "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: Pope:1960:MPA
author: D. A. Pope and M. L. Stein
title: Multiple Precision Arithmetic
journal: j-CACM
volume: 3
number: 12
pages: 652--654
month: dec
monthnumber: 12
year: 1960
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: D. A. Pope and M. L. Stein
rawtitle: Multiple Precision Arithmetic
entry:
@Article{Pope:1960:MPA,
  author =       "D. A. Pope and M. L. Stein",
  title =        "Multiple Precision Arithmetic",
  journal =      j-CACM,
  volume =       "3",
  number =       "12",
  pages =        "652--654",
  month =        dec,
  year =         "1960",
  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;
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  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: incollection
filename: fparith.bib
label: Reitwiesner:1960:BA
author: G. W. Reitwiesner
title: Binary arithmetic
crossref: Alt:1960:AC
pages: 231--308
year: 1960
bibdate: Sat May 18 14:36:56 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.18 14:36:56 ???
acknowledgement: ack-nhfb
rawauthor: G. W. Reitwiesner
rawtitle: Binary arithmetic
entry:
@InCollection{Reitwiesner:1960:BA,
  author =       "G. W. Reitwiesner",
  title =        "Binary arithmetic",
  crossref =     "Alt:1960:AC",
  pages =        "231--308",
  year =         "1960",
  bibdate =      "Sat May 18 14:36:56 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Sarafyan:1960:DCS
author: Diran Sarafyan
title: Divisionless computation of square roots through continued squaring
journal: j-CACM
volume: 3
number: 5
pages: 319--321
month: may
monthnumber: 5
year: 1960
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65.00
MRnumber: 22\#8639
bibdate: Fri Nov 25 18:19:26 MST 2005
bibtimestamp: 2005.11.25 18:19:26 MST
fjournal: Communications of the ACM
keywords: $sqrt (x)$; elementary functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Diran Sarafyan
rawtitle: Divisionless computation of square roots through continued squaring
bibsource:
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entry:
@Article{Sarafyan:1960:DCS,
  author =       "Diran Sarafyan",
  title =        "Divisionless computation of square roots through
                 continued squaring",
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  number =       "5",
  pages =        "319--321",
  month =        may,
  year =         "1960",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.00",
  MRnumber =     "22\#8639",
  bibdate =      "Fri Nov 25 18:19:26 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
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  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions",
  ZMreviewer =   "M. Lotkin",
}


bibtype: article
filename: fparith.bib
label: Silver:1960:LER
author: Roland Silver
title: Letter to the Editor: Rounding in Floating-Point Arithmetic
journal: j-CACM
volume: 3
number: 12
pages: A9--A9
month: dec
monthnumber: 12
year: 1960
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:29 MST 2005
bibtimestamp: 2005.11.25 18:19:29 MST
fjournal: Communications of the ACM
keywords: floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Roland Silver
rawtitle: Letter to the {Editor}: Rounding in Floating-Point Arithmetic
bibsource:
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entry:
@Article{Silver:1960:LER,
  author =       "Roland Silver",
  title =        "Letter to the {Editor}: Rounding in Floating-Point
                 Arithmetic",
  journal =      j-CACM,
  volume =       "3",
  number =       "12",
  pages =        "A9--A9",
  month =        dec,
  year =         "1960",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:29 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
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  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: Sklansky:1960:CSA
author: J. Sklansky
title: Conditional Sum Addition Logic
journal: j-TRANS-IRE
volume: EC-9
number: 2
pages: 226--230
month: jun
monthnumber: 6
year: 1960
bibdate: Fri Nov 09 19:17:08 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 19:17:08 ???
fjournal: Transactions of the IRE
acknowledgement: ack-nhfb
rawauthor: J. Sklansky
rawtitle: Conditional Sum Addition Logic
entry:
@Article{Sklansky:1960:CSA,
  author =       "J. Sklansky",
  title =        "Conditional Sum Addition Logic",
  journal =      j-TRANS-IRE,
  volume =       "EC-9",
  number =       "2",
  pages =        "226--230",
  month =        jun,
  year =         "1960",
  bibdate =      "Fri Nov 09 19:17:08 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Transactions of the IRE",
}


bibtype: article
filename: fparith.bib
label: Traub:1960:CNM
author: J. F. Traub
title: Comments on a recent paper [``A New Method of Computation of Square Roots Without Using Division'']
journal: j-CACM
volume: 3
number: 2
pages: 86--86
month: feb
monthnumber: 2
year: 1960
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:25 MST 2005
bibtimestamp: 2005.11.25 18:19:25 MST
note: See cite Sarafyan:1959:NMC.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: J. F. Traub
rawnote: See \cite{Sarafyan:1959:NMC}.
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Traub60; 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

rawtitle:
Comments on a recent paper [{``A New Method of Computation of Square Roots Without Using Division''}]

entry:
@Article{Traub:1960:CNM,
  author =       "J. F. Traub",
  title =        "Comments on a recent paper [{``A New Method of
                 Computation of Square Roots Without Using
                 Division''}]",
  journal =      j-CACM,
  volume =       "3",
  number =       "2",
  pages =        "86--86",
  month =        feb,
  year =         "1960",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:25 MST 2005",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Traub60;
                 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 \cite{Sarafyan:1959:NMC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Traub60",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Traub60",
}


bibtype: article
filename: fparith.bib
label: Wadey:1960:FA
author: W. G. Wadey
title: Floating-Point Arithmetics
journal: j-J-ACM
volume: 7
number: 2
pages: 129--139
month: apr
monthnumber: 4
year: 1960
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
MRclass: 65.00 (68.00)
MRnumber: 22\#6090
bibdate: Fri Dec 08 14:44:46 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 14:44:46 ???
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
reviewer: C. B. Haselgrove
rawauthor: W. G. Wadey
rawtitle: Floating-Point Arithmetics
abstract:
Three types of floating-point arithmetics with error control are discussed and compared with conventional floating-point arithmetic. General multiplication and division shift criteria are derived (for any base) for Metropolis-style arithmetics. The limitations and most suitable range of application for each arithmetic are discussed.

rawabstract:
Three types of floating-point arithmetics with error control are discussed and compared with conventional floating-point arithmetic. General multiplication and division shift criteria are derived (for any base) for Metropolis-style arithmetics. The limitations and most suitable range of application for each arithmetic are discussed.

entry:
@Article{Wadey:1960:FA,
  author =       "W. G. Wadey",
  title =        "Floating-Point Arithmetics",
  journal =      j-J-ACM,
  volume =       "7",
  number =       "2",
  pages =        "129--139",
  month =        apr,
  year =         "1960",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "65.00 (68.00)",
  MRnumber =     "22\#6090",
  bibdate =      "Fri Dec 08 14:44:46 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Three types of floating-point arithmetics with error
                 control are discussed and compared with conventional
                 floating-point arithmetic. General multiplication and
                 division shift criteria are derived (for any base) for
                 Metropolis-style arithmetics. The limitations and most
                 suitable range of application for each arithmetic are
                 discussed.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
  reviewer =     "C. B. Haselgrove",
  xxmonth =      "none",
  xxnumber =     "none",
}


bibtype: article
filename: fparith.bib
label: Wilkinson:1960:EAF
author: J. H. Wilkinson
title: Error Analysis of Floating-Point Computation
journal: j-NUM-MATH
volume: 2
pages: 319--340
month: dec
monthnumber: 12
year: 1960
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 65.00
MRnumber: MR0116477 (22 \#7264)
MRreviewer: C. B. Haselgrove
bibdate: Fri May 14 17:18:08 2010
bibtimestamp: 2010.05.14 17:18:08 ???
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: J. H. Wilkinson
rawtitle: Error Analysis of Floating-Point Computation
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Wilkinson:1960:EAF,
  author =       "J. H. Wilkinson",
  title =        "Error Analysis of Floating-Point Computation",
  journal =      j-NUM-MATH,
  volume =       "2",
  pages =        "319--340",
  month =        dec,
  year =         "1960",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.00",
  MRnumber =     "MR0116477 (22 \#7264)",
  MRreviewer =   "C. B. Haselgrove",
  bibdate =      "Fri May 14 17:18:08 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.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: Amble:1961:AFP
author: O. Amble and Jan V. Garwick
title: On the Accuracy of Floating Point Computers [BIT bf 1(2), 1961, pp. 87--88]
journal: j-NORDISK-TIDSKR-INFORM-BEHAND
volume: 1
number: 3
pages: 220--222
month: sep
monthnumber: 9
year: 1961
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01933434
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 18:52:07 MST 2006
bibtimestamp: 2006.01.04 18:52:07 MST
note: See cite Garwick:1961:AFP,Garwick:1961:RAF.
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=3&spage=220
keywords: floating-point accuracy; floating-point arithmetic
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: O. Amble and Jan V. Garwick
rawnote: See \cite{Garwick:1961:AFP,Garwick:1961:RAF}.
rawtitle: On the Accuracy of Floating Point Computers {[BIT {\bf 1}(2), 1961, pp. 87--88]}
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=3; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Amble:1961:AFP,
  author =       "O. Amble and Jan V. Garwick",
  title =        "On the Accuracy of Floating Point Computers {[BIT {\bf
                 1}(2), 1961, pp. 87--88]}",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "1",
  number =       "3",
  pages =        "220--222",
  month =        sep,
  year =         "1961",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01933434",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:07 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Garwick:1961:AFP,Garwick:1961:RAF}.",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=3&spage=220",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point accuracy; floating-point arithmetic",
  xxpages =      "220--221??",
}


bibtype: techreport
filename: fparith.bib
label: Anonymous:1961:MCM
author: Anonymous
title: Modern Computing Methods
type: Notes on Applied Science
number: 16
institution: National Physical Laboratory
address: Her Majesty's Stationery Office, London
pages: 220--222
year: 1961
bibdate: Fri Aug 20 10:05:25 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.08.20 10:05:25 ???
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
rawauthor: Anonymous
rawtitle: Modern Computing Methods
entry:
@TechReport{Anonymous:1961:MCM,
  author =       "Anonymous",
  title =        "Modern Computing Methods",
  type =         "Notes on Applied Science",
  number =       "16",
  institution =  "National Physical Laboratory",
  address =      "Her Majesty's Stationery Office, London",
  year =         "1961",
  bibdate =      "Fri Aug 20 10:05:25 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: Avizienis:1961:SDN
author: Algirdas Avizienis
title: Signed-Digit Number Representations for Fast Parallel Arithmetic
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-10
number: 3
pages: 389--400
month: sep
monthnumber: 9
year: 1961
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1961.5219227
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 14:45:04 MDT 2011
bibtimestamp: 2011.07.14 14:45:04 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219227
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: Algirdas Avi{\v{z}}ienis
rawtitle: Signed-Digit Number Representations for Fast Parallel Arithmetic
entry:
@Article{Avizienis:1961:SDN,
  author =       "Algirdas Avi{\v{z}}ienis",
  title =        "Signed-Digit Number Representations for Fast Parallel
                 Arithmetic",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-10",
  number =       "3",
  pages =        "389--400",
  month =        sep,
  year =         "1961",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1961.5219227",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 14:45:04 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=5219227",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Cheney:1961:DCB
author: Philip Warren Cheney
title: A Digital Correlator Based on the Residue Number System
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-10
number: 1
pages: 63--70
month: mar
monthnumber: 3
year: 1961
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1961.5219154
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 14:45:02 MDT 2011
bibtimestamp: 2011.07.14 14:45:02 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219154
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: Philip Warren Cheney
rawtitle: A Digital Correlator Based on the Residue Number System
abstract:
A system design for a digital correlator based on the application of the residue number system for computation is presented. Areas of investigation include sampling, analog-to-residue conversion, logical design of the arithmetic units, residue-to-analog conversion, and modes of operation of the proposed digital correlator. The advantages of speed of computation and simplicity of logic due to the use of a residue number system are shown to result in a significantly faster and simpler system than if a conventional number system were used. The resulting digital correlator is designed for megacycle sampling and computation with a 0.1 per cent system precision.

rawabstract:
A system design for a digital correlator based on the application of the residue number system for computation is presented. Areas of investigation include sampling, analog-to-residue conversion, logical design of the arithmetic units, residue-to-analog conversion, and modes of operation of the proposed digital correlator. The advantages of speed of computation and simplicity of logic due to the use of a residue number system are shown to result in a significantly faster and simpler system than if a conventional number system were used. The resulting digital correlator is designed for megacycle sampling and computation with a 0.1 per cent system precision.

entry:
@Article{Cheney:1961:DCB,
  author =       "Philip Warren Cheney",
  title =        "A Digital Correlator Based on the Residue Number
                 System",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-10",
  number =       "1",
  pages =        "63--70",
  month =        mar,
  year =         "1961",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1961.5219154",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 14:45:02 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=5219154",
  abstract =     "A system design for a digital correlator based on the
                 application of the residue number system for
                 computation is presented. Areas of investigation
                 include sampling, analog-to-residue conversion, logical
                 design of the arithmetic units, residue-to-analog
                 conversion, and modes of operation of the proposed
                 digital correlator. The advantages of speed of
                 computation and simplicity of logic due to the use of a
                 residue number system are shown to result in a
                 significantly faster and simpler system than if a
                 conventional number system were used. The resulting
                 digital correlator is designed for megacycle sampling
                 and computation with a 0.1 per cent system precision.",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Cheney:1961:TNA
author: E. W. Cheney and H. L. Loeb
title: Two new algorithms for rational approximation
journal: j-NUM-MATH
volume: 3
number: 1
pages: 72--75
month: dec
monthnumber: 12
year: 1961
CODEN: NUMMA7
DOI: https://doi.org/10.1007/BF01386002
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Sun Oct 17 19:01:15 MDT 1999
bibtimestamp: 1999.10.17 19:01:15 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: E. W. Cheney and H. L. Loeb
rawtitle: Two new algorithms for rational approximation
bibsource:
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/nummath.bib

entry:
@Article{Cheney:1961:TNA,
  author =       "E. W. Cheney and H. L. Loeb",
  title =        "Two new algorithms for rational approximation",
  journal =      j-NUM-MATH,
  volume =       "3",
  number =       "1",
  pages =        "72--75",
  month =        dec,
  year =         "1961",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01386002",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Oct 17 19:01:15 MDT 1999",
  bibsource =    "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/nummath.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: article
filename: fparith.bib
label: Clarkson:1961:DMI
author: W. K. Clarkson
title: A Divisionless Method of Integer Conversion
journal: j-CACM
volume: 4
number: 7
pages: 315--316
month: jul
monthnumber: 7
year: 1961
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Sep 08 08:14:59 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.08 08:14:59 ???
fjournal: Communications of the ACM
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/cacm
rawauthor: W. K. Clarkson
rawtitle: A Divisionless Method of Integer Conversion
entry:
@Article{Clarkson:1961:DMI,
  author =       "W. K. Clarkson",
  title =        "A Divisionless Method of Integer Conversion",
  journal =      j-CACM,
  volume =       "4",
  number =       "7",
  pages =        "315--316",
  month =        jul,
  year =         "1961",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 08:14:59 1994",
  bibsource =    "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: Cox:1961:NMP
author: Albert G. Cox and H. A. Luther
title: A Note on Multiple Precision Arithmetic
journal: j-CACM
volume: 4
number: 8
pages: 353--353
month: aug
monthnumber: 8
year: 1961
CODEN: CACMA2
DOI: https://doi.org/10.1145/366678.366693
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Sat Dec 03 14:07:44 2005
bibtimestamp: 2005.12.03 14:07:44 ???
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Albert G. Cox and H. A. Luther
rawtitle: A Note on Multiple Precision Arithmetic
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:
Since computers have means to detect overflow on addition or subtraction, this can be used in a multiple precision addition-subtraction subroutine to obviate a sign analysis. Consider all integers in the computer to be expressed ``radix t'', that is, in the form $ a = a_0 + a_1 t + cdots + a_n t^n $ where $ a_i $ are of like sign and have magnitudes less than $t$. $t$ is a positive integer determined by the word length of the computer. Consider the expression $ c = a pm b = (a_0 pm b_0) + (a_1 pm b_1)t + cdots + (a_n pm b_n)t^n$. Here $ a_i pm b_i$ may exceed the storage capacity of one word or may have a sign different from $c$.

rawabstract:
Since computers have means to detect overflow on addition or subtraction, this can be used in a multiple precision addition-subtraction subroutine to obviate a sign analysis. Consider all integers in the computer to be expressed ``radix t'', that is, in the form $ a = a_0 + a_1 t + \cdots + a_n t^n $ where $ a_i $ are of like sign and have magnitudes less than $t$. $t$ is a positive integer determined by the word length of the computer. Consider the expression $ c = a \pm b = (a_0 \pm b_0) + (a_1 \pm b_1)t + \cdots + (a_n \pm b_n)t^n$. Here $ a_i \pm b_i$ may exceed the storage capacity of one word or may have a sign different from $c$.

entry:
@Article{Cox:1961:NMP,
  author =       "Albert G. Cox and H. A. Luther",
  title =        "A Note on Multiple Precision Arithmetic",
  journal =      j-CACM,
  volume =       "4",
  number =       "8",
  pages =        "353--353",
  month =        aug,
  year =         "1961",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/366678.366693",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sat Dec 03 14:07:44 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 =     "Since computers have means to detect overflow on
                 addition or subtraction, this can be used in a multiple
                 precision addition-subtraction subroutine to obviate a
                 sign analysis. Consider all integers in the computer to
                 be expressed ``radix t'', that is, in the form $ a =
                 a_0 + a_1 t + \cdots + a_n t^n $ where $ a_i $ are of
                 like sign and have magnitudes less than $t$. $t$ is a
                 positive integer determined by the word length of the
                 computer. Consider the expression $ c = a \pm b = (a_0
                 \pm b_0) + (a_1 \pm b_1)t + \cdots + (a_n \pm b_n)t^n$.
                 Here $ a_i \pm b_i$ may exceed the storage capacity of
                 one word or may have a sign different from $c$.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: article
filename: fparith.bib
label: Croy:1961:RTM
author: John E. Croy
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-10
number: 4
pages: 777--777
month: dec
monthnumber: 12
year: 1961
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1961.5219286
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 14:45:05 MDT 2011
bibtimestamp: 2011.07.14 14:45:05 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219286
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: John E. Croy
title:
Rapid Technique of Manual or Machine Binary-to-Decimal Integer Conversion Using Decimal Radix Arithmetic

rawtitle:
Rapid Technique of Manual or Machine Binary-to-Decimal Integer Conversion Using Decimal Radix Arithmetic

entry:
@Article{Croy:1961:RTM,
  author =       "John E. Croy",
  title =        "Rapid Technique of Manual or Machine Binary-to-Decimal
                 Integer Conversion Using Decimal Radix Arithmetic",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-10",
  number =       "4",
  pages =        "777--777",
  month =        dec,
  year =         "1961",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1961.5219286",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 14:45:05 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=5219286",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Freiman:1961:SAC
author: C. V. Freiman
title: Statistical analysis of certain binary division algorithms
journal: j-IRE-PROC
volume: 49
number: 1
pages: 91--103
month: jan
monthnumber: 1
year: 1961
bibdate: Mon Sep 16 16:12:21 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.09.16 16:12:21 ???
fjournal: IRE Proceedings
acknowledgement: ack-sfo
rawauthor: C. V. Freiman
rawtitle: Statistical analysis of certain binary division algorithms
entry:
@Article{Freiman:1961:SAC,
  author =       "C. V. Freiman",
  title =        "Statistical analysis of certain binary division
                 algorithms",
  journal =      j-IRE-PROC,
  volume =       "49",
  number =       "1",
  pages =        "91--103",
  month =        jan,
  year =         "1961",
  bibdate =      "Mon Sep 16 16:12:21 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "IRE Proceedings",
  xxnote =       "Check author name: I have found this paper cited both
                 as Freiman and as Frieman?? Hennessy and Patterson
                 \cite{Hennessy:2002:CAQ} have Freiman.",
}


bibtype: techreport
filename: fparith.bib
label: Garner:1961:RNS
title: Residue number systems for computers
type: ASD Technical Report
number: 61-483
institution: Electronic Technology Laboratory, The University of Michigan
address: Ann Arbor, MI, USA
pages: 91--103
month: oct
monthnumber: 10
year: 1961
bibdate: Thu Nov 18 09:27:06 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.11.18 09:27:06 ???
URL: http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txt
acknowledgement: ack-nhfb
rawtitle: Residue number systems for computers
author:
H. L. Garner and R. F. Arnold and B. C. Benson and C. G. Brockus and R. J. Gonzalez and D. P. Rozenberg

abstract:
The purpose of the research performed under this contract was to investigate the feasibility of residue number systems in their applications to digital computers. The problems of such an application are the ones of magnitude determination, sign determination, overflow, scaling, and division. These problems are not independent, but are found to be quite interrelated. A theoretical treatment of residue number systems is given which lays the foundation for a unified study of the complete problem. Treatments of an organizational nature are given which deal with multiplication, division, and scaling. The matter of correlating the theoretical and organizational studies to physical realizations involving networks is treated also. The question of whether the residue number system can be successfully applied to general purpose computers is still an open one. Their application to special purpose machines is considered both feasible and practical.

remark:
This report represents the results of research performed by the group at The University of Michigan under the direction of Professor H. L. Garner. Concurrently, research on the same subject was being conducted at Harvard University under the direction of Professor Howard Aiken, and at the Lockheed Missile System Division under the direction of Dr. Richard Tanaka. There was a considerable exchange of information among the above groups during the course of the research effort. The efforts attained exhibit little overlap, rather they are complementary. A portion of this report was extracted from the doctoral dissertation of D. P. Rozenberg. His work was supported by this contract, and led to the Ph.D..

rawabstract:
The purpose of the research performed under this contract was to investigate the feasibility of residue number systems in their applications to digital computers. The problems of such an application are the ones of magnitude determination, sign determination, overflow, scaling, and division. These problems are not independent, but are found to be quite interrelated. A theoretical treatment of residue number systems is given which lays the foundation for a unified study of the complete problem. Treatments of an organizational nature are given which deal with multiplication, division, and scaling. The matter of correlating the theoretical and organizational studies to physical realizations involving networks is treated also. The question of whether the residue number system can be successfully applied to general purpose computers is still an open one. Their application to special purpose machines is considered both feasible and practical.

rawauthor:
H. L. Garner and R. F. Arnold and B. C. Benson and C. G. Brockus and R. J. Gonzalez and D. P. Rozenberg

entry:
@TechReport{Garner:1961:RNS,
  author =       "H. L. Garner and R. F. Arnold and B. C. Benson and C.
                 G. Brockus and R. J. Gonzalez and D. P. Rozenberg",
  title =        "Residue number systems for computers",
  type =         "{ASD} Technical Report",
  number =       "61-483",
  institution =  "Electronic Technology Laboratory, The University of
                 Michigan",
  address =      "Ann Arbor, MI, USA",
  month =        oct,
  year =         "1961",
  bibdate =      "Thu Nov 18 09:27:06 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txt",
  abstract =     "The purpose of the research performed under this
                 contract was to investigate the feasibility of residue
                 number systems in their applications to digital
                 computers. The problems of such an application are the
                 ones of magnitude determination, sign determination,
                 overflow, scaling, and division. These problems are not
                 independent, but are found to be quite interrelated. A
                 theoretical treatment of residue number systems is
                 given which lays the foundation for a unified study of
                 the complete problem. Treatments of an organizational
                 nature are given which deal with multiplication,
                 division, and scaling. The matter of correlating the
                 theoretical and organizational studies to physical
                 realizations involving networks is treated also. The
                 question of whether the residue number system can be
                 successfully applied to general purpose computers is
                 still an open one. Their application to special purpose
                 machines is considered both feasible and practical.",
  acknowledgement = ack-nhfb,
  remark =       "This report represents the results of research
                 performed by the group at The University of Michigan
                 under the direction of Professor H. L. Garner.
                 Concurrently, research on the same subject was being
                 conducted at Harvard University under the direction of
                 Professor Howard Aiken, and at the Lockheed Missile
                 System Division under the direction of Dr. Richard
                 Tanaka. There was a considerable exchange of
                 information among the above groups during the course of
                 the research effort. The efforts attained exhibit
                 little overlap, rather they are complementary. A
                 portion of this report was extracted from the doctoral
                 dissertation of D. P. Rozenberg. His work was supported
                 by this contract, and led to the Ph.D..",
}


bibtype: article
filename: fparith.bib
label: Garwick:1961:AFP
author: Jan V. Garwick
title: The Accuracy of Floating Point Computers
journal: j-NORDISK-TIDSKR-INFORM-BEHAND
volume: 1
number: 2
pages: 87--88
month: jun
monthnumber: 6
year: 1961
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01939221
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 18:52:07 MST 2006
bibtimestamp: 2006.01.04 18:52:07 MST
note: See also comment and reply cite Amble:1961:AFP,Garwick:1961:RAF.
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=2&spage=87
keywords: floating-point accuracy; floating-point arithmetic
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Jan V. Garwick
rawnote: See also comment and reply \cite{Amble:1961:AFP,Garwick:1961:RAF}.
rawtitle: The Accuracy of Floating Point Computers
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=2; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Garwick:1961:AFP,
  author =       "Jan V. Garwick",
  title =        "The Accuracy of Floating Point Computers",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "1",
  number =       "2",
  pages =        "87--88",
  month =        jun,
  year =         "1961",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01939221",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:07 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also comment and reply
                 \cite{Amble:1961:AFP,Garwick:1961:RAF}.",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=2&spage=87",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point accuracy; floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Garwick:1961:RAF
author: J. V. Garwick
title: Reply to ``On the Accuracy of Floating Point Computers'' [BIT bf 1(3), 1961, pp. 220--221]
journal: j-NORDISK-TIDSKR-INFORM-BEHAND
volume: 1
number: 3
pages: 222--222
year: 1961
CODEN: BITTEL, NBITAB
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Mon Nov 16 14:36:22 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1998.11.16 14:36:22 ???
note: See cite Garwick:1961:AFP,Amble:1961:AFP.
keywords: floating-point accuracy; floating-point arithmetic
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: J. V. Garwick
rawnote: See \cite{Garwick:1961:AFP,Amble:1961:AFP}.
rawtitle: Reply to {``On the Accuracy of Floating Point Computers'' [BIT {\bf 1}(3), 1961, pp. 220--221]}
entry:
@Article{Garwick:1961:RAF,
  author =       "J. V. Garwick",
  title =        "Reply to {``On the Accuracy of Floating Point
                 Computers'' [BIT {\bf 1}(3), 1961, pp. 220--221]}",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "1",
  number =       "3",
  pages =        "222--222",
  year =         "1961",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Mon Nov 16 14:36:22 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Garwick:1961:AFP,Amble:1961:AFP}.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point accuracy; floating-point arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Henderson:1961:RCE
author: D. S. Henderson
booktitle: Proceedings of the 1961 16th ACM national meeting
title: Residue class error checking codes
publisher: pub-ACM
address: pub-ACM:adr
pages: 132.101--132.104
year: 1961
DOI: https://doi.org/10.1145/800029.808563
bibdate: Thu Aug 07 19:04:58 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2008.08.07 19:04:58 ???
keywords: decimal arithmetic
acknowledgement: ack-nhfb
rawauthor: D. S. Henderson
rawbooktitle: {Proceedings of the 1961 16th ACM national meeting}
rawtitle: Residue class error checking codes
abstract:
Error checking codes based on residues have the advantage over parity-based codes of monitoring arithmetic as well as transmission operations. Codes may be devised to detect burst-type errors, to correct single errors in a binary arithmetic operation, to correct burst errors and finally to correct any single-digit error in a decimal operation.

rawabstract:
Error checking codes based on residues have the advantage over parity-based codes of monitoring arithmetic as well as transmission operations. Codes may be devised to detect burst-type errors, to correct single errors in a binary arithmetic operation, to correct burst errors and finally to correct any single-digit error in a decimal operation.

entry:
@InProceedings{Henderson:1961:RCE,
  author =       "D. S. Henderson",
  booktitle =    "{Proceedings of the 1961 16th ACM national meeting}",
  title =        "Residue class error checking codes",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "132.101--132.104",
  year =         "1961",
  DOI =          "https://doi.org/10.1145/800029.808563",
  bibdate =      "Thu Aug 07 19:04:58 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Error checking codes based on residues have the
                 advantage over parity-based codes of monitoring
                 arithmetic as well as transmission operations. Codes
                 may be devised to detect burst-type errors, to correct
                 single errors in a binary arithmetic operation, to
                 correct burst errors and finally to correct any
                 single-digit error in a decimal operation.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal arithmetic",
}


bibtype: article
filename: fparith.bib
label: Kettel:1961:AAM
author: E. Kettel and W. Schneider
title: An Accurate Analog Multiplier and Divider
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-10
number: 2
pages: 269--272
month: jun
monthnumber: 6
year: 1961
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1961.5219198
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 14:45:03 MDT 2011
bibtimestamp: 2011.07.14 14:45:03 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219198
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: E. Kettel and W. Schneider
rawtitle: An Accurate Analog Multiplier and Divider
entry:
@Article{Kettel:1961:AAM,
  author =       "E. Kettel and W. Schneider",
  title =        "An Accurate Analog Multiplier and Divider",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-10",
  number =       "2",
  pages =        "269--272",
  month =        jun,
  year =         "1961",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1961.5219198",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 14:45:03 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=5219198",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Knuth:1961:EIN
author: Donald E. Knuth
title: Errata: ``An imaginary number system''
journal: j-CACM
volume: 4
number: 8
pages: 355--355
month: aug
monthnumber: 8
year: 1961
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Tue Jan 09 07:10:22 1996
bibtimestamp: 1996.01.09 07:10:22 ???
note: See cite Knuth:1960:INS.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Donald E. Knuth
rawnote: See \cite{Knuth:1960:INS}.
rawtitle: Errata: {``An imaginary number system''}
bibsource:
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Knuth:1961:EIN,
  author =       "Donald E. Knuth",
  title =        "Errata: {``An imaginary number system''}",
  journal =      j-CACM,
  volume =       "4",
  number =       "8",
  pages =        "355--355",
  month =        aug,
  year =         "1961",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Jan 09 07:10:22 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Knuth:1960:INS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: article
filename: fparith.bib
label: Kovatch:1961:HEA
author: G. Kovatch and W. E. Meserve
title: The Hall-Effect Analog Multiplier
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-10
number: 3
pages: 512--515
month: sep
monthnumber: 9
year: 1961
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1961.5219240
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 14:45:04 MDT 2011
bibtimestamp: 2011.07.14 14:45:04 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219240
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: G. Kovatch and W. E. Meserve
rawtitle: The {Hall-Effect} Analog Multiplier
entry:
@Article{Kovatch:1961:HEA,
  author =       "G. Kovatch and W. E. Meserve",
  title =        "The {Hall-Effect} Analog Multiplier",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-10",
  number =       "3",
  pages =        "512--515",
  month =        sep,
  year =         "1961",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1961.5219240",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 14:45:04 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=5219240",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Lehman:1961:STH
author: M. Lehman and N. Burla
title: Skip Techniques for High-Speed Carry-Propagation in Binary Arithmetic Units
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-10
number: 4
pages: 691--698
month: dec
monthnumber: 12
year: 1961
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1961.5219274
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 14:45:04 MDT 2011
bibtimestamp: 2011.07.14 14:45:04 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219274
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: M. Lehman and N. Burla
rawtitle: Skip Techniques for High-Speed Carry-Propagation in Binary Arithmetic Units
entry:
@Article{Lehman:1961:STH,
  author =       "M. Lehman and N. Burla",
  title =        "Skip Techniques for High-Speed Carry-Propagation in
                 Binary Arithmetic Units",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-10",
  number =       "4",
  pages =        "691--698",
  month =        dec,
  year =         "1961",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1961.5219274",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 14:45:04 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=5219274",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: MacSorley:1961:HSA
author: O. L. MacSorley
title: High-speed arithmetic in binary computers
journal: j-IRE-PROC
volume: 49
pages: 67--91
month: jan
monthnumber: 1
year: 1961
bibdate: Sat May 18 14:34:55 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.18 14:34:55 ???
note: Reprinted in cite Swartzlander:1976:CDD.
fjournal: IRE Proceedings
acknowledgement: ack-nhfb
rawauthor: O. L. MacSorley
rawnote: Reprinted in \cite{Swartzlander:1976:CDD}.
rawtitle: High-speed arithmetic in binary computers
entry:
@Article{MacSorley:1961:HSA,
  author =       "O. L. MacSorley",
  title =        "High-speed arithmetic in binary computers",
  journal =      j-IRE-PROC,
  volume =       "49",
  number =       "??",
  pages =        "67--91",
  month =        jan,
  year =         "1961",
  bibdate =      "Sat May 18 14:34:55 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite{Swartzlander:1976:CDD}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Proceedings",
}


bibtype: book
filename: fparith.bib
label: Morrison:1961:CBP
editor: Philip Morrison and Emily Morrison
title: Charles Babbage on the principles and development of the calculator: and other seminal writings
publisher: pub-DOVER
address: pub-DOVER:adr
pages: xxxviii + 400
year: 1961
ISBN: 0-486-24691-4 (paperback) OR 0486246914 (paperback)
ISBN13: 978-0-486-24691-8 (paperback) OR 9780486246918 (paperback)
LCCN: QA75 .C52 1961
bibdate: Sat Jan 12 22:30:15 MST 2013
bibtimestamp: 2013.01.12 22:30:15 MST
subject: Calculators; Babbage, Charles
acknowledgement: ack-nhfb
subjectdates: Charles Babbage (26 December 1791--18 October 1871)
raweditor: Philip Morrison and Emily Morrison
rawtitle: {Charles Babbage} on the principles and development of the calculator: and other seminal writings
bibsource:
clio-db.cc.columbia.edu:7090/Voyager; https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib; https://www.math.utah.edu/pub/tex/bib/adabooks.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

TOC:
Chapters from Passages from the life of a philosopher Selections from Babbage's calculating engines Appendix of miscellaneous papers

rawTOC:
Chapters from Passages from the life of a philosopher \\ Selections from Babbage's calculating engines \\ Appendix of miscellaneous papers

entry:
@Book{Morrison:1961:CBP,
  editor =       "Philip Morrison and Emily Morrison",
  title =        "{Charles Babbage} on the principles and development of
                 the calculator: and other seminal writings",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xxxviii + 400",
  year =         "1961",
  ISBN =         "0-486-24691-4 (paperback)",
  ISBN-13 =      "978-0-486-24691-8 (paperback)",
  LCCN =         "QA75 .C52 1961",
  bibdate =      "Sat Jan 12 22:30:15 MST 2013",
  bibsource =    "clio-db.cc.columbia.edu:7090/Voyager;
                 https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
                 https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$7.95",
  acknowledgement = ack-nhfb,
  subject =      "Calculators; Babbage, Charles",
  subject-dates = "Charles Babbage (26 December 1791--18 October 1871)",
  tableofcontents = "Chapters from Passages from the life of a
                 philosopher \\
                 Selections from Babbage's calculating engines \\
                 Appendix of miscellaneous papers",
}


bibtype: article
filename: fparith.bib
label: Nadler:1961:DSR
author: Morton Nadler
title: Division and square root in the quater-imaginary number system
journal: j-CACM
volume: 4
number: 4
pages: 192--193
month: apr
monthnumber: 4
year: 1961
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65.99
MRnumber: 23\#B555
bibdate: Fri Nov 25 18:19:32 MST 2005
bibtimestamp: 2005.11.25 18:19:32 MST
note: See cite Knuth:1960:INS.
fjournal: Communications of the ACM
keywords: $sqrt (x)$; elementary functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Morton Nadler
rawnote: See \cite{Knuth:1960:INS}.
rawtitle: Division and square root in the quater-imaginary number system
entry:
@Article{Nadler:1961:DSR,
  author =       "Morton Nadler",
  title =        "Division and square root in the quater-imaginary
                 number system",
  journal =      j-CACM,
  volume =       "4",
  number =       "4",
  pages =        "192--193",
  month =        apr,
  year =         "1961",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.99",
  MRnumber =     "23\#B555",
  bibdate =      "Fri Nov 25 18:19:32 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Knuth:1960:INS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions",
  ZMreviewer =   "C. B. Haselgrove",
}


bibtype: article
filename: fparith.bib
label: Pinkham:1961:DFS
author: Roger S. Pinkham
title: On the Distribution of First Significant Digits
journal: j-ANN-MATH-STAT
volume: 32
number: 4
pages: 1223--1230
month: dec
monthnumber: 12
year: 1961
CODEN: AASTAD
ISSN: 0003-4851 (print), 2168-8990 (electronic) OR 00034851 (print), 21688990 (electronic)
ISSNL: 0003-4851 OR 00034851
bibdate: Thu Feb 15 15:07:57 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.02.15 15:07:57 ???
URL: http://links.jstor.org/sici?sici=0003-4851%28196112%2932%3A4%3C1223%3AOTDOFS%3E2.0.CO%3B2-T
fjournal: Annals of Mathematical Statistics
keywords: Benford's Law; Law of Anomalous Numbers; Zipf's Law
acknowledgement: ack-nhfb
journalURL: http://projecteuclid.org/all/euclid.aoms/
rawauthor: Roger S. Pinkham
rawtitle: On the Distribution of First Significant Digits
abstract:
It has been noticed by astute observers that well used tables of logarithms are invariably dirtier at the front than at the back. Upon reflection one is led to inquire whether there are more physical constants with low order first significant digits than high. Actual counts by Benford [2] show that not only is this the case but that it seems to be an empirical truth that whenever one has a large body of physical data, Farmer's Almanac, Census Reports, Chemical Rubber Handbook, etc., the proportion of these data with first significant digit $n$ or less is approximately $ log _10(n + 1) $. Any reader formerly unaware of this ``peculiarity'' will find an actual sampling experiment wondrously tantalizing. Thus, for example, approximately $ 0.7 $ of the physical constants in the Chemical Rubber Handbook begin with $4$ or less ($ log _10(4 + 1) = 0.699 $). This is to be contrasted with the widespread intuitive evaluation $ 4 / 9 $ ths.

remark:
From p. 1223: ``ldots the proportion of these data with first significant digit $n$ or less is approximately $ log _10(n + 1) $.''par ldots ``The only distribution for first significant digits which is invariant under scale change of the underlying distribution is $ log _10(n + 1) $. Contrary to suspicion this is a non-trivial mathematical result, for the variable $n$ is discrete.''.par From p. 1230: ``The foregoing results bear on questions of round-off in computing machines. Since $ d(u v) = u d v + v d u $, the error resulting from multiplying two rounded numbers will be governed primarily by the first significant digits of the two numbers being multiplied. Now the distribution of first significant digits, favoring as it does low order digits, tends to produce less error than would be the case if first significant digits were uniform as has sometimes been assumed.''par Cited in cite Sterbenz:1974:FPC.

rawabstract:
It has been noticed by astute observers that well used tables of logarithms are invariably dirtier at the front than at the back. Upon reflection one is led to inquire whether there are more physical constants with low order first significant digits than high. Actual counts by Benford [2] show that not only is this the case but that it seems to be an empirical truth that whenever one has a large body of physical data, Farmer's Almanac, Census Reports, Chemical Rubber Handbook, etc., the proportion of these data with first significant digit $n$ or less is approximately $ \log_{10}(n + 1) $. Any reader formerly unaware of this ``peculiarity'' will find an actual sampling experiment wondrously tantalizing. Thus, for example, approximately $ 0.7 $ of the physical constants in the Chemical Rubber Handbook begin with $4$ or less ($ \log_{10}(4 + 1) = 0.699 $). This is to be contrasted with the widespread intuitive evaluation $ 4 / 9 $ ths.

entry:
@Article{Pinkham:1961:DFS,
  author =       "Roger S. Pinkham",
  title =        "On the Distribution of First Significant Digits",
  journal =      j-ANN-MATH-STAT,
  volume =       "32",
  number =       "4",
  pages =        "1223--1230",
  month =        dec,
  year =         "1961",
  CODEN =        "AASTAD",
  ISSN =         "0003-4851 (print), 2168-8990 (electronic)",
  ISSN-L =       "0003-4851",
  bibdate =      "Thu Feb 15 15:07:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://links.jstor.org/sici?sici=0003-4851%28196112%2932%3A4%3C1223%3AOTDOFS%3E2.0.CO%3B2-T",
  abstract =     "It has been noticed by astute observers that well used
                 tables of logarithms are invariably dirtier at the
                 front than at the back. Upon reflection one is led to
                 inquire whether there are more physical constants with
                 low order first significant digits than high. Actual
                 counts by Benford [2] show that not only is this the
                 case but that it seems to be an empirical truth that
                 whenever one has a large body of physical data,
                 Farmer's Almanac, Census Reports, Chemical Rubber
                 Handbook, etc., the proportion of these data with first
                 significant digit $n$ or less is approximately $
                 \log_{10}(n + 1) $. Any reader formerly unaware of this
                 ``peculiarity'' will find an actual sampling experiment
                 wondrously tantalizing. Thus, for example,
                 approximately $ 0.7 $ of the physical constants in the
                 Chemical Rubber Handbook begin with $4$ or less ($
                 \log_{10}(4 + 1) = 0.699 $). This is to be contrasted
                 with the widespread intuitive evaluation $ 4 / 9 $
                 ths.",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Mathematical Statistics",
  journal-URL =  "http://projecteuclid.org/all/euclid.aoms/",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "From p. 1223: ``\ldots{} the proportion of these data
                 with first significant digit $n$ or less is
                 approximately $ \log_{10}(n + 1) $.''\par

                 \ldots{} ``The only distribution for first significant
                 digits which is invariant under scale change of the
                 underlying distribution is $ \log_{10}(n + 1) $.
                 Contrary to suspicion this is a non-trivial
                 mathematical result, for the variable $n$ is
                 discrete.''.\par

                 From p. 1230: ``The foregoing results bear on questions
                 of round-off in computing machines. Since $ d(u v) = u
                 d v + v d u $, the error resulting from multiplying two
                 rounded numbers will be governed primarily by the first
                 significant digits of the two numbers being multiplied.
                 Now the distribution of first significant digits,
                 favoring as it does low order digits, tends to produce
                 less error than would be the case if first significant
                 digits were uniform as has sometimes been
                 assumed.''\par

                 Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Rabinowitz:1961:MPD
author: Philip Rabinowitz
title: Multiple-Precision Division
journal: j-CACM
volume: 4
number: 2
pages: 98--98
month: feb
monthnumber: 2
year: 1961
CODEN: CACMA2
DOI: https://doi.org/10.1145/366105.366171
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Sep 08 00:29:25 1994
bibtimestamp: 1994.09.08 00:29:25 ???
fjournal: Communications of the ACM
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Philip Rabinowitz
rawtitle: Multiple-Precision Division
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

entry:
@Article{Rabinowitz:1961:MPD,
  author =       "Philip Rabinowitz",
  title =        "Multiple-Precision Division",
  journal =      j-CACM,
  volume =       "4",
  number =       "2",
  pages =        "98--98",
  month =        feb,
  year =         "1961",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/366105.366171",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 00:29:25 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/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: article
filename: fparith.bib
label: Saltman:1961:RCT
author: Roy G. Saltman
title: Reducing Computing Time for Synchronous Binary Division
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-10
number: 2
pages: 169--174
month: jun
monthnumber: 6
year: 1961
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1961.5219186
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 14:45:03 MDT 2011
bibtimestamp: 2011.07.14 14:45:03 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219186
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: Roy G. Saltman
rawtitle: Reducing Computing Time for Synchronous Binary Division
entry:
@Article{Saltman:1961:RCT,
  author =       "Roy G. Saltman",
  title =        "Reducing Computing Time for Synchronous Binary
                 Division",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-10",
  number =       "2",
  pages =        "169--174",
  month =        jun,
  year =         "1961",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1961.5219186",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 14:45:03 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=5219186",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Spielberg:1961:ECF
author: Kurt Spielberg
title: Efficient Continued Fraction Approximations To Elementary Functions
journal: j-MATH-COMPUT
volume: 15
number: 76
pages: 409--417
month: oct
monthnumber: 10
year: 1961
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-nj
ajournal: Math. Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: Kurt Spielberg
rawtitle: Efficient Continued Fraction Approximations To Elementary Functions
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database

entry:
@Article{Spielberg:1961:ECF,
  author =       "Kurt Spielberg",
  title =        "Efficient Continued Fraction Approximations To
                 Elementary Functions",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "76",
  pages =        "409--417",
  month =        oct,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: fparith.bib
label: Spielberg:1961:RPS
author: K. Spielberg
journal: j-J-ACM
volume: 8
number: 4
pages: 613--627
month: oct
monthnumber: 10
year: 1961
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Sat Dec 09 14:01:44 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 14:01:44 ???
fjournal: Journal of the ACM
acknowledgement: ack-nj
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
rawauthor: K. Spielberg
title:
Representation of Power Series in Terms of Polynomials, Rational Approximations and Continued Fractions

rawtitle:
Representation of Power Series in Terms of Polynomials, Rational Approximations and Continued Fractions

entry:
@Article{Spielberg:1961:RPS,
  author =       "K. Spielberg",
  title =        "Representation of Power Series in Terms of
                 Polynomials, Rational Approximations and Continued
                 Fractions",
  journal =      j-J-ACM,
  volume =       "8",
  number =       "4",
  pages =        "613--627",
  month =        oct,
  year =         "1961",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Sat Dec 09 14:01:44 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 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",
}


bibtype: article
filename: fparith.bib
label: Thacher:1961:ISR
author: Henry C. Thacher, Jr.
title: Iterated Square Root Expansions for the Inverse Cosine and Inverse Hyperbolic Cosine
journal: j-MATH-COMPUT
volume: 15
number: 76
pages: 399--403
month: oct
monthnumber: 10
year: 1961
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: Henry C. {Thacher, Jr.}
rawtitle: Iterated Square Root Expansions for the Inverse Cosine and Inverse Hyperbolic Cosine
entry:
@Article{Thacher:1961:ISR,
  author =       "Henry C. {Thacher, Jr.}",
  title =        "Iterated Square Root Expansions for the Inverse Cosine
                 and Inverse Hyperbolic Cosine",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "76",
  pages =        "399--403",
  month =        oct,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "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: techreport
filename: fparith.bib
label: Weik:1961:TSD
author: Martin H. Weik
title: A Third Survey of Domestic Electronic Digital Computing Systems
type: Report
number: 1115
institution: Ballistic Research Laboratories
address: Aberdeen Proving Ground, MD, USA
pages: 1131
month: mar
monthnumber: 3
year: 1961
bibdate: Fri Nov 28 19:37:51 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 19:37:51 ???
acknowledgement: ack-mfc
rawauthor: Martin H. Weik
rawtitle: A Third Survey of Domestic Electronic Digital Computing Systems
abstract:
Based on the results of a third survey, the engineering and programming characteristics of two hundred twenty-two different electronic digital computing systems are given. The data are presented from the point of view of application, numerical and arithmetic characteristics, input, output and storage systems, construction and checking features, power, space, weight, and site preparation and personnel requirements, production records, cost and rental rates, sale and lease policy, reliability, operating experience, and time availability, engineering modifications and improvements and other related topics. An analysis of the survey data, fifteen comparative tables, a discussion of trends, a revised bibliography, and a complete glossary of computer engineering and programming terminology are included.

rawabstract:
Based on the results of a third survey, the engineering and programming characteristics of two hundred twenty-two different electronic digital computing systems are given. The data are presented from the point of view of application, numerical and arithmetic characteristics, input, output and storage systems, construction and checking features, power, space, weight, and site preparation and personnel requirements, production records, cost and rental rates, sale and lease policy, reliability, operating experience, and time availability, engineering modifications and improvements and other related topics. An analysis of the survey data, fifteen comparative tables, a discussion of trends, a revised bibliography, and a complete glossary of computer engineering and programming terminology are included.

entry:
@TechReport{Weik:1961:TSD,
  author =       "Martin H. Weik",
  title =        "A Third Survey of Domestic Electronic Digital
                 Computing Systems",
  type =         "Report",
  number =       "1115",
  institution =  "Ballistic Research Laboratories",
  address =      "Aberdeen Proving Ground, MD, USA",
  pages =        "1131",
  month =        mar,
  year =         "1961",
  bibdate =      "Fri Nov 28 19:37:51 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Based on the results of a third survey, the
                 engineering and programming characteristics of two
                 hundred twenty-two different electronic digital
                 computing systems are given. The data are presented
                 from the point of view of application, numerical and
                 arithmetic characteristics, input, output and storage
                 systems, construction and checking features, power,
                 space, weight, and site preparation and personnel
                 requirements, production records, cost and rental
                 rates, sale and lease policy, reliability, operating
                 experience, and time availability, engineering
                 modifications and improvements and other related
                 topics. An analysis of the survey data, fifteen
                 comparative tables, a discussion of trends, a revised
                 bibliography, and a complete glossary of computer
                 engineering and programming terminology are included.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Wilson:1961:ARB
author: J. B. Wilson and R. S. Ledley
title: An Algorithm for Rapid Binary Division
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-10
number: 4
pages: 662--670
month: dec
monthnumber: 12
year: 1961
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1961.5219271
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 14:45:04 MDT 2011
bibtimestamp: 2011.07.14 14:45:04 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219271
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: J. B. Wilson and R. S. Ledley
rawtitle: An Algorithm for Rapid Binary Division
entry:
@Article{Wilson:1961:ARB,
  author =       "J. B. Wilson and R. S. Ledley",
  title =        "An Algorithm for Rapid Binary Division",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-10",
  number =       "4",
  pages =        "662--670",
  month =        dec,
  year =         "1961",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1961.5219271",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 14:45:04 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=5219271",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: inproceedings
filename: fparith.bib
label: Ashenhurst:1962:MIA
author: R. L. Ashenhurst
title: The Maniac III Arithmetic System
crossref: AFIPS:1962:APS
pages: 192--202
year: 1962
bibdate: Wed Feb 14 17:14:21 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.02.14 17:14:21 ???
acknowledgement: ack-nhfb
rawauthor: R. L. Ashenhurst
rawtitle: The {Maniac III} Arithmetic System
entry:
@InProceedings{Ashenhurst:1962:MIA,
  author =       "R. L. Ashenhurst",
  title =        "The {Maniac III} Arithmetic System",
  crossref =     "AFIPS:1962:APS",
  pages =        "192--202",
  year =         "1962",
  bibdate =      "Wed Feb 14 17:14:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: fparith.bib
label: Buchholz:1962:PCS
editor: Werner Buchholz
title: Planning a Computer System: Project Stretch
publisher: pub-MCGRAW-HILL
address: pub-MCGRAW-HILL:adr
pages: xvii + 322
year: 1962
LCCN: 1876
bibdate: Fri Nov 19 10:02:31 MST 2010
bibtimestamp: 2010.11.19 10:02:31 MST
URL: http://ed-thelen.org/comp-hist/IBM-7030-Planning-McJones.pdf
subject: Computer architecture
acknowledgement: ack-nhfb
raweditor: Werner Buchholz
rawtitle: Planning a Computer System: {Project Stretch}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib; https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib; library.ox.ac.uk:210/ADVANCE

note:
This important book is the primary description of the influential IBM 7030 Stretch computer, written by its architects.

remark:
The text of the book is in the public domain, with the permission of the author in 2003. See cite MacKenzie:1991:IAL for a remark about the noisy mode for floating-point arithmetic in the IBM 7030 Stretch. That mode is first mentioned on page 25 of this book, and described in detail on page 102, which states: ``By definition of ordinary normalized FLP operations, numbers are frequently extended on the right by attaching zeros. During addition the n-digit operand that is not preshifted is extended with n zeros, so as to provide the extra positions to which the preshifted operand can be added. Any operand or result that is shifted left to be normalized requires a corresponding number of zeros to be shifted in at the right. Both sets of zeros tend to produce numbers smaller in absolute value than they would have been if more digits had been carried. In the noisy mode these numbers are simply extended with 1's instead of zeros (1's in a binary machine, 9's in a decimal machine). So all numbers tend to be too large in absolute value. The true value, if there had been no significance loss, should lie between these two extremes. Hence, two runs, one made without and one made with the noisy mode, should show differences in result that indicate which digits may have been affected by significance loss. The principal weakness of the noisy-mode procedure is that it requires two runs for the same problem. A much less important weakness is that the loss of significance cannot be guaranteed to show up --- it merely has a very high probability of showing up --- whereas built-in significance checks can be made slightly pessimistic, so that actual significance loss will not be greater than indicated. On the other hand, little extra hardware and no extra storage are required for the noisy-mode approach. Furthermore, significance loss is relatively rare, so that running a problem twice when Significance loss is suspected does not pose a serious problem. What is serious is the possibility of unsuspected significance loss. In discussions of significance two points are often overlooked. The first of these is trivial: the best way of ensuring significant results is to use an adequate number of fraction digits. The second is almost equally mundane: for a given procedure, normalized FLP arithmetic will ordinarily produce the greatest precision possible for the number of fraction digits used. Normalized FLP arithmetic has been criticized with respect to significance loss, because such loss is not indicated by the creation of leading zeros, as it is with fixed-point arithmetic. In other words, the contention is not that normalized FLP arithmetic is more prone to significance loss than equivalent fixed-point arithmetic, which would be untrue, but that an equivalent indication of such loss is not provided. Loss of significance, however, is also a serious problem in fixed-point arithmetic; multiplication and division do not handle it at all correctly by means of leading zeros. (In particular, fixed-point multiplication may lead to serious or even total significance loss, which would not have occurred with normalized FLP arithmetic: and although leading zeros in addition and subtraction of fixed-point operands do give correct significance indications, the use of other operations and of built-in scaling loops frequently destroys entirely the leading-zeros method of counting significance.)''

TOC:
Foreword v Preface vii 1. Project Stretch 1 [by W. Buchholz] 2. Architectural Philosophy 5 [by F. P. Brooks, Jr.] 2.1. The Two Objectives of Project Stretch 5 2.2. Resources 6 2.3. Guiding Principles 7 2.4. Contemporary Trends in Computer Architecture 10 2.5. Hindsight 15 3. System Summary of IBM 7030 17 [by W. Buchholz] 3.1. System Organization 17 3.2. Memory Units 17 3.3. Index Memory 19 3.4. Special Registers 19 3.5. Input and Output Facilities 19 3.6. High-speed Disk Units 20 3.7. Central Processing Unit 20 3.8. Instruction Controls 21 3.9. Index-arithmetic Unit 21 3.10. Instruction Look-ahead 21 3.11. Arithmetic Unit 22 3.12. Instruction Set 24 3.13. Data Arithmetic 24 3.14. Radix-conversion Operations 27 3.15. Connective Operations 27 3.16. Index-arithmetic Operations 27 3.17. Branching Operations 28 3.18. Transmission Operations 28 3.19. Input-Output Operations 29 3.20. New Features 29 3.21. Performance 32 4. Natural Data Units 33 [by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz] 4.1. Lengths and Structures of Natural Data Units 33 4.2. Procedures for Specifying Natural Data Units 36 4.3. Data Hierarchies 39 4.4. Classes of Operations 40 5. Choosing a Number Base 42 [by W. Buchholz] 5.1. Introduction 42 5.2. Information Content 45 5.3. Arithmetic Speed 49 5.4. Numerical Data 50 5.5. Nonnumerical Data 51 5.6. Addresses 52 5.7. Transformation 53 5.8. Partitioning of Memory 54 5.9. Program Interpretation 56 5.10. Other Number Bases 58 5.11. Conclusion 58 6. Character Set 60 [by R. W. Bemer and W. Buchholz] 6.1. Introduction 60 6.2. Size of Set 62 6.3. Subsets 62 6.4. Expansion of Set 63 6.5. Code 63 6.6. Parity Bit 66 6.7. Sequence 66 6.8. Blank 67 6.9. Decimal Digits 68 6.10. Typewriter Keyboard 68 6.11. Adjacency 69 6.12. Uniqueness 69 6.13. Signs 70 6.14. Tape-recording Convention 71 6.15. Card-punching Convention 71 6.16. List of 7030 Character Set 72 7. Variable-field-length Operation 75 [by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz] 7.1. Introduction 75 7.2. Addressing of Variable-field-length Data 76 7.3. Field Length 77 7.4. Byte Size 78 7.5. Universal Accumulator 79 7.6. Accumulator Operand 79 7.7. Binary and Decimal Arithmetic 80 7.8. Integer Arithmetic 81 7.9. Numerical Signs 82 7.10. Indicators 84 7.11. Arithmetical Operations 85 7.12. Radix-conversion Operation 87 7.13. Logical Connectives of Two Variables 87 7.14. Connective Operations 89 8. Floating-point Operation 92 [by S. G. Campbell] General Discussion 8.1. Problems of Fixed-point Arithmetic 92 8.2. Floating-point Arithmetic 94 8.3. Normalization 97 8.4. Floating-point Singularities 98 8.5. Range and Precision 99 8.6. Round-off Error 100 8.7. Significance Checks 101 8.8. Forms of Floating-point Arithmetic 103 8.9. Structure of Floating-point Data 104 Floating-point Features of the 7030 8.10. Floating-point Instruction Format 106 8.11. Floating-point Data Formats 106 8.12. Singular Floating-point Numbers 108 8.13. Indicators 112 8.14. Universal Accumulator 113 8.15. Fraction Arithmetic 114 8.16. Floating-point-arithmetic Operations 114 8.17. Fixed-point Arithmetic Using Unnormalized Floating-point Operations 118 8.18. Special Functions and Forms of Arithmetic 119 8.19. Multiple-precision Arithmetic 119 8.20. General Remarks 121 9. Instruction Formats 122 [by W. Buchholz] 9.1. Introduction 122 9.2. Earlier Instruction Languages 122 9.3. Evolution of the Single-address Instruction 124 9.4. Implied Addresses 125 9.5. Basic 7030 Instruction Formats 126 9.6. Instruction Efficiency 127 9.7. The Simplicity of Complexity 131 9.8. Relationship to Automatic Programming Languages 132 10. Instruction Sequencing 133 [by F. P. Brooks, Jr.] 10.1. Modes of Instruction Sequencing 133 10.2. Instruction Counter 134 10.3. Unconditional Branching 135 10.4. Conditional Branching 136 10.5. Program-interrupt System 136 10.6. Components of the Program-interrupt System 137 10.7. Examples of Program-interrupt Techniques 140 10.8. Execute Instructions 146 10.9. Execute Operations in the 7030 148 11. Indexing 150 [by G. P. Blaauw] 11.1. Introduction 150 11.2. Indexing Functions 151 11.3. Instruction Format for Indexing 155 11.4. Incrementing 157 11.5. Counting 159 11.6. Advancing by One 161 11.7. Progressive Indexing 161 11.8. Data Transmission 162 11.9. Data Ordering 163 11.10. Refilling 165 11.11. Indirect Addressing and Indirect Indexing 167 11.12. Indexing Applications 169 11.13. Record-handling Applications 172 11.14. File Maintenance 175 11.15. Subroutine Control 177 11.16. Conclusion 178 12. Input-Output Control 179 [by W. Buchholz] 12.1. A Generalized Approach to Connecting Input-Output and External Storage 179 12.2. Input-Output Instructions 180 12.3. Defining the Memory Area 181 12.4. Writing and Reading 182 12.5. Controlling and Locating 183 12.6. An Alternative Approach 184 12.7. Program Interruptions 184 12.8. Buffering 180 12.9. Interface 188 12.10. Operator Control of Input-Output Units 190 13. Multiprogramming 192 [by E. F. Codd, E. S. Lowry, E. McDonough, and C. A. Scalzi] 13.1. Introduction 192 13.2. Multiprogramming Requirements 193 13.3. 7030 Features that Assist Multiprogramming 195 13.4. Programmed Logic 197 13.5. Concluding Remarks 200 13.6. References 201 14. The Central Processing Unit 202 [by E. Bloch] 14.1. Concurrent System Operation 202 14.2. Concurrency within the Central Processing Unit 204 14.3. Data Flow 204 14.4. Arithmetic Unit 208 14.5. Checking 216 14.6. Component Count 216 14.7. Performance 217 14.8. Circuits 218 14.9. Packaging 223 15. The Look-ahead Unit 228 [by R. S. Balance, J. Cocke, and H. G. Kolsky] 15.1. General Description 228 15.2. Timing-simulation Program 230 15.3. Description of the Look-ahead Unit 238 15.4. Forwarding 240 15.5. Counter Sequences 241 15.6. Recovery after Interrupt 246 15.7. A Look-back at the Look-ahead 247 16. The Exchange 248 [by W. Buchholz] 16.1. General Description 248 16.2. Starting a WRITE or READ Operation 250 16.3. Data Transfer during Writing 250 16.4. Data Transfer during Reading 251 16.5. Terminating a WRITE or READ Operation 252 16.6. Multiple Operations 252 16.7. CONTROL and LOCATE Operations 252 16.8. Interrogating the Control Word 253 16.9. Forced Termination 253 17. A Nonarithmetical System Extension 254 [by S. G. Campbell, P.S. Herwitz, and J. H. Pomerene] 17.1. Nonarithmetical Processing 254 17.2. The Set-up Mode 258 17.3. Byte-sequence Formation 259 17.4. Pattern Selection 260 17.5. Transformation Facilities 261 17.6. Statistical Aids 263 17.7. The BYTE-BY-BYTE Instruction 263 17.8. Monitoring for Special Conditions 264 17.9. Instruction Set 265 17.10. Collating Operations 266 17.11. Table Look-up Operations 267 17.12. Example 267 Appendix A. Summary Data 273 A.1. List of the Larger IBM Stored-program Computers 273 A.2. Instruction Formats 275 A.3. List of Registers and Special Addresses 276 A.4. Summary of Operations and Modifiers 277 A.5. Summary of Indicators 287 Appendix B. Programming Examples 292 Notation 292 B.1. Polynomial Evaluation 295 B.2. Cube-root Extraction 296 B.3. Matrix Multiplication 298 B.4. Conversion of Decimal Numbers to a Floating-point Normalized Vector 299 B.5. Editing a Typed Message 301 B.6. Transposition of a Large Bit Matrix 303 Index 305

rawnote:
This important book is the primary description of the influential IBM 7030 Stretch computer, written by its architects.

rawTOC:
Foreword v \\ Preface vii \\ 1. Project Stretch 1 \\ [by W. Buchholz] \\ 2. Architectural Philosophy 5 \\ [by F. P. Brooks, Jr.] \\ 2.1. The Two Objectives of Project Stretch 5 \\ 2.2. Resources 6 \\ 2.3. Guiding Principles 7 \\ 2.4. Contemporary Trends in Computer Architecture 10 \\ 2.5. Hindsight 15 \\ 3. System Summary of IBM 7030 17 \\ [by W. Buchholz] \\ 3.1. System Organization 17 \\ 3.2. Memory Units 17 \\ 3.3. Index Memory 19 \\ 3.4. Special Registers 19 \\ 3.5. Input and Output Facilities 19 \\ 3.6. High-speed Disk Units 20 \\ 3.7. Central Processing Unit 20 \\ 3.8. Instruction Controls 21 \\ 3.9. Index-arithmetic Unit 21 \\ 3.10. Instruction Look-ahead 21 \\ 3.11. Arithmetic Unit 22 \\ 3.12. Instruction Set 24 \\ 3.13. Data Arithmetic 24 \\ 3.14. Radix-conversion Operations 27 \\ 3.15. Connective Operations 27 \\ 3.16. Index-arithmetic Operations 27 \\ 3.17. Branching Operations 28 \\ 3.18. Transmission Operations 28 \\ 3.19. Input-Output Operations 29 \\ 3.20. New Features 29 \\ 3.21. Performance 32 \\ 4. Natural Data Units 33 \\ [by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz] \\ 4.1. Lengths and Structures of Natural Data Units 33 \\ 4.2. Procedures for Specifying Natural Data Units 36 \\ 4.3. Data Hierarchies 39 \\ 4.4. Classes of Operations 40 \\ 5. Choosing a Number Base 42 \\ [by W. Buchholz] \\ 5.1. Introduction 42 \\ 5.2. Information Content 45 \\ 5.3. Arithmetic Speed 49 \\ 5.4. Numerical Data 50 \\ 5.5. Nonnumerical Data 51 \\ 5.6. Addresses 52 \\ 5.7. Transformation 53 \\ 5.8. Partitioning of Memory 54 \\ 5.9. Program Interpretation 56 \\ 5.10. Other Number Bases 58 \\ 5.11. Conclusion 58 \\ 6. Character Set 60 \\ [by R. W. Bemer and W. Buchholz] \\ 6.1. Introduction 60 \\ 6.2. Size of Set 62 \\ 6.3. Subsets 62 \\ 6.4. Expansion of Set 63 \\ 6.5. Code 63 \\ 6.6. Parity Bit 66 \\ 6.7. Sequence 66 \\ 6.8. Blank 67 \\ 6.9. Decimal Digits 68 \\ 6.10. Typewriter Keyboard 68 \\ 6.11. Adjacency 69 \\ 6.12. Uniqueness 69 \\ 6.13. Signs 70 \\ 6.14. Tape-recording Convention 71 \\ 6.15. Card-punching Convention 71 \\ 6.16. List of 7030 Character Set 72 \\ 7. Variable-field-length Operation 75 \\ [by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz] \\ 7.1. Introduction 75 \\ 7.2. Addressing of Variable-field-length Data 76 \\ 7.3. Field Length 77 \\ 7.4. Byte Size 78 \\ 7.5. Universal Accumulator 79 \\ 7.6. Accumulator Operand 79 \\ 7.7. Binary and Decimal Arithmetic 80 \\ 7.8. Integer Arithmetic 81 \\ 7.9. Numerical Signs 82 \\ 7.10. Indicators 84 \\ 7.11. Arithmetical Operations 85 \\ 7.12. Radix-conversion Operation 87 \\ 7.13. Logical Connectives of Two Variables 87 \\ 7.14. Connective Operations 89 \\ 8. Floating-point Operation 92 \\ [by S. G. Campbell] \\ General Discussion \\ 8.1. Problems of Fixed-point Arithmetic 92 \\ 8.2. Floating-point Arithmetic 94 \\ 8.3. Normalization 97 \\ 8.4. Floating-point Singularities 98 \\ 8.5. Range and Precision 99 \\ 8.6. Round-off Error 100 \\ 8.7. Significance Checks 101 \\ 8.8. Forms of Floating-point Arithmetic 103 \\ 8.9. Structure of Floating-point Data 104 \\ Floating-point Features of the 7030 \\ 8.10. Floating-point Instruction Format 106 \\ 8.11. Floating-point Data Formats 106 \\ 8.12. Singular Floating-point Numbers 108 \\ 8.13. Indicators 112 \\ 8.14. Universal Accumulator 113 \\ 8.15. Fraction Arithmetic 114 \\ 8.16. Floating-point-arithmetic Operations 114 \\ 8.17. Fixed-point Arithmetic Using Unnormalized \\ Floating-point Operations 118 \\ 8.18. Special Functions and Forms of Arithmetic 119 \\ 8.19. Multiple-precision Arithmetic 119 \\ 8.20. General Remarks 121 \\ 9. Instruction Formats 122 \\ [by W. Buchholz] \\ 9.1. Introduction 122 \\ 9.2. Earlier Instruction Languages 122 \\ 9.3. Evolution of the Single-address Instruction 124 \\ 9.4. Implied Addresses 125 \\ 9.5. Basic 7030 Instruction Formats 126 \\ 9.6. Instruction Efficiency 127 \\ 9.7. The Simplicity of Complexity 131 \\ 9.8. Relationship to Automatic Programming Languages 132 \\ 10. Instruction Sequencing 133 \\ [by F. P. Brooks, Jr.] \\ 10.1. Modes of Instruction Sequencing 133 \\ 10.2. Instruction Counter 134 \\ 10.3. Unconditional Branching 135 \\ 10.4. Conditional Branching 136 \\ 10.5. Program-interrupt System 136 \\ 10.6. Components of the Program-interrupt System 137 \\ 10.7. Examples of Program-interrupt Techniques 140 \\ 10.8. Execute Instructions 146 \\ 10.9. Execute Operations in the 7030 148 \\ 11. Indexing 150 \\ [by G. P. Blaauw] \\ 11.1. Introduction 150 \\ 11.2. Indexing Functions 151 \\ 11.3. Instruction Format for Indexing 155 \\ 11.4. Incrementing 157 \\ 11.5. Counting 159 \\ 11.6. Advancing by One 161 \\ 11.7. Progressive Indexing 161 \\ 11.8. Data Transmission 162 \\ 11.9. Data Ordering 163 \\ 11.10. Refilling 165 \\ 11.11. Indirect Addressing and Indirect Indexing 167 \\ 11.12. Indexing Applications 169 \\ 11.13. Record-handling Applications 172 \\ 11.14. File Maintenance 175 \\ 11.15. Subroutine Control 177 \\ 11.16. Conclusion 178 \\ 12. Input-Output Control 179 \\ [by W. Buchholz] \\ 12.1. A Generalized Approach to Connecting \\ Input-Output and External Storage 179 \\ 12.2. Input-Output Instructions 180 \\ 12.3. Defining the Memory Area 181 \\ 12.4. Writing and Reading 182 \\ 12.5. Controlling and Locating 183 \\ 12.6. An Alternative Approach 184 \\ 12.7. Program Interruptions 184 \\ 12.8. Buffering 180 \\ 12.9. Interface 188 \\ 12.10. Operator Control of Input-Output Units 190 \\ 13. Multiprogramming 192 \\ [by E. F. Codd, E. S. Lowry, E. McDonough, and C. A. Scalzi] \\ 13.1. Introduction 192 \\ 13.2. Multiprogramming Requirements 193 \\ 13.3. 7030 Features that Assist Multiprogramming 195 \\ 13.4. Programmed Logic 197 \\ 13.5. Concluding Remarks 200 \\ 13.6. References 201 \\ 14. The Central Processing Unit 202 \\ [by E. Bloch] \\ 14.1. Concurrent System Operation 202 \\ 14.2. Concurrency within the Central Processing Unit 204 \\ 14.3. Data Flow 204 \\ 14.4. Arithmetic Unit 208 \\ 14.5. Checking 216 \\ 14.6. Component Count 216 \\ 14.7. Performance 217 \\ 14.8. Circuits 218 \\ 14.9. Packaging 223 \\ 15. The Look-ahead Unit 228 \\ [by R. S. Balance, J. Cocke, and H. G. Kolsky] \\ 15.1. General Description 228 \\ 15.2. Timing-simulation Program 230 \\ 15.3. Description of the Look-ahead Unit 238 \\ 15.4. Forwarding 240 \\ 15.5. Counter Sequences 241 \\ 15.6. Recovery after Interrupt 246 \\ 15.7. A Look-back at the Look-ahead 247 \\ 16. The Exchange 248 \\ [by W. Buchholz] \\ 16.1. General Description 248 \\ 16.2. Starting a WRITE or READ Operation 250 \\ 16.3. Data Transfer during Writing 250 \\ 16.4. Data Transfer during Reading 251 \\ 16.5. Terminating a WRITE or READ Operation 252 \\ 16.6. Multiple Operations 252 \\ 16.7. CONTROL and LOCATE Operations 252 \\ 16.8. Interrogating the Control Word 253 \\ 16.9. Forced Termination 253 \\ 17. A Nonarithmetical System Extension 254 \\ [by S. G. Campbell, P.S. Herwitz, and J. H. Pomerene] \\ 17.1. Nonarithmetical Processing 254 \\ 17.2. The Set-up Mode 258 \\ 17.3. Byte-sequence Formation 259 \\ 17.4. Pattern Selection 260 \\ 17.5. Transformation Facilities 261 \\ 17.6. Statistical Aids 263 \\ 17.7. The BYTE-BY-BYTE Instruction 263 \\ 17.8. Monitoring for Special Conditions 264 \\ 17.9. Instruction Set 265 \\ 17.10. Collating Operations 266 \\ 17.11. Table Look-up Operations 267 \\ 17.12. Example 267 \\ Appendix A. Summary Data 273 \\ A.1. List of the Larger IBM Stored-program Computers 273 \\ A.2. Instruction Formats 275 \\ A.3. List of Registers and Special Addresses 276 \\ A.4. Summary of Operations and Modifiers 277 \\ A.5. Summary of Indicators 287 \\ Appendix B. Programming Examples 292 \\ Notation 292 \\ B.1. Polynomial Evaluation 295 \\ B.2. Cube-root Extraction 296 \\ B.3. Matrix Multiplication 298 \\ B.4. Conversion of Decimal Numbers to a \\ Floating-point Normalized Vector 299 \\ B.5. Editing a Typed Message 301 \\ B.6. Transposition of a Large Bit Matrix 303 \\ Index 305

entry:
@Book{Buchholz:1962:PCS,
  editor =       "Werner Buchholz",
  title =        "Planning a Computer System: {Project Stretch}",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xvii + 322",
  year =         "1962",
  LCCN =         "1876",
  bibdate =      "Fri Nov 19 10:02:31 MST 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
                 library.ox.ac.uk:210/ADVANCE",
  note =         "This important book is the primary description of the
                 influential IBM 7030 Stretch computer, written by its
                 architects.",
  URL =          "http://ed-thelen.org/comp-hist/IBM-7030-Planning-McJones.pdf",
  acknowledgement = ack-nhfb,
  remark =       "The text of the book is in the public domain, with the
                 permission of the author in 2003.

                 See \cite{MacKenzie:1991:IAL} for a remark about the
                 noisy mode for floating-point arithmetic in the IBM
                 7030 Stretch. That mode is first mentioned on page 25
                 of this book, and described in detail on page 102,
                 which states:

                 ``By definition of ordinary normalized FLP operations,
                 numbers are frequently extended on the right by
                 attaching zeros. During addition the n-digit operand
                 that is not preshifted is extended with n zeros, so as
                 to provide the extra positions to which the preshifted
                 operand can be added. Any operand or result that is
                 shifted left to be normalized requires a corresponding
                 number of zeros to be shifted in at the right. Both
                 sets of zeros tend to produce numbers smaller in
                 absolute value than they would have been if more digits
                 had been carried. In the noisy mode these numbers are
                 simply extended with 1's instead of zeros (1's in a
                 binary machine, 9's in a decimal machine). So all
                 numbers tend to be too large in absolute value. The
                 true value, if there had been no significance loss,
                 should lie between these two extremes. Hence, two runs,
                 one made without and one made with the noisy mode,
                 should show differences in result that indicate which
                 digits may have been affected by significance loss.

                 The principal weakness of the noisy-mode procedure is
                 that it requires two runs for the same problem. A much
                 less important weakness is that the loss of
                 significance cannot be guaranteed to show up --- it
                 merely has a very high probability of showing up ---
                 whereas built-in significance checks can be made
                 slightly pessimistic, so that actual significance loss
                 will not be greater than indicated. On the other hand,
                 little extra hardware and no extra storage are required
                 for the noisy-mode approach. Furthermore, significance
                 loss is relatively rare, so that running a problem
                 twice when Significance loss is suspected does not pose
                 a serious problem. What is serious is the possibility
                 of unsuspected significance loss.

                 In discussions of significance two points are often
                 overlooked. The first of these is trivial: the best way
                 of ensuring significant results is to use an adequate
                 number of fraction digits. The second is almost equally
                 mundane: for a given procedure, normalized FLP
                 arithmetic will ordinarily produce the greatest
                 precision possible for the number of fraction digits
                 used. Normalized FLP arithmetic has been criticized
                 with respect to significance loss, because such loss is
                 not indicated by the creation of leading zeros, as it
                 is with fixed-point arithmetic. In other words, the
                 contention is not that normalized FLP arithmetic is
                 more prone to significance loss than equivalent
                 fixed-point arithmetic, which would be untrue, but that
                 an equivalent indication of such loss is not provided.
                 Loss of significance, however, is also a serious
                 problem in fixed-point arithmetic; multiplication and
                 division do not handle it at all correctly by means of
                 leading zeros. (In particular, fixed-point
                 multiplication may lead to serious or even total
                 significance loss, which would not have occurred with
                 normalized FLP arithmetic: and although leading zeros
                 in addition and subtraction of fixed-point operands do
                 give correct significance indications, the use of other
                 operations and of built-in scaling loops frequently
                 destroys entirely the leading-zeros method of counting
                 significance.)''",
  subject =      "Computer architecture",
  tableofcontents = "Foreword v \\
                 Preface vii \\
                 1. Project Stretch 1 \\
                 [by W. Buchholz] \\
                 2. Architectural Philosophy 5 \\
                 [by F. P. Brooks, Jr.] \\
                 2.1. The Two Objectives of Project Stretch 5 \\
                 2.2. Resources 6 \\
                 2.3. Guiding Principles 7 \\
                 2.4. Contemporary Trends in Computer Architecture 10
                 \\
                 2.5. Hindsight 15 \\
                 3. System Summary of IBM 7030 17 \\
                 [by W. Buchholz] \\
                 3.1. System Organization 17 \\
                 3.2. Memory Units 17 \\
                 3.3. Index Memory 19 \\
                 3.4. Special Registers 19 \\
                 3.5. Input and Output Facilities 19 \\
                 3.6. High-speed Disk Units 20 \\
                 3.7. Central Processing Unit 20 \\
                 3.8. Instruction Controls 21 \\
                 3.9. Index-arithmetic Unit 21 \\
                 3.10. Instruction Look-ahead 21 \\
                 3.11. Arithmetic Unit 22 \\
                 3.12. Instruction Set 24 \\
                 3.13. Data Arithmetic 24 \\
                 3.14. Radix-conversion Operations 27 \\
                 3.15. Connective Operations 27 \\
                 3.16. Index-arithmetic Operations 27 \\
                 3.17. Branching Operations 28 \\
                 3.18. Transmission Operations 28 \\
                 3.19. Input-Output Operations 29 \\
                 3.20. New Features 29 \\
                 3.21. Performance 32 \\
                 4. Natural Data Units 33 \\
                 [by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
                 \\
                 4.1. Lengths and Structures of Natural Data Units 33
                 \\
                 4.2. Procedures for Specifying Natural Data Units 36
                 \\
                 4.3. Data Hierarchies 39 \\
                 4.4. Classes of Operations 40 \\
                 5. Choosing a Number Base 42 \\
                 [by W. Buchholz] \\
                 5.1. Introduction 42 \\
                 5.2. Information Content 45 \\
                 5.3. Arithmetic Speed 49 \\
                 5.4. Numerical Data 50 \\
                 5.5. Nonnumerical Data 51 \\
                 5.6. Addresses 52 \\
                 5.7. Transformation 53 \\
                 5.8. Partitioning of Memory 54 \\
                 5.9. Program Interpretation 56 \\
                 5.10. Other Number Bases 58 \\
                 5.11. Conclusion 58 \\
                 6. Character Set 60 \\
                 [by R. W. Bemer and W. Buchholz] \\
                 6.1. Introduction 60 \\
                 6.2. Size of Set 62 \\
                 6.3. Subsets 62 \\
                 6.4. Expansion of Set 63 \\
                 6.5. Code 63 \\
                 6.6. Parity Bit 66 \\
                 6.7. Sequence 66 \\
                 6.8. Blank 67 \\
                 6.9. Decimal Digits 68 \\
                 6.10. Typewriter Keyboard 68 \\
                 6.11. Adjacency 69 \\
                 6.12. Uniqueness 69 \\
                 6.13. Signs 70 \\
                 6.14. Tape-recording Convention 71 \\
                 6.15. Card-punching Convention 71 \\
                 6.16. List of 7030 Character Set 72 \\
                 7. Variable-field-length Operation 75 \\
                 [by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
                 \\
                 7.1. Introduction 75 \\
                 7.2. Addressing of Variable-field-length Data 76 \\
                 7.3. Field Length 77 \\
                 7.4. Byte Size 78 \\
                 7.5. Universal Accumulator 79 \\
                 7.6. Accumulator Operand 79 \\
                 7.7. Binary and Decimal Arithmetic 80 \\
                 7.8. Integer Arithmetic 81 \\
                 7.9. Numerical Signs 82 \\
                 7.10. Indicators 84 \\
                 7.11. Arithmetical Operations 85 \\
                 7.12. Radix-conversion Operation 87 \\
                 7.13. Logical Connectives of Two Variables 87 \\
                 7.14. Connective Operations 89 \\
                 8. Floating-point Operation 92 \\
                 [by S. G. Campbell] \\
                 General Discussion \\
                 8.1. Problems of Fixed-point Arithmetic 92 \\
                 8.2. Floating-point Arithmetic 94 \\
                 8.3. Normalization 97 \\
                 8.4. Floating-point Singularities 98 \\
                 8.5. Range and Precision 99 \\
                 8.6. Round-off Error 100 \\
                 8.7. Significance Checks 101 \\
                 8.8. Forms of Floating-point Arithmetic 103 \\
                 8.9. Structure of Floating-point Data 104 \\
                 Floating-point Features of the 7030 \\
                 8.10. Floating-point Instruction Format 106 \\
                 8.11. Floating-point Data Formats 106 \\
                 8.12. Singular Floating-point Numbers 108 \\
                 8.13. Indicators 112 \\
                 8.14. Universal Accumulator 113 \\
                 8.15. Fraction Arithmetic 114 \\
                 8.16. Floating-point-arithmetic Operations 114 \\
                 8.17. Fixed-point Arithmetic Using Unnormalized \\
                 Floating-point Operations 118 \\
                 8.18. Special Functions and Forms of Arithmetic 119 \\
                 8.19. Multiple-precision Arithmetic 119 \\
                 8.20. General Remarks 121 \\
                 9. Instruction Formats 122 \\
                 [by W. Buchholz] \\
                 9.1. Introduction 122 \\
                 9.2. Earlier Instruction Languages 122 \\
                 9.3. Evolution of the Single-address Instruction 124
                 \\
                 9.4. Implied Addresses 125 \\
                 9.5. Basic 7030 Instruction Formats 126 \\
                 9.6. Instruction Efficiency 127 \\
                 9.7. The Simplicity of Complexity 131 \\
                 9.8. Relationship to Automatic Programming Languages
                 132 \\
                 10. Instruction Sequencing 133 \\
                 [by F. P. Brooks, Jr.] \\
                 10.1. Modes of Instruction Sequencing 133 \\
                 10.2. Instruction Counter 134 \\
                 10.3. Unconditional Branching 135 \\
                 10.4. Conditional Branching 136 \\
                 10.5. Program-interrupt System 136 \\
                 10.6. Components of the Program-interrupt System 137
                 \\
                 10.7. Examples of Program-interrupt Techniques 140 \\
                 10.8. Execute Instructions 146 \\
                 10.9. Execute Operations in the 7030 148 \\
                 11. Indexing 150 \\
                 [by G. P. Blaauw] \\
                 11.1. Introduction 150 \\
                 11.2. Indexing Functions 151 \\
                 11.3. Instruction Format for Indexing 155 \\
                 11.4. Incrementing 157 \\
                 11.5. Counting 159 \\
                 11.6. Advancing by One 161 \\
                 11.7. Progressive Indexing 161 \\
                 11.8. Data Transmission 162 \\
                 11.9. Data Ordering 163 \\
                 11.10. Refilling 165 \\
                 11.11. Indirect Addressing and Indirect Indexing 167
                 \\
                 11.12. Indexing Applications 169 \\
                 11.13. Record-handling Applications 172 \\
                 11.14. File Maintenance 175 \\
                 11.15. Subroutine Control 177 \\
                 11.16. Conclusion 178 \\
                 12. Input-Output Control 179 \\
                 [by W. Buchholz] \\
                 12.1. A Generalized Approach to Connecting \\
                 Input-Output and External Storage 179 \\
                 12.2. Input-Output Instructions 180 \\
                 12.3. Defining the Memory Area 181 \\
                 12.4. Writing and Reading 182 \\
                 12.5. Controlling and Locating 183 \\
                 12.6. An Alternative Approach 184 \\
                 12.7. Program Interruptions 184 \\
                 12.8. Buffering 180 \\
                 12.9. Interface 188 \\
                 12.10. Operator Control of Input-Output Units 190 \\
                 13. Multiprogramming 192 \\
                 [by E. F. Codd, E. S. Lowry, E. McDonough, and C. A.
                 Scalzi] \\
                 13.1. Introduction 192 \\
                 13.2. Multiprogramming Requirements 193 \\
                 13.3. 7030 Features that Assist Multiprogramming 195
                 \\
                 13.4. Programmed Logic 197 \\
                 13.5. Concluding Remarks 200 \\
                 13.6. References 201 \\
                 14. The Central Processing Unit 202 \\
                 [by E. Bloch] \\
                 14.1. Concurrent System Operation 202 \\
                 14.2. Concurrency within the Central Processing Unit
                 204 \\
                 14.3. Data Flow 204 \\
                 14.4. Arithmetic Unit 208 \\
                 14.5. Checking 216 \\
                 14.6. Component Count 216 \\
                 14.7. Performance 217 \\
                 14.8. Circuits 218 \\
                 14.9. Packaging 223 \\
                 15. The Look-ahead Unit 228 \\
                 [by R. S. Balance, J. Cocke, and H. G. Kolsky] \\
                 15.1. General Description 228 \\
                 15.2. Timing-simulation Program 230 \\
                 15.3. Description of the Look-ahead Unit 238 \\
                 15.4. Forwarding 240 \\
                 15.5. Counter Sequences 241 \\
                 15.6. Recovery after Interrupt 246 \\
                 15.7. A Look-back at the Look-ahead 247 \\
                 16. The Exchange 248 \\
                 [by W. Buchholz] \\
                 16.1. General Description 248 \\
                 16.2. Starting a WRITE or READ Operation 250 \\
                 16.3. Data Transfer during Writing 250 \\
                 16.4. Data Transfer during Reading 251 \\
                 16.5. Terminating a WRITE or READ Operation 252 \\
                 16.6. Multiple Operations 252 \\
                 16.7. CONTROL and LOCATE Operations 252 \\
                 16.8. Interrogating the Control Word 253 \\
                 16.9. Forced Termination 253 \\
                 17. A Nonarithmetical System Extension 254 \\
                 [by S. G. Campbell, P.S. Herwitz, and J. H. Pomerene]
                 \\
                 17.1. Nonarithmetical Processing 254 \\
                 17.2. The Set-up Mode 258 \\
                 17.3. Byte-sequence Formation 259 \\
                 17.4. Pattern Selection 260 \\
                 17.5. Transformation Facilities 261 \\
                 17.6. Statistical Aids 263 \\
                 17.7. The BYTE-BY-BYTE Instruction 263 \\
                 17.8. Monitoring for Special Conditions 264 \\
                 17.9. Instruction Set 265 \\
                 17.10. Collating Operations 266 \\
                 17.11. Table Look-up Operations 267 \\
                 17.12. Example 267 \\
                 Appendix A. Summary Data 273 \\
                 A.1. List of the Larger IBM Stored-program Computers
                 273 \\
                 A.2. Instruction Formats 275 \\
                 A.3. List of Registers and Special Addresses 276 \\
                 A.4. Summary of Operations and Modifiers 277 \\
                 A.5. Summary of Indicators 287 \\
                 Appendix B. Programming Examples 292 \\
                 Notation 292 \\
                 B.1. Polynomial Evaluation 295 \\
                 B.2. Cube-root Extraction 296 \\
                 B.3. Matrix Multiplication 298 \\
                 B.4. Conversion of Decimal Numbers to a \\
                 Floating-point Normalized Vector 299 \\
                 B.5. Editing a Typed Message 301 \\
                 B.6. Transposition of a Large Bit Matrix 303 \\
                 Index 305",
}


bibtype: incollection
filename: fparith.bib
label: Campbell:1962:FPO
author: S. G. Campbell
editor: Werner Buchholz
booktitle: Planning a Computer System: Project Stretch
title: Floating-Point Operation
publisher: pub-MCGRAW-HILL
address: pub-MCGRAW-HILL:adr
pages: 92--121
year: 1962
LCCN: QA76.8.I2 I5
bibdate: Wed Feb 14 17:24:27 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2007.02.14 17:24:27 ???
subject: IBM 7030 (Computer); IBM Stretch
acknowledgement: ack-nhfb
bookpages: 322
rawauthor: S. G. Campbell
rawbooktitle: Planning a Computer System: {Project Stretch}
raweditor: Werner Buchholz
rawtitle: Floating-Point Operation
entry:
@InCollection{Campbell:1962:FPO,
  author =       "S. G. Campbell",
  editor =       "Werner Buchholz",
  booktitle =    "Planning a Computer System: {Project Stretch}",
  title =        "Floating-Point Operation",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  bookpages =    "322",
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  year =         "1962",
  LCCN =         "QA76.8.I2 I5",
  bibdate =      "Wed Feb 14 17:24:27 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "IBM 7030 (Computer); IBM Stretch",
}


bibtype: article
filename: fparith.bib
label: Cantor:1962:LEF
author: D. Cantor and G. Estrin and R. Turn
title: Logarithmic and Exponential Function Evaluation in a Variable Structure Digital Computer
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-11
number: 2
pages: 155--164
month: apr
monthnumber: 4
year: 1962
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1962.5219348
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 09:11:49 MDT 2011
bibtimestamp: 2011.07.14 09:11:49 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219348
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nj
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: D. Cantor and G. Estrin and R. Turn
rawtitle: Logarithmic and Exponential Function Evaluation in a Variable Structure Digital Computer
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/ieeetranscomput.bib

entry:
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  author =       "D. Cantor and G. Estrin and R. Turn",
  title =        "Logarithmic and Exponential Function Evaluation in a
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bibtype: techreport
filename: fparith.bib
label: Descloux:1962:REF
author: J. Descloux
title: Remarks on errors in first order iterative processes with floating-point computers
institution: University of Illinois Graduate College, Digital Computer Laboratory
address: Urbana, IL, USA
pages: 7
year: 1962
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Electronic digital computers.; Numerical calculations.
remark: Supported by: National Science Foundation under grant G16489. ``March 22, 1962.''
acknowledgement: ack-nhfb
rawauthor: J. Descloux
rawtitle: Remarks on errors in first order iterative processes with floating-point computers
series:
Report / University of Illinois, Digital Computer Laboratory; no. 113 Report (University of Illinois (Urbana-Champaign campus). Digital Computer Laboratory); no. 113.

entry:
@TechReport{Descloux:1962:REF,
  author =       "J. Descloux",
  title =        "Remarks on errors in first order iterative processes
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  institution =  "University of Illinois Graduate College, Digital
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  address =      "Urbana, IL, USA",
  pages =        "7",
  year =         "1962",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
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  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers.; Numerical
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  remark =       "Supported by: National Science Foundation under grant
                 G16489. ``March 22, 1962.''",
}


bibtype: article
filename: fparith.bib
label: Fischler:1962:TRA
author: M. A. Fischler and E. A. Poe
title: Threshold Realization of Arithmetic Circuits
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-11
number: 2
pages: 287--288
month: apr
monthnumber: 4
year: 1962
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1962.5219366
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 09:11:50 MDT 2011
bibtimestamp: 2011.07.14 09:11:50 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219366
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: M. A. Fischler and E. A. Poe
rawtitle: Threshold Realization of Arithmetic Circuits
entry:
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  author =       "M. A. Fischler and E. A. Poe",
  title =        "Threshold Realization of Arithmetic Circuits",
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  volume =       "EC-11",
  number =       "2",
  pages =        "287--288",
  month =        apr,
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  DOI =          "https://doi.org/10.1109/TEC.1962.5219366",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 09:11:50 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
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  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219366",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
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bibtype: article
filename: fparith.bib
label: Fraser:1962:CRA
author: W. Fraser and J. F. Hart
title: On the computation of rational approximations to continuous functions
journal: j-CACM
volume: 5
number: 7
pages: 401--403
month: jul
monthnumber: 7
year: 1962
CODEN: CACMA2
DOI: https://doi.org/10.1145/368273.368578
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:39 MST 2005
bibtimestamp: 2005.11.25 18:19:39 MST
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: W. Fraser and J. F. Hart
rawtitle: On the computation of rational approximations to continuous functions
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

keywords:
$abs (x)$; $cos (x)$; $Gamma (1+x)$; $sin (x)$; elementary functions; Remes algorithm; special functions

entry:
@Article{Fraser:1962:CRA,
  author =       "W. Fraser and J. F. Hart",
  title =        "On the computation of rational approximations to
                 continuous functions",
  journal =      j-CACM,
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  number =       "7",
  pages =        "401--403",
  month =        jul,
  year =         "1962",
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  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:39 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;
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  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\abs(x)$; $\cos(x)$; $\Gamma(1+x)$; $\sin(x)$;
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}


bibtype: article
filename: fparith.bib
label: Grau:1962:FNR
author: A. A. Grau
title: On a floating-point number representation for use with algorithmic languages
journal: j-CACM
volume: 5
number: 3
pages: 160--161
month: mar
monthnumber: 3
year: 1962
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 68.00
MRnumber: 26\#4506
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: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
reviewer: R. L. Ashenhurst
rawauthor: A. A. Grau
rawtitle: On a floating-point number representation for use with algorithmic languages
abstract:
Algorithmic languages, such as ALGOL, make provision for two types of numbers, real and integer, which are usually implemented on the computer by means of floating-point and fixed-point numbers respectively. The concepts real and integer, however, are taken from mathematics, where the set of integers forms a proper subset of the set of real numbers. In implementation a real problem is posed by the fact that the set of fixed-point numbers is not a proper subset of the set of floating-point numbers; this problem becomes very apparent in attempts to implement ALGOL 60. Furthermore, the em one mathematical operation of addition is implemented in the machine by one of em two machine operations, fixed-point addition or floating-point addition.

rawabstract:
Algorithmic languages, such as ALGOL, make provision for two types of numbers, real and integer, which are usually implemented on the computer by means of floating-point and fixed-point numbers respectively. The concepts real and integer, however, are taken from mathematics, where the set of integers forms a proper subset of the set of real numbers. In implementation a real problem is posed by the fact that the set of fixed-point numbers is not a proper subset of the set of floating-point numbers; this problem becomes very apparent in attempts to implement ALGOL 60. Furthermore, the {\em one\/} mathematical operation of addition is implemented in the machine by one of {\em two\/} machine operations, fixed-point addition or floating-point addition.

entry:
@Article{Grau:1962:FNR,
  author =       "A. A. Grau",
  title =        "On a floating-point number representation for use with
                 algorithmic languages",
  journal =      j-CACM,
  volume =       "5",
  number =       "3",
  pages =        "160--161",
  month =        mar,
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  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Algorithmic languages, such as ALGOL, make provision
                 for two types of numbers, real and integer, which are
                 usually implemented on the computer by means of
                 floating-point and fixed-point numbers respectively.
                 The concepts real and integer, however, are taken from
                 mathematics, where the set of integers forms a proper
                 subset of the set of real numbers. In implementation a
                 real problem is posed by the fact that the set of
                 fixed-point numbers is not a proper subset of the set
                 of floating-point numbers; this problem becomes very
                 apparent in attempts to implement ALGOL 60.
                 Furthermore, the {\em one\/} mathematical operation of
                 addition is implemented in the machine by one of {\em
                 two\/} machine operations, fixed-point addition or
                 floating-point addition.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  reviewer =     "R. L. Ashenhurst",
}


bibtype: article
filename: fparith.bib
label: Guffin:1962:CSL
author: Ronald M. Guffin
title: A Computer for Solving Linear Simultaneous Equations Using the Residue Number System
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-11
number: 2
pages: 164--173
month: apr
monthnumber: 4
year: 1962
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1962.5219349
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 09:11:49 MDT 2011
bibtimestamp: 2011.07.14 09:11:49 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219349
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: Ronald M. Guffin
rawtitle: A Computer for Solving Linear Simultaneous Equations Using the Residue Number System
entry:
@Article{Guffin:1962:CSL,
  author =       "Ronald M. Guffin",
  title =        "A Computer for Solving Linear Simultaneous Equations
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  volume =       "EC-11",
  number =       "2",
  pages =        "164--173",
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bibtype: book
filename: fparith.bib
label: Hamming:1962:NMS
author: R. W. (Richard Wesley) Hamming
title: Numerical methods for scientists and engineers
publisher: pub-MCGRAW-HILL
address: pub-MCGRAW-HILL:adr
pages: 411
year: 1962
LCCN: QA297 .H28
bibdate: Fri Aug 20 09:12:08 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.08.20 09:12:08 MDT
series: International series in pure and applied mathematics
remark: Cited in cite Sterbenz:1974:FPC.
subject: Numerical analysis; Electronic digital computers
acknowledgement: ack-nhfb
rawauthor: R. W. (Richard Wesley) Hamming
rawtitle: Numerical methods for scientists and engineers
entry:
@Book{Hamming:1962:NMS,
  author =       "R. W. (Richard Wesley) Hamming",
  title =        "Numerical methods for scientists and engineers",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "411",
  year =         "1962",
  LCCN =         "QA297 .H28",
  bibdate =      "Fri Aug 20 09:12:08 MDT 2010",
  bibsource =    "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 =       "Cited in \cite{Sterbenz:1974:FPC}.",
  subject =      "Numerical analysis; Electronic digital computers",
}


bibtype: article
filename: fparith.bib
label: Jones:1962:FPF
author: F. B. Jones and A. W. Wymore
title: Floating Point Feature on the IBM Type 1620
journal: j-IBM-TDB
volume: 05-62
pages: 43--46
month: may
monthnumber: 5
year: 1962
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Fri Nov 28 11:26:02 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 11:26:02 ???
fjournal: IBM Technical Disclosure Bulletin
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: F. B. Jones and A. W. Wymore
rawtitle: Floating Point Feature on the {IBM Type 1620}
remark:
The IBM 1620 normalized variable-precision arithmetic provides up to 100 decimal digits with an exponent range of $ pm 99 $.

entry:
@Article{Jones:1962:FPF,
  author =       "F. B. Jones and A. W. Wymore",
  title =        "Floating Point Feature on the {IBM Type 1620}",
  journal =      j-IBM-TDB,
  volume =       "05-62",
  pages =        "43--46",
  month =        may,
  year =         "1962",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Fri Nov 28 11:26:02 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 =       "The IBM 1620 normalized variable-precision arithmetic
                 provides up to 100 decimal digits with an exponent
                 range of $ \pm 99 $.",
}


bibtype: article
filename: fparith.bib
label: Karatsuba:1962:MMN
author: A. Karatsuba and Y. Ofman
title: Multiplication of multidigit numbers on automata
journal: j-DOKL-AKAD-NAUK
volume: 145
pages: 293--294
year: 1962
CODEN: DANKAS
ISSN: 0002-3264 OR 00023264
bibdate: Tue Jul 05 10:35:11 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.05 10:35:11 ???
fjournal: Doklady Akademii nauk SSSR
acknowledgement: ack-nhfb
journalURL: http://istina.msu.ru/journals/366838/
rawauthor: A. Karatsuba and Y. Ofman
rawtitle: Multiplication of multidigit numbers on automata
entry:
@Article{Karatsuba:1962:MMN,
  author =       "A. Karatsuba and Y. Ofman",
  title =        "Multiplication of multidigit numbers on automata",
  journal =      j-DOKL-AKAD-NAUK,
  volume =       "145",
  number =       "??",
  pages =        "293--294",
  month =        "????",
  year =         "1962",
  CODEN =        "DANKAS",
  ISSN =         "0002-3264",
  bibdate =      "Tue Jul 05 10:35:11 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Doklady Akademii nauk SSSR",
  journal-URL =  "http://istina.msu.ru/journals/366838/",
}


bibtype: article
filename: fparith.bib
label: Keir:1962:DOD
author: Y. A. Keir and P. W. Cheney and M. Tannenbaum
title: Division and overflow detection in residue number systems
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-11
number: 4
pages: 501--507
month: aug
monthnumber: 8
year: 1962
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1962.5219389
ISSN: 0367-9950 OR 03679950
MRclass: 68.00
MRnumber: MR0150990 (27 \#976)
MRreviewer: N. H. Choksy
bibdate: Thu Jul 14 09:11:51 MDT 2011
bibtimestamp: 2011.07.14 09:11:51 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219389
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: Y. A. Keir and P. W. Cheney and M. Tannenbaum
rawtitle: Division and overflow detection in residue number systems
entry:
@Article{Keir:1962:DOD,
  author =       "Y. A. Keir and P. W. Cheney and M. Tannenbaum",
  title =        "Division and overflow detection in residue number
                 systems",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-11",
  number =       "4",
  pages =        "501--507",
  month =        aug,
  year =         "1962",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1962.5219389",
  ISSN =         "0367-9950",
  MRclass =      "68.00",
  MRnumber =     "MR0150990 (27 \#976)",
  MRreviewer =   "N. H. Choksy",
  bibdate =      "Thu Jul 14 09:11:51 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=5219389",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Kesner:1962:FPA
author: O. Kesner
title: Floating-point arithmetic in COBOL
journal: j-CACM
volume: 5
number: 5
pages: 269--271
month: may
monthnumber: 5
year: 1962
CODEN: CACMA2
DOI: https://doi.org/10.1145/367710.367739
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:38 MST 2005
bibtimestamp: 2005.11.25 18:19:38 MST
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: O. Kesner
rawtitle: Floating-point arithmetic in {COBOL}
entry:
@Article{Kesner:1962:FPA,
  author =       "O. Kesner",
  title =        "Floating-point arithmetic in {COBOL}",
  journal =      j-CACM,
  volume =       "5",
  number =       "5",
  pages =        "269--271",
  month =        may,
  year =         "1962",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/367710.367739",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:38 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: Knuth:1962:EPC
author: Donald E. Knuth
title: Evaluation of polynomials by computer
journal: j-CACM
volume: 5
number: 12
pages: 595--599
month: dec
monthnumber: 12
year: 1962
CODEN: CACMA2
DOI: https://doi.org/10.1145/355580.369074
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 68.00 (12.00)
MRnumber: 27 \#970
bibdate: Thu Dec 08 11:11:03 2005
bibtimestamp: 2005.12.08 11:11:03 ???
note: See letter cite Knuth:1963:LEE.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Donald E. Knuth
rawnote: See letter \cite{Knuth:1963:LEE}.
rawtitle: Evaluation of polynomials by computer
bibsource:
http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; MathSciNet database

remark:
The author that Motzkin (1962) showed that Horner's rule for polynomial evaluation may not be optimal, and develops the idea further for arbitrary polynomials, but also observes that the coefficients of the revised polynomials may be difficult to find. He also asks about, but does not answer, the question of error analysis of the various methods.

entry:
@Article{Knuth:1962:EPC,
  author =       "Donald E. Knuth",
  title =        "Evaluation of polynomials by computer",
  journal =      j-CACM,
  volume =       "5",
  number =       "12",
  pages =        "595--599",
  month =        dec,
  year =         "1962",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355580.369074",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "68.00 (12.00)",
  MRnumber =     "27 \#970",
  bibdate =      "Thu Dec 08 11:11:03 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  note =         "See letter \cite{Knuth:1963:LEE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "The author that Motzkin (1962) showed that Horner's
                 rule for polynomial evaluation may not be optimal, and
                 develops the idea further for arbitrary polynomials,
                 but also observes that the coefficients of the revised
                 polynomials may be difficult to find. He also asks
                 about, but does not answer, the question of error
                 analysis of the various methods.",
}


bibtype: article
filename: fparith.bib
label: Lake:1962:LEH
author: G. T. Lake
title: Letter to the Editor: Hardware Conversion of Decimal and Binary Numbers
journal: j-CACM
volume: 5
number: 9
pages: 468--469
month: sep
monthnumber: 9
year: 1962
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 28 18:16:30 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 18:16:30 ???
fjournal: Communications of the ACM
keywords: decimal floating-point arithmetic
acknowledgement: ack-mfc
journalURL: https://dl.acm.org/loi/cacm
rawauthor: G. T. Lake
rawtitle: Letter to the Editor: Hardware Conversion of Decimal and Binary Numbers
entry:
@Article{Lake:1962:LEH,
  author =       "G. T. Lake",
  title =        "Letter to the Editor: Hardware Conversion of Decimal
                 and Binary Numbers",
  journal =      j-CACM,
  volume =       "5",
  number =       "9",
  pages =        "468--469",
  month =        sep,
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 28 18:16:30 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: Lynch:1962:WBD
author: W. C. Lynch
title: On a Wired-In Binary-to-Decimal Conversion Scheme
journal: j-CACM
volume: 5
number: 3
pages: 159--159
month: mar
monthnumber: 3
year: 1962
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 28 18:21:41 2003
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2003.11.28 18:21:41 ???
fjournal: Communications of the ACM
keywords: decimal floating-point arithmetic
acknowledgement: ack-mfc
journalURL: https://dl.acm.org/loi/cacm
rawauthor: W. C. Lynch
rawtitle: On a Wired-In Binary-to-Decimal Conversion Scheme
entry:
@Article{Lynch:1962:WBD,
  author =       "W. C. Lynch",
  title =        "On a Wired-In Binary-to-Decimal Conversion Scheme",
  journal =      j-CACM,
  volume =       "5",
  number =       "3",
  pages =        "159--159",
  month =        mar,
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 28 18:21:41 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "decimal floating-point arithmetic",
}


bibtype: article
filename: fparith.bib
label: MacSorley:1962:RBA
author: O. L. MacSorley
title: Review: booktitle An Algorithm for Rapid Binary Division, by J. B. Wilson and R. S. Ledley
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-11
number: 3
pages: 420--420
month: jun
monthnumber: 6
year: 1962
CODEN: IRELAO
ISSN: 0367-9950 OR 03679950
bibdate: Sat Jul 16 20:52:08 2011
bibtimestamp: 2011.07.16 20:52:08 ???
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: O. L. MacSorley
rawtitle: Review: \booktitle{An Algorithm for Rapid Binary Division}, by {J. B. Wilson and R. S. Ledley}
entry:
@Article{MacSorley:1962:RBA,
  author =       "O. L. MacSorley",
  title =        "Review: \booktitle{An Algorithm for Rapid Binary
                 Division}, by {J. B. Wilson and R. S. Ledley}",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-11",
  number =       "3",
  pages =        "420--420",
  month =        jun,
  year =         "1962",
  CODEN =        "IRELAO",
  ISSN =         "0367-9950",
  bibdate =      "Sat Jul 16 20:52:08 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: McGee:1962:BM
author: W. C. McGee
title: A Binary Multiplication
journal: j-SIAM-REVIEW
volume: 4
number: 3
pages: 256--256
year: 1962
CODEN: SIREAD
DOI: https://doi.org/10.1137/1004066
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Thu Mar 27 09:04:54 MDT 2014
bibtimestamp: 2014.03.27 09:04:54 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
onlinedate: July 1962
rawauthor: W. C. McGee
rawtitle: A Binary Multiplication
bibsource:
http://epubs.siam.org/toc/siread/4/3; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

entry:
@Article{McGee:1962:BM,
  author =       "W. C. McGee",
  title =        "A Binary Multiplication",
  journal =      j-SIAM-REVIEW,
  volume =       "4",
  number =       "3",
  pages =        "256--256",
  month =        "????",
  year =         "1962",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1004066",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:04:54 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/4/3;
                 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 1962",
}


bibtype: article
filename: fparith.bib
label: Meggitt:1962:PDP
author: J. E. Meggitt
title: Pseudo Division and Pseudo Multiplication Processes
journal: j-IBM-JRD
volume: 6
number: 2
pages: 210--226
month: apr
monthnumber: 4
year: 1962
CODEN: IBMJAE
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
bibdate: Thu Sep 1 10:15:31 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 10:15:31 ???
fjournal: IBM Journal of Research and Development
acknowledgement: ack-nj
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
rawauthor: J. E. Meggitt
rawtitle: Pseudo Division and Pseudo Multiplication Processes
entry:
@Article{Meggitt:1962:PDP,
  author =       "J. E. Meggitt",
  title =        "Pseudo Division and Pseudo Multiplication Processes",
  journal =      j-IBM-JRD,
  volume =       "6",
  number =       "2",
  pages =        "210--226",
  month =        apr,
  year =         "1962",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Thu Sep 1 10:15:31 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 Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}


bibtype: article
filename: fparith.bib
label: Metze:1962:CBD
author: Gernot Metze
title: A Class of Binary Divisions Yielding Minimally Represented Quotients
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-11
number: 6
pages: 761--764
month: dec
monthnumber: 12
year: 1962
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1962.5219460
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 09:11:53 MDT 2011
bibtimestamp: 2011.07.14 09:11:53 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219460
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: Gernot Metze
rawtitle: A Class of Binary Divisions Yielding Minimally Represented Quotients
entry:
@Article{Metze:1962:CBD,
  author =       "Gernot Metze",
  title =        "A Class of Binary Divisions Yielding Minimally
                 Represented Quotients",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-11",
  number =       "6",
  pages =        "761--764",
  month =        dec,
  year =         "1962",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1962.5219460",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 09:11:53 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=5219460",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Mitchell:1962:CMD
author: John N. Mitchell
title: Computer Multiplication and Division Using Binary Logarithms
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-11
number: 4
pages: 512--517
month: aug
monthnumber: 8
year: 1962
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1962.5219391
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 09:11:51 MDT 2011
bibtimestamp: 2011.07.14 09:11:51 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219391
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: John N. Mitchell
rawtitle: Computer Multiplication and Division Using Binary Logarithms
abstract:
A method of computer multiplication and division is proposed which uses binary logarithms. The logarithm of a binary number may be determined approximately from the number itself by simple shifting and counting. A simple add or subtract and shift operation is all that is required to multiply or divide. Since the logarithms used are approximate there can be errors in the result. An error analysis is given and a means of reducing the error for the multiply operation is show

rawabstract:
A method of computer multiplication and division is proposed which uses binary logarithms. The logarithm of a binary number may be determined approximately from the number itself by simple shifting and counting. A simple add or subtract and shift operation is all that is required to multiply or divide. Since the logarithms used are approximate there can be errors in the result. An error analysis is given and a means of reducing the error for the multiply operation is show

entry:
@Article{Mitchell:1962:CMD,
  author =       "John N. Mitchell",
  title =        "Computer Multiplication and Division Using Binary
                 Logarithms",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-11",
  number =       "4",
  pages =        "512--517",
  month =        aug,
  year =         "1962",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1962.5219391",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 09:11:51 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=5219391",
  abstract =     "A method of computer multiplication and division is
                 proposed which uses binary logarithms. The logarithm of
                 a binary number may be determined approximately from
                 the number itself by simple shifting and counting. A
                 simple add or subtract and shift operation is all that
                 is required to multiply or divide. Since the logarithms
                 used are approximate there can be errors in the result.
                 An error analysis is given and a means of reducing the
                 error for the multiply operation is show",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Rozier:1962:DBC
author: Charles P. Rozier
title: Decimal-to-Binary Conversion Using Octal Radix Arithmetic
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-11
number: 5
pages: 708--709
month: oct
monthnumber: 10
year: 1962
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1962.5219436
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 09:11:52 MDT 2011
bibtimestamp: 2011.07.14 09:11:52 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219436
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nhfb
journalURL: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: Charles P. Rozier
rawtitle: Decimal-to-Binary Conversion Using Octal Radix Arithmetic
entry:
@Article{Rozier:1962:DBC,
  author =       "Charles P. Rozier",
  title =        "Decimal-to-Binary Conversion Using Octal Radix
                 Arithmetic",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-11",
  number =       "5",
  pages =        "708--709",
  month =        oct,
  year =         "1962",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1962.5219436",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 09:11:52 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=5219436",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: fparith.bib
label: Shanks:1962:CD
author: Daniel Shanks and John W. Wrench, Jr.
title: Calculation of $ pi $ to 100,000 Decimals
journal: j-MATH-COMPUT
volume: 16
number: 77
pages: 76--99
month: jan
monthnumber: 1
year: 1962
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: Daniel Shanks and John W. {Wrench, Jr.}
rawtitle: Calculation of $ \pi $ to 100,000 Decimals
entry:
@Article{Shanks:1962:CD,
  author =       "Daniel Shanks and John W. {Wrench, Jr.}",
  title =        "Calculation of $ \pi $ to 100,000 Decimals",
  journal =      j-MATH-COMPUT,
  volume =       "16",
  number =       "77",
  pages =        "76--99",
  month =        jan,
  year =         "1962",
  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: misc
filename: fparith.bib
label: Sierra:1962:FDP
author: Huberto M. Sierra
title: Floating Decimal Point Arithmetic Control Means for Calculator
pages: 76--99
day: 5
month: jun
monthnumber: 6
year: 1962
bibdate: Sat Mar 24 05:59:45 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2018.03.24 05:59:45 ???
URL: https://patents.google.com/patent/US3037701A
acknowledgement: ack-nhfb
howpublished: US Patent 3,037,701
rawauthor: Huberto M. Sierra
rawtitle: Floating Decimal Point Arithmetic Control Means for Calculator
abstract:
The invention relates to digital computers and more particularly to digital computers for making calculations with numbers having a wide range of values with a limited number of digit storing positions.

remark:
US Patent filed 21 November 1956, granted to IBM on 5 June 1962, expired 5 June 1979 (17 years after grant). This may be the earliest US patent on floating-point arithmetic.

rawabstract:
The invention relates to digital computers and more particularly to digital computers for making calculations with numbers having a wide range of values with a limited number of digit storing positions.

entry:
@Misc{Sierra:1962:FDP,
  author =       "Huberto M. Sierra",
  title =        "Floating Decimal Point Arithmetic Control Means for
                 Calculator",
  howpublished = "US Patent 3,037,701",
  day =          "5",
  month =        jun,
  year =         "1962",
  bibdate =      "Sat Mar 24 05:59:45 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://patents.google.com/patent/US3037701A",
  abstract =     "The invention relates to digital computers and more
                 particularly to digital computers for making
                 calculations with numbers having a wide range of values
                 with a limited number of digit storing positions.",
  acknowledgement = ack-nhfb,
  remark =       "US Patent filed 21 November 1956, granted to IBM on 5
                 June 1962, expired 5 June 1979 (17 years after grant).
                 This may be the earliest US patent on floating-point
                 arithmetic.",
}


bibtype: article
filename: fparith.bib
label: Smith:1962:ACDa
author: Robert L. Smith
title: Algorithm 116: Complex Division
journal: j-CACM
volume: 5
number: 8
pages: 435--435
month: aug
monthnumber: 8
year: 1962
CODEN: CACMA2
DOI: https://doi.org/10.1145/368637.368661
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:40 MST 2005
bibtimestamp: 2005.11.25 18:19:40 MST
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Robert L. Smith
rawtitle: {Algorithm 116}: {Complex} Division
entry:
@Article{Smith:1962:ACDa,
  author =       "Robert L. Smith",
  title =        "{Algorithm 116}: {Complex} Division",
  journal =      j-CACM,
  volume =       "5",
  number =       "8",
  pages =        "435--435",
  month =        aug,
  year =         "1962",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/368637.368661",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:40 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: Spielberg:1962:PCF
author: Kurt Spielberg
title: Polynomial and Continued-Fraction Approximations for Logarithmic Functions
journal: j-MATH-COMPUT
volume: 16
number: 78
pages: 205--217
month: apr
monthnumber: 4
year: 1962
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-nj
ajournal: Math. Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: Kurt Spielberg
rawtitle: Polynomial and Continued-Fraction Approximations for Logarithmic Functions
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database

entry:
@Article{Spielberg:1962:PCF,
  author =       "Kurt Spielberg",
  title =        "Polynomial and Continued-Fraction Approximations for
                 Logarithmic Functions",
  journal =      j-MATH-COMPUT,
  volume =       "16",
  number =       "78",
  pages =        "205--217",
  month =        apr,
  year =         "1962",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: fparith.bib
label: Wynn:1962:AAP
author: P. Wynn
title: An Arsenal of ALGOL Procedures for Complex Arithmetic
journal: j-NORDISK-TIDSKR-INFORM-BEHAND
volume: 2
number: 4
pages: 232--255
month: dec
monthnumber: 12
year: 1962
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01940171
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 18:52:07 MST 2006
bibtimestamp: 2006.01.04 18:52:07 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=2&issue=4&spage=232
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: P. Wynn
rawtitle: An Arsenal of {ALGOL} Procedures for Complex Arithmetic
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=2&issue=4; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

keywords:
ALGOL; complex arithmetic; confluence hypergeometric function; continued fractions; incomplete beta function; incomplete gamma function; Stieltjes $S$-fractions; Weber parabolic cylinder function

entry:
@Article{Wynn:1962:AAP,
  author =       "P. Wynn",
  title =        "An Arsenal of {ALGOL} Procedures for Complex
                 Arithmetic",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "2",
  number =       "4",
  pages =        "232--255",
  month =        dec,
  year =         "1962",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01940171",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:07 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=2&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=2&issue=4&spage=232",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "ALGOL; complex arithmetic; confluence hypergeometric
                 function; continued fractions; incomplete beta
                 function; incomplete gamma function; Stieltjes
                 $S$-fractions; Weber parabolic cylinder function",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: incollection
filename: fparith.bib
label: Zuse:1962:ERE
author: K. Zuse
editor: W. Hoffman
booktitle: Digitale Informationswandler
publisher: Vieweg & Sohn, GmbH
address: Braunschweig, West Germany
pages: 508--532
year: 1962
bibdate: Wed Oct 13 11:23:04 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2010.10.13 11:23:04 ???
note: Reprinted in cite [ 4.3]Randell:1982:ODC. Translated by Mr. and Mrs. P. Jones.
language: German
acknowledgement: ack-nhfb
rawauthor: K. Zuse
rawbooktitle: {Digitale Informationswandler}
raweditor: W. Hoffman
rawnote: Reprinted in \cite[\S 4.3]{Randell:1982:ODC}. Translated by Mr. and Mrs. P. Jones.
title:
Entwicklungslinien einer Rechengerate-Entwicklung von der Mechanik zur Elektronik. (German) [Lines of development of computing equipment development from mechanics to electronics]

rawtitle:
{Entwicklungslinien einer Rechenger{\"a}te-Entwicklung von der Mechanik zur Elektronik}. ({German}) [Lines of development of computing equipment development from mechanics to electronics]

entry:
@InCollection{Zuse:1962:ERE,
  author =       "K. Zuse",
  editor =       "W. Hoffman",
  booktitle =    "{Digitale Informationswandler}",
  title =        "{Entwicklungslinien einer Rechenger{\"a}te-Entwicklung
                 von der Mechanik zur Elektronik}. ({German}) [Lines of
                 development of computing equipment development from
                 mechanics to electronics]",
  publisher =    "Vieweg \& Sohn, GmbH",
  address =      "Braunschweig, West Germany",
  pages =        "508--532",
  year =         "1962",
  bibdate =      "Wed Oct 13 11:23:04 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 4.3]{Randell:1982:ODC}.
                 Translated by Mr. and Mrs. P. Jones.",
  acknowledgement = ack-nhfb,
  language =     "German",
}


bibtype: article
filename: fparith.bib
label: Bemer:1963:NRT
author: R. W. Bemer
title: A Note on Range Transformations for Square Root and Logarithm
journal: j-CACM
volume: 6
number: 6
pages: 306--307
month: jun
monthnumber: 6
year: 1963
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:47 MST 2005
bibtimestamp: 2005.11.25 18:19:47 MST
fjournal: Communications of the ACM
keywords: $log (x)$; $sqrt (x)$; elementary functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: R. W. Bemer
rawtitle: A Note on Range Transformations for Square Root and Logarithm
entry:
@Article{Bemer:1963:NRT,
  author =       "R. W. Bemer",
  title =        "A Note on Range Transformations for Square Root and
                 Logarithm",
  journal =      j-CACM,
  volume =       "6",
  number =       "6",
  pages =        "306--307",
  month =        jun,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:47 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 =     "$\log(x)$; $\sqrt(x)$; elementary functions",
}


bibtype: article
filename: fparith.bib
label: Clenshaw:1963:ASF
author: C. W. Clenshaw and G. F. Miller and M. Woodger
title: Algorithms for Special Functions I
journal: j-NUM-MATH
volume: 4
pages: 403--419
year: 1963
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Fri Sep 16 10:21:31 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 10:21:31 ???
fjournal: Numerische Mathematik
acknowledgement: ack-nj
journalURL: http://link.springer.com/journal/211
rawauthor: C. W. Clenshaw and G. F. Miller and M. Woodger
rawtitle: Algorithms for Special Functions {I}
entry:
@Article{Clenshaw:1963:ASF,
  author =       "C. W. Clenshaw and G. F. Miller and M. Woodger",
  title =        "Algorithms for Special Functions {I}",
  journal =      j-NUM-MATH,
  volume =       "4",
  pages =        "403--419",
  year =         "1963",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Fri Sep 16 10:21:31 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: Daly:1963:HSA
author: W. G. Daly and J. F. Kruy
title: A High-Speed Arithmetic Unit Using Tunnel Diodes
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-12
number: 5
pages: 503--511
month: oct
monthnumber: 10
year: 1963
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1963.263644
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 08:10:42 MDT 2011
bibtimestamp: 2011.07.14 08:10:42 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037964
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: W. G. Daly and J. F. Kruy
rawtitle: A High-Speed Arithmetic Unit Using Tunnel Diodes
entry:
@Article{Daly:1963:HSA,
  author =       "W. G. Daly and J. F. Kruy",
  title =        "A High-Speed Arithmetic Unit Using Tunnel Diodes",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-12",
  number =       "5",
  pages =        "503--511",
  month =        oct,
  year =         "1963",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1963.263644",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 08:10:42 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=4037964",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: fparith.bib
label: Descloux:1963:NRE
author: J. Descloux
title: Note on the Round-Off Errors in Iterative Processes
journal: j-MATH-COMPUT
volume: 17
number: 81
pages: 18--27
month: jan
monthnumber: 1
year: 1963
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: J. Descloux
rawtitle: Note on the Round-Off Errors in Iterative Processes
entry:
@Article{Descloux:1963:NRE,
  author =       "J. Descloux",
  title =        "Note on the Round-Off Errors in Iterative Processes",
  journal =      j-MATH-COMPUT,
  volume =       "17",
  number =       "81",
  pages =        "18--27",
  month =        jan,
  year =         "1963",
  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: Dietmeyer:1963:CPN
author: Donald L. Dietmeyer
title: Conversion from Positive to Negative and Imaginary Radix
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-12
number: 1
pages: 20--22
month: feb
monthnumber: 2
year: 1963
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1963.263391
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 08:10:36 MDT 2011
bibtimestamp: 2011.07.14 08:10:36 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037765
fjournal: IEEE Transactions on Electronic Computers
keywords: imaginary base; negative base
acknowledgement: ack-nhfb
rawauthor: Donald L. Dietmeyer
rawtitle: Conversion from Positive to Negative and Imaginary Radix
entry:
@Article{Dietmeyer:1963:CPN,
  author =       "Donald L. Dietmeyer",
  title =        "Conversion from Positive to Negative and Imaginary
                 Radix",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-12",
  number =       "1",
  pages =        "20--22",
  month =        feb,
  year =         "1963",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1963.263391",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 08:10:36 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=4037765",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
  keywords =     "imaginary base; negative base",
}


bibtype: article
filename: fparith.bib
label: Eisman:1963:PER
author: S. H. Eisman
title: Polynomial Evaluation Revisited
journal: j-CACM
volume: 6
number: 7
pages: 384--385
month: jul
monthnumber: 7
year: 1963
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Sep 1 10:15:41 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.01 10:15:41 ???
fjournal: Communications of the ACM
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/cacm
rawauthor: S. H. Eisman
rawtitle: Polynomial Evaluation Revisited
entry:
@Article{Eisman:1963:PER,
  author =       "S. H. Eisman",
  title =        "Polynomial Evaluation Revisited",
  journal =      j-CACM,
  volume =       "6",
  number =       "7",
  pages =        "384--385",
  month =        jul,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:15:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: article
filename: fparith.bib
label: Eve:1963:SAI
author: J. Eve
title: Starting Approximations for the Iterative Calculation of Square Roots
journal: j-COMP-J
volume: 6
number: 3
pages: 274--276
month: nov
monthnumber: 11
year: 1963
CODEN: CMPJA6
DOI: https://doi.org/10.1093/comjnl/6.3.274
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Dec 4 14:47:30 MST 2012
bibtimestamp: 2012.12.04 14:47:30 MST
fjournal: The Computer Journal
acknowledgement: ack-nhfb
journalURL: http://comjnl.oxfordjournals.org/
rawauthor: J. Eve
rawtitle: Starting Approximations for the Iterative Calculation of Square Roots
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://comjnl.oxfordjournals.org/content/6/3.toc; http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_03/; https://www.math.utah.edu/pub/tex/bib/compj1960.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 are given which, in conjunction with a well-known iterative process, lead to square root approximations, with a relative error in the range $ (2^-55, 2^-45) $, at the expense of three divisions. More accurate approximations are given which require in addition a single multiplication.

rawabstract:
Several starting approximations are given which, in conjunction with a well-known iterative process, lead to square root approximations, with a relative error in the range $ (2^{-55}, 2^{-45}) $, at the expense of three divisions. More accurate approximations are given which require in addition a single multiplication.

entry:
@Article{Eve:1963:SAI,
  author =       "J. Eve",
  title =        "Starting Approximations for the Iterative Calculation
                 of Square Roots",
  journal =      j-COMP-J,
  volume =       "6",
  number =       "3",
  pages =        "274--276",
  month =        nov,
  year =         "1963",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/6.3.274",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:30 MST 2012",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://comjnl.oxfordjournals.org/content/6/3.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_03/;
                 https://www.math.utah.edu/pub/tex/bib/compj1960.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 are given which, in
                 conjunction with a well-known iterative process, lead
                 to square root approximations, with a relative error in
                 the range $ (2^{-55}, 2^{-45}) $, at the expense of
                 three divisions. More accurate approximations are given
                 which require in addition a single multiplication.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}


bibtype: book
filename: fparith.bib
label: Flores:1963:LCA
author: I. Flores
title: The Logic of Computer Arithmetic
publisher: pub-PH
address: pub-PH:adr
pages: xii + 493
year: 1963
LCCN: QA76.5 .F46
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: I. Flores
rawtitle: The Logic of Computer Arithmetic
entry:
@Book{Flores:1963:LCA,
  author =       "I. Flores",
  title =        "The Logic of Computer Arithmetic",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xii + 493",
  year =         "1963",
  LCCN =         "QA76.5 .F46",
  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: Geier:1963:ACD
author: A. Geier and I. Sturz
journal: An. Univ. Timisoara Ser. Sti. Mat.-Fiz.
volume: 1
pages: 133--139
year: 1963
MRclass: 68.00
MRnumber: 30\#3588
bibdate: Fri Dec 08 13:52:47 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 13:52:47 ???
acknowledgement: ack-nhfb
reviewer: R. N. Goss
rawauthor: A. Geier and I. Sturz
title:
The approximate calculation of a definite integral with automatic choice of integration steps (intervals). The program for the computer $ rm MECIPTI $ in a floating point regime. (Romanian)

rawtitle:
The approximate calculation of a definite integral with automatic choice of integration steps (intervals). The program for the computer {$ {\rm MECIPTI} $} in a floating point regime. ({Romanian})

entry:
@Article{Geier:1963:ACD,
  author =       "A. Geier and I. Sturz",
  title =        "The approximate calculation of a definite integral
                 with automatic choice of integration steps (intervals).
                 The program for the computer {$ {\rm MECIPTI} $} in a
                 floating point regime. ({Romanian})",
  journal =      "An. Univ. Timi{\c{s}}oara Ser. {\c{S}}ti. Mat.-Fiz.",
  volume =       "1",
  pages =        "133--139",
  year =         "1963",
  MRclass =      "68.00",
  MRnumber =     "30\#3588",
  bibdate =      "Fri Dec 08 13:52:47 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  reviewer =     "R. N. Goss",
}


bibtype: article
filename: fparith.bib
label: Goldstein:1963:SAD
author: Max Goldstein
title: Significance arithmetic on a digital computer
journal: j-CACM
volume: 6
number: 3
pages: 111--117
month: mar
monthnumber: 3
year: 1963
CODEN: CACMA2
DOI: https://doi.org/10.1145/366274.366339
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:45 MST 2005
bibtimestamp: 2005.11.25 18:19:45 MST
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Max Goldstein
rawtitle: Significance arithmetic on a digital computer
abstract:
The 7090 at NYU has been modified to include a ``Significance Mode'' of operation which is intended to facilitate the identification of significant bits in the results of floating-point arithmetic operations. The manner in which floating-point arithmetic is handled in this mode is discussed. Several numerical experiments using this mode are described and comparisons are made with the ordinary ``normalized mode.'' Examples include power series evaluation, linear equations solution, determinant evaluation and matrix inversion.

rawabstract:
The 7090 at NYU has been modified to include a ``Significance Mode'' of operation which is intended to facilitate the identification of significant bits in the results of floating-point arithmetic operations. The manner in which floating-point arithmetic is handled in this mode is discussed. Several numerical experiments using this mode are described and comparisons are made with the ordinary ``normalized mode.'' Examples include power series evaluation, linear equations solution, determinant evaluation and matrix inversion.

entry:
@Article{Goldstein:1963:SAD,
  author =       "Max Goldstein",
  title =        "Significance arithmetic on a digital computer",
  journal =      j-CACM,
  volume =       "6",
  number =       "3",
  pages =        "111--117",
  month =        mar,
  year =         "1963",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/366274.366339",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:45 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 =     "The 7090 at NYU has been modified to include a
                 ``Significance Mode'' of operation which is intended to
                 facilitate the identification of significant bits in
                 the results of floating-point arithmetic operations.
                 The manner in which floating-point arithmetic is
                 handled in this mode is discussed. Several numerical
                 experiments using this mode are described and
                 comparisons are made with the ordinary ``normalized
                 mode.'' Examples include power series evaluation,
                 linear equations solution, determinant evaluation and
                 matrix inversion.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: article
filename: fparith.bib
label: Knuth:1963:LEE
author: Donald E. Knuth
title: Letter to the Editor: Evaluation of polynomials by computer
journal: j-CACM
volume: 6
number: 2
pages: 51--51
month: feb
monthnumber: 2
year: 1963
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Tue Dec 26 16:31:38 1995
bibtimestamp: 1995.12.26 16:31:38 ???
note: See cite Knuth:1962:EPC.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: http://dl.acm.org/pub.cfm?id=J782
rawauthor: Donald E. Knuth
rawnote: See \cite{Knuth:1962:EPC}.
rawtitle: Letter to the {Editor}: {Evaluation} of polynomials by computer
bibsource:
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Knuth:1963:LEE,
  author =       "Donald E. Knuth",
  title =        "Letter to the {Editor}: {Evaluation} of polynomials by
                 computer",
  journal =      j-CACM,
  volume =       "6",
  number =       "2",
  pages =        "51--51",
  month =        feb,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Dec 26 16:31:38 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Knuth:1962:EPC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}


bibtype: article
filename: fparith.bib
label: Krishnamurthy:1963:CMD
author: E. V. Krishnamurthy
title: On Computer Multiplication and Division Using Binary Logarithms
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-12
number: 3
pages: 319--320
month: jun
monthnumber: 6
year: 1963
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1963.263572
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 08:10:39 MDT 2011
bibtimestamp: 2011.07.14 08:10:39 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037874
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: E. V. Krishnamurthy
rawtitle: On Computer Multiplication and Division Using Binary Logarithms
entry:
@Article{Krishnamurthy:1963:CMD,
  author =       "E. V. Krishnamurthy",
  title =        "On Computer Multiplication and Division Using Binary
                 Logarithms",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-12",
  number =       "3",
  pages =        "319--320",
  month =        jun,
  year =         "1963",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1963.263572",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 08:10:39 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=4037874",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: fparith.bib
label: Lehman:1963:MAB
author: M. Lehman
title: The Minimization of Assimilations in Binary Carry-Storage Arithmetic Units
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-12
number: 4
pages: 409--410
month: aug
monthnumber: 8
year: 1963
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1963.263479
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 08:10:40 MDT 2011
bibtimestamp: 2011.07.14 08:10:40 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037921
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: M. Lehman
rawtitle: The Minimization of Assimilations in Binary Carry-Storage Arithmetic Units
entry:
@Article{Lehman:1963:MAB,
  author =       "M. Lehman",
  title =        "The Minimization of Assimilations in Binary
                 Carry-Storage Arithmetic Units",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-12",
  number =       "4",
  pages =        "409--410",
  month =        aug,
  year =         "1963",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1963.263479",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 08:10:40 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=4037921",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: fparith.bib
label: Lehmer:1963:RDO
author: D. H. Lehmer
title: R63--17 Division and Overflow Detection in Residue Number Systems
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-12
number: 1
pages: 36--37
month: feb
monthnumber: 2
year: 1963
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1963.263493
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 08:10:36 MDT 2011
bibtimestamp: 2011.07.14 08:10:36 MDT
fjournal: IEEE Transactions on Electronic Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: D. H. Lehmer
rawtitle: {R63--17} Division and Overflow Detection in Residue Number Systems
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037786; http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4037754

entry:
@Article{Lehmer:1963:RDO,
  author =       "D. H. Lehmer",
  title =        "{R63--17} Division and Overflow Detection in Residue
                 Number Systems",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-12",
  number =       "1",
  pages =        "36--37",
  month =        feb,
  year =         "1963",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1963.263493",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 08:10:36 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=4037786;
                 http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4037754",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
  keywords =     "residue arithmetic; residue number system",
}


bibtype: article
filename: fparith.bib
label: Lindamood:1963:MCO
author: George E. Lindamood and George Shapiro
title: Magnitude Comparison and Overflow Detection in Modular Arithmetic Computers
journal: j-SIAM-REVIEW
volume: 5
number: 4
pages: 342--350
year: 1963
CODEN: SIREAD
DOI: https://doi.org/10.1137/1005095
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Thu Mar 27 09:05:07 MDT 2014
bibtimestamp: 2014.03.27 09:05:07 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
onlinedate: October 1963
rawauthor: George E. Lindamood and George Shapiro
rawtitle: Magnitude Comparison and Overflow Detection in Modular Arithmetic Computers
bibsource:
http://epubs.siam.org/toc/siread/5/4; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

entry:
@Article{Lindamood:1963:MCO,
  author =       "George E. Lindamood and George Shapiro",
  title =        "Magnitude Comparison and Overflow Detection in Modular
                 Arithmetic Computers",
  journal =      j-SIAM-REVIEW,
  volume =       "5",
  number =       "4",
  pages =        "342--350",
  month =        "????",
  year =         "1963",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1005095",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:05:07 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/5/4;
                 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 =   "October 1963",
}


bibtype: article
filename: fparith.bib
label: Metropolis:1963:BOU
author: N. Metropolis and R. L. Ashenhurst
title: Basic Operations in an Unnormalized Arithmetic System
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-12
number: 6
pages: 896--904
month: dec
monthnumber: 12
year: 1963
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1963.263593
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 08:10:44 MDT 2011
bibtimestamp: 2011.07.14 08:10:44 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038037
fjournal: IEEE Transactions on Electronic Computers
keywords: MANIAC III
remark: Cited in cite Sterbenz:1974:FPC.
ZMnumber: 0124.07910
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753
rawauthor: N. Metropolis and R. L. Ashenhurst
rawtitle: Basic Operations 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; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib

abstract:
A particular set of unnormalized arithmetic operations termed ``basic'' are described, in the context of the University of Chicago Maniac III Computer. Each basic operation involves three operand words and generates two result words, all in unnormalized floating point format. The use of these operations in the implementation of multi-precision arithmetic is explained; in particular, it is demonstrated that multiprecision division can be effected in a nontentative manner with their aid.

rawabstract:
A particular set of unnormalized arithmetic operations termed ``basic'' are described, in the context of the University of Chicago Maniac III Computer. Each basic operation involves three operand words and generates two result words, all in unnormalized floating point format. The use of these operations in the implementation of multi-precision arithmetic is explained; in particular, it is demonstrated that multiprecision division can be effected in a nontentative manner with their aid.

entry:
@Article{Metropolis:1963:BOU,
  author =       "N. Metropolis and R. L. Ashenhurst",
  title =        "Basic Operations in an Unnormalized Arithmetic
                 System",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-12",
  number =       "6",
  pages =        "896--904",
  month =        dec,
  year =         "1963",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1963.263593",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 08:10:44 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 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=4038037",
  ZMnumber =     "0124.07910",
  abstract =     "A particular set of unnormalized arithmetic operations
                 termed ``basic'' are described, in the context of the
                 University of Chicago Maniac III Computer. Each basic
                 operation involves three operand words and generates
                 two result words, all in unnormalized floating point
                 format. The use of these operations in the
                 implementation of multi-precision arithmetic is
                 explained; in particular, it is demonstrated that
                 multiprecision division can be effected in a
                 nontentative manner with their aid.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753",
  keywords =     "MANIAC III",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: book
filename: fparith.bib
label: Mood:1963:ITS
author: Alexander McFarlane Mood and Franklin A. Graybill
title: Introduction to the theory of statistics
publisher: pub-MCGRAW-HILL
address: pub-MCGRAW-HILL:adr
edition: Second
pages: 443
year: 1963
LCCN: HA29 .M75 1963
bibdate: Fri Aug 20 10:02:03 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.08.20 10:02:03 MDT
series: McGraw-Hill series in probability and statistics
remark: Cited in cite Sterbenz:1974:FPC.
subject: Mathematical statistics
acknowledgement: ack-nhfb
rawauthor: Alexander McFarlane Mood and Franklin A. Graybill
rawtitle: Introduction to the theory of statistics
entry:
@Book{Mood:1963:ITS,
  author =       "Alexander McFarlane Mood and Franklin A. Graybill",
  title =        "Introduction to the theory of statistics",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  edition =      "Second",
  pages =        "443",
  year =         "1963",
  LCCN =         "HA29 .M75 1963",
  bibdate =      "Fri Aug 20 10:02:03 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "McGraw-Hill series in probability and statistics",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
  subject =      "Mathematical statistics",
}


bibtype: article
filename: fparith.bib
label: Stern:1963:CSR
author: T. E. Stern and R. M. Lerner
title: A circuit for the square root of the sum of the squares
journal: j-PROC-IEEE
volume: 51
number: 4
pages: 593--596
month: apr
monthnumber: 4
year: 1963
CODEN: IEEPAD
ISSN: 0018-9219 (print), 1558-2256 (electronic) OR 00189219 (print), 15582256 (electronic)
ISSNL: 0018-9219 OR 00189219
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: Proceedings of the IEEE
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5
rawauthor: T. E. Stern and R. M. Lerner
rawtitle: A circuit for the square root of the sum of the squares
entry:
@Article{Stern:1963:CSR,
  author =       "T. E. Stern and R. M. Lerner",
  title =        "A circuit for the square root of the sum of the
                 squares",
  journal =      j-PROC-IEEE,
  volume =       "51",
  number =       "4",
  pages =        "593--596",
  month =        apr,
  year =         "1963",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "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",
  summary =      "A piecewise-linear network can produce an output
                 proportional to the square root of the sum of the
                 squares of a set of input voltages, using resistors and
                 diodes alone. The required relationship between
                 voltages can be represented by a multi- \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Stroud:1963:MPF
author: A. H. Stroud and D. Secrest
title: A multiple-precision floating-point interpretive program for the Control Data 1604
journal: j-COMP-J
volume: 6
number: 1
pages: 62--66
month: apr
monthnumber: 4
year: 1963
CODEN: CMPJA6
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Fri Sep 29 08:55:45 MDT 2000
bibtimestamp: 2000.09.29 08:55:45 MDT
fjournal: The Computer Journal
acknowledgement: ack-nhfb
journalURL: http://comjnl.oxfordjournals.org/
rawauthor: A. H. Stroud and D. Secrest
rawtitle: A multiple-precision floating-point interpretive program for the {Control Data} 1604
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/060062.sgm.abs.html; http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/62.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/63.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/64.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/65.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/66.tif

entry:
@Article{Stroud:1963:MPF,
  author =       "A. H. Stroud and D. Secrest",
  title =        "A multiple-precision floating-point interpretive
                 program for the {Control Data} 1604",
  journal =      j-COMP-J,
  volume =       "6",
  number =       "1",
  pages =        "62--66",
  month =        apr,
  year =         "1963",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:55:45 MDT 2000",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/060062.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/62.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/63.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/64.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/65.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/66.tif",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}


bibtype: article
filename: fparith.bib
label: Svoboda:1963:AD
author: A. Svoboda
title: An algorithm for division
journal: j-INF-PROCESS-MACH
volume: 9
pages: 25--33
year: 1963
CODEN: IPRMDD
ISSN: 0373-885X OR 0373885X
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: Information processing machines
acknowledgement: ack-sfo
rawauthor: A. Svoboda
rawtitle: An algorithm for division
entry:
@Article{Svoboda:1963:AD,
  author =       "A. Svoboda",
  title =        "An algorithm for division",
  journal =      j-INF-PROCESS-MACH,
  volume =       "9",
  number =       "??",
  pages =        "25--33",
  month =        "????",
  year =         "1963",
  CODEN =        "IPRMDD",
  ISSN =         "0373-885X",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "Information processing machines",
}


bibtype: inproceedings
filename: fparith.bib
label: Wilkinson:1963:PSA
author: J. H. Wilkinson
title: Plane rotations in floating-point arithmetic
crossref: Metropolis:1963:PFS
pages: 185--198
year: 1963
MRclass: 65.35
MRnumber: 28\#1744
bibdate: Fri Dec 8 08:24:14 1995
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1995.12.08 08:24:14 ???
acknowledgement: ack-nhfb
reviewer: A. S. Householder
rawauthor: J. H. Wilkinson
rawtitle: Plane rotations in floating-point arithmetic
entry:
@InProceedings{Wilkinson:1963:PSA,
  author =       "J. H. Wilkinson",
  title =        "Plane rotations in floating-point arithmetic",
  crossref =     "Metropolis:1963:PFS",
  pages =        "185--198",
  year =         "1963",
  MRclass =      "65.35",
  MRnumber =     "28\#1744",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  reviewer =     "A. S. Householder",
}


bibtype: article
filename: fparith.bib
label: Aiken:1964:PAC
author: H. H. Aiken and A. G. Oettinger and T. C. Bartee
title: Proposed automatic calculating machine
journal: j-IEEE-SPECTRUM
volume: 1
number: 8
pages: 62--69
month: aug
monthnumber: 8
year: 1964
CODEN: IEESAM
DOI: https://doi.org/10.1109/MSPEC.1964.6500770
ISSN: 0018-9235 (print), 1939-9340 (electronic) OR 00189235 (print), 19399340 (electronic)
ISSNL: 0018-9235 OR 00189235
bibdate: Tue Jan 14 11:14:17 2020
bibtimestamp: 2020.01.14 11:14:17 ???
fjournal: IEEE Spectrum
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6
rawauthor: H. H. Aiken and A. G. Oettinger and T. C. Bartee
rawtitle: Proposed automatic calculating machine
bibsource:
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/ieeespectrum1960.bib; https://www.math.utah.edu/pub/tex/bib/master.bib

note:
Previously unpublished memorandum written by Aiken and dated by an unknown recipient as 4 November 1937. Reprinted in cite [ 5.1]Randell:1982:ODC.

abstract:
Here presented is the memorandum that 20 years ago initiated a series of events whose revolutionary implications are only beginning to manifest themselves a description of the first large-scale general-purpose automatic digital computer. Twenty years ago, on August 7, 1944, Mark I, the first large-scale general-purpose automatic digital computer ever to be put in operation was dedicated at Harvard University by James B. Conant, then president of Harvard, and the late Thomas J. Watson, founder of IBM.

remark:
Pages 66--69 discuss computation of the elementary functions with minimal intermediate storage: recipes are given for integral and fractional power, log, exponential, trigonometric, inverse trigonometric, hyperbolic, and inverse hyperbolic. Mention is also made of the probability integral, elliptic functions, and Bessel functions, but the text says they will be discussed later (meaning, in a future publication). The methods involve recurrences and series summations, and thus, can be regarded as precision independent.

rawabstract:
Here presented is the memorandum that 20 years ago initiated a series of events whose revolutionary implications are only beginning to manifest themselves a description of the first large-scale general-purpose automatic digital computer. Twenty years ago, on August 7, 1944, Mark I, the first large-scale general-purpose automatic digital computer ever to be put in operation was dedicated at Harvard University by James B. Conant, then president of Harvard, and the late Thomas J. Watson, founder of IBM.

rawnote:
Previously unpublished memorandum written by Aiken and dated by an unknown recipient as 4 November 1937. Reprinted in \cite[\S 5.1]{Randell:1982:ODC}.

entry:
@Article{Aiken:1964:PAC,
  author =       "H. H. Aiken and A. G. Oettinger and T. C. Bartee",
  title =        "Proposed automatic calculating machine",
  journal =      j-IEEE-SPECTRUM,
  volume =       "1",
  number =       "8",
  pages =        "62--69",
  month =        aug,
  year =         "1964",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.1964.6500770",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Tue Jan 14 11:14:17 2020",
  bibsource =    "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/ieeespectrum1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "Previously unpublished memorandum written by Aiken and
                 dated by an unknown recipient as 4 November 1937.
                 Reprinted in \cite[\S 5.1]{Randell:1982:ODC}.",
  abstract =     "Here presented is the memorandum that 20 years ago
                 initiated a series of events whose revolutionary
                 implications are only beginning to manifest themselves
                 a description of the first large-scale general-purpose
                 automatic digital computer. Twenty years ago, on August
                 7, 1944, Mark I, the first large-scale general-purpose
                 automatic digital computer ever to be put in operation
                 was dedicated at Harvard University by James B. Conant,
                 then president of Harvard, and the late Thomas J.
                 Watson, founder of IBM.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  remark =       "Pages 66--69 discuss computation of the elementary
                 functions with minimal intermediate storage: recipes
                 are given for integral and fractional power, log,
                 exponential, trigonometric, inverse trigonometric,
                 hyperbolic, and inverse hyperbolic. Mention is also
                 made of the probability integral, elliptic functions,
                 and Bessel functions, but the text says they will be
                 discussed later (meaning, in a future publication). The
                 methods involve recurrences and series summations, and
                 thus, can be regarded as precision independent.",
}


bibtype: manual
filename: fparith.bib
label: Anonymous:1964:PPF
author: Anonymous
organization: General Precision, Inc.
address: West Lafayette, IN, USA
pages: 45
year: 1964
bibdate: Mon May 06 10:24:31 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.06 10:24:31 ???
remark: Program no. H1-02.0
acknowledgement: ack-nhfb
rawauthor: Anonymous
title:
PINT: Purdue floating point interpretive system: for the RPC 4000 General Precision electronic computer

keywords:
Electronic digital computers --- Programming.; Purdue University School of Electrical Engineering; RPC 4000 (Computer)

rawtitle:
{PINT}: {Purdue} floating point interpretive system: for the {RPC 4000 General Precision} electronic computer

entry:
@Manual{Anonymous:1964:PPF,
  author =       "Anonymous",
  title =        "{PINT}: {Purdue} floating point interpretive system:
                 for the {RPC 4000 General Precision} electronic
                 computer",
  organization = "General Precision, Inc.",
  address =      "West Lafayette, IN, USA",
  pages =        "45",
  year =         "1964",
  bibdate =      "Mon May 06 10:24:31 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming.; Purdue
                 University School of Electrical Engineering; RPC 4000
                 (Computer)",
  remark =       "Program no. H1-02.0",
}


bibtype: article
filename: fparith.bib
label: Ashenhurst:1964:FEU
author: R. L. Ashenhurst
title: Function Evaluation in Unnormalized Arithmetic
journal: j-J-ACM
volume: 11
number: 2
pages: 168--187
month: apr
monthnumber: 4
year: 1964
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Thu Nov 03 22:33:52 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.11.03 22:33:52 ???
fjournal: Journal of the ACM
acknowledgement: ack-nhfb
journalURL: http://portal.acm.org/browse_dl.cfm?idx=J401
rawauthor: R. L. Ashenhurst
rawtitle: Function Evaluation in Unnormalized Arithmetic
entry:
@Article{Ashenhurst:1964:FEU,
  author =       "R. L. Ashenhurst",
  title =        "Function Evaluation in Unnormalized Arithmetic",
  journal =      j-J-ACM,
  volume =       "11",
  number =       "2",
  pages =        "168--187",
  month =        apr,
  year =         "1964",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Thu Nov 03 22:33:52 1994",
  bibsource =    "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: Baer:1964:MPA
author: Robert M. Baer and Martin G. Redlich
journal: j-CACM
volume: 7
number: 11
pages: 657--659
month: nov
monthnumber: 11
year: 1964
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65.25
MRnumber: 31\#865
bibdate: Mon Oct 24 09:33:02 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.10.24 09:33:02 MDT
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Robert M. Baer and Martin G. Redlich
title:
Multiple-precision arithmetic and the exact calculation of the $ 3 - j $, $ 6 - j $ and $ 9 - j $ symbols

abstract:
Described in this paper is a system of general-purpose multiple-precision fixed-point routines and their use in subroutines which calculate exactly the quantum-mechanical 3-j, 6-j and 9-j symbols of large arguments.

rawabstract:
Described in this paper is a system of general-purpose multiple-precision fixed-point routines and their use in subroutines which calculate exactly the quantum-mechanical 3-j, 6-j and 9-j symbols of large arguments.

rawtitle:
Multiple-precision arithmetic and the exact calculation of the $ 3 - j $, $ 6 - j $ and $ 9 - j $ symbols

entry:
@Article{Baer:1964:MPA,
  author =       "Robert M. Baer and Martin G. Redlich",
  title =        "Multiple-precision arithmetic and the exact
                 calculation of the $ 3 - j $, $ 6 - j $ and $ 9 - j $
                 symbols",
  journal =      j-CACM,
  volume =       "7",
  number =       "11",
  pages =        "657--659",
  month =        nov,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.25",
  MRnumber =     "31\#865",
  bibdate =      "Mon Oct 24 09:33:02 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Described in this paper is a system of general-purpose
                 multiple-precision fixed-point routines and their use
                 in subroutines which calculate exactly the
                 quantum-mechanical 3-j, 6-j and 9-j symbols of large
                 arguments.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: mastersthesis
filename: fparith.bib
label: Bookhart:1964:SFP
author: Thomas Woodward Bookhart
title: A study of floating point arithmetic
type: Thesis (M.S. in Math.)
school: Georgia Institute of Technology
address: Atlanta, GA, USA
pages: 51
year: 1964
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Electronic digital computers.; Number theory.; Numerical calculations --- Computer programs.
acknowledgement: ack-nhfb
rawauthor: Thomas Woodward Bookhart
rawtitle: A study of floating point arithmetic
entry:
@MastersThesis{Bookhart:1964:SFP,
  author =       "Thomas Woodward Bookhart",
  title =        "A study of floating point arithmetic",
  type =         "Thesis ({M.S. in Math.})",
  school =       "Georgia Institute of Technology",
  address =      "Atlanta, GA, USA",
  pages =        "51",
  year =         "1964",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers.; Number theory.;
                 Numerical calculations --- Computer programs.",
}


bibtype: article
filename: fparith.bib
label: Brooker:1964:PPS
author: R. A. Brooker
title: A programming package for some general modes of arithmetic
journal: j-CACM
volume: 7
number: 2
pages: 119--127
month: feb
monthnumber: 2
year: 1964
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Oct 24 09:33:00 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.10.24 09:33:00 MDT
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: R. A. Brooker
rawtitle: A programming package for some general modes of arithmetic
abstract:
An interpretive programming package is described for computation with operands which may be real, complex, single or double precision, or real multiple precision. It also performs operations on matrices formed from these elements. A simple language structure is used to describe the computation.

rawabstract:
An interpretive programming package is described for computation with operands which may be real, complex, single or double precision, or real multiple precision. It also performs operations on matrices formed from these elements. A simple language structure is used to describe the computation.

entry:
@Article{Brooker:1964:PPS,
  author =       "R. A. Brooker",
  title =        "A programming package for some general modes of
                 arithmetic",
  journal =      j-CACM,
  volume =       "7",
  number =       "2",
  pages =        "119--127",
  month =        feb,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Oct 24 09:33:00 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "An interpretive programming package is described for
                 computation with operands which may be real, complex,
                 single or double precision, or real multiple precision.
                 It also performs operations on matrices formed from
                 these elements. A simple language structure is used to
                 describe the computation.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: manual
filename: fparith.bib
label: Burroughs:1964:BBI
author: Burroughs Corporation
title: Burroughs B5500 Information Processing Systems Reference Manual
organization: Burroughs Corporation
address: Detroit, MI, USA
pages: 119--127
year: 1964
bibdate: Wed Nov 22 21:15:11 2006
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2006.11.22 21:15:11 ???
keywords: decimal floating-point arithmetic
acknowledgement: ack-nhfb
rawauthor: {Burroughs Corporation}
rawtitle: {Burroughs B5500} Information Processing Systems Reference Manual
remark:
The B5500 uses a decimal integer or fixed-point coefficient of 21 or 22 digits, with an exponent range of $ pm 63 $.

entry:
@Manual{Burroughs:1964:BBI,
  author =       "{Burroughs Corporation}",
  title =        "{Burroughs B5500} Information Processing Systems
                 Reference Manual",
  organization = "Burroughs Corporation",
  address =      "Detroit, MI, USA",
  year =         "1964",
  bibdate =      "Wed Nov 22 21:15:11 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  remark =       "The B5500 uses a decimal integer or fixed-point
                 coefficient of 21 or 22 digits, with an exponent range
                 of $ \pm 63 $.",
}


bibtype: article
filename: fparith.bib
label: Cody:1964:DPS
author: W. J. Cody, Jr.
title: Double-Precision Square Root for the CDC-3600
journal: j-CACM
volume: 7
number: 12
pages: 715--718
month: dec
monthnumber: 12
year: 1964
CODEN: CACMA2
DOI: https://doi.org/10.1145/355588.365122
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: $sqrt(x)$; CDC 3600; elementary functions
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/cacm
rawauthor: W. J. {Cody, Jr.}
rawtitle: Double-Precision Square Root for the {CDC-3600}
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
In January of 1960, the late Hans J. Maehly completed a summary of approximations to the elementary functions for the CDC-1604 computer. The approximations and techniques suggested by Maehly are equally applicable to the second large computer in the CDC line, the 3600. Unlike the 1604, however, the 3600 has built-in double-precision floating-point arithmetic. The present work, largely inspired by the successes of Maehly and his associates, concerns the extension of one of Maehly's ideas to a double-precision subroutine for the 3600.

rawabstract:
In January of 1960, the late Hans J. Maehly completed a summary of approximations to the elementary functions for the CDC-1604 computer. The approximations and techniques suggested by Maehly are equally applicable to the second large computer in the CDC line, the 3600. Unlike the 1604, however, the 3600 has built-in double-precision floating-point arithmetic. The present work, largely inspired by the successes of Maehly and his associates, concerns the extension of one of Maehly's ideas to a double-precision subroutine for the 3600.

entry:
@Article{Cody:1964:DPS,
  author =       "W. J. {Cody, Jr.}",
  title =        "Double-Precision Square Root for the {CDC-3600}",
  journal =      j-CACM,
  volume =       "7",
  number =       "12",
  pages =        "715--718",
  month =        dec,
  year =         "1964",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355588.365122",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:15:43 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In January of 1960, the late Hans J. Maehly completed
                 a summary of approximations to the elementary functions
                 for the CDC-1604 computer. The approximations and
                 techniques suggested by Maehly are equally applicable
                 to the second large computer in the CDC line, the 3600.
                 Unlike the 1604, however, the 3600 has built-in
                 double-precision floating-point arithmetic. The present
                 work, largely inspired by the successes of Maehly and
                 his associates, concerns the extension of one of
                 Maehly's ideas to a double-precision subroutine for the
                 3600.",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$sqrt(x)$; CDC 3600; elementary functions",
}


bibtype: article
filename: fparith.bib
label: Cowgill:1964:LEB
author: D. Cowgill
title: Logic Equations for a Built-In Square Root Method
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-13
number: 2
pages: 156--157
month: apr
monthnumber: 4
year: 1964
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1964.263791
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 06:56:59 MDT 2011
bibtimestamp: 2011.07.14 06:56:59 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038119
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: D. Cowgill
rawtitle: Logic Equations for a Built-In Square Root Method
entry:
@Article{Cowgill:1964:LEB,
  author =       "D. Cowgill",
  title =        "Logic Equations for a Built-In Square Root Method",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-13",
  number =       "2",
  pages =        "156--157",
  month =        apr,
  year =         "1964",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1964.263791",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:56:59 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=4038119",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: fparith.bib
label: Eve:1964:EP
author: J. Eve
title: The Evaluation of Polynomials
journal: j-NUM-MATH
volume: 6
pages: 17--21
year: 1964
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Fri Sep 16 10:21:47 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.16 10:21:47 ???
fjournal: Numerische Mathematik
acknowledgement: ack-nj
journalURL: http://link.springer.com/journal/211
rawauthor: J. Eve
rawtitle: The Evaluation of Polynomials
entry:
@Article{Eve:1964:EP,
  author =       "J. Eve",
  title =        "The Evaluation of Polynomials",
  journal =      j-NUM-MATH,
  volume =       "6",
  pages =        "17--21",
  year =         "1964",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Fri Sep 16 10:21:47 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 =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  xxmonth =      "(none)",
  xxnumber =     "(none)",
}


bibtype: mastersthesis
filename: fparith.bib
label: Goldschmidt:1964:ADC
author: Robert E. Goldschmidt
title: Applications of Division by Convergence
type: Thesis (M.S.)
school: Department of Electrical Engineering, Massachusetts Institute of Technology
address: Cambridge, MA, USA
pages: 44
month: jun
monthnumber: 6
year: 1964
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 ???
URL: https://dspace.mit.edu/handle/1721.1/11113
acknowledgement: ack-sfo
advisor: Alfred K. Susskind
rawauthor: Robert E. Goldschmidt
rawtitle: Applications of Division by Convergence
remark:
This thesis introduced the quadratically convergent Goldschmidt algorithm for iterative division, as an alternative to Newton--Raphson iteration: see cite Flynn:1966:VHS, Anderson:1967:ISMb, Flynn:1970:DFI, Ito:1995:EIAb, Oberman:1996:FIR, Ercegovac:1999:IGD, Ercegovac:2000:IGD, Gallagher:2000:FTN, Even:2003:PEA, Markstein:2004:SDS, Even:2005:PEA, Piso:2006:OMD, Schulte:2007:FPD, Kong:2008:RMI, Piso:2008:FOS, Piso:2008:NRA, Ruiz:2008:EIR, Kong:2010:RMR, Kong:2011:GDM, Piso:2011:VLG, Panhaleux:2012:CFP for improvements and error analysis. For computing $ Q = N / D $, Newton--Raphson starts with $ Y approx 1 / D $, and iterates $ Y leftarrow (2 - Y D) Y $, or equivalently, $ Y leftarrow Y - (Y (Y D - 1)) $. With the same starting point, Goldschmidt instead iterates $ N leftarrow N Y $, $ D leftarrow D Y $, $ Y = 2 - D $, which converges to $ Y = 1 $. When parallel multipliers are available, the two multiplies can be done at the same time, whereas Newton--Raphson requires two sequential multiplies. In addition, the update $ 2 D $ can be computed in hardware by a fast bitwise two's complement operation, instead of a slower floating-point subtraction. The Goldschmidt algorithm has been used in CPUs of the IBM S/360 model 91 and the AMD K7. Unfortunately, unlike Newton--Raphson, each iteration of the Goldschmidt algorithm increases rounding error. Numerical tests of the Goldschmidt algorithm show worst-case errors in ulps roughly equal to the number of iterations. Without an FMA, the Newton--Raphson worst case errors are about 1.7 ulps, and with an FMA, about 1.0 ulps. In hardware in both cases, a few bits of extra intermediate precision can lead to correctly rounded results. Without extra precision, additional fixups are needed for correct rounding.

entry:
@MastersThesis{Goldschmidt:1964:ADC,
  author =       "Robert E. Goldschmidt",
  title =        "Applications of Division by Convergence",
  type =         "Thesis ({M.S.})",
  school =       "Department of Electrical Engineering, Massachusetts
                 Institute of Technology",
  address =      "Cambridge, MA, USA",
  pages =        "44",
  month =        jun,
  year =         "1964",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://dspace.mit.edu/handle/1721.1/11113",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  advisor =      "Alfred K. Susskind",
  remark =       "This thesis introduced the quadratically convergent
                 Goldschmidt algorithm for iterative division, as an
                 alternative to Newton--Raphson iteration: see
                 \cite{Flynn:1966:VHS, Anderson:1967:ISMb,
                 Flynn:1970:DFI, Ito:1995:EIAb, Oberman:1996:FIR,
                 Ercegovac:1999:IGD, Ercegovac:2000:IGD,
                 Gallagher:2000:FTN, Even:2003:PEA, Markstein:2004:SDS,
                 Even:2005:PEA, Piso:2006:OMD, Schulte:2007:FPD,
                 Kong:2008:RMI, Piso:2008:FOS, Piso:2008:NRA,
                 Ruiz:2008:EIR, Kong:2010:RMR, Kong:2011:GDM,
                 Piso:2011:VLG, Panhaleux:2012:CFP} for improvements and
                 error analysis. For computing $ Q = N / D $,
                 Newton--Raphson starts with $ Y \approx 1 / D $, and
                 iterates $ Y \leftarrow (2 - Y D) Y $, or equivalently,
                 $ Y \leftarrow Y - (Y (Y D - 1)) $. With the same
                 starting point, Goldschmidt instead iterates $ N
                 \leftarrow N Y $, $ D \leftarrow D Y $, $ Y = 2 - D $,
                 which converges to $ Y = 1 $. When parallel multipliers
                 are available, the two multiplies can be done at the
                 same time, whereas Newton--Raphson requires two
                 sequential multiplies. In addition, the update $ 2 D $
                 can be computed in hardware by a fast bitwise two's
                 complement operation, instead of a slower
                 floating-point subtraction. The Goldschmidt algorithm
                 has been used in CPUs of the IBM S/360 model 91 and the
                 AMD K7. Unfortunately, unlike Newton--Raphson, each
                 iteration of the Goldschmidt algorithm increases
                 rounding error. Numerical tests of the Goldschmidt
                 algorithm show worst-case errors in ulps roughly equal
                 to the number of iterations. Without an FMA, the
                 Newton--Raphson worst case errors are about 1.7 ulps,
                 and with an FMA, about 1.0 ulps. In hardware in both
                 cases, a few bits of extra intermediate precision can
                 lead to correctly rounded results. Without extra
                 precision, additional fixups are needed for correct
                 rounding.",
}


bibtype: article
filename: fparith.bib
label: Gram:1964:RZF
author: Christian Gram
title: On the Representation of Zero in Floating-Point Arithmetic
journal: j-NORDISK-TIDSKR-INFORM-BEHAND
volume: 4
number: 3
pages: 156--161
month: sep
monthnumber: 9
year: 1964
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01956026
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 68.00
MRnumber: 29\#5412
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 ???
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=4&issue=3&spage=156
keywords: floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Christian Gram
rawtitle: On the Representation of Zero in Floating-Point Arithmetic
entry:
@Article{Gram:1964:RZF,
  author =       "Christian Gram",
  title =        "On the Representation of Zero in Floating-Point
                 Arithmetic",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "4",
  number =       "3",
  pages =        "156--161",
  month =        sep,
  year =         "1964",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01956026",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "68.00",
  MRnumber =     "29\#5412",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=4&issue=3&spage=156",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point arithmetic; rounding errors",
}


bibtype: article
filename: fparith.bib
label: Gregory:1964:FAN
author: Robert T. Gregory and James L. Raney
title: Floating-point arithmetic with $ 84 $-bit numbers
journal: j-CACM
volume: 7
pages: 10--13
year: 1964
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 68.00
MRnumber: 30\#2706
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: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Robert T. Gregory and James L. Raney
rawtitle: Floating-point arithmetic with $ 84 $-bit numbers
entry:
@Article{Gregory:1964:FAN,
  author =       "Robert T. Gregory and James L. Raney",
  title =        "Floating-point arithmetic with $ 84 $-bit numbers",
  journal =      j-CACM,
  volume =       "7",
  pages =        "10--13",
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "68.00",
  MRnumber =     "30\#2706",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "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: book
filename: fparith.bib
label: Henrici:1964:ENA
author: Peter Henrici
title: Elements of numerical analysis
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xv + 328
year: 1964
LCCN: QA297 .H4
bibdate: Fri Aug 20 09:17:19 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.08.20 09:17:19 MDT
subject: Numerical analysis
acknowledgement: ack-nhfb
rawauthor: Peter Henrici
rawtitle: Elements of numerical analysis
remark:
Based on the author's lecture notes for a course entitled em Numerical Mathematical Analysis at the University of California, Los Angeles. Cited in cite Sterbenz:1974:FPC.

entry:
@Book{Henrici:1964:ENA,
  author =       "Peter Henrici",
  title =        "Elements of numerical analysis",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xv + 328",
  year =         "1964",
  LCCN =         "QA297 .H4",
  bibdate =      "Fri Aug 20 09:17:19 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "Based on the author's lecture notes for a course
                 entitled {\em Numerical Mathematical Analysis\/} at the
                 University of California, Los Angeles. Cited in
                 \cite{Sterbenz:1974:FPC}.",
  subject =      "Numerical analysis",
}


bibtype: article
filename: fparith.bib
label: Jacobsohn:1964:SFM
author: D. Jacobsohn
title: A Suggestion for a Fast Multiplier
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-13
number: 6
pages: 754--754
month: dec
monthnumber: 12
year: 1964
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1964.263942
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 06:57:06 MDT 2011
bibtimestamp: 2011.07.14 06:57:06 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038318
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: D. Jacobsohn
rawtitle: A Suggestion for a Fast Multiplier
entry:
@Article{Jacobsohn:1964:SFM,
  author =       "D. Jacobsohn",
  title =        "A Suggestion for a Fast Multiplier",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-13",
  number =       "6",
  pages =        "754--754",
  month =        dec,
  year =         "1964",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1964.263942",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:57:06 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=4038318",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: book
filename: fparith.bib
label: Khinchin:1964:CF
author: Aleksandr Iakovlevich Khinchin
title: Continued fractions
publisher: P. Noordhoff
address: Groningen, The Netherlands
pages: 101
year: 1964
LCCN: QA295 .K513 1964a
bibdate: Fri Nov 30 06:55:53 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2007.11.30 06:55:53 MST
note: Translated by Peter Wynn
acknowledgement: ack-nhfb
authordates: 1894--1959
rawauthor: Aleksandr Iakovlevich Khinchin
rawnote: Translated by Peter Wynn
rawtitle: Continued fractions
URL:
http://www.loc.gov/catdir/description/dover032/97008056.html; http://www.loc.gov/catdir/toc/dover031/97008056.html

entry:
@Book{Khinchin:1964:CF,
  author =       "Aleksandr Iakovlevich Khinchin",
  title =        "Continued fractions",
  publisher =    "P. Noordhoff",
  address =      "Groningen, The Netherlands",
  pages =        "101",
  year =         "1964",
  LCCN =         "QA295 .K513 1964a",
  bibdate =      "Fri Nov 30 06:55:53 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Translated by Peter Wynn",
  URL =          "http://www.loc.gov/catdir/description/dover032/97008056.html;
                 http://www.loc.gov/catdir/toc/dover031/97008056.html",
  acknowledgement = ack-nhfb,
  author-dates = "1894--1959",
}


bibtype: article
filename: fparith.bib
label: Klokacev:1964:RNF
author: I. V. Klokacev
title: A refinement of the normalized floating point number notation on digital computers. (Russian)
journal: Z. Vycisl. Mat. i Mat. Fiz.
volume: 4
pages: 192--194
year: 1964
MRclass: 68.00
MRnumber: 28\#4694
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
rawauthor: I. V. Kloka{\v{c}}ev
rawtitle: A refinement of the normalized floating point number notation on digital computers. ({Russian})
entry:
@Article{Klokacev:1964:RNF,
  author =       "I. V. Kloka{\v{c}}ev",
  title =        "A refinement of the normalized floating point number
                 notation on digital computers. ({Russian})",
  journal =      "{\v{Z}}. Vy{\v{c}}isl. Mat. i Mat. Fiz.",
  volume =       "4",
  pages =        "192--194",
  year =         "1964",
  MRclass =      "68.00",
  MRnumber =     "28\#4694",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}


bibtype: article
filename: fparith.bib
label: Kundu:1964:TMD
author: P. Kundu and S. Banerji
title: Transistorized Multiplier and Divider and Its Applications
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-13
number: 3
pages: 288--295
month: jun
monthnumber: 6
year: 1964
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1964.263919
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 06:57:00 MDT 2011
bibtimestamp: 2011.07.14 06:57:00 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038157
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: P. Kundu and S. Banerji
rawtitle: Transistorized Multiplier and Divider and Its Applications
entry:
@Article{Kundu:1964:TMD,
  author =       "P. Kundu and S. Banerji",
  title =        "Transistorized Multiplier and Divider and Its
                 Applications",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-13",
  number =       "3",
  pages =        "288--295",
  month =        jun,
  year =         "1964",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1964.263919",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:57:00 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=4038157",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: fparith.bib
label: Lamson:1964:DAD
author: Roger C. Lamson
title: A Division Algorithm for a Digital Differential Analyzer
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-13
number: 1
pages: 54--55
month: feb
monthnumber: 2
year: 1964
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1964.263838
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 06:56:57 MDT 2011
bibtimestamp: 2011.07.14 06:56:57 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038079
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: Roger C. Lamson
rawtitle: A Division Algorithm for a Digital Differential Analyzer
entry:
@Article{Lamson:1964:DAD,
  author =       "Roger C. Lamson",
  title =        "A Division Algorithm for a Digital Differential
                 Analyzer",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-13",
  number =       "1",
  pages =        "54--55",
  month =        feb,
  year =         "1964",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1964.263838",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:56:57 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=4038079",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: fparith.bib
label: Lynn:1964:REM
author: M. Stuart Lynn
title: On the Round-Off Error in the Method of Successive Over-Relaxation
journal: j-MATH-COMPUT
volume: 18
number: 85
pages: 36--49
month: jan
monthnumber: 1
year: 1964
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: M. Stuart Lynn
rawtitle: On the Round-Off Error in the Method of Successive Over-Relaxation
entry:
@Article{Lynn:1964:REM,
  author =       "M. Stuart Lynn",
  title =        "On the Round-Off Error in the Method of Successive
                 Over-Relaxation",
  journal =      j-MATH-COMPUT,
  volume =       "18",
  number =       "85",
  pages =        "36--49",
  month =        jan,
  year =         "1964",
  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: book
filename: fparith.bib
label: Maley:1964:MDC
author: Gerald A. Maley and Edward J. Skiko
title: Modern digital computers
publisher: pub-PH
address: pub-PH:adr
pages: xiv + 216
year: 1964
LCCN: QA76.5 .M192
bibdate: Thu Nov 18 10:04:00 MST 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.11.18 10:04:00 MST
series: Prentice-Hall electrical engineering series
keywords: binary arithmetic
subject: Electronic digital computers
acknowledgement: ack-nhfb
rawauthor: Gerald A. Maley and Edward J. Skiko
rawtitle: Modern digital computers
entry:
@Book{Maley:1964:MDC,
  author =       "Gerald A. Maley and Edward J. Skiko",
  title =        "Modern digital computers",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xiv + 216",
  year =         "1964",
  LCCN =         "QA76.5 .M192",
  bibdate =      "Thu Nov 18 10:04:00 MST 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Prentice-Hall electrical engineering series",
  acknowledgement = ack-nhfb,
  keywords =     "binary arithmetic",
  subject =      "Electronic digital computers",
}


bibtype: book
filename: fparith.bib
label: McCracken:1964:NMF
author: Daniel D. McCracken and William S. Dorn
title: Numerical methods and FORTRAN programming, with applications in engineering and science
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xii + 457
year: 1964
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: Numerical analysis --- Data processing.; Fortran (Computer program language)
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
rawauthor: Daniel D. McCracken and William S. Dorn
rawtitle: Numerical methods and {FORTRAN} programming, with applications in engineering and science
entry:
@Book{McCracken:1964:NMF,
  author =       "Daniel D. McCracken and William S. Dorn",
  title =        "Numerical methods and {FORTRAN} programming, with
                 applications in engineering and science",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xii + 457",
  year =         "1964",
  bibdate =      "Sat Jan 27 13:40:57 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Numerical analysis --- Data processing.; {Fortran}
                 (Computer program language)",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: fparith.bib
label: Merrill:1964:IDC
author: Roy D. Merrill
title: Improving Digital Computer Performance Using Residue Number Theory
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-13
number: 2
pages: 93--101
month: apr
monthnumber: 4
year: 1964
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1964.263776; https://doi.org/10.1109/PGEC.1964.263777
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 06:56:58 MDT 2011
bibtimestamp: 2011.07.14 06:56:58 MDT
fjournal: IEEE Transactions on Electronic Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: Roy D. Merrill
rawtitle: Improving Digital Computer Performance Using Residue Number Theory
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038105; http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4038099

entry:
@Article{Merrill:1964:IDC,
  author =       "Roy D. Merrill",
  title =        "Improving Digital Computer Performance Using Residue
                 Number Theory",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-13",
  number =       "2",
  pages =        "93--101",
  month =        apr,
  year =         "1964",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1964.263776;
                 https://doi.org/10.1109/PGEC.1964.263777",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:56:58 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=4038105;
                 http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4038099",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Residue arithmetic has the interesting characteristic
                 that in multiplication, addition and subtraction any
                 digit in the result is dependent only on its two
                 corresponding operand digits. Consequently, for these
                 operations, residue arithmetic is \ldots{}",
}


bibtype: article
filename: fparith.bib
label: Miller:1964:ESD
author: R. H. Miller
title: An example in ``significant-digit'' arithmetic
journal: j-CACM
volume: 7
number: 1
pages: 21--21
month: jan
monthnumber: 1
year: 1964
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon Oct 24 09:33:00 MDT 2005
bibsource: http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2005.10.24 09:33:00 MDT
fjournal: Communications of the ACM
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: R. H. Miller
rawtitle: An example in ``significant-digit'' arithmetic
abstract:
Different methods of handling the summing process for the geometric series are shown to give results indicating widely differing significances when carried out in a machine incorporating ``significant-digit'' arithmetic.

rawabstract:
Different methods of handling the summing process for the geometric series are shown to give results indicating widely differing significances when carried out in a machine incorporating ``significant-digit'' arithmetic.

entry:
@Article{Miller:1964:ESD,
  author =       "R. H. Miller",
  title =        "An example in ``significant-digit'' arithmetic",
  journal =      j-CACM,
  volume =       "7",
  number =       "1",
  pages =        "21--21",
  month =        jan,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Oct 24 09:33:00 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Different methods of handling the summing process for
                 the geometric series are shown to give results
                 indicating widely differing significances when carried
                 out in a machine incorporating ``significant-digit''
                 arithmetic.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: mastersthesis
filename: fparith.bib
label: Moss:1964:RDC
author: George Joseph Moss, Jr.
title: Recording digital counter with floating point output format
type: Thesis (M.S.)
school: University of Maryland
address: College Park, MD, USA
pages: 155
year: 1964
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: George Joseph {Moss, Jr.}
rawtitle: Recording digital counter with floating point output format
entry:
@MastersThesis{Moss:1964:RDC,
  author =       "George Joseph {Moss, Jr.}",
  title =        "Recording digital counter with floating point output
                 format",
  type =         "Thesis ({M.S.})",
  school =       "University of Maryland",
  address =      "College Park, MD, USA",
  pages =        "155",
  year =         "1964",
  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: Rice:1964:AFV
author: John R. Rice
title: The Approximation of Functions
volume: 1
publisher: pub-AW
address: pub-AW:adr
pages: various
year: 1964
LCCN: QA221 .R5 V.1-2
bibdate: Fri Dec 08 13:02:52 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 13:02:52 ???
acknowledgement: ack-nj
rawauthor: John R. Rice
rawtitle: The Approximation of Functions
entry:
@Book{Rice:1964:AFV,
  author =       "John R. Rice",
  title =        "The Approximation of Functions",
  volume =       "1",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "various",
  year =         "1964",
  LCCN =         "QA221 .R5 V.1-2",
  bibdate =      "Fri Dec 08 13:02:52 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: Santos:1964:BVB
author: J. Santos and H. Arango
title: Base $3$ vs Base $2$ Synchronous Arithmetic Units
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-13
number: 5
pages: 608--609
month: oct
monthnumber: 10
year: 1964
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1964.263734
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 06:57:04 MDT 2011
bibtimestamp: 2011.07.14 06:57:04 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038256
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: J. Santos and H. Arango
rawtitle: Base $3$ vs Base $2$ Synchronous Arithmetic Units
entry:
@Article{Santos:1964:BVB,
  author =       "J. Santos and H. Arango",
  title =        "Base $3$ vs Base $2$ Synchronous Arithmetic Units",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-13",
  number =       "5",
  pages =        "608--609",
  month =        oct,
  year =         "1964",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1964.263734",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:57:04 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=4038256",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: fparith.bib
label: Stein:1964:DCM
author: M. L. Stein
title: Divide-and-Correct Methods for Multiple Precision Division
journal: j-CACM
volume: 7
number: 8
pages: 472--474
month: aug
monthnumber: 8
year: 1964
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: M. L. Stein
rawtitle: Divide-and-Correct Methods for Multiple Precision Division
entry:
@Article{Stein:1964:DCM,
  author =       "M. L. Stein",
  title =        "Divide-and-Correct Methods for Multiple Precision
                 Division",
  journal =      j-CACM,
  volume =       "7",
  number =       "8",
  pages =        "472--474",
  month =        aug,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  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: mastersthesis
filename: fparith.bib
label: Sweo:1964:SFP
author: David Ernest Sweo
title: A study of floating point arithmetic with the residue number system
type: Thesis (M.S.)
school: UCLA - Engineering
address: Los Angeles, CA, USA
pages: 89
year: 1964
bibdate: Sat Feb 24 15:01:45 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1996.02.24 15:01:45 MST
keywords: Congruences and residues.; Electronic digital computers --- Programming.
acknowledgement: ack-nhfb
rawauthor: David Ernest Sweo
rawtitle: A study of floating point arithmetic with the residue number system
entry:
@MastersThesis{Sweo:1964:SFP,
  author =       "David Ernest Sweo",
  title =        "A study of floating point arithmetic with the residue
                 number system",
  type =         "Thesis ({M.S.})",
  school =       "UCLA - Engineering",
  address =      "Los Angeles, CA, USA",
  pages =        "89",
  year =         "1964",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Congruences and residues.; Electronic digital
                 computers --- Programming.",
}


bibtype: article
filename: fparith.bib
label: Wallace:1964:SFM
author: C. S. Wallace
title: A Suggestion for a Fast Multiplier
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-13
number: 1
pages: 14--17
month: feb
monthnumber: 2
year: 1964
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1964.263830
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 06:56:56 MDT 2011
bibtimestamp: 2011.07.14 06:56:56 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038071
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: C. S. Wallace
rawtitle: A Suggestion for a Fast Multiplier
entry:
@Article{Wallace:1964:SFM,
  author =       "C. S. Wallace",
  title =        "A Suggestion for a Fast Multiplier",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-13",
  number =       "1",
  pages =        "14--17",
  month =        feb,
  year =         "1964",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1964.263830",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:56:56 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=4038071",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: fparith.bib
label: Wolfe:1964:RTE
author: Jack M. Wolfe
title: Reducing Truncation Errors by Programming
journal: j-CACM
volume: 7
number: 6
pages: 355--356
month: jun
monthnumber: 6
year: 1964
CODEN: CACMA2
DOI: https://doi.org/10.1145/512274.512287
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:54 MST 2005
bibtimestamp: 2005.11.25 18:19:54 MST
fjournal: Communications of the ACM
keywords: floating-point arithmetic; truncation errors
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Jack M. Wolfe
rawtitle: Reducing Truncation Errors by Programming
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://portal.acm.org/; 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 accumulating a sum such as in a numerical integration with a large number of intervals, the sum itself becomes much larger than the individual addends. This may produce a less accurate sum as the number of intervals is increased. Separate variables can be established as accumulators to hold partial sums within various distinct intervals. Thus, the extensive successive truncations are eliminated.

remark:
This algorithm is a precursor of Kahan's compensated summation algorithm cite Kahan:1965:PFR; see cite [p. 384]Lange:2020:NDF for a discussion.

rawabstract:
In accumulating a sum such as in a numerical integration with a large number of intervals, the sum itself becomes much larger than the individual addends. This may produce a less accurate sum as the number of intervals is increased. Separate variables can be established as accumulators to hold partial sums within various distinct intervals. Thus, the extensive successive truncations are eliminated.

entry:
@Article{Wolfe:1964:RTE,
  author =       "Jack M. Wolfe",
  title =        "Reducing Truncation Errors by Programming",
  journal =      j-CACM,
  volume =       "7",
  number =       "6",
  pages =        "355--356",
  month =        jun,
  year =         "1964",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/512274.512287",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:54 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://portal.acm.org/;
                 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 accumulating a sum such as in a numerical
                 integration with a large number of intervals, the sum
                 itself becomes much larger than the individual addends.
                 This may produce a less accurate sum as the number of
                 intervals is increased. Separate variables can be
                 established as accumulators to hold partial sums within
                 various distinct intervals. Thus, the extensive
                 successive truncations are eliminated.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "floating-point arithmetic; truncation errors",
  remark =       "This algorithm is a precursor of Kahan's compensated
                 summation algorithm \cite{Kahan:1965:PFR}; see \cite[p.
                 384]{Lange:2020:NDF} for a discussion.",
}


bibtype: article
filename: fparith.bib
label: Ashenhurst:1965:EEC
author: R. L. Ashenhurst and N. Metropolis
title: Error Estimation in Computer Calculation
journal: j-AMER-MATH-MONTHLY
volume: 72
number: 2 (Part 2)
pages: 47--58
year: 1965
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 65.80
MRnumber: MR0192671 (33 \#896)
MRreviewer: James H. Wilkinson
bibdate: Fri Jan 12 11:37:56 1996
bibtimestamp: 1996.01.12 11:37:56 ???
fjournal: The American Mathematical Monthly
keywords: error estimation; floating-point arithmetic
ZMnumber: 0216.49602
acknowledgement: ack-jr
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: R. L. Ashenhurst and N. Metropolis
rawtitle: Error Estimation in Computer Calculation
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

note:
Reprinted in Department of Economics, Graduate School of Business, University of Chicago, Center for Mathematical Studies in Business and Economics, number 45.

rawnote:
Reprinted in Department of Economics, Graduate School of Business, University of Chicago, Center for Mathematical Studies in Business and Economics, number 45.

entry:
@Article{Ashenhurst:1965:EEC,
  author =       "R. L. Ashenhurst and N. Metropolis",
  title =        "Error Estimation in Computer Calculation",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "72",
  number =       "2 (Part 2)",
  pages =        "47--58",
  year =         "1965",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "65.80",
  MRnumber =     "MR0192671 (33 \#896)",
  MRreviewer =   "James H. Wilkinson",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in Department of Economics, Graduate School
                 of Business, University of Chicago, Center for
                 Mathematical Studies in Business and Economics, number
                 45.",
  ZMnumber =     "0216.49602",
  acknowledgement = ack-jr,
  fjournal =     "The American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  keywords =     "error estimation; floating-point arithmetic",
}


bibtype: inproceedings
filename: fparith.bib
label: Ashenhurst:1965:EIU
author: R. L. Ashenhurst
editor: L. B. Rall
booktitle: Error in digital computation
title: Experimental investigation of unnormalized arithmetic
publisher: pub-WILEY
address: pub-WILEY:adr
pages: 3--37
year: 1965
bibdate: Thu Nov 8 14:49:59 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.08 14:49:59 ???
keywords: ARI FLP
acknowledgement: ack-nhfb
rawauthor: R. L. Ashenhurst
rawbooktitle: Error in digital computation
raweditor: L. B. Rall
rawtitle: Experimental investigation of unnormalized arithmetic
entry:
@InProceedings{Ashenhurst:1965:EIU,
  author =       "R. L. Ashenhurst",
  editor =       "L. B. Rall",
  booktitle =    "Error in digital computation",
  title =        "Experimental investigation of unnormalized
                 arithmetic",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "3--37",
  year =         "1965",
  bibdate =      "Thu Nov 8 14:49:59 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARI FLP",
}


bibtype: inproceedings
filename: fparith.bib
label: Ashenhurst:1965:TAE
author: R. L. Ashenhurst
editor: L. B. Rall
booktitle: Error in digital computation
title: Techniques for automatic error monitoring and control
publisher: pub-WILEY
address: pub-WILEY:adr
pages: 43--59
year: 1965
bibdate: Tue Oct 9 09:42:56 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.10.09 09:42:56 ???
keywords: ARI FLP
acknowledgement: ack-nhfb
rawauthor: R. L. Ashenhurst
rawbooktitle: Error in digital computation
raweditor: L. B. Rall
rawtitle: Techniques for automatic error monitoring and control
entry:
@InProceedings{Ashenhurst:1965:TAE,
  author =       "R. L. Ashenhurst",
  editor =       "L. B. Rall",
  booktitle =    "Error in digital computation",
  title =        "Techniques for automatic error monitoring and
                 control",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "43--59",
  year =         "1965",
  bibdate =      "Tue Oct 9 09:42:56 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARI FLP",
}


bibtype: article
filename: fparith.bib
label: Atrubin:1965:ODR
author: A. J. Atrubin
title: A One-Dimensional Real-Time Iterative Multiplier
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-14
number: 3
pages: 394--399
month: jun
monthnumber: 6
year: 1965
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1965.264145
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 06:26:33 MDT 2011
bibtimestamp: 2011.07.14 06:26:33 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038457
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: A. J. Atrubin
rawtitle: A One-Dimensional Real-Time Iterative Multiplier
entry:
@Article{Atrubin:1965:ODR,
  author =       "A. J. Atrubin",
  title =        "A One-Dimensional Real-Time Iterative Multiplier",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "3",
  pages =        "394--399",
  month =        jun,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264145",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:33 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=4038457",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: fparith.bib
label: Blum:1965:EAP
author: B. I. Blum
title: An Extended Arithmetic Package
journal: j-CACM
volume: 8
number: 5
pages: 318--320
month: may
monthnumber: 5
year: 1965
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Sep 8 08:20:53 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 1994.09.08 08:20:53 ???
fjournal: Communications of the ACM
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/cacm
rawauthor: B. I. Blum
rawtitle: An Extended Arithmetic Package
entry:
@Article{Blum:1965:EAP,
  author =       "B. I. Blum",
  title =        "An Extended Arithmetic Package",
  journal =      j-CACM,
  volume =       "8",
  number =       "5",
  pages =        "318--320",
  month =        may,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 8 08:20:53 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 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: Combet:1965:CBT
author: M. Combet and H. Van Zonneveld and L. Verbeek
title: Computation of the Base Two Logarithm of Binary Numbers
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-14
number: 6
pages: 863--867
month: dec
monthnumber: 12
year: 1965
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1965.264080
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 06:26:41 MDT 2011
bibtimestamp: 2011.07.14 06:26:41 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038605
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: M. Combet and H. {Van Zonneveld} and L. Verbeek
rawtitle: Computation of the Base Two Logarithm of Binary Numbers
entry:
@Article{Combet:1965:CBT,
  author =       "M. Combet and H. {Van Zonneveld} and L. Verbeek",
  title =        "Computation of the Base Two Logarithm of Binary
                 Numbers",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "6",
  pages =        "863--867",
  month =        dec,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264080",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:41 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=4038605",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: fparith.bib
label: Dadda:1965:SSP
author: Luigi Dadda
title: Some Schemes for Parallel Multipliers
journal: j-ALTA-FREQ
volume: 34
pages: 349--356
month: mar
monthnumber: 3
year: 1965
CODEN: ALFRAJ
ISSN: 0002-6557 OR 00026557
ISSNL: 0002-6557 OR 00026557
bibdate: Fri Nov 09 10:47:42 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 10:47:42 ???
note: Reprinted in cite [pages 118--225]Swartzlander:1990:CAa.
URL: http://en.wikipedia.org/wiki/Dadda_multiplier; http://en.wikipedia.org/wiki/luigi_dadda
fjournal: Alta frequenza
acknowledgement: ack-nhfb
authordates: 29 April 1923--26 October 2012
rawauthor: Luigi Dadda
rawnote: Reprinted in \cite[pages 118--225]{Swartzlander:1990:CAa}.
rawtitle: Some Schemes for Parallel Multipliers
remark:
According to an ARITH'21 conference attendee, this is a recommended article for understanding the Wallace and Dadda multipliers.

entry:
@Article{Dadda:1965:SSP,
  author =       "Luigi Dadda",
  title =        "Some Schemes for Parallel Multipliers",
  journal =      j-ALTA-FREQ,
  volume =       "34",
  number =       "??",
  pages =        "349--356",
  month =        mar,
  year =         "1965",
  CODEN =        "ALFRAJ",
  ISSN =         "0002-6557",
  ISSN-L =       "0002-6557",
  bibdate =      "Fri Nov 09 10:47:42 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[pages
                 118--225]{Swartzlander:1990:CAa}.",
  URL =          "http://en.wikipedia.org/wiki/Dadda_multiplier;
                 http://en.wikipedia.org/wiki/luigi_dadda",
  acknowledgement = ack-nhfb,
  author-dates = "29 April 1923--26 October 2012",
  fjournal =     "Alta frequenza",
  remark =       "According to an ARITH'21 conference attendee, this is
                 a recommended article for understanding the Wallace and
                 Dadda multipliers.",
}


bibtype: article
filename: fparith.bib
label: Deiters:1965:ODD
author: Robert M. Deiters
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-14
number: 3
pages: 456--463
month: jun
monthnumber: 6
year: 1965
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1965.264153
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 06:26:34 MDT 2011
bibtimestamp: 2011.07.14 06:26:34 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038465
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: Robert M. Deiters
title:
Optimum Design of a Diode Squarer by Applying the Criterion of Square Root of the Integral of Per Cent Error Squared

rawtitle:
Optimum Design of a Diode Squarer by Applying the Criterion of Square Root of the Integral of Per Cent Error Squared

entry:
@Article{Deiters:1965:ODD,
  author =       "Robert M. Deiters",
  title =        "Optimum Design of a Diode Squarer by Applying the
                 Criterion of Square Root of the Integral of Per Cent
                 Error Squared",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "3",
  pages =        "456--463",
  month =        jun,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264153",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:34 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=4038465",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: fparith.bib
label: Dodd:1965:RSB
author: George G. Dodd
title: Remarks on Simulation of Boolean Functions
journal: j-CACM
volume: 8
number: 8
pages: 517--517
month: aug
monthnumber: 8
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 18:20:01 MST 2005
bibtimestamp: 2005.11.25 18:20:01 MST
fjournal: Communications of the ACM
keywords: Boolean operations; decimal arithmetic
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: George G. Dodd
rawtitle: Remarks on Simulation of {Boolean} Functions
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

abstract:
Recently M. Morris Mano presented a method for performing Boolean OR, AND and NOT operations by means of arithmetic and conditional transfer operations in a decimal computer lacking builtin logical instructions.

rawabstract:
Recently M. Morris Mano presented a method for performing Boolean OR, AND and NOT operations by means of arithmetic and conditional transfer operations in a decimal computer lacking builtin logical instructions.

entry:
@Article{Dodd:1965:RSB,
  author =       "George G. Dodd",
  title =        "Remarks on Simulation of {Boolean} Functions",
  journal =      j-CACM,
  volume =       "8",
  number =       "8",
  pages =        "517--517",
  month =        aug,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:01 MST 2005",
  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",
  abstract =     "Recently M. Morris Mano presented a method for
                 performing Boolean OR, AND and NOT operations by means
                 of arithmetic and conditional transfer operations in a
                 decimal computer lacking builtin logical
                 instructions.",
  acknowledgement = ack-nhfb,
  checked =      "19940407",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Boolean operations; decimal arithmetic",
  sjb =          "Commenting on \cite{Mano:1965:PSB}.",
}


bibtype: article
filename: fparith.bib
label: Earle:1965:LCS
author: J. G. Earle
title: Latched Carry-Save Adder
journal: j-IBM-TDB
volume: 7
pages: 909--910
month: mar
monthnumber: 3
year: 1965
CODEN: IBMTAA
ISSN: 0018-8689 OR 00188689
bibdate: Fri Nov 09 10:49:36 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2007.11.09 10:49:36 ???
fjournal: IBM Technical Disclosure Bulletin
acknowledgement: ack-nhfb
rawauthor: J. G. Earle
rawtitle: Latched Carry-Save Adder
entry:
@Article{Earle:1965:LCS,
  author =       "J. G. Earle",
  title =        "Latched Carry-Save Adder",
  journal =      j-IBM-TDB,
  volume =       "7",
  number =       "??",
  pages =        "909--910",
  month =        mar,
  year =         "1965",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Fri Nov 09 10:49:36 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Technical Disclosure Bulletin",
}


bibtype: incollection
filename: fparith.bib
label: Garner:1965:NSA
author: H. L. Garner
title: Number systems and arithmetic
crossref: Alt:1965:AC
volume: 6
pages: 131--194
year: 1965
bibdate: Sat May 18 14:18:19 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/fparith.bib
bibtimestamp: 2002.05.18 14:18:19 ???
acknowledgement: ack-nhfb
rawauthor: H. L. Garner
rawtitle: Number systems and arithmetic
entry:
@InCollection{Garner:1965:NSA,
  author =       "H. L. Garner",
  title =        "Number systems and arithmetic",
  crossref =     "Alt:1965:AC",
  volume =       "6",
  pages =        "131--194",
  year =         "1965",
  bibdate =      "Sat May 18 14:18:19 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: fparith.bib
label: Garner:1965:RID
author: H. L. Garner
title: R65-22 Improving Digital Computer Performance Using Residue Number Theory
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-14
number: 2
pages: 277--277
month: apr
monthnumber: 4
year: 1965
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1965.263975
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 06:26:23 MDT 2011
bibtimestamp: 2011.07.14 06:26:23 MDT
fjournal: IEEE Transactions on Electronic Computers
keywords: residue arithmetic; residue number system
acknowledgement: ack-nhfb
rawauthor: H. L. Garner
rawtitle: {R65-22} Improving Digital Computer Performance Using Residue Number Theory
URL:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038430; http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753; http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4038385

entry:
@Article{Garner:1965:RID,
  author =       "H. L. Garner",
  title =        "{R65-22} Improving Digital Computer Performance Using
                 Residue Number Theory",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "2",
  pages =        "277--277",
  month =        apr,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.263975",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:23 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=4038430;
                 http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4038385",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
  keywords =     "residue arithmetic; residue number system",
}


bibtype: article
filename: fparith.bib
label: Hammel:1965:RLC
author: D. Hammel
title: R65-54 The Logic of Computer Arithmetic
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-14
number: 4
pages: 670--670
month: aug
monthnumber: 8
year: 1965
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1965.264031
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 06:26:40 MDT 2011
bibtimestamp: 2011.07.14 06:26:40 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038535
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: D. Hammel
rawtitle: {R65-54} The Logic of Computer Arithmetic
entry:
@Article{Hammel:1965:RLC,
  author =       "D. Hammel",
  title =        "{R65-54} The Logic of Computer Arithmetic",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "4",
  pages =        "670--670",
  month =        aug,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264031",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:40 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=4038535",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: fparith.bib
label: Hammer:1965:BRBa
author: Preston C. Hammer
journal: j-TECHNOMETRICS
volume: 7
number: 1
pages: 82--82
month: feb
monthnumber: 2
year: 1965
CODEN: TCMTA2
DOI: https://doi.org/10.2307/1266139
ISSN: 0040-1706 (print), 1537-2723 (electronic) OR 00401706 (print), 15372723 (electronic)
ISSNL: 0040-1706 OR 00401706
bibdate: Sat Jun 21 13:17:45 MDT 2014
bibtimestamp: 2014.06.21 13:17:45 MDT
URL: http://www.jstor.org/stable/1266139
fjournal: Technometrics
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00401706.html
rawauthor: Preston C. Hammer
title:
Book Review: booktitle Experimental Arithmetic, High Speed Computing and Mathematics by N. C. Metropolis; A. H. Taub; John Todd; C. B. Tompkins

bibsource:
http://www.jstor.org/journals/00401706.html; http://www.jstor.org/stable/i254241; https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib

rawtitle:
Book Review: {{\booktitle{Experimental Arithmetic, High Speed Computing and Mathematics}} by N. C. Metropolis; A. H. Taub; John Todd; C. B. Tompkins}

entry:
@Article{Hammer:1965:BRBa,
  author =       "Preston C. Hammer",
  title =        "Book Review: {{\booktitle{Experimental Arithmetic,
                 High Speed Computing and Mathematics}} by N. C.
                 Metropolis; A. H. Taub; John Todd; C. B. Tompkins}",
  journal =      j-TECHNOMETRICS,
  volume =       "7",
  number =       "1",
  pages =        "82--82",
  month =        feb,
  year =         "1965",
  CODEN =        "TCMTA2",
  DOI =          "https://doi.org/10.2307/1266139",
  ISSN =         "0040-1706 (print), 1537-2723 (electronic)",
  ISSN-L =       "0040-1706",
  bibdate =      "Sat Jun 21 13:17:45 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00401706.html;
                 http://www.jstor.org/stable/i254241;
                 https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib",
  URL =          "http://www.jstor.org/stable/1266139",
  acknowledgement = ack-nhfb,
  fjournal =     "Technometrics",
  journal-URL =  "http://www.jstor.org/journals/00401706.html",
}


bibtype: article
filename: fparith.bib
label: Hammer:1965:BRBb
author: Preston C. Hammer
journal: j-TECHNOMETRICS
volume: 7
number: 1
pages: 82--82
month: feb
monthnumber: 2
year: 1965
CODEN: TCMTA2
ISSN: 0040-1706 (print), 1537-2723 (electronic) OR 00401706 (print), 15372723 (electronic)
ISSNL: 0040-1706 OR 00401706
bibdate: Tue Mar 20 13:44:52 2007
bibtimestamp: 2007.03.20 13:44:52 ???
URL: http://links.jstor.org/sici?sici=0040-1706%28196502%297%3A1%3C82%3AEAHSCA%3E2.0.CO%3B2-9
fjournal: Technometrics
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00401706.html
rawauthor: Preston C. Hammer
title:
Book Review: booktitle Experimental Arithmetic, High Speed Computing and Mathematics by N. C. Metropolis, A. H. Taub, John Todd, and C. B. Tompkins

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib

rawtitle:
Book Review: {{\booktitle{Experimental Arithmetic, High Speed Computing and Mathematics}} by N. C. Metropolis, A. H. Taub, John Todd, and C. B. Tompkins}

entry:
@Article{Hammer:1965:BRBb,
  author =       "Preston C. Hammer",
  title =        "Book Review: {{\booktitle{Experimental Arithmetic,
                 High Speed Computing and Mathematics}} by N. C.
                 Metropolis, A. H. Taub, John Todd, and C. B.
                 Tompkins}",
  journal =      j-TECHNOMETRICS,
  volume =       "7",
  number =       "1",
  pages =        "82--82",
  month =        feb,
  year =         "1965",
  CODEN =        "TCMTA2",
  ISSN =         "0040-1706 (print), 1537-2723 (electronic)",
  ISSN-L =       "0040-1706",
  bibdate =      "Tue Mar 20 13:44:52 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib",
  URL =          "http://links.jstor.org/sici?sici=0040-1706%28196502%297%3A1%3C82%3AEAHSCA%3E2.0.CO%3B2-9",
  acknowledgement = ack-nhfb,
  fjournal =     "Technometrics",
  journal-URL =  "http://www.jstor.org/journals/00401706.html",
}


bibtype: article
filename: fparith.bib
label: Hamming:1965:NLB
author: R. W. Hamming and W. L. Mammel
title: A Note on the Location of the Binary Point in a Computing Machine
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-14
number: 2
pages: 260--261
month: apr
monthnumber: 4
year: 1965
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1965.264258
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=4038414
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: R. W. Hamming and W. L. Mammel
rawtitle: A Note on the Location of the Binary Point in a Computing Machine
bibsource:
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib

remark:
The authors consider the low-level multiplication circuit efficiency of placing the binary point before or after the first bit. If the leading bit is equally likely to be a 0 or a 1, then their analysis shows that it is better to place the point before the leading bit. However, they report that a more likely distribution is logarithmic (as predicted by Benford's Law, although the Newcomb / Benford work is neither mentioned nor cited), in which case there is no advantage for either choice of placement of the binary point. The conclude that it would be humane to place it after the leading digit, by analogy with how people learn decimal arithmetic.

entry:
@Article{Hamming:1965:NLB,
  author =       "R. W. Hamming and W. L. Mammel",
  title =        "A Note on the Location of the Binary Point in a
                 Computing Machine",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "2",
  pages =        "260--261",
  month =        apr,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264258",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 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=4038414",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
  remark =       "The authors consider the low-level multiplication
                 circuit efficiency of placing the binary point before
                 or after the first bit. If the leading bit is equally
                 likely to be a 0 or a 1, then their analysis shows that
                 it is better to place the point before the leading bit.
                 However, they report that a more likely distribution is
                 logarithmic (as predicted by Benford's Law, although
                 the Newcomb / Benford work is neither mentioned nor
                 cited), in which case there is no advantage for either
                 choice of placement of the binary point. The conclude
                 that it would be humane to place it after the leading
                 digit, by analogy with how people learn decimal
                 arithmetic.",
}


bibtype: article
filename: fparith.bib
label: Ikebe:1965:NTP
author: Yasuhiko Ikebe
title: Note on Triple-Precision Floating-Point Arithmetic with 132-Bit Numbers
journal: j-CACM
volume: 8
number: 3
pages: 175--177
month: mar
monthnumber: 3
year: 1965
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 68.00
MRnumber: 30\#2707
bibdate: Fri Dec 08 14:32:51 1995
bibtimestamp: 1995.12.08 14:32:51 ???
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Yasuhiko Ikebe
rawtitle: Note on Triple-Precision Floating-Point Arithmetic with 132-Bit Numbers
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
In a recent paper, Gregory and Raney described a technique for double-precision floating-point arithmetic. A similar technique can be developed for triple-precision floating-point arithmetic and its is the purpose of this note to describe this technique. Only the multiplication and the division algorithms are described, since the addition-subtraction algorithm can be obtained by a trivial modification of the algorithm in Gregory's and Raney's paper.

rawabstract:
In a recent paper, Gregory and Raney described a technique for double-precision floating-point arithmetic. A similar technique can be developed for triple-precision floating-point arithmetic and its is the purpose of this note to describe this technique. Only the multiplication and the division algorithms are described, since the addition-subtraction algorithm can be obtained by a trivial modification of the algorithm in Gregory's and Raney's paper.

entry:
@Article{Ikebe:1965:NTP,
  author =       "Yasuhiko Ikebe",
  title =        "Note on Triple-Precision Floating-Point Arithmetic
                 with 132-Bit Numbers",
  journal =      j-CACM,
  volume =       "8",
  number =       "3",
  pages =        "175--177",
  month =        mar,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "68.00",
  MRnumber =     "30\#2707",
  bibdate =      "Fri Dec 08 14:32:51 1995",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In a recent paper, Gregory and Raney described a
                 technique for double-precision floating-point
                 arithmetic. A similar technique can be developed for
                 triple-precision floating-point arithmetic and its is
                 the purpose of this note to describe this technique.
                 Only the multiplication and the division algorithms are
                 described, since the addition-subtraction algorithm can
                 be obtained by a trivial modification of the algorithm
                 in Gregory's and Raney's paper.",
  acknowledgement = ack-nhfb,
  checked =      "19940404",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: article
filename: fparith.bib
label: James:1965:GSR
author: Wendy James and P. Jarratt
journal: j-MATH-COMPUT
volume: 19
number: 91
pages: 497--500
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
fjournal: Mathematics of Computation
acknowledgement: ack-nj
ajournal: Math. Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: Wendy James and P. Jarratt
title:
The Generation of Square Roots on a Computer with Rapid Multiplication Compared with Division (in Technical Notes and Short Papers)

bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/fparith.bib; JSTOR database

rawtitle:
The Generation of Square Roots on a Computer with Rapid Multiplication Compared with Division (in {Technical Notes and Short Papers})

entry:
@Article{James:1965:GSR,
  author =       "Wendy James and P. Jarratt",
  title =        "The Generation of Square Roots on a Computer with
                 Rapid Multiplication Compared with Division (in
                 {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "91",
  pages =        "497--500",
  month =        jul,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


